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Physico- Chemical
Diagnostics of Plasmas
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PROCEEDINGS OF
THE FIFTH BIENNIAL
GAS DYNAMICS SYMPOSIUM
Edited by-
Thomas P. Anderson,
Robert W. Springer,
Richard C. Warder, Jr.
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Physico-Chemical Diagnostics of Plasmas
The American Institute
of Aeronautics and Astronautics
AND
The Gas Dynamics Laboratory
Northwestern University
Physico-Chemical
Diagnostics of Plasmas
Proceedings of the Fifth Biennial Gas Dynamics Symposium
EDITORS
Thomas P. Anderson
Robert W. Springer
Richard C. Warder, Jr.
NORTHWESTERN UNIVERSITY PRESS
Evanston
LIBRARY OF CONGRESS CATALOG CARD NUMBER: 64-14121
Printed in Great Britain
PREFACE
In 1955 The American Institute of Aeronautics and Astronautics
(then The American Rocket Society) and Northwestern University
initiated a series of biennial symposia on gas dynamics to deal with
recent and specialized fundamental aspects of jet propulsion. Since
then these meetings have widened in scope to stay abreast of
advances in science and technology. Thus previous symposia have
treated Aerothermochemistry (1955), Transport Properties in Gases
(1957), Dynamics of Conducting Gases (1959), and Magnetohydro-
dynamics (1960).
The present volume constitutes the Proceedings of the Fifth
Biennial Gas Dynamics Symposium which was held in Evanston
on August 14, 15, and 16, 1963. Continuing along the lines estab-
lished by the earlier meetings — that of treating interdisciplinary
topics of current interest to the scientist-engineer — the theme of
this symposium was the physico-chemical diagnostics of plasmas.
Nearly all aspects of experimental plasma diagnostics were dis-
cussed in the twenty-one papers presented. The topics include both
research papers and reviews of the current state-of-the-art.
The contributions to this volume have been edited as little as
possible and no attempt has been made to change the style and
nomenclature of the various authors. The editors hope that this
volume will prove to be a useful reference for the fields considered.
THOMAS P. ANDERSON
ROBERT W. SPRINGER
KICHARD C. WARDER, JR.
Evanston, Illinois
November, 1963
ACKNOWLEDGMENTS
Acknowledgment of each of the great number of people who
contributed to the success of this symposium is not possible beyond
this general thank you. However, the editors would like to note
the contributions of some who deserve special mention.
First of all we thank Professor Ah Bulent Cambel, who initiated
the Gas Dynamics Symposium and has continued to serve as Co-
Chairman of the Symposium Committee, for his cooperation and
advice in the organization of this meeting and the publication of
this volume.
The speakers were of course essential and deserve particular
thanks for the time and effort spent in the preparation and presenta-
tion of the various studies. Also deserving of special note are the
session chairmen, Daniel Bershader, Eino Latvala, Martin Lessen,
and Henri Hodara, for their able guidance of the sessions' business.
Robert B. Banks gave a very interesting banquet speech and his
effort in this regard, along with that of Martin Lessen who served
as Toastmaster, was appreciated.
Thanks are extended to the staff of the American Institute of
Aeronautics and Astronautics, in particular to James J. Harford
and Miss Bobbie Chifos; to J. Roscoe Miller, President of North-
western University, who gave the opening remarks; and to Mrs.
Ethel Majerus and the rest of the secretarial staff of the Gas
Dynamics Laboratory. The following students gave valuable
assistance: Daniel P. Aeschhman, James M. Berry, Charles A.
Boitnott, David L. Hector, William F. Hug, and Said E. Matar.
Finally, the financial aspects of such a meeting are no small
matter, and we would like to acknowledge the generosity of the
following government and industrial sponsors for their support,
without which the symposium would not have been possible.
vu
ACKNOWLEDGMENTS
Government Sponsors:
Advanced Research Projects Agency
National Aeronautics and Space
Administration
United States Air Force, Office
of Scientific Research
United States Army Research
Office (Durham)
United States Navy, Office
of Naval Research
Industrial Sponsors:
Aerojet-General Corporation
Aerospace Corporation
The Bendix Corporation
The Boeing Company
Ford Motor Company
The Garrett Corporation
General Motors Corporation
International Harvester Company
Ling-Temco-Vought, Incorporated
Litton Systems, Incorporated
North American Aviation, Incorpo-
rated
Northrop Corporation
Phillips Petroleum Company
The Pure Oil Company
Radio Corporation of America
Republic Aviation Corporation
Texaco, Incorporated
Thiokol Chemical Corporation
THE EDITORS
CONTENTS
PREFACE v
ACKNOWLEDGMENTS vii
Charles B. wharton: Plasma Diagnostic Techniques ... 3
JOHN a. Thornton: Electric and Electromagnetic Sl<ock Tubes . . 27
h. x. olsex: The Measurement of Argon Transition Probabilities
and Computation of Thermodynamic Properties of the Argon
Plasma 47
j. h. de leeuw: Electrostatic Plasma Probes 65
pattl c. wilbek: Experimental Investigation of the Characteristics of
a Langmuir Probe in Ionized Low-Density Flows ... 97
eobebt betchov and eugene b. turner: Measurements of MHD
Turbulence with Magnetic Probes 113
R. M. Montgomery and R. a. holmes: Some Experiments in Radio-
Frequency Diagnostics of Partially -Ionized Plasmas ... 131
w. k. mcgregor: Spectroscopic Measurements in Plasmas . . . 143
kenneth m. FOREMAN and Maurice E. levy: Comparative Spectro-
scopic Studies of Elertromagnetkally-Briven Hypersonic
Waves in Elemental Gases and Detonable Mixtures . . . 167
Robert b. spiers, jr, and Charles husson: Development of a Rocket-
borne Spertroradiometer to Measure the Radiation Environ-
ment of a Reentry Vehicle 187
m. r. denison and r. w. ziemer: Investigation of the Phenomena
in Crossed- Field Plasma Accelerators 201
alan f. klein: A Survey of Optical Interferometry as Applied to
Plasma Studies 233
koichi oshima: Microwave Diagnostics of a Partly-Ionized Flow
in the Presence of a Magnetic Field 247
charles e. shepard and velvin r. watson: Performance of a
Constricted-Arc Discharge in a Supersonic Nozzle . . . 261
PHILIP BROCKMAN, ROBERT V. HESS, and EICHABD E. WEINSTEIN:
Measurements and Theoretical Interpretation of Hall Currents
for Steady Axial Discharges in Radial Magnetic Fields . . 273
1*
1 IX
CONTENTS
steege t. demetriades: Momentum Transfer to Plasmas by
Lorentz Forces 297
L. J. krzycki, H. m. laksen, and w. M. byrne, jr.: Magnetohydro-
dynamic Power Generation from a Supersonic Rocket
Exhaust 329
a. i. carswell, m. p. bachynski, and g. G. cloutier: Micro-
wave Measurements of Electromagnetic Properties of Plasma
Flow-Fields 355
allen e. ftths: Flight Instrumentation for the Reentry Plasma
Sheath 383
boris ragent: X-Ray Densitometer for Use in Plasma Streams . 403
t. Herbert dimmock and william r. kineyko: Ionization Profiles
in Low- Pressure Exhausts 423
Physico-Chemical Diagnostics of Plasmas
1. Charles B. Wharton: Plasma
Diagnostic Techniques
12? The study of plasma diagnostics is concerned with making
significant, non-perturbing measurements of plasma. The term
"diagnostics" implies that compatible conclusions are drawn simul-
taneously from several observed symptoms. Ideally, the diagnostic
measurements from any one plasma event should be self-sufficient,
without relying on the repetition of successive events. This qualification
may require the data-producing instrument to have large bandwidth
and dynamic range {and, perhaps multiple-channel capabilities) so
that it can respond to rapid fluctuations.
A number of techniques have been widely developed, while others,
although they tnay have intrinsic merit, for some reason or other have
not had as wide an application. Some external measurements, notably
microwave diagnostics, optical spectroscopy, and interferometry and
radiometry, essentially do not perturb the plasma. Others involve
internal probing, such as Langmuir probes, magnetic probes, RF
probes, and particle beams, leading to various degrees of perturbation.
This paper presents a catalog of a number of useful techniques,
grouped according to the quantities measured. Certain of the methods
that have been extensively developed or have considerable potential are
then expanded upon in detail. A number of illustrative examples are
given and comparisons of techniques are made where possible. Photo-
graphs and sketches of some of the instruments are shown.
A number of interesting plasma diagnostic techniques have evolved over the
last few years. Some have found wide application while others are lacking in some
respect. Some measurements involve internal probing, such as Langmuir and
magnetic probes, with the possibility of severely perturbing the plasma. Others
are external measurements, such as microwave or optical probing and optical
spectroscopy. In the latter methods the technology of the method itself is as
complicated as the applications to plasma diagnostics. Other techniques are useful
only in dense plasmas or in hot plasmas or in plasmas confined by an intense
magnetic field. To sort out the measurements useful for a given kind of deter-
mination a brief survey of several techniques, grouped according to the quantities
measured, is given in sections 1 through 9. Certain of the methods that have been
extensively developed or have considerable potential are then expanded upon in
the rest of the paper.
ed. note: Dr. Wharton is at the General Atomic Division, General Dynamics
Corporation, San Diego, California.
3
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
1. Electron Density and Distribution
a) Microwave interferometer; 10 10 <w e < 10 14 /cm 3
b) Microwave cavity perturbation; \0 a <n e < 10 12 /cm 3
c) RF conductivity probes; 10 8 <w e < 10 15 /cm 3 ; for high collision rates
d) Microwave scattering; 10 12 <n e < 10 14 /cm 3 ; sensitive to instabilities
e) Optical interferometer; 10 14 < n e < 10 19 /cm 3
f) Optical Faraday rotation; n e > 10 le /cm 3 for 10,000 gauss
g) Optical spectroscopic intensities; n e > 10 13 ; equilibrium plasmas
h) Optical scattering; 10 14 < n e < 10 19 /cm 3
i) Optical Balmer series limit; 10 13 <n e < 10 15 /cm 3
j) Particle collectors; 10 " 6 < J e < 1 amp/cm 2 ; yields product qn e v
k) Electron or ion beam scattering; sensitive to potential fluctuations
2. Electron Temperature
a) Microwave radiation intensities; Te>0.1 eV; stable plasmas
b) Doppler broadening of cyclotron radiation line; Te >50 eV.
c) Infrared and optical intensities; Te>\Q eV; equilibrium plasmas
d) X-ray intensities; Te>6 keV; wall problems
e) Relative intensities of spectral lines; 1 < Te < 50 eV.
f ) Relative intensities of bremsstrahlung and recombination radiation
g) Doppler broadening of optical (Thomson) scattering; Te>5 eV.
h) Langmuir probes; 0.1 <Te< 1000 eV; moderate densities
3. Ion Density and Distribution
a) Stark broadening of spectral lines; Mj > 10 15 /cm 3
b) Langmuir probes, single and double
c) Electron, ion, neutral atom, or neutron beam probes; Wj>10 14 /cm 3
d) Diamagnetic effect (requires knowledge of temperature)
e) Alfven and sound wave propagation; dense plasmas
f ) Calorimetry (requires knowledge of temperature)
g) Radioactive gas tracers and collimated detectors
h) Charge-exchange neutral detectors
4. Ion Temperature and Energy
a) Calorimetry; total energy and momentum
b) Doppler broadening of spectral lines; T t >5 eV
c) External energy-momentum analyzer; samples escaping ions
d) Time-of- flight; gives particle or shock-front velocity
e) Diamagnetic effect; use magnetic probes inside and outside plasma
5. Neutral Density, Distribution, and Identity
a) Shielded ionization gauge
b) Ion or neutral atom beam scattering
c) Rayleigh scattering and resonance absorption of infrared and light photons
by bound electrons
d) Schlieren and Mach-Zehnder photography
e) Charge-exchange detectors; fast neutrals
f) Molecular resonance spectroscopy; RF and infrared
g) Re-ionization by delayed ionizing pulses
wharton: Plasma Diagnostic Techniques
6. Drift Velocity, Shock Velocity, Rotation, and Thrust
a) Doppler frequency of reflected microwaves
b) Doppler shift of synchrotron radiation
c) Doppler shift of spectral lines
d) Ballistics and calorimetry
e) Time-flight; probes, light, and microwave sampling
f ) Nonreciprocity of phase shift for space charge and EM wave propagation
7. Instabilities and Turbulence
a) Electron and ion energy- momentum analysis; external measurement
b) Microwave radiation (nonthermal effects)
c) Microwave scattering from turbulence
d) Electron and ion beam scattering
e) Fast photography; time-resolved spectroscopy and total light; high densities
f ) Magnetic probes and Rogowski loops
g) RF and Langmuir probes
h) External voltage-current measurements
i) X-rays (if high-energy electrons are generated)
j ) Neutron energy analysis (if high-energy ions are present)
8. Sheath Regions
a) Langmuir probes
b) RF probes (sheath oscillations and space charge waves)
c) Electron and ion beam probes
d) Microwave scattering from sheath oscillations
9. Constituent Identity (Purity)
a) Optical and atomic-resonance spectroscopy
b) Ion cyclotron resonance absorption; e/wi ratio
c) Magnetic analyzer; escaping ions
d) Mass spectrometer; neutral gas
10. Microwave Diagnostics
The standard techniques of interferometry and radiometry are useful in many
plasma experiments (1, 2). Equipment in the spectrum of 1 cm to 4 mm wavelength
is found to be convenient for a variety of plasma experiments.
Small-diameter, high-density plasmas require the highest frequencies available
to have w > a> p , to avoid scattering and to have as many wavelengths as possible
inside the plasma. Horn or other antennas must be kept small to provide narrow
probing areas. The surrounding walls will then have to be coated with nonreflecting
surfaces (commercially available) to inhibit stray reflection of the noncaptured part
of the wave beam. Larger, lower density plasma experiments require lower
frequencies.
The quantities measurable are the electron density, its spatial distribution, the
cross section and collision frequency for momentum transfer, the electron tempera-
ture, the presence of certain plasma oscillation modes and instabilities, the drift
velocities of electron streams, the velocity and position in time of wriggling
columns, shock fronts, etc., and the local magnetic field strength — all as functions
PHYSICO-CHEJIICAL DIAGNOSTICS OF PLASMAS
of time. A composite microwave interferometer and radiometer system is shown
in Figure 1. Not all of the components are necessary for some measurements.
Some additional components will be needed for the measurement of Faraday
rotation and shock-front velocity. Two or more systems, at different frequencies,
BALANCED IN 26
MIXER (2).
yfv PAD
DUAL BEAM SCOPE
CHAN B
6254
K — BAND
KLYSTRON
POWER
SUPPLY
u L F {ZM'- — <
A fit
SAWTOOTH
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VIDEO
AMPLIFIER
FIGURE 1. Composite microwave interferometer and radiometer for plasma diagnostics.
The zebra stripe data presentation is generated.
running simultaneously are always preferred. Often the same radiators and circuits
can be used for both frequencies by sorting out the waves at the detectors with
filters.
This method of diagnostics does not perturb the plasma and has very short
resolving times. The components are all available and the techniques well
established.
10a. Microwave Transmission
A review of the relationships on which the techniques are based will be useful
here to show how they are applied. Many of the relationships are exceedingly
complicated, and the reader is referred to the references for their derivations. The
plasma frequency, the natural oscillation frequency, is
\mej
(1)
When a magnetic field is present in the plasma, the microwave conductivity is
anisotropic. The index of refraction then must be described by tensors. Certain
wave-polarizations, however, remain unchanged as they propagate and the index
of refraction can then be written algebraically. These waves are called characteristic
waves. A plane, transverse-electromagnetic (TEM) wave, incident at an angle 6
(in respect to the magnetic field) on a plasma will generate a pair of these character-
istic waves, each one having completely different properties. In optics the wave
whartox : Plasma Diagnostic Technique*
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PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
which is most nearly like that in the absence of the magnetic field is called the
"ordinary wave". The other wave is the "extraordinary wave".
The cyclotron frequency, the angular frequency at which electrons spiral in a
magnetic field, is
*. = W. = -a
Expressed in megacycles and gauss
ft = 2-82?
(2)
(3)
Figure 2 shows the intersection loci of the index of refraction, N, with the cut-
off plane, (jV = 0), for some characteristic waves. The plus sign (taken from a + in
the equation for refractive index) corresponds to the ordinary wave; the minus
sign to the extraordinary. The angles indicated are for 8, 0° being along B. The
ranges of index are indicated in the various zones. The resonances are difficult to
observe in practice. The electron density always falls to a low value at the walls of
an experiment, so that a wave must go through a cutoff region to reach a resonance
region, unless the magnetic field is increasing outwardly in a certain way. Synchro-
tron radiation emanating from a plasma thus is found to lie within a narrow
cone about the field lines. "Whistler mode" propagation also is explained by this
effect. Internal mode conversion and evanescent coupling through thin cutoff
regions do allow resonances to be seen for waves propagating across field lines,
especially at high plasma temperatures.
Figure 3a shows the real index, N, or $' for waves propagating in a plasma as a
function of plasma density, for plasmas having various spatial distributions.
For propagation along magnetic field lines (8 = 0°) the characteristic waves are
circularly polarized, contrarotating. They propagate at different velocities, so that
when they re-emerge from the plasma the reconstituted plane wave has had its
1.0
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of density.
wharton: Plasma Diagnostic Techniques
V
= - LY
2c l
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N
(5)
Equations (4) and (5) a
FIGURE 3b. Phaseshift data presented as interferometer fringes at frequencies of 70 Go
and 90 Gc. At the top the plasma was in helium at 80 microns pressure. The bottom
fringes were obtained after 200 microns of argon had been added, showing the effect of
collisions.
plane of polarization rotated. This phenomenon is known as the Faraday effect.
The angle of rotation for a non-uniform path. L. is
1 t l
</, = -- [N + (Z)-N_(Z)]dZ radians (4)
where A% and JV_ are the indexes of refraction of the two characteristic waves
(functions of position). If the path lias uniform density
L ,
— degrees
trictly valid only if the wave damping is small. If the
damping of one wave i> larger than that of the other the emerging wave is not
plane, but clliptically. polarized. Properly interpreted measurements thus are able
to determine the density and its spatial distribution along the field hues, and the
collision rates. If one wave is completely cut off. the emerging wave is circularly
polarized. In Figure 2 the shaded triangle defined by co 6 /oj>1.0. tu'i or > 2.0.
and the A' cutoff line, for # = . represents such a medium. The index. A T . is quite
large, so that the plasma wavelength is short and waves cling closely to field lines.
This wave type lias been called variously "Whistler mode", "ducted-wave mode".
and "high-density-window mode". Experimentally it can be seen only if the electron
collision rate is low. since the damping is relatively large.
If the electrons are drifting, say to the right along a plasma column, the cyclotron
frequency as measured from right to left will be higher than that from left to right,
due to Doppler shift. The indexes and the Faraday rotation also will be
nonreciprocal. The drift velocity is thus measurable.
When the density in a moving plasma front, such as a shock front or a wriggling
arc column, is above cutoff, the reflected wave will be Doppler shifted and a
Doppler radar system gives the instantaneous velocity. Occasionally velocities
10
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
measured in this way do not agree with those obtained optically or with probes.
Supposedly, the velocities of charged particles (microwave) and excited particles
(light emission) are not the same as the front expands.
10b. Microwave Radiation
Radiation emanating from the plasma bears a relationship to the density and
temperature.
Blackbody Radiation: A dense plasma whose electrons have a thermal distribu-
tion (thermalization times short compared to characteristic plasma transients)
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whartok: Plasma Diagnostic Techniques
11
will radiate much as a blackbody in the microwave spectrum. If the collision rate is
high or the radiation is viewed at a frequency near a resonance, the plasma appears
opaque. The radiated power density per frequency interval A/ is then
AP = 8nkT e (f 2 jc 2 )Af watts/m 2 (6)
where T e is the electron kinetic temperature in degrees Kelvin.
k = 1.38 x 10 _23 joule/°K, Boltzmann's constant
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12 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
If the radiating surface is viewed by a directive antenna, which sees only the
surface, the directivity just cancels the frequency dependence of equation (6) and
the blackbody power received is
P b6 = fcT e A/watts (7)
A region which is not totally opaque loses some of its power "out the back door".
The received power is then
r bb JO
exp(-2az)d(-2ag) (8)
where a is the absorption coefficient, a function of n and v. (See Figure 3.) A
microwave radiometer is sketched in Figure 4.
Other Radiations: Electrons orbiting in a magnetic field emit synchrotron
radiation, which is peaked at the electron gyrofrequency, co b , and its harmonics. If
the electron density is high and no cooperative effects operate, the self- absorption
limits the radiation intensity to the blackbody level shown earlier.
If the cooperative effects, due to violent oscillations and instabilities, are present,
the radiation intensity scales as %1 where n c is the number of in-phase radiators.
Incoherent radiation scales as n. The radiation intensity from cooperative effects
thus has little to do with the electron temperature. Fortunately, the radiations
from cooperative oscillations are trapped within the plasma region and seldom are
coupled to external radiation fields, so that radiometry still yields valid electron
temperatures in most cases.
10c. Microwave Scattering
The scattering from individual electrons, that is, Thomson scattering, has a very
small cross section
<7r = yrg (9)
where r = 2.8xl0~ 15 meter, the electron radius. When plasma waves or other
density fluctuations are present, however, the cross section may be enhanced by
as much as 10 6 or so and the scattered signal emerges in only a narrow cone about
the Bragg scattering angle (3, 4). The spectrum of scattered waves will contain
sidebands similar to a phase modulation spectrum, where the modulation frequency
is that of the plasma waves. Figure 5 shows the block diagram of a microwave
scattering system, with a typical spectrum shown in the inset.
11. Optical and Infrared Probing
Probing by means of light beams is in principle very similar to microwave
probing and the bulk of the theory applies. The techniques differ somewhat, but
numerous parallels can be drawn.
Optical interferometers that are direct analogs of the microwave interferometer
are useful for dense plasma measurements. The Mach-Zehnder interferometer
sketched in Figure 6 is an example (5). A monochromatic light source is required;
the smaller the wavelength spread, the sharper the interferences. Optical masers,
or lasers, intrinsically are excellent monochromatic sources, but for transient
events it is difficult to achieve accurate timing without elaborate pumping and
triggering arrangements. A number of pulsed and C.W. lasers are now available
commercially (6) covering wavelength ranges from 6900 A to 72,000 A (7.2 ^i).
Spark and arc-light sources, followed by a filter or monochromator are also useful
wharton: Plasma Diagnostic Techniques
13
OPTICAL ARRANGEMENT TOR MACH ZEMMXR INTERFEROMETER
J t
?
CTfflS
?
\ \
? -----
?
FIGURE 6. Mach-Zehnder interferometer used for studies of plasma refractive index.
(After Ascoli-Bartoli, Frascati, Rome, Italy.)
for interferometers of medium resolution. Magnesium electrode spark sources
can produce microsecond pulses of intense light, having jitter times of only a few
nanoseconds. A wratten filter accepts the 3838 A line, rejecting the others, as well
as plasma-generated light. The light from the source must be much more intense
than that from the plasma, of course, at the wavelength of interest.
A tabulation of some useful intense monochromatic light sources is given in
Table I, together with wavelengths of peak outputs. Also shown are the oscillation
frequencies, the corresponding plasma cutoff densities, and the electron densities
required to give 90° of phaseshift in a 10-cm path.
TABLE I. SEVERAL INTENSE LIGHT SOURCES FOR OPTICAL PROBING, GIVING WAVELENGTHS
FREQUENCIES, CORRESPONDING PLASMA CUTOFF DENSITIES ?l c , AND ELECTRON DENSITIES
GIVING 90° OF PHASESHIFT IN A 10-Cm PATH LENGTH.
Light Source.
Wavelength
(microns)
Wave
Frequency
(ops)
Plasma
Cutoff
Density
(no. /cm 3 )
Plasma Density
for AO = 90°
in L= 10 cm
(no. /cm 3 )
Microwave
Mg spark
Hg" 8 arc
Ruby/cr 3 laser
Rb 85 flash lamp
Xenon flash lamp
GaAs junction
CaWo 4 /Nd 3 laser
He-Ne gas laser
CaF 2 /TJ 3 laser
Cs vapor laser
10,000
1,000
0.3838
0.4358
0.6943
0.7800
0.7948
0.8200
0.90
1.06
1.153
1.207
2.6
3.20
7.18
3.3 x 10 10
3.3 x 10"
7.83 x 10"
6.89x10"
4.33 x 10"
3.85 x 10"
3.78 x 10"
3.66 x 10"
3.34 x 10"
2.83 x 10"
2.60x10"
2.48 x 10"
1.15 x 10"
9.37 x 10"
4.18x10"
1.35 x 10"
1.35x10"
7.73 x 10 21
5.89 x 102i
2.32 x 10 21
1.835 x 102i
1.77 x 102i
1.66 x 10 21
1.38 x 102i
9.9 x 10 20
8.40 x 1020
7.61 x 10 20
1.64X10 20
1.09x102°
2.17x10"
1.5x10"
1.5xl0i2
1.48x10"
8.05 x 10"
7.16x10"
7.04 x 10"
6.8 x 10"
6.2 x 10"
5.25 x 10"
4.85 x 10"
4.6 x 10"
2.13 x 10"
1.74x10"
7.78x10"
14
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
A 1 -microsecond recording of the interferences obtained by an interferometer
from a dense plasma jet expanding into a low-pressure chamber is shown in
Figure 7. The shock waves and turbulence are plainly visible.
A similar optical arrangement is used for Schlieren photography, except that
changes in refractive index are recorded as modulations of light intensity, rather
than interference fringes. An experimental arrangement for studying shock waves
can be made up rather simply with lenses and a knife edge (7). The light source is a
spark between tungsten electrodes in nitrogen. The accurate timing necessary to
follow the fast front is obtained by a Kerr cell light shutter. A typical photograph
is shown in Figure 8, showing the sharp electron density gradient in the "snow
plow" front.
FIGURE 7. Interference fringes obtained by a Mach Zehnder interferometer viewing
a plasma jet expanding into a low-pressure chamber. (Courtesy Prof. D. Bershader,
Stanford University.)
Optical Faraday rotation can be used to study dense plasmas in strong magnetic
fields (8). The total rotation is given by Equation (5), where the collisionless linear
approximation is easily justified for these frequencies. Equation (5) then reduces to
180° \ ?
B\B R
1 - B*jB)
(10)
where B is the magnetic field and B R is the magnetic field necessary to give gyro
resonance, B R = w b mje. As an example, the plasma density in a 10-cm path with
20 kilogauss applied, necessary to give 90° of rotation at A = 2.6 microns, is
4.36 x 10 ,8 /cm 3 . The sensitivity increases in direct proportion to the density, the
wharton ; Plasma Diagnostic Techniques
15
path length, and the magnetic field applied. Crossed polarization plates, sensitive
to rotation as small as 5% are experimentally feasible.
12. Conductivity Probes
Plasmas having high collision rates have appreciable real components of conduc-
tivity. A small RF coil immersed in such a plasma will induce currents in the
plasma. The current is complex, the real part extracting power and the imaginary
part changing the coil's effective inductance by diamagnetic effects. In Figure 9
FIGURE 8. Schlieren photographs of a current sheet, traveling at 7 cm usee between
parallel plates in a plasma accelerator. (Courtesy R. Lovberg. General Atomic, San Diego,
California. I
the unloaded coil is resonated at the drive frequency / . The plasma current then
both detunes and de-Q's the circuit much as in the ease of resonant cavities. When
v?w and w r ?w. the major effect of the plasma on the coil is in lowering its Q. If
the coil is immersed in the plasma so that the plasma conductivity a is uniform in
space, the change in Q is approximately
1
Qi(t)
i
aJt)
(11)
In most experiments, however, u is not uniform, since the coil is mounted on a
form or otherwise obstructs the plasma. Calibration is then conveniently carried
out with ionic solutions (9). whose conductivities can be measured directly with a
platinum electrode conductivity cell. For example, the data of Figure 9 was
16
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
CONDUCTIVITY, MHOS/METER
FIGURE 9. RF conductivity probe calibration data. The changes in Q of resonant cir-
cuits due to the conductivity of enclosed ionic solutions are shown for frequencies of
1, 5, and 14 Mc. (After Wharton, Hawke, and Katz 1982.)
whartox: Plasma Diagnostic Techniques
obtained in an experiment at Livermore (10) from a coil wrapped around a section
of pyrex plasma chamber which had been removed and filled with a conducting
solution. The Q was measured by observing the width ?/ at half-height of the
frequency response, where
? - L TO
The center frequency / was held constant by trimming C x slightly as the conduc-
tivity was varied. Q was 105 for the 5-Mc coil and 85 for the 14-Mc coil, with
distilled water in the chamber. A Faraday screen inside the coil helped reduce
electrostatic effects between the coil and the solution, and later when the assembly
was used to study high density plasmas.
13. Langmuir Probes
\ conducting probe immersed in a plasma will emit or collect current, depending
upon the voltage impressed (11). The technique has been extensively used and in
many cases the quantities measured compare very well with those obtained by other
means (12).
13a. Single Langmuir Probes
Typical characteristics for a single probe, whose dimensions are small compared
to electron and ion mean-free paths, are shown for a plasma in the absence of
magnetic field, in Figure 10.
The probe potential is measured in respect to some convenient, fixed-potential
point, such as the anode or walls of a discharge tube or a floating "wall probe"
which has an area at least 50 times as large as the probe itself.
When the probe potential V is made very negative aU electrons are repelled and
only ions collected. The random ion current passing through an area A in the
plasma is related to the ion density and the velocity
_ 7 + _ n + v th w+ l 2kT (13)
J+ ~ A, ~ 4 4 V m +
where i + is the random ion current, amp,
J + is the random ion current density, amp/m 2 ,
A? is the area of the probe, m 2 ,
m + is the ion mass, 1.67 x 10" 27 kgm for protons,
n + is the ion density, no./m 3 ,
?; lfc = (2ifcT/m + ) 1,2 = mean kinetic ion velocity, m/sec.
Equation (13) would be valid also for ion current collected by a probe if the
presence of the probe caused no perturbation in the surrounding random plasma
currents. The probe does perturb the plasma, however. The volume which the
probe occupies provides an energy sink for all particles which strike it and the
fringing fields extend for a considerable distance into the surroundings (13). As a
result, the collected ion current density seems to be more a function of the electron
temperature than of the ion temperature. This effect is due to the formation of a
positive sheath around the probe. The extent of the sheath's influence is determined
by the electron temperature. For T t <T e the ion current density is nearly in-
dependent of the ion temperature, and equation (13) can be modified to (14)
J + ~ 0An + /^ amp/m 2 (14)
18
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
J (CURRENT DENSITY)
VOLTS
LOG J_L- J +
10 VOLTS
LINEAR CHARACTERISTIC.
LOGARITHMIC CHARACTERISTIC
10 20 i '30 i?0 VOLTS
-i r-
DOUBLE FLOATING PROBE CHARACTERISTIC
FIGURE 10. Langmuir probe characteristics plotted on linear and logarithmic scales.
If secondary electrons are emitted by the collected ions they also give a positive
current indistinguishable from the ion current.
When V is made less negative, a few of the high-energy electrons are collected,
partially cancelling the positive ion current. As the potential is changed further in
the positive direction, the random ion and electron currents collected just cancel.
This probe-plasma potential, V F in Figure 10, is the "floating potential". For a
thermalized plasma this voltage is approximately \1cT e (expressed in electron volts).
Increasing V beyond V F results in a steep rise in electron current, in region II.
This current eventually saturates at the "space potential" value, V s , due to space-
charge limitation in current collection. According to the sketch in Figure 10, we
have V s = 0. In region II the probe electron current follows a logarithmic dependence
ln/e = + (w) F+ln ^ J ° < 15 )
where A, is the area of the probe sheathe A p ,
wharton : Plasma Diagnostic Technique.
19
FIGURE 11. Probe and waveguide assemblies mounted in tubing introduced through a
vacuum wall with Wilson seals. (Courtesy General Atomic, San Diego, California.)
J is the random electron current density, amp/ni 2 ; J =J S + '?/_ I.
i is the electron charge. 1.6 x 10~ 19 coulomb,
kT e is expressed in electron volts.
The total probe current is the difference between the electron current and ion
current. Since it is the total probe current. I, that is measured, to find I,, in
equation (15) we write
I e = I+\J + \ and J C =J + \J^\
(16)
20 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Equation (16) implies that the probe sheath is thin compared to probe dimensions,
so that A s xA? and is constant in size. In many experiments the sheath thickness
X<0.1 mm and we are justified in using equation (16).
When we plot the logarithm of J e versus probe voltage V or display the current
on an oscilloscope having a logarithmic amplifier, as in Figure 10, the slope yields
the electron temperature
T dV ~ AF cY (17)
J *-d[ln(J+|J + |)]~A[ln(,/+|J + |)] eV ( >
The slope of Figure 10 corresponds to ~1.5 eV.
Increasing the probe voltage beyond V s does not cause J to rise much higher than
J s , due to spacecharge. The spacecharge saturation current is
I s = J s A s zJ A s = ^ 2 -^ (18)
Comparing equation (18) with equation (14) we note that
(19)
J + ~ V 2m e
13b. Single Probe with a Magnetic Field
When a magnetic field is present, conditions alter. Since the effective mean-free-
paths may now compare to prove dimensions, the electron spacecharge saturation
current is reduced. It is only the mobility transverse to the field which is impaired,
however, and electrons may flow along the lines essentially unimpeded, so that the
probe may actually be sampling the conditions in the plasma some distance away.
There may also be a "short-circuiting" effect if magnetic lines connect the probe
with conducting surfaces, so that current can flow in the conductor across the field
lines.
Since the ion gyro radius is much bigger than that of electrons, the ion saturation
current, J + , is not affected much until the field strength is fairly large.
By ordering the axis of the probe either along or across the field lines, the
collection of electrons across and along field lines, respectively, may be observed.
The /- V slopes at low current values are essentially the same and at moderate field
strengths the log-plot still yields valid electron temperatures (14).
Figure 11 shows two Langmuir probes and two microwave horns mounted in
movable vacuum seals that permit positioning the probes anywhere inside a
chamber within 0.05 inch.
13c. Double Floating Probes
To avoid drawing the large electron currents of region III in Figure 10 the double
floating probe technique is useful (15). Two probes, ordinarily of equal area, are
inserted into the plasma and the difference in current due to an applied voltage
difference is measured.
13d. Double Probes, No Magnetic Field
In the absence of a magnetic field the characteristics look similar to the bottom
graph of Figure 10. For equal probe areas the top and bottom parts are symmetrical
and represent only the magnitude of the saturated ion current. This is so since the
difference of the probe currents must be zero and when the negative probe reaches
wharton: Plasma Diagnostic Techniques 9\
ion saturation the current of the positive probe must also saturate. The saturation
value is again given by equation (14) if the electron temperature is known. Since a
plasma is grossly neutral we may presume that n e = n + .
To find the electron temperature we may use equation (15) again. It will be
convenient to rewrite it in the notation used in the bottom graph of Figure 10
We shall be very general and presume that the probe areas are not equal and
therefore I pl # I p2 .
Since the net current to the system must be zero,
^>i + -fp 2 = 2 I v = I ei + I e 2 = AJ o exp (<j>V -,) + J^o exp (<f>V 2 ) (20)
where A 12 is the area of the respective probes,
J is the random electron space current density,
V 12 is the plasma-to-probe potential,
v D =v 2 -v lt
■* D = *pl *el = le2~-lp2>
9 kT e T e (eV) ~ T e (-K)'
The logarithm of equation (20) is
The slope of equation (21) plotted against V D yields the electron temperature, just
as in section 13a.
13e. Double Probes in a Magnetic Field
Double probes are not influenced as much by magnetic fields as are single probes.
The collected current is governed by ion mobility and it is not until the magnetic
field strength is very large (several thousand gauss) that the ion gyro radius is as
small as the probe size.
When the field is large so that the collected ion current is limited by the orbital
motion, the Mott-Smith (16) theory applies. For large negative potentials (large
sheath thickness) the slope of ion current squared versus voltage gives the ion
density
d(Jf) 2e 3 ?
ir = - ^ "? (22)
14. Plasma Wave and Resonant Probes
When plasma waves or oscillations are present they may be detected with
probes. Spacecharge waves may also be launched with probes, but this method of
launching tends to excite all modes. Langmuir-type probes having coaxial shields
brought up near the collecting surface are adequate for many measurements up to
frequencies of 1000 Mc (17). A pair of small disc probes has been used successfully
to measure w p in dilute plasma (18) and, in fact, wire and disc probes were used in
experiments that probably were the first microwave diagnostic measurements (9).
Probes fed by resonant transmission lines (19) permit measurement of the plasma
impedance, wave damping, and wavelength. Probes loosely coupled to a tunable
filter, such as a motor-driven coaxial resonator (20), permit rapid analysis of the
frequency spectrum of oscillations picked up in the plasma, or as a means to filter
received signals. The movable probes shown in Figure 11 were used for these
purposes, as well as for Langmuir probes.
22 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
15. Magnetic Probes
Small inductive probes immersed in the plasma will have voltages induced in
them by changes in the local magnetic field, dBjdt (21, 22). Field sensitive elements,
such as Hall current probes, measure the instantaneous magnitude of the magnetic
field, B . Magnetic probes may be made as small as 1 mm in diameter and grouped
i n x-y-z arrays to measure three-dimensional field configurations (23). Current
density contours and the presence of hydromagnetic instabilities in dense plasmas
are measured by a linear array across current channels. The data can be displayed
by rapid sampling. The output voltage of the coil-type probe may be integrated
to yield the magnitude of field. The resulting signals are very small (depending on
the integration time) and care must be used to avoid stray pickup. Hall probes have
outputs of a volt or so, response times up into the megacycle range, and are easily
calibrated with a standard magnet. They are somewhat temperature- sensitive.
Another kind of coil assembly that measures rates of change in enclosed current
channels is the Rogowsky loop or girdle (24). The assembly consists of two sets of
coils, one around the entire experimental region and the other around only the
current channel or a part of it. The difference in induced voltage represents the
currents not enclosed, such as wall currents. The coils may be segmented, with leads
brought out separately, to indicate current profiles.
Low inductance coils can also be used to pick up high-frequency fluctuations,
such as those associated with ion wave instabilities or ion cyclotron frequency
instabilities. These frequencies are typically from 10 kc to 10 Mc.
16. Optical Spectroscopy
Spectroscopic observations have been extensively used for plasma studies,
especially for equilibrium plasmas, where the Saha conditions apply (25). A great
deal of work has been done in applying the "standard techniques" of Doppler
broadening, Stark broadening, Zeeman splitting, and line identification to the
understanding of intense discharges. For atoms that exhibit first-order Stark
effect, some idea of the ion density can be derived through application of microfield
theories from measurements on the extent of the profile wings. The use of a
Fabry-Perot interferometer increases the resolution (26).
The thermal Doppler broadening of such lines as the ionized He II 4686 A pro-
vides direct measure of the mean kinetic energy of the ions, when no mass motions
are present. Presuming equilibrium, the Doppler width is (27)
AAo = v* = 1 /2*T, (23)
Ac c \ m i
The line half width then becomes
2A'A = 1.67AA D = 7.1x10
7 V A
where A is the ion mass relative to hydrogen. This is typically a fraction of an
Angstrom at temperatures of 10 6 °K .
Stark broadening becomes measurable only at ion densities above 10 1 /cm .
Below this density (and even above, if the ion temperature is high) the Doppler
broadening dominates.
Electron density in hydrogenic plasmas can be measured by observing the
t>-i : n: — T'v.n in <- T-oonhmWp llnp ia somewhat below the theoretical
-DctllUCi !5Cllt.tt Ul unco. ai'V' ai*uu .i/.?.. i ?. — - -
wharton: Plasma Diagnostic Techniques 23
limit because of the smearing of emission wavelengths due to the microfields. The
last resolvable line is given by Inglis and Teller (28)
.i.i ^ js m n e e - — ^ (24)
(25)
a m.
or when expressed in terms of density
~ 1Q23
W e ~ ATI 5/2
x? m
where a is the atomic Bohr radius,
Z is the atomic number,
N m is the total quantum number of the last distinguishable line,
e is the electron charge,
n e is the electron density.
For hydrogen when H 20 can just be resolved, the density is n,^3x 10 13 /cm 3 . The
Balmer limit is at Ax 3650 A.
At high temperatures the plasma is almost totally ionized and very little visible
light is emitted. Most of the faint emission then appears in the ultraviolet and
special techniques must then be used (29). In some experiments there are impurities
such as O or C whose radiation can be viewed, or impurities such as He or A may be
added.
17. Fast Photography
Discharges which emit intense light, such as pinches and shocks, may be studied
with time-resolved photography. The diameter of the luminous column may be
recorded as a function of time by sweeping the image of a viewing slit with a
rotating mirror. Framed pictures may also be taken with Kerr cells, image-con-
verter tubes, and rotating-mirror framing cameras. The lines of a spectrometer may
be scanned by the use of rotating slits or mirrors, to give time-resolved spectra.
Such measurements of the luminous features of discharges must be backed up bv
other measurements. For example, in shock tubes "precursors" and other fast
ionization and excitation fronts often precede the main shock front. The details of
constriction often follow the dips of current in fast pinches and the development of
instabilities is easily discernible.
REFERENCES
1. Wharton, C. B., "Microwave Diagnostics for Controlled Fusion Research",
Univ. of California Radiation Lab. Report UCRL-4836 (Rev.) (September
1957).
2. Heald, M. A., and Wharton, C. B., Plasma Diagnostics with Microwaves
(to be published by John Wiley and Sons, 1964).
3. Drummond, W. E., "Microwave Scattering from Unstable Plasma Waves",
Phys. Fluids, 5, 9, 1133 (1962).
4. Boley, F. J., "Scattering of Microwave Radiation by a Plasma Column",
Nature, 182, 790 (1958).
5. Ascoli-Bartoli et al., "Interferometric Study of a RF Discharge", paper
presented at VI Inter. Conf. on Ionization Phen. in Gases, Paris, 1963.
6. Serchuck, A., "Commercially Available Optical Masers", Microwave, 1,
54-57 (1962).
2 +
24 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
7. Lovberg, R., "Acceleration of a Plasma by Displacement Currents Resulting
from Ionization", paper presented at VI Inter. Conf. on Ionization Phen. in
Gases, Paris, 1963.
8. Dougal, A. A., "Optical Maser Probing Theory for Magnetoplasma Diag-
nostics", paper presented at 4th Symposium on Engineering Aspects of
Magnetohydrodynamics, Univ. of California, Berkeley, 1963.
9. van der Pol, B., "The Influence of an Ionized Gas on the Propagation of
Electromagnetic Waves" (Thesis, Utrecht University, The Netherlands,
April, 1920).
10. Wharton, C. B., and Hawke, R., "Calibration of RF Conductivity Probes by
Immersion in Ionic Solutions", Univ. of California, Lawrence Radiation Lab.
Electronics Engineering Report (July, 1962).
11. Tonks, L., and Langmuir, I., "Theory of the Arc Plasma", Phys. Rev., 34, 876
(1929).
12. Schulz, G. J., and Brown, S. C, "Microwave Study of Positive Ion Collection
by Probes", Phys. Rev., 98, 6, 1642^9 (June, 1955).
13. Generalov, N. P., "The Theory of Probes", J. Nuclear Energy, 9, 148 (1959),
translated from Atomnaya Energiya, 4, 183 (1958).
14. Bohm, D., Burhop, E. H. S., and Massey, H. S. W., "Use of Probes for Plasma
Exploration", in A. Guthrie and R. K. Wakerling, eds., The Characteristics
of Electrical Discharges in Magnetic Fields (New York: McGraw-Hill, 1949),
Chapters 2 and 9.
15. Johnson, E. 0., and Malter, L., "A Floating Double Probe Method for Measure-
ments in Gas Discharges", Phys. Rev., 80, 58 (1950).
16. Langmuir, I., and Mott-Smith, H., "Studies of Electric Discharges in Gases at
Low Pressures", Gen. Elect. Rev., 27, 449, 538, 616, 762, 810 (1924).
17. Bailey, R. A., and Emeleus, K. G., "Plasma Electron Oscillations", Proc. Roy.
Irish Acad., 57A, 53 (May, 1955).
18. Yeung, T. H. Y., and Sayers, J., "An RF Probe Technique for the Measure-
ment of Plasma Electron Concentrations in the Presence of Negative Ions",
Proc. Phys. Soc. (England) N451B, 70, 663 (1957).
19. Levitskii, I., and Shashurin, S., "Resonant Microwave Probe for Measuring
Charge Density in a Plasma", Zh. Tekh. Fiz. {USSR), 31, 4, 436 (1961).
20. Malmberg, J. et al., "A Collisionless Plasma for Wave Propagation Studies",
paper presented at VI Inter. Conf. on Ionization Phen. in Gases, Paris, 1963.
21. Lovberg, R., "The Use of Magnetic Probes in Plasma", Ann. Phys. (New
York), 8, 3, 311 (November, 1959).
22. Colgate, S. A., "A Summary of the Berkeley and Livermore Pinch Programs",
Proc. 2nd U.N. Conf. on Peaceful Uses of Atomic Energy (Geneva) P/1064 and
P/369, 32, 123-139 (1958).
23. Pollock, H., Goldman, L., and Westendorp, W., "Multiple Magnetic Probe
Measurements in Compressed Deuterium Plasma", Bull. Amer. Phys. Soc, 5,
337-383 (1960).
24. Golovin, I. N. et al., "Stable Plasma Column in a Longitudinal Magnetic
Field", Proc. 2nd U.N. Conf. on Peaceful Uses of Atomic Energy (Geneva)
P/2226, 32, 72-81 (1958).
25. Griem, H., and Kolb, A., "Advances in the Theory of Broadening of Spectral
Lines", paper presented at IV Inter. Conf. on Ioniz. Phen. in Gases, Uppsala,
Sweden, 1959.
26. Gardner, A. et al., "Diagnostic Measurements on the P^ Steady State Plasma",
Univ. of California Radiation Lab. Report UCRL-6562 (October, 1961).
wharton: Plasma Diagnostic Techniques
27. Wulff, H., "Plasma Diagnostics by Spectroscopical Means", Nuclear Instru-
ments and Methods, 4, 352 (1959).
28. Inglis, D. R., and Teller, E., "Ionic Depression of Series Limits in One-electron
Spectra", Astrophys. J., 90, 439 (1939).
29. Kelly, R. L., "A Grazing Incidence Vacuum Spectrograph of Simple Design",
Stanford Research Institute Report SD-3006-2 TR1 (December, 1959).
2. John A. Thornton: Electric and
Electromagnetic Shock Tubes
12? The classical diaphragm shock tube presents serious limitations
in the production of very high temperatures and velocities. Accordingly,
electric and electromagnetic shock tubes have received considerable
attention as devices capable of generating shock waves both of extremely
high Mach numbers, up to several hundred, and of extremely high
temperatures, over one hundred thousand degrees Kelvin. Recent
investigations have indicated several characteristics, such as electron-
driven shocks, precursor effects, and driver-driven gas mixing, which
affect the applicability of these shock tubes as research tools. These
investigations are surveyed and consideration is given to the poten-
tialities, limitations, and design trends which they suggest for electric
and EM shock tubes as laboratory devices. Finally, important
diagnostic techniques are surveyed.
INTRODUCTION AND GENERAL DISCUSSION
An electric shock tube is defined as a shock tube in which the driving energy is
imparted to the gas by electric means, and an electromagnetic or EM shock tube as
a device in which the driving energy is imparted to the gas by both electric and
magnetic means. The emphasis in this paper is directed at the electric and EM
shock tubes as laboratory devices for experimental studies in plasma physics
although it is to be noted that the driving processes in many of the pulsed-plasma
accelerator concepts being investigated for propulsion applications are very similar
to those in EM shock tubes.
The conventional gas-driven diaphragm shock tube has become a very important
research tool in experimental gas dynamics because the thermodynamic state of the
shocked gas is completely defined, in principle, at least, by three easy-to-measure
parameters: the pressure and temperature in the expansion chamber and the shock
velocity (1-4). Nevertheless, such shock tubes are severely limited in producing
high-velocity, highly-ionized plasmas. To understand these limitations and the
potentialities of electric and EM shock tubes, it is profitable to consider briefly the
classical shock tube formalism. Figure 1 is a sketeh of the theoretical pressure
distribution in a classical shock tube shortly after the diaphragm has been broken.
The regions defined in this figure have become incorporated into standard shock
tube nomenclature as subscripts and will be used throughout this paper.
According to a linearized perfect gas analysis, the shock Mach number M s is a
function of the initial pressure ratio Pijp x and the species of the gases in the driver
ed. note: Dr. Thornton is with the Space Sciences Laboratory, Litton Systems, Inc.,
Beverly Hills, California. This work was performed under the sponsorship
of the Air Force Office of Scientific Research under grant No. AFOSR
62-307.
27
28
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
INITIAL DIAPHRAGM POSITION
i:kexpak[)kd
driver gas
(REGION 4)
FOOT OF RAREFACTION
WAVE
CONTACT SURFACE
EXPANDED / DRIVEN
DRIVER /OR SHOCKED
GAS C GAS
(REGION 3) S (REGION 2)
SHOCK
FRONT
BACKGROUND GAS
(REGION 1)
X —
FIGURE 1. Pressure distribution in a diaphragm shock tube (theoretical).
section (region 4) and the expansion section (region 2); it is given implicitly by the
following equation:
2y 4 /(y 4 -l)
(1)
Pi
Pi
2y 1 M s 2 -(y 1 -l)
yi + l
(y 4 -l) o,/ J_\
where a is the sonic velocity and y is the ratio of specific heats. Equation (1) can be
thought of as defining the regime of performance of the classical shock tube con-
cept (see Figure 2). This regime is bounded by two extremes in the shock tube
driving potential; at one extreme the pressure ratio Pijp-i is due to a density-
generated pressure in the driver (p 4 ) and at the other extreme to a thermal-
generated pressure in the driver gas. The low performance curve on the left in
Figure 2 represents a density-driven shock tube with identical gas species at
identical temperatures on both sides of the diaphragm and is defined by setting
Ni>N lt yi = y 4 , and T i = T 1 = T, and noting that a=VyRT in equation (1)
(N = particle number density). The high performance curve corresponds to a
thermal-driven shock tube with identical gas species at identical densities on both
sides of the diaphragm and is defined by setting T i >T 1 ,y 1 =y i , and N i = N 1 .
It is easily shown that in the limit of an infinite pressure ratio the maximum
obtainable shock Mach number is independent of the pressure ratio and depends
primarily on the sonic velocities in the driver and driven gases (1). Accordingly,
diaphragm shock tube performance is improved by using light gases such as
hydrogen or helium in the driver; in addition, the driver gas is often heated by
combustion or by an electric discharge technique (4). Theoretical performance
curves for several driver configurations are shown in Figure 2, where it can be seen
that they simply tend to make the shock tube performance curve approach that of
the thermal shock tube. Equation (1) has been solved for a thermal shock tube with
a y of 5/3, yielding (5)
0.77
where m t is the ion mass. Equation (2) can be written as
M s = — s = oW- 4 ^ = 0.60(^l
?i W \Pil
1/2
(2)
(3)
Indeed, the thermal shock tube, in which the driving pressure is generated entirely
by the temperature and which has, therefore, the highest possible driver-section
Thornton : Electric and Electromagnetic Shock Tvhes
29
11 r
10 [-DENSITY-DRIVEN
SHOCK TUBES
* N
7, = 7,=-|- AIR-AIR
10" -
10
10
10"
10
10"
10'
10
- a V? =i . "V? -i.if
AIR-AIR*
'V?=3.16/
'4
COMBUSTION-DRIVEN
(70% H e IN STOICHIOMETRIC
? MIXTURE OF \\ z AND 2 )*
FIGURE 2. Diaphragm shock tube performance (theoretical).
sonic velocity for a given gas species and pressure, constitutes the performance
limit for the classical shock tube concept and accordingly might be called the
idealized shock tube.
The simple electric shock tube such as the T-tube shown in Figure 3 is an
example of a thermal shock tube. The potential energy is stored in power storage
capacitors and enters the gas in a very short time via an electric discharge, thereby
generating a high temperature plasma in the electrode region. This discharge
ELECTRODES
GLASS TUBE
TO
VACUUM
PUMP
FIGURE 3. Fowler's T-tube apparatus.
30 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
plasma then constitutes the driver gas of the electric shock tube. In the EM shock
tube the discharge plasma is in effect given an additional acceleration by the
interaction of a magnetic field with the discharge current. Although the electric
discharge produces a thermal driver and makes the electric and EM shock tubes
capable of extremely high Mach numbers, it also introduces several serious com-
plications which affect their applicability as research tools. These characteristics,
outlined as follows, are discussed in more detail in subsequent sections:
(1) Even though much research has been done on the electric discharge, it
remains one of the least understood of nature's phenomena. Thus it is not
possible to predict the conditions in the discharge plasma from the initial
conditions of capacitor energy and ambient pressure, and reproducibility is
often poor.
(2) A high driver-section sonic velocity is desirable for high shock velocities;
however, coupled with the short lengths of the driver plasma and the short
periods of coupling between the magnetic field and the discharge plasma in
most EM configurations, this results in severe shock velocity attenuation.
(3) Measurements in electric shock tubes are usually made at points much
closer to the electrode region than to the diaphragm in classical shock tubes
in corresponding measurements. This results in a short region of shocked gas.
Also, the ambient pressures employed in electric shock tubes are generally
less by orders of magnitude than the pressures employed in diaphragm shock
tubes. Accordingly, under some conditions the discharge plasma may be out
of equilibrium during the acceleration and expansion processes. Also, the
contact surface breaks down, and at low pressures a complete mixing of the
driver and driven gases occurs. Not only are the shocked gases perturbed
from behind by the breakdown of the contact surface, but also the cold gas
ahead of the shock front is perturbed by the absorption of ultraviolet and
X-ray radiation from the discharge. Therefore the Rankine-Hugoniot
equations generally cannot be used with a simple measurement of the shock
velocity and ambient pressure to compute the thermodynamic state of the
gas behind the shock front.
DEVELOPMENT OF ELECTRIC AND ELECTROMAGNETIC
SHOCK TUBES
While the diaphragm shock tube seems to have been a rather logical invention
extending from the definition of a shock wave, the electric shock tube was dis-
covered in 1951 by R. G. Fowler and his students (6-7), who were using the
T-tube arrangement shown in Figure 3 to investigate the luminosity which
invaded branch paths after low pressure gaseous discharges. They observed this
luminosity in the side arm of the T-tube, attributed it to a violent expansion of the
ion cloud created in the discharge, and concluded that the expansion frequently
generates luminosity-producing shock waves with Mach numbers as high as 30.
Recognizing the possibilities of an electric shock tube for aerodynamic investiga-
tions, Fowler's group continued their work (8-10).
Elsewhere, however, diaphragm shock tubes were considered adequate for
generating the thermodynamic states of interest at that time (Mach 20 and less)
and they continued to dominate the scene for the next five years. By 1955 the
increased interest in controlled thermonuclear fusion, space propulsion, and
hypersonic aerodynamics (particularly reentry problems) made it desirable to
produce in the laboratory high temperature plasmas, often with extremely high
thorntos: Electric, and Electromagnetic Shock Tubes
31
VACUUM LINE
BACK STRIP
TEST GAS FEED LINE
FIGURE 4. Electromagnetic T-tube.
velocities. In 1956 Kolb added an external magnetic field to Fowler's T-tube
(11-12), thus forming the first EM shock tube. The field was provided by coupling
a backstrap or coil to the primary discharge or by a separate but synchronized
current source. The primary circuit backstrap type of the EM T-tube is shown in
Figure 4.
Soon many additional EM shock tube geometries were developed. Blackman
discharged a low-inductance condenser through a single-turn copper coil wrapped
SPARK GAP
SWITCH
RETURN
STRAP
(1 OF 6)
PYREX
EXPANSION
TUBE
CENTER \RING
ELECTRODE ELECTRODE
FIGURE 5. Conical electromagnetic shock tube.
32
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
around a straight glass tube and generated reasonably plane shock waves (13).
The group at AVCO developed an annular electromagnetic shock tube (MAST)
which has produced strong one-dimensional shock waves of over 200 (14-15).
The MAST has been used in a continuing research program to study the structure
of strong shock waves propagating into a transverse magnetic field (16-18).
Josephson developed the conical configuration shown in Figure 5 in attempting to
obtain less contamination of the gas (19). A group at Lockheed conducted experi-
ments using EM T-tubes, conical tubes, and the cylindrical configuration shown
in Figure 6 (20-22).
REAR INSULATOR
- CYLINDRICAL ELECTRODE
PYREX
EXPANSION
TUBE
CENTER ELECTRODE
SPARK GAP SWITCH
FIGURE 6. Cylindrical electrode electromagnetic shock tube.
In subsequent years many investigations have been conducted, not only in the
"laboratories where these original geometries were developed but also in other
industrial and university laboratories in this country and abroad, as summarized
in Table I. In a number of the early investigations it was enthusiastically assumed
that many of the desirable characteristics of the classical shock tubes would also be
applicable to the electric and EM shock tubes. Later investigations discovered the
limitations listed in the introduction.
Recent reports describe new configurations attempting to minimize the
limitations and to make electric and EM shock tubes more useful laboratory tools.
Smy (23) reports a new EM shock tube designed with a Mylar diaphragm separa-
ting the electrode region from the expansion tube. A dense gas such as nitrogen is
used as the driver to impede the attenuation process. It was noted in the preceding
section that the result of a very high sonic velocity in the driver is a high initial
shock velocity and a high rate of shock velocity attenuation. Thus Smy s intention
was to reduce the velocity attenuation at the expense of the initial shock velocity.
Also his diaphragm shields the cold gas from precursor radiation originating in the
electric discharge.
It might be said that Smy's modifications are moving in the direction ot a
compromise between the EM shock tube and classical gas-driven shock tube.
Indeed this is the case in a new configuration developed by Camm and Rose (24).
Energy densities of up to 400 J/cc are discharged into a helium filled driver section
10J inches long. The helium, which is initially at a pressure of a few hundred psi, is
raised to 10,000 to 20,000 psi and a temperature of 10,000 to 20,000°K. The high
pressure bursts a scribed diaphragm and drives a shock wave with velocities as high
as 43 000 ft/sec down a 20-ft expansion tube filled with air. Electrical heating of the
driver in a classical shock tube is not new (4), but the Camm-Rose tube is believed
to be the first of this type in which the major component of the driving pressure is
thermal-generated, and accordingly we classify it as an electric shock tube. Initial
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36 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
tests indicate that the average shock velocity attenuation is low and that test
time intervals between the shock front and contact surface approach theoretical
values. However, despite the fact that their shock tube is a recent innovation,
Camm and Rose conclude that the device is operating near the limits of test time
and velocity which can be expected from a shock tube operating in this manner,
since radiation effects appear to make it difficult to maintain the driver temperature
above 20,000°K regardless of the initial conditions.
Recently Fowler has tested an electric shock tube with a segmented many-
electrode driver section 1 m long (25). Early experiments indicate that shock
Mach numbers of several hundred can be obtained. The long driver section
maintains a high electron temperature (estimated ~10 6 °K), and preliminary tests
indicate that shock velocity attenuation is small.
THE ELECTRIC DISCHARGE AND THE SHOCK EXPANSION
During the low pressure gaseous discharge in an electric or EM shock tube, the
electric field imparts the capacitor energy preferentially to the electrons. This is
due to the inertial effect which prevents the ions from being accelerated between
collisions to the same velocity as the electrons. Thus, at the conclusion of the
discharge, if the pressure is low, the electron temperature may be several orders of
magnitude greater than the neutral or ion temperature. The characteristic time for
thermal equilibration between electrons and ions in a fully-ionized gas is a function
of ljN e and T e 3 ' 2 and a weak function of T t for T e > T t (26). For example, in an
argon plasma with an electron temperature of 20,000°K, an ion temperature of
about 1000°K, and an electron density of 10 17 electrons/cc, the thermal equili-
bration times have been estimated to be of the order of 0.1 [xsec; but when N e = 10 15 ,
the equilibration times can be of the order of 10 jxsec (27). Under such conditions
the electron partial pressure in the driver plasma is indeed the primary source of
shock motion for sustained lengths of time. The instantaneous total pressure in the
driver plasma is the sum of the partial pressures of the electrons and the heavy
particles. Therefore, because of the competing processes of energy injection and
thermal equilibration, it is possible under certain conditions of tube size and
voltage for the total pressure to exhibit two maximums, the first giving rise to the
electron-driven shock wave and the second resulting from equilibration and
providing the source for a second shock wave which we shall arbitrarily call the
"hydrodynamically-driven shock wave" because the driver plasma is now in or
near thermal equilibrium.
The existence of electron-driven shock waves was first recognized by Fowler (28),
who observed that in small-diameter electric shock tubes (~1 mm) and at low
pressures (~1 mm Hg) electron-driven shock waves would propagate from the
electrode region at times which were nearly an order of magnitude too brief for
thermal equilibration. In larger diameter tubes at low pressures, two shock fronts
were observed: an electron- driven front followed by a hydrodynamic shock front.
In these large diameter tubes at higher pressures only the hydrodynamic fronts
were observed.
Fowler concluded experimentally (28) that the velocity of the electron-driven
shock fronts can be approximated bv
where a i = {kT e jm i ) 112 is the effective sonic velocity of the non-equilibrium driver.
The similarity between equation (4) and equation (2) for the thermal shock tube
thorntos: Electric and Electromagnetic Shock Tubes 37
The energy exchange process in the EM shock tube is complicated by the
coupling provided by interaction between the discharge current and the magnetic
field and is therefore very sensitive to the electrode geometry. While various
attempts have been made to uncouple the magnetic and thermal driving processes
for the purpose of analysis (29-34), the emphasis here will be on the qualitative
features of the problem. In effect a "glob" of driver plasma is created by the electric
discharge and is driven from the electrode region by the magnetic field.
In most configurations the magnetic acceleration is of limited duration. After
that the moving plasma undergoes an expansion which approaches that of a one-
dimensional blast wave because of the short length of the glob of accelerated plasma
(21, 35-37).
In the conical configuration the driver plasma is compressed as it is driven from
the electrode region. This increase in the density of the driver plasma thereby
increases the rate of thermal equilibration and decreases the threshold pressure
below which electron-driven shock waves are expected. Though electron driven
shock waves have been reported in conical tubes (28), evidence of thermal equili-
bration has been found at a point 8 inches from the ring electrode in a 3-inch
diameter tube operating with argon at an ambient pressure of 50 [A-Hg (27).
Fowler (38) has noted that although the driving effect of the magnetic field in the
EM T-tube can be thought of as forcing the discharge current loop into the side
arm, where its driving effect is replaced by a rail-type drive produced by the
efforts of the hairpin current to straighten itself, the major effect of the magnetic
field may be to force hot electrons of the main discharge into the side arm where
their electron pressure supplies a drive which is not weakened by expansion as in
the classical shock tube. The blast wave nature of the ensuing shock motion
would then be explained by noting that T e ccEccVlx where E is the electric
field strength at the shock front, V is the voltage on the capacitors, and x
is the position of the shock. The electron-driven shock front would then exhibit
the same velocity attenuation characteristics as the blast wave, i.e., V s ccx' 1!2
[equation (4)].
In general the highest velocities are obtained when the electrode geometry is
designed for an effective transmission-line or rail-type drive in which the magnetic
forces are more fully utilized (39). The MAST is such a device. The discharge
begins as a radial current in the annulus between concentric electrode cylinders.
The current sheet is then driven outward by the interaction between these radial
currents and the azimuthal fields which are present in the region between the
electrodes, and into an annular expansion tube with non-conducting walls. Thus,
as the drive progresses, two concentric axial sheet-current arcs form to connect the
electrodes with the propagating radial arc.
During the initial phases of the electric discharge, the electron temperature can
become very high resulting in large radiation losses and the removal of large
amounts of contaminants from the tube walls. Cases have been reported (40) in
which impurities have been vaporized from the driver section in sufficient amounts
to counteract the rarefaction waves and significantly reduce shock velocity
attenuation. Experiments show high levels of silicon wall impurities even in the
conical EM shock tubes which were designed to minimize this effect (27). These
contaminants increase radiation losses from the driver. Estimates made from data
obtained in electric (41) and conical-type EM (27) shock tubes indicate that only
1°, or 2°? of the stored capacitor energy can be accounted for in thermal and
kinetic energy of the expanding plasma, It is interesting to note that the rate of
shock velocity attenuation is not affected by radiation losses under most shock
tube operating conditions (37).
38
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
PRECURSOR EFFECTS
We shall define a precursor effect as any effect which results in a perturbation
of the state of the background gas ahead of a shock front. It is difficult to generalize
on precursor observations reported in the literature, because many of the papers
do not itemize information such as electrode material or the existence of ground
loops in the shock tube circuit — information which can be important in determining
what precursor process dominates in a given situation. However, precursor
phenomena can be attributed to three general processes — electron diffusion,
radiation, or breakdown waves — and have been observed in conventional, electric,
and electromagnetic shock tubes. Electron diffusion appears to be the dominant
mechanism in diaphragm shock tubes (42-44), although radiation effects have been
reported (45-47). Radiation and breakdown waves are the principal causes of
precursor effects in electric and EM shock tubes.
Radiation from the high temperature gaseous discharge results in photoelectric
emission from metallic surfaces within the shock tube and pre-excitation of the
background gas due to absorption. Radiation investigations generally consist of
three parts: (1) postulation of a type of radiation which would result in the
observed perturbation of the cold gas; (2) an experiment to show that the observed
phenomenon was not caused by fast electrons escaping from the highly ionized
plasma; and (3) an experiment to identify the source of the radiation. Although
photoelectric emission was observed in the first electric shock tube (8), recent
investigations have verified the existence of unbroadened precursor line emission
from the cold gas ahead of the shock front in both the T- (48) and conical (49) EM
shock tubes. The primary source of this precursor effect has been traced to radiation
emitted from the discharge region (50); and since the cold low pressure gas ahead
of the shock front is optically thin to radiation in the visible region, the source
must be attributed to radiation in the vacuum ultraviolet (A < 2000 A) or the
X-ray regions (A <50 A). Although kinetic models have been suggested (48-49) for
the absorption of ultraviolet radiation and the ultimate emission of the observed
line radiation, X-rays have been found prominent in forming an ionizing precursor
disturbance which travels through the background gas during the electric discharge
(51). This X-ray effect was observed in a conical EM shock tube, where the back-
ground gas faces the positive center electrode, when the discharge voltage was
above the threshold value needed to produce K a radiation from the positive elec-
trode. Radiation precursor effects have been found to be strongly dependent on
the impurity level in the background gas (85).
When electric or EM shock tubes are operated at low pressures, stray currents
have been observed to propagate downstream to grounded points along the
expansion tube such as vacuum system junctions (27, 52-53). Such currents, and
other propagating disturbances which cannot be attributed to radiation processes,
will be classified as breakdown waves. For example, an electrostatic disturbance
with associated faint luminous front has been reported (54) moving ahead of the
shock at approximately 3 x 10 7 cm/sec in a conical tube, and Kerr cell studies (55)
have shown what appeared to be the formation of a precursor boundary layer on
the surface of a probe placed in a cylindrical type tube. Luminosity producing
precursor waves have been observed (56) leaving the electrode region of the
segmented electrode electric shock tube immediately after the discharge and
moving more than a meter into the field-free region at velocities of 10 8 cm/sec.
The waves are attributed (57) to the very high electron pressure which develops in
such a device.
thorntox : Electric and Electromagnetic Shock Tubes 39
It is very difficult to make accurate quantitative judgments of how much these
precursor processes perturb the cold gas. Although microwave experiments can be
used to obtain information on the electron density [10 10 -10 13 cm" 3 (85-86)], it is
difficult to estimate the degree of excitation of the bound states since the back-
ground gas is not in equilibrium. The internal excitation of the bound states can
have a pronounced effect on the thermodynamic state which develops behind the
shock front (58-59). It should be noted, however, that under some low pressure
operating conditions contact surface breakdown would make it impossible to use
the Rankine-Hugoniot equations even if the state ahead of the shock front were
accurately known.
CONTACT SURFACE BREAKDOWN
The concept of a contact surface originates from the diaphragm shock tube
formalism and is defined as the diffusion interface which separates the gas which
was originally in the electrode region from that originally in the expansion tube.
The low pressures at which electric and EM shock tubes are often operated result
in a breakdown of the contact surface. The importance of this effect has been
illustrated by the experimental observations of Fowler (8), using electric shock
tubes, and of Chang (60), Cloupeau (52, 61-64), and this author (27), using EM
shock tubes. Fowler, Chang, and Cloupeau investigated the behavior of the shock
and contact surfaces as they were reflected from an obstacle or another shock front.
Chang identified the shock front by mounting a piezoelectric pressure probe in the
end plate of the shock tube. Fowler (8) and Cloupeau (52) identified the source of
the radiation by placing different gas species in the electrode and expansion tube
regions and making time-resolved spectroscopic observations. This investigator,
using time resolved spectroscopy, found evidence of impurities from the discharge
region throughout the slug of accelerated plasma in a conical EM shock tube.
The results of these observations can be summarized as follows:
(1) The dynamics of the driver and driven gases and the existence of a luminous
well-defined shock- heated region are very dependent on the ambient pressure,
test gas species, and firing voltage.
(2) At high pressures no luminosity is observed from the shocked gas even after
the shock is reflected, although the driver plasma is clearly luminous.
Spectroscopic investigations at these conditions in EM shock tubes show that,
although the contact surface has not broken down, some of the driven gas is
passing through the contact surface rather than being compressed in front
of it,
(3) As the pressure is lowered while the test gas and firing voltage are kept
identical with (2), above, the reflected shock becomes visible; and finally,
after continuing to lower the pressure one reaches a point where luminosity
can be observed from behind the shock front as it separates and moves ahead
of the contact surface. (The distance which the driver plasma propagates
downstream and the point of onset of the luminosity from behind the shock
front are very dependent on the test gas species and firing voltage.) Spectro-
scopic studies in EM shock tubes show that at these conditions there exists a
region of pure shocked gas followed by the driver plasma, mixed with some
of the driven gas. As the pressure is further reduced the primary shock front
becomes progressively more luminous and the contact surface becomes
indistinguishable. Under these conditions spectroscopic investigations in an
EM T-tube show that the contact surface has completely broken down and
that the driver plasma species can be found at the shock front (65).
40 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
The cause of the complete mixing is not clear at this point. It has been observed
at pressures which, in terms of equilibration times, are marginal for the existence
of electron driven shock waves. However, it has been noted in the preceding section
that a high electron pressure may be maintained at the leading edge of the plasma
as long as the discharge current continues to flow. Streak photographs indicate that
the current was still flowing when the mixing was observed. Cloupeau has suggested
that the discharge plasma may move into the tube as a projectile (or a group of
projectiles), creating a shock wave whose front stays scarcely detached from the
projectile. This model is very similar to Fowler's proposed theory for electron
driven shock waves (66) in which it is assumed that a hot electron gas expands
down the tube pulling a cold positive ion wind by the action of Coulomb forces.
All electron-neutral collisions are neglected except for ionizing ones, so that an
incident neutral atom passes through the front and continues at a constant velocity
until it is ionized.
Several other mechanisms might be suggested to explain the contact surface
breakdown. The deflection of the discharge current by the magnetic field may
cause a turbulent mixing of the driver and driven gases. This process may be
important in the conical tube where mixing has been observed in plasmas which
appear to be in thermal equilibrium. Other possibilities might be a boundary layer
allowing driven gas to escape past the contact surface (67) or a diffusion process,
since under some conditions the density of the driven gas at the contact surface will
be higher than that of the higher temperature driver plasma. The diffusion process
is of particular interest since, when two fluids are accelerated in a direction per-
pendicular to their interface and in a direction from the less dense to the more
dense, small irregularities in the interfacial boundary grow exponentially and
turbulence develops (Taylor instability) (68). Kerr cell photographs show that the
shape of the luminous front often is not reproducible and appears turbulent in
form (55, 87).
CONCLUSIONS
Electric and EM shock tubes are capable of generating gas samples with higher
temperatures and velocities than can be obtained in conventional gas-driven
diaphragm shock tubes. However, the simple electric and EM shock tubes of the
T-, cylindrical, and conical types are not suited for quantitative aerodynamic
studies because of the brevity of available test times and the blast wave nature of
the expansion, resulting in severe gradients in the thermodynamic state; nor are
they suited for chemical kinetic studies involving the reactions in the shock front,
because of precursor effects and contact surface mixing. Nevertheless, simple
electric and EM shock tubes are very useful when a high-temperature, high-
velocity gas sample is required. For example, EM T-tubes have been used for
measuring Stark profiles of helium and hydrogen lines in the visible spectrum (69),
and for ultraviolet line profile and oscillator strength measurements (70, 88).
Conical EM tubes have been used for semiquantitative magnetoaerodynamic
studies (71), for studying a small wire-resistance heat transfer gauge (72) and an
infrared heat transfer gauge (73), and to inject plasma samples into both cusp and
perpendicular magnetic fields (74-75). The simplicity and low cost of these shock
tubes make them particularly suitable for educational laboratories (76).
Although the Rankine-Hugoniot equations cannot be used to determine
accurately the thermodynamic state of the plasma sample (77), this information
can be obtained experimentally. Optical interferometers have been suceessfullv
thorxton : EUctric and Electromagnetic Shock Tubes 41
used to make time-resolved electron density measurements (77-78). Time-
integrated spectroscopy is useful in determining the impurities which are present,
and time-resolved line emission spectroscopy can be used to obtain the electron
temperature and density and the atom and ion densities throughout the accelerated
plasma if the electron density is high enough to insure a Boltzmann distribution
over the bound states (79). Time resolved spectroscopic measurements can be
made either by placing a rotating mirror or drum camera in series with the spectro-
graph, or by mounting one or more photomultipliers behind slits in the focal plane
of the spectrograph and feeding their outputs to oscilloscopes. Since a spectro-
graph with a small aperture ratio is required to expose the photographic film, the
photomultiplier method is recommended when spatial resolution is important.
Both smear camera (58) and photomultiplier techniques have been used to make
time-resolved line profile measurements (80). Microwave techniques such as inter-
ferometry. attenuation, and phase shift have been used to measure plasma
velocities (20) and to investigate electron densities (81). The microwave techniques
are limited by rather poor spatial resolution but are particularly well suited for
precursor measurements where spatial resolution is not important and where
electron densities are too low for quantitative spectroscopic studies. Several other
diagnostic tools such as piezoelectric crystals, magnetic probes, and magnetic
microphones have been used in electric and EM shock tube studies. These are
summarized in Table I. Although there have been a limited number of experi-
mental investigations of the thermodynamic states which are generated in electric
and EM shock tubes, these studies show that collision-dominated equilibrium
plasmas can be generated, and that in general the temperatures are higher than the
values predicted by the Rankine-Hugoniot equations. Typical data obtained with
EM shock tubes using the time resolved spectroscopic technique are summarized
in Table II.
Densities (cm'
Electron
Electron
Atom
First ion
Ref.
Tube typerf
Test gas
temp, (ev)
density
density
density
(82)
A
Hydrogen
2.4
2.5 x 10 17
(58)
A
Helium
3.98
1.2 xlO 17
6.7 x 10 13
8.2 x 10 16
(27)
B
Argon
1.27
9.3 xlO 16
6.5 xlO 16
9.3 x 10 16
(59)
C
Helium
~4
~10 17
(83)
A
Helium
4.3
5x10"
t A = EM T-tube; B = conical tube; C = conical electrodeless.
The purpose of this paper has been to try to summarize the recent developments
in electric and EM shock tube research. These developments have had the effect of
providing a better understanding of the limitations of the original conical and
T-tube geometries and to suggest modifications which make more effective use of
the phenomena which are occurring. Accordingly, it is of interest to speculate on
what future trends might be expected. It is believed that work may develop in
two directions. One direction may be toward a compromise with the diaphragm
shock tube in order to develop a shock tube with a clean shock front for high-
temperature studies in chemical kinetics. The new AVCO tube is a device of this
nature (24). The other direction may be on the development of plasma accelerators
42 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
for the generation and acceleration of sufficiently long plasma samples for flow
studies. In such devices the emphasis would be on the preparation of a plasma
specimen followed by magnetic acceleration rather than depending on the action
of a shock front. Another line of development may follow Fowler's new segmented-
electrode electric shock tube, which takes advantage of the concept of an electron-
driven shock front. Axial magnetic fields along the expansion tube may be used to
reduce heat transfer to the walls (84).
ACKNOWLEDGMENTS
Much of the material presented in this paper was gathered while the author was
associated with the Northwestern University Gas Dynamics Laboratory, and he
wishes to express his appreciation to Dr. Ali Bulent Cambel, Laboratory Director,
for his interest and helpful suggestions.
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the Theory of Shock Wave Propagation and Channel Formation in Spark
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44
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
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39
Fowler, R. G., "Origin of the Driving Force in Electromagnetic Shock Tubes",
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41 Fowler, R. G., and Turner, E. B., "Magnetically Insulated Shock Tube ,
Phys. Fluids, 4, 5, 544 (1961).
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' Phys. Fluids, 5, 7, 824 (1962).
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' Tube", Applied Physics Laboratory, Report No. CM-903, Johns Hopkins
University (1957). . ,
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Shocks", Phys. Fluids, 2, 5, 576 (1959).
Analytical work by Biberman and Veklenko, Soviet Phys. JETP, and recent
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the shock may contribute significantly to the perturbation of the gas directly
in front of the shock.
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Shocktubes", Bull. Am. Phys. Soc, 8, 2, 167 (1963).
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53 Byron, S., private communication.
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thoenton : Electric and Electromagnetic Shock Tubes 45
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65. Time resolved spectroscopy by B. D. Edwards, Nature, 196, 833 (1962), in
which all permutations of hydrogen and argon at 1 mm Hg placed on
each side of a diaphragm 17 cm from the electrodes in an EM T-tube showed no
indication of driver plasma downstream of diaphragm. It is difficult to ascer-
tain the role which the diaphragm played in inhibiting the motion of the driver
gas. Cloupeau (51) used a diffusion interface to initially separate the gases in
the electrode region and expansion tube.
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Phys. Fluids, 4, 6, 767 (1961).
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a Perpendicular Magnetic Field", Bull. Am. Phys. Soc., 8, 162 (1963).
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77. There are preliminary indications of density ratio agreement with the Rankine-
Hugoniot equations at large distances from the electrode region and P x =
2 mm Hg. Klein, A. F., Phys. Fluids, 6, 310 (1963).
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Radiat. Transfer, 2, 4, 477 (1962).
80. Cunningham, S. P., Scott, F. R., and Wenzel, R. F., "Time Behavior of
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(1960). ' '
81. Takeda, S., "Microwave Study of Plasmas Produced by Electromagnetically
Driven Shock Waves", Bull. Am. Phys. Soc., 8, 130 (1963).
46 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
82. Wiese, W., Berg, H. F., and Griem, H. R., "Measurements of Temperatures
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120, 4, 1079 (1960).
83. Barnard, A. J., Cormack, G. D., and Simkinson, W. V., "Spectroscopic Studies
of Helium and Argon Plasmas Produced by Electromagnetically Driven Shock
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Phys. Fluids, 4, 5, 544 (1961).
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trically Driven Shock Tube," paper presented at 5th Annual Meeting,
Div. of Plasma Physics of the Amer. Phys. Soc, San Diego, California,
November 6-9, 1964.
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Effect", paper presented at Vlth Inter. Conf. on Ionization Phen. in Gases,
July 8-13, 1963.
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Electromagnetic Shock Tubes", paper presented at Vlth Inter. Conf. on
Ionization Phen. in Gases, July 8-13, 1963.
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Electromagnetic Shock Tube", paper presented at Vlth Inter. Conf. on
Ionization Phen. in Gases, July 8-13, 1963.
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3. H. N. Olsen: The Measurement of
Argon Transition Probabilities
and Computation of
Thermodynamic Properties of
the Argon Plasma
\2i After considerable discussion by a number of authors it is now
generally agreed that for plasmas having electron densities below a
critical value of ~ 10 19 cm' 3 the correction for the lowering of the
ionization potential should be determined from the Debye-Huckel
limiting law corrections to the internal energy. The mathematical form
of the correction is obtained automatically when the Saha equation is
derived by extremizing the free energy.
Numerous attempts at a direct measurement of the lowering of the
ionization potential have been made with widely differing results. A
common error is the failure to recognize the fundamental difference
between the value determined from radiation measurements and that
which appears in the Saha equation. It has been pointed out earlier by
the author that an experimental check of the theoretical value to be used
in the Saha equation is difficult and can probably be made only by
comparing it with the value required to bring computed densities into
agreement with experimental values measured by some method which is
independent of the computed composition.
In this paper the agreement between a measured and computed ionic
transition probability is used as a crude criterion for selecting the
Debye-Huckel polarization theory as the best basis for treating the
plasma corrections. Results of the work are (1) a computed composition
of the atmospheric pressure argon plasma, (2) corrected partition
functions, (3) absolute values of transition probabilities, and (4)
corrected thermodynamic properties of the plasma.
INTRODUCTION
In order to determine the best possible values for spontaneous transition
probabilities from measured absolute spectral line intensities emitted from a
thermal arc plasma it was essential that the highest possible accuracy be attained
in the theoretical calculation of the plasma composition. Several studies have
treated the corrections which must be considered in computing the composition of
ed. note: Dr. Olsen is at the Northrop Space Laboratories, Northrop Corporation,
Hawthorne, California.
47
48
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
a laboratory plasma: lowering of the ionization potential, cutoff of the partition
function, and the Debye polarization contribution to the total pressure.
After considerable discussion by several people studying the problem, it is now
generally accepted that for plasmas having electron densities below a critical value
of about 10 19 cm" 3 , the correction for the lowering of the ionization potential
should be determined from the Debye-Hiickel limiting law corrections to the
internal energy. This correction leads automatically to a lowering of the ionization
potential when the Saha equation is derived by extremizing the free energy.
In evaluating the internal partition functions it is conventional (1, 2) to sum
over the unperturbed energy levels up to the effective ionization limit denned by
the lowered ionization potential. Griem (2) has estimated the errors resulting from
such a cutoff in the case of hydrogen and points out that it will rarely exceed one-
tenth of one per cent in normal laboratory plasmas. He states, therefore, that it
hardly seems justified to replace the straightforward cutoff by more involved
methods.
Whereas corrections for the ionization-potential lowering and partition-Junction
cutoff have generally been considered, the pressure corrections in the equations of
state are seldom considered in the computation of plasma compositions. Duclos
and Cambel (3) have reviewed this problem in great detail and have shown that in
most laboratory plasmas the Debye-Hiickel limiting laws are generally applicable.
As pointed out by Griem (2), and found also to be the case in the work reported
here, this correction will never amount to more than a few per cent. Thus errors
due to uncertainties in the correction can generally be neglected.
Numerous attempts at a direct measure of the lowering of the ionization potential
have been made with widely differing results. A common error is the failure to
recognize the difference between the AF R which is determined from radiation
measurements and the AF, which appears in the Saha equation. This distinction
was first pointed out by Ecker and Wiezel (4), and later by Olsen (1). In the latter
paper it was also pointed out that an experimental check of the theoretical value
for AV S is difficult and can probably be made only by comparing it with the
value required to bring computed densities into agreement with experimental values
measured by some method which is independent of the computed composition. In
the present paper the agreement between a measured and computed ionic line
transition probability is used as a crude criterion for selecting the best method for
treating the plasma corrections. Results of this work are: (1) a computed com-
position of the atmospheric-pressure argon plasma; (2) corrected partition func-
tions; (3) absolute values for transition probabilities; and (4) corrected
thermodynamic properties of the plasma.
PLASMA COMPOSITION
Detailed calculations of the plasma composition involve reversible ionization
reactions of the form
L^l^W-l^l + M-e^-AF,
(1)
where [A t ] represents the initial particle, [A l + 1 ] the next fold ionized particle, and
[e] the electron liberated by the process which consumes a quantity of energy,
e(F-AF), where V x is the free particle ionization potential and AF t is the
lowering caused by the interaction of the neighboring plasma particles. There are z
such reactions, where i is an integer ranging from 1 to z. and z is the highest fold ot
ionization existing in the plasma.
olsen: Measurement of Argon Transition Probabilities 49
Under the assumption of LTE, quasineutrality, and the applicabihty of Dalton's
law, the system of equations to be solved may be written as follows: "
?±l? = F i( T) = ^^(T)?p[-,(F I -AF J )/W]
(2)
where A(T) = 2[27rmlh 2 ] 3 2 (kT) 5 2 = 6.5180x lO" 7 !"" the u t are the internal
electron partition functions, and all pressures are in atmospheres. The z Saha
equations are combined with the quasineutrality condition (conservation of charge)
P.= 2(?-1)P, (3)
and Dalton's Law (conservation of particles)
P = P, + P D
where
p, = 2 *' p <
i=l
and the added pressure term P D is due to the Debye-Hiickel polarization.
It is now generally accepted that the Debye-Hiickel limiting law corrections
to the internal energy, free energv, and pressure may be determined as follows
(I, 2, 3, 4):
_-kT -kTV -kT ...
^-^rW *°-l&rW PdSS uJP (5)
where V is the volume and D the Debye radius given by
kT
D =
4we 2 2 n t Zi
and the sum is over all particles of charge Z t including the electrons. In the process
of deriving the Saha equation by extremizing the free energy with respect to the
ionization process given by equation (1), a correction in the direction of lowering
the ionization potential enters in the amount of
AF f = i-i, i=l,2,... S (6)
This leads to a value that is, by about a factor of 4, smaller than the value given
by the Unsold (5) relation which considers only the microfield of the nearest ion —
much in the same manner as an electric field lowers the work function at a surface.
Ecker and Weizel (4) proceeded to add the Debye polarization term equation (6)
to the Unsold relation giving what is now recognized as too large a correction for
any laboratory plasma.
Ecker and Kroll (6) have recently treated this problem in theoretical detail
confirming the conclusion of Duclos and Cambel that there is a critical electron
density below which only the polarization term is to be retained. The Unsold
relation has been erroneously used almost consistently in the earlier published
works on plasma spectroscopy.
The partition functions appearing in equation (2) are given by
u i = J^g u exp(-EJkT) (7)
50
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
where g u are the statistical weights and E u are the unperturbed excitation
energies of the levels I of species i. Because of the nonconvergence of this sum at
temperatures above about 15,000°K in argon, it must be cut off at some upper
energy level E Uc which fulfills the condition i7 ii , ( ,^e(F i — AF,).
Griem (2) has considered in detail all of the above internally consistent corrections
for the Saha equation, the equations of state, and the partition functions, and has
shown that errors due to remaining uncertainties in the corrections are usually
below one per cent. With the above corrections given, the final set of equations to
be solved is given below:
3/2
P = P e
Kf,^^)/!^
3(ifcT) s
Pet U+VJC, 2^
(8)
where C,-= J~[ (F,IP e ), the F t are given by equation (2), and
AF i =
kT
^i(j+i)A/2^
i=i
(9)
Equation (8) must first be iteratively solved for P e from which all of the species'
partial pressures can subsequently be determined according to
Px-Pe ZjCji Pi + i = PiCi for
1,2,
z-1
(10)
where the subscript 1 is associated with the neutral atoms to be consistent with
standard spectroscopic notation. An iterative computation of these equations has
been programmed for the IBM 7090 to give particle number densities, partition
functions, lowering of ionization potentials, and the effective charge of the ions.
The numerical results are tabulated in Tables I and II.
TRANSITION PROBABILITIES
Detailed methods for obtaining transition probabilities from measured line
intensities using the 400-amp argon arc plasma at a total pressure of 1.1 atmos-
pheres have been thoroughly described in a recent paper (7). In that work a novel
method for determining transition probabilities from measured emission co-
efficients of a prominent pair of lines defined as reference lines (A6965 Arl and
A4806 Aril) was presented. This method has been advantageously employed here
to confirm the theoretical conclusions regarding methods to be applied in correcting
the computed plasma compositions.
The emission coefficient of a spectral line emitted in watt/(cm 3 -steradian) by a
particle of number density n t from a volume unit at temperature T°K is defined as
(11)
St-A^K^expi-EJkT)]
where #, = 1.582 x 10- 2 % m /A) A, g m is the statistical weight of the upper energy
level E im and A is the wavelength in cm. The portion of equation (11) in brackets is
defined as the normalized emission coefficient (S*[) which can be calculated directly
from the plasma composition.
Figure 1 is a plot of the measured emission coefficients of the above reference
lines emitted by the 1.1-atmosphere argon plasma. This plot can be represented
by the following parametric equations:
x = \ogS 1 = log^+logS?
y = logS 2 = \ogA 2 + logS$
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56
olsex: Measurement of Argon Transition Probabilities
57
5
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\6965 Arl EMISSION COEFFICIENT <S. 0&. S )
FIGURE 1. Log-log plot of measured absolute emission coefficients (S t ) and theoretical
normalized emission coefficients (S1[) for atomic (I) and ionic (II) spectral lines emitted
from a 1.1 -atmosphere argon plasma. The arrows demonstrate the method used to
determine absolute transition probabilities (A t ).
58 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
If the transition probabilities are normalized to unity, a similar plot of the nor-
malized emission coefficients is obtained as shown in Figure 1 where the results of
two different methods for correcting the composition are indicated. There are two
principal advantages in this type of plot. First of all, since the parameter on the
experimental curve is temperature (or plasma radius) the results of measurements
of both lines at common points throughout the entire plasma as well as measure-
ments made in different arcs at the same total pressure can be readily compared.
Secondly, as can be seen by the equations (12) and as indicated in Figure 1, the
numerical factors required to shift the theoretical curve to best fit the experimental
points are precisely the transition probabilities sought.
The experimental points plotted in Figure 1 represent averages of at least six
independent measurements. By independent, it is meant that intensities of the two
lines were measured at the same position in a given arc, but that each set of
measurements was made in a different arc in the sense that it had been re-struck
with replaced electrodes at the same current and pressure. Measurements in the
same arc were also made at three different positions along the arc axis; the points
at the top of the curve were measured near the cathode and those at the bottom
midway between the electrodes. The deviation of experimental points toward
lower values for the A6965 Arl line at the lower temperature has been explained (7)
by absorption of the cooler layers of gas through which one must look to observe
the core of the plasma.
The solid curve through the experimental points represents the best fit of the
normalized emission coefficients which correspond with the plasma composition
corrected according to the now accepted Debye-Hiickel theory for the lowering
of the ionization potential. Because of the similarity in shapes of the theoretical
curves, both can be fitted — with practically the same degree of precision — to the
experimental points resulting in the following A -values in units of sec" 1 .
A 1 A 2
Ecker-Weizel 0.67 x 10 7 9.20 x 10 7
Debye-Hiickel 0.57 x 10 7 7.86 x 10 7
A theoretical value of 7.88 x 10 7 sec -1 has been computed from intermediate
coupling line strengths calculated by Garstang (8). The excellent agreement
between this value and the experimental value obtained from the plasma composi-
tion based on the theoretically accepted Debye-Hiickel polarization correction
represents the first experimental evidence in support of the theory. In all fairness,
these results should be looked upon only as indications at this time since the
accuracy of the theoretical A -value is not considered by Garstang to be better than
50 per cent, and we are trying to separate an effect which differs by 15 per cent.
The results do show, however, that the experimental precision is sufficient to
observe the difference between the two corrections provided a more precise
theoretical ^4-value can be obtained. The observed agreement between measured
and computed ^4-values, coupled with the state of the theory on plasma corrections,
was at the very least a guide in selecting the correct theory applied in determining
the composition of the plasma and its thermodynamic properties.
THERMODYNAMIC PROPERTIES
Using the computed particle densities, partition functions, and AV the following
have been computed: heat content, Gibbs free energy, entropy, and constant
pressure specific heat. The computations include the contributions from trans-
lation, ionization, internal excitation, mixing (in the case of the entropy and free
energy) and Debye-Hiickel polarization. The equations used in ail computations
OLSE3S? : Measurement of Argon Transition Probabilities
59
are given below where M is the molecular weight in grams/mole, R is the gas
constant expressed in ergs/mole, k is Boltzmann's constant, and h is Planck's
constant. It should be noted that the partition functions and their derivatives with
respect to temperature were determined first on a per-particle basis and then
multiplied by the number of particles per gram to give the corresponding totals.
Since the derivatives should be evaluated at constant volume rather than constant
pressure this can introduce some error. However, as is shown in Figure 2, the
rv!3
KG /GRAM
30 40
TEMPERATURE
FIGURE 2. Temperature dependence of relative contributions to total computed heat
content of a 1 -atmosphere argon plasma.
60
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
contributions of internal excitations to the total heat content under the conditions
covered here are practically negligible. The error introduced by the incorrect
differentiation may, therefore, certainly be neglected.
Heat content
_ 5 RT
trans o yr '
-"ion —
R
MkP, (=
RT 2 ^ d
H ? = MP,l Pi dT lnUi
2 p i I e(V-iAV); H D =
4RT IP
M
m
Gibbs free energy
_ RT
M
0,,
[in P,-|ln T + (K e -K a ) ^ + K^
where K e = — f In (2<nm e k 5la lh z ) and K a =-% In (2TTm a k 5l3 jh 2 )
RT
^lnt = —
""mix = —
Entropy
MP,
RT
MP,
2 Pi In u i + P e In %
s = i
J P t In (PJP,) + P e In (P e jP,)
""ion — "ion
Or.
- 3 /7
s t .
Sint - MP
5R _G^
21
R
T
R ?&- / d \
MP, A Pt [ ln Ui + T dT ln Ui J + P e ln
q ^"mix .
°mix — rp '
Sd= "It
Specific heat at constant pressure
5R_ n _ RT
2M :
C,
trans — ?it> ^int — TffT
2*.
d d 2
2 dT lnUi + T df 2lnUi
l0n ~ dT '
C D
dT
The totals of each of the thermodynamic properties computed for the atmospheric
pressure argon plasma are given in Table III, along with the mass density p in
grams/cm 3 , molar volume V in cm 3 , the molecular weight M in grams/mole, and
the ideal gas pressure P, and Debye-Hiickel pressure corrections P D in atmospheres
for temperatures in the range of 4000 to 50,000°K. All energies are referred to as
zero at the absolute temperature zero.
ACKNOWLEDGMENTS
I wish to acknowledge the support of the Lockheed California Company of
Burbank, California, in programming and performing the machine computations
of the plasma compositions prior to my joining the Northrop Space Laboratories.
The measured absolute line intensities were taken from work reported previously
as completed at the Linde Company Speedway Laboratories, Indianapolis,
Indiana.
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63
64 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
REFERENCES
1. Olsen, H. N., "Partition Function Cutoff and Lowering of the Ionization
Potential in an Argon Plasma", Phys. Rev., 124, 1703 (1961).
2. Griem, H. R., "High-Density Corrections in Plasma Spectroscopy", Phys. Rev.,
128, 997 (1962). ?
3. Duclos, D. P., and Cambel, A. B., "The Equation of State of an Ionized Gas ,
Z. Naturforsch., 16a, 711 (1961).
4. Ecker, G., and Weizel, W., "Partition Functions and Ionization Potentials of
Atoms in the Interior of a Plasma", Ann. Physik, 17, 126 (1956).
5. Unsold, A., "On the Calculation of Partition Functions for Atoms and Ions in
a Partially Ionized Gas", Z. Astrophys., 24, 355 (1948).
6. Ecker, G., and Kroll, W., "Lowering of the Ionization Energy for a Plasma in
Thermodynamic Equilibrium", Phys. Fluids, 6, 62 (1963).
7. Olsen, H. N., "Measurement of Argon Transition Probabilities using the Ther-
mal Arc Plasma as a Radiation Source", J. Quant. Spectrosc. Radiat. Transfer,
3, 596 (1963).
8. Garstang, R. H., "Intermediate Coupling Line Strengths", Mon. Not. R. Astr.
Soc, 114, 118 (1954).
4. J. H. de Leeuw: Electrostatic
Plasma Probes
\H A brief review is given of the use of electrostatic probes for the
measurement of plasma properties. A central problem is the theoretical
interpretation of the measured probe characteristic. The available
treatments for a variety of plasma conditions are discussed. In addition,
the sources of error and the practical form and arrangement of probes
are considered.
1. INTRODUCTION
The use of electrostatic probes constitutes possibly one of the earliest techniques
for the study of plasmas. Essentially, the method is based on the interpretation of
the current collected by a small probe in the plasma as a function of the voltage
applied to the probe. Basically, then, the use of such probes is attractive because it
requires only relatively simple equipment. On the other hand, there are problems
in their use. Many secondary phenomena often introduce errors in the measurements
and problems also arise as a result of the absence of available theory for probe
operation— theory valid to cover all conditions that may be encountered in
practice.
Although electrostatic probes were already used late in the last century,
there did not exist any adequate theory until the classical work by Langmuir
(1), who laid the basis for the theory of probe operation for electropositive
stationary plasmas when the collection of charged particles takes place under
essentially collision-free conditions. In low-pressure gas discharges probes can be
made small enough to satisfy these conditions and the "Langmuir" probe was
used extensively in the investigation of such discharges with a considerable
measure of success. Loeb (2) has given a comprehensive review of all aspects
of probe use in 1955. However, the problem of the interpretation of probe read-
ings is still the subject of investigation and it is not completely solved for the
entire range of plasma conditions at the present time. This is hardly surprising
in view of the fact that the behavior of the probe depends on a considerable
number of parameters.
(a) In the first place, when the probe is at a potential different from
that of the local plasma, when it is negative with respect to it, for instance,
electrons will be repelled and positive ions will be attracted to it. This
creates a region near the probe, a sheath, in which there exists a net charge
density in contrast to the body of the plasma in which neutrality prevails.
ed. note: Professor de Leeuw is with the Institute of Aerophysics, University of
Toronto, Toronto, Canada. This work was supported in part by the
U.S. Air Force Office of Scientific Research, under Grant AF-AFOSR
366-63.
65
66 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
The thickness of the sheath depends on the Debye length which for the
electrons is given by
A D = 70 /— e
(m) (1.1)
where T e = electron temperature
n e = electron number density
This sheath has the effect of shielding the plasma from the disturbing probe
potential; it is therefore to be expected that the ratio of Debye length to the
probe radius, r p , will be of significance.
(b) Secondly, the motion of the charged particles in the field near the probe
will be modified by collisions. The probe's current- voltage curve will therefore
depend on the electron and ion mean free paths relative to the probe size.
(c) A third parameter will be the ratio of electron and ion temperatures.
Since the energy exchange between the light electrons and much heavier ions
is relatively poor, it often happens that these two species can have appreciably
different temperatures. In low-pressure gas discharges, where the energy is
primarily fed to the electrons, it is, for instance, usual to find electron energy
orders of magnitude larger than those of the ions. Conversely, it is possible to
have larger ion energies when the energy loss is primarily from the electrons
as in extremely high temperature plasmas.
(d) A fourth parameter, of special interest at our laboratory where plasma
flows are studied, is the effect of plasma mass motion relative to the probe as
it can be indicated by a Mach number or the speed ratio of directed velocity
relative to a mean random speed of the ions.
(e) Further complications arise when electronegative ions are present in
considerable number. This occurs in discharges when electron-attaching
species are present. Such ions are also present in the ionosphere.
(f ) Finally, the presence of magnetic fields will influence the motion and
hence the collection of charged particles. The electrons are especially sensitive
because at relatively weak magnetic fields these will have gyromagnetic radii
comparable to the probe and sheath sizes.
In this paper the characteristics of probes in stationary plasmas will be discussed.
The cylindrical probe is of special interest, since it is reasonable to expect that
under collision-free conditions, when the probe axis is parallel to the flow direction,
such a probe will measure the plasma properties even in a moving plasma. In
addition, some aspects of the influence of flow velocity on probe behavior for other
shapes or orientations will be discussed.
2. INTERPRETATION OF SINGLE-PROBE CHARACTERISTIC
The single probe is used with a circuit as indicated in Figure 1. The voltage on
the probe is varied with respect to one of the electrodes of the arc or discharge and
the current to the probe is measured. The probe itself can be plane, cylindrical, or
spherical in shape. A typical probe characteristic is shown in Figure 2a. The
potential at which the current is zero is called the floating potential, V F . At this
potential most of the electrons are repelled by the probe to provide a balance of
electron and ion currents, and at more negative potentials practically all electrons
are prevented from reaching the probe and only positive ions are collected. The
probe is surrounded by an ion sheath and the dependence of current on voltage is a
de leeuw: Electrostatic Plasma Probes
67
probe
*rrr//////.
cylindrical probe
spherical probe
;;;;;;
//////
plane probes
FIGURE 1. Probes and basic circuit.
rather weak one. For increasing potentials more and more of the electrons will
reach the probe, resulting in a rapidly increasing electron current. When the probe
is at the plasma potential, V m , the probe collects both ions and electrons from the
plasma without the aid of electric fields. This means that as a result of the greater
random speed of the electrons, the probe is drawing a negative current, much
larger than the magnitude of the ion current at negative potentials. For potentials
positive with respect to F.,, the ions are repelled and an electron sheath controls
the magnitude of the "saturation" electron current.
electron
current
retarding field
region
ion- sheathed
operation
electrons emitted
from probe surface
by ion bombardment
FIGURE 2a
ion
current
\
electron- sheathed
operation
V probe potential
Probe characteristics.
68
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
100
C
0)
!h
3
o
C
o
-t-?
o
m
10
0. 1
0.01
/
/
/
/ /
1 /
1 /
1/
1/
0.001
1 2 3 4 5
Probe voltage (arbitrary)
FIGURE 2b. Single probe characteristics.
The interpretation of the probe characteristic will be discussed first. We will
assume that collision-free conditions exist, so that the ion and electron mean free
paths are to be larger than the probe and sheath size, and that secondary phenomena
are absent.
2.1. ELECTRON COLLECTION AT RETARDING POTENTIALS
When the probe is slightly negative with respect to the plasma potential some,
but not all, electrons will be prevented from reaching the probe, because those
electrons having sufficient energy in the direction towards the probe, i.e.,
\m e c z ei > ejFp-Fooj (2.1.1)
de leettw: Electrostatic Plasma Probes 69
will be able to reach the probe if the potential distribution is assumed to be
monotonic. The total electron current will therefore be an integral over the
distribution function,
l e = — = en*
^00 & 00 /?OO
cjdc (2.1.2)
J Cx J — to J — CO
where I e = electron current density,
■&~ e — total electron current,
A= probe area,
n m = undisturbed electron number density,
/= distribution function
If the electron collision frequency is high it may be expected that the electron
distribution function is Maxwellian and equation (2.1.2) may be written
| J, | = en,
W27rm e eXp L kT e J (2 - L3)
which is true independent of probe shape, as shown by Langmuir and Mott-Smith
(3).
Taking the logarithm of equation (2.1.3) this becomes
H/.|-^(F,-F.) + m(e^V^ <*■">
Assuming that V x is a constant and differentiating with respect to V? leads to
dln\I e \ e__ 11,700
dV p kT~ T e
(2.1.5)
so that a linear dependence of In | I e \ on voltage indicates a Maxwellian distribution
and the slope of this straight line yields the electron temperature.
The electron current is obtained from the probe current by noting that
|^ e | = |^|+^ + (2.1.6)
In order to obtain 3~ e the ion current has to be known. The ion current depends in
general on voltage and some extrapolation from the measured ion current at large
negative potentials is therefore in order. However, when X D jr v is small this varia-
tion is not too severe and furthermore in the characteristic of a single probe the
electron current becomes much larger than the ion current as the plasma potential
is approached, so that the extrapolation error in ^" + will not be important.
A completely analogous situation exists for the ion collection at slightly positive
potentials. Unfortunately, in the normal use of a probe, the ion contribution to the
probe current near plasma potential is masked by that of the electrons. However,
when the Debye lengths in the plasma are relatively large, it is possible to separate
the two current components by the use of fine grids. Boyd (4) made attempts,
which were partly successful, to do this in the laboratory. More recently this
technique has been applied for the investigation of the ionosphere where the Debye
length is of the order of a few centimeters. The use of such multi-electrode probes
will be discussed in section 5.
When the distribution function is not Maxwellian, but still isotropic, the probe
characteristic in the retarding field region can be used to find the shape of the
distribution function. A method to do this is given in reference (3) by relating
70 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
the second derivative of the probe current with respect to voltage to the distribution
function in the form
d 2 \^e\ _ Aen^ I e tiv —V \ (2 1.7)
Sloane and McGregor (5) following a suggestion by Emeleus indicated an experi-
mental method, later improved by Boyd and Twiddy (6), to obtain the second
derivative directly. They measure the d-c collected current without and with a
small superimposed sinusoidal a-c signal of amplitude AF at various values of the
d-c voltage. They showed that the difference in d-c collected current is given by the
expression
= (APT^ (2 . L8)
d0 4 dVl K '
where (V p —V x ) is the voltage equivalent of the electron kinetic energy. This
method was also suggested as a means of finding the value of V x , the plasma
potential, in reference (5), by taking as the value of V x , that value of V p for which
the amplitude of the a-c variation in the current disappears.
It should be pointed out that the theoretical basis for the use of superimposed
voltage fluctuations rests on the assumption of quasi-stationary conditions, so that
when the frequency of the fluctuations becomes comparable to the electron plasma
frequency the method loses its validity.
As a matter of fact, the resonance that occurs at plasma frequency is a useful
indicator of electron density as Takayama, Ikegami, and Miazaki (7) have pointed
out and as shown in careful experiments by Cairns (8). However, as long as the
applied frequency is much lower than the plasma frequency the above method is
indeed valid and independent of frequency.
2.2 SPACE POTENTIAL AND OPERATION AT POSITIVE
POTENTIALS
When the probe potential is at the local plasma potential, there are no electric
fields around the probe and it will accept the random fluxes of electrons and ions
normally incident on it, i.e., per unit area n m \/kT e \2-nm e electrons and
n*, Vic f^]2nm^ + ions will be collected. It is clear that the electron current will far
outweigh the ion current because their ratio is Vm + T e lni e T + . Consequently,
unless T + ?T e the current collected at space potential is in good approximation
entirely due to the electrons, so that the current at plasma potential gives
information about the charged particle density since
^ = o.^eV— ? (2.2.1)
and the value of T e can be determined from the retarding field region.
As soon as V v becomes larger than V *,, ions are repelled and an electron sheath
forms which will control the collection of electrons. It is normally assumed that
when T + IT e <l the electrons reach the sheath edge at their normal random
current density so that
^, = eA, na> J^r = OAn.eA.J^ (2.2.2)
de leeuw: Electrostatic Plasma Probes 71
where A s is the effective collection area at the sheath edge. Since the sheath
thickness will grow with increasing voltage, for instance, for a thin sheath which
may be approximated by a plane sheath, the thickness is given by
(V P -V*? I2 Y 12
q fa r (2-2.3)
d? =
the electron current will depend on voltage through the dependence of A s on the
sheath thickness. This dependence is a much weaker one, though, than the
exponential dependence in the retarding field region. This simple picture of electron
collection is not quite correct, as will be discussed in section 2.4. However, the
procedure for finding the electron current at space potential described in the
following rests on an extrapolation from the electron current curve to the value at
plasma potential and the description here is adequate for the purpose.
The change in dependence of I e on F p shows on the logarithmic plot of current
versus voltage as a change from a steep straight line to a much less steep curve at
V p > V^. For thin sheaths under ideal conditions this change is abrupt and there is
little difficulty in fixing the value of V x . In reality the curve often changes rather
more smoothly as a result of secondary effects to be discussed in section 4 and it is
customary to locate plasma potential at the intersection of the straight line in the
retarding field region and a reasonable straight line through the data for V p > V x .
When the sheath is not very thin with respect to the probe, say for Debye
lengths Ao^rg- r p , the curve shows a pronounced rounding even under ideal condi-
tions and the plasma potential should be taken at the point where the measured
curve starts to deviate from the straight line representing the exponential increase
of the electron current. However, since secondary effects may be present there
is an inherent uncertainty in the value of V x , with a corresponding uncertainty in
the electron density determination when equation (2.2.1) is used. It is partly for
this reason that the accuracy of the probe method is limited in many cases.
2.3. ION COLLECTION AT LARGE NEGATIVE POTENTIALS
When the probe is strongly negative with respect to the plasma potential
virtually all electrons will be repelled. This will be the case when e| V p — V x \?kT e
and as a result the electrons will take on an equilibrium Boltzmann distribution
when the distribution function far from the probe is Maxwellian, i.e.,
exp
For the case of very low charged particle density, such that the Debye length is
very much larger than the probe radius, the collection of ions will be controlled by
the essentially unshielded Coulomb potential of the probe. In reference (3) the ion
collection for a spherical probe under these conditions is given by the relation
in which V = kT + je the voltage equivalent of the ion energy when the ions are
Maxwellian and A = probe area. Similarly, a cylindrical probe would collect
^^ An 4S- + M-^r < 2 - 3 - 3 >
72 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
It must be noted that the collection depends only on the probe voltage and not on
the ratio A D /r p . These equations are valid only when the Debye length is so large
that everywhere in the field around the probe the following inequality is satisfied
A test could be made by using different sized probes to experimentally show the
independence of the results on
An
When the inequality, equation (2.3.4), is not fulfilled the analysis of the problem
of ion collection is very complicated and only approximate solutions are available.
Bohm, Burhop, and Massey (9) treated the problem of a spherical probe by using
equation (2.3.1) for the electron density and assuming that the field around the
probe could be represented by an extremely thin sheath surrounded by quasi-
neutral plasma. In addition, the assumption was made that the ions at infinity had
random motion but were all mono-energetic. Their results showed that the electric
field in the quasi-neutral plasma region attained an infinite slope as a function of
position and they located the sheath edge at the position where this occurred. For
zero energy ions this procedure resulted in a potential at the sheath edge of
I ^ c — l^oo I = 2 kT e l e which showed that the plasma region cannot support more
than this potential difference. T*~hm (10) derived a criterion for the formation of a
sheath indicating that the potential should be larger or equal to this value. So for
the zero energy case these two criteria lead to the conclusion that at the sheath
edge this value of the potential must exist, meaning that the plasma beyond the
sheath is significantly disturbed. In the first place the charged particle density will
be smaller than at infinity as a result of the Boltzmannian distribution of
electrons and secondly the ions will have been accelerated towards the probe so
that they enter the sheath with a finite energy corresponding to \kT e .
The calculations for two different ion energies gave the following results :
Ihrp \ 1/2
ion energy 0.01ifcT e &~ + = 0.57n a el — e -\ A (2.3.5)
/I./71 \ 1/2
ion energy 0.5kT e &~ + = 0.54w 0O el — e \ A (2.3.6)
The implication of these calculations is that for the case of thin sheaths the ion
current is controlled by the electron temperature alone as long as T + jT e < 1.
Allen, Boyd, and Reynolds (11) refined the analysis for zero energy ions by
removing the assumption of a quasi-neutral plasma region. Their results, repro-
duced in Figure 3, show that at values for ^" + /^ D of about 10 4 , where ^ D repre-
sents essentially the random ion current passing through a Debye sphere, the
plasma solution of reference (10) is indeed a good one. For smaller values of this
ratio, i.e., larger ratios of X D lr v , the approximation becomes increasingly less valid
and their full analysis has to be used. Their solution for the thin sheath case for
zero energy ions is given by
— e A (2.3.7)
m +
and is in good agreement with equation (2.3.5) and applicable for ^ + /^~ D >10 4
or A D /V P < 0.01.
de leetjw: Electrostatic Plasma Probes
73
PLASMA, SOLUTION
*/j D = I0 8
Wj D = to*
FIGURE 3. The electrostatic field near a spherical Langmuir probe.
For ratios of A D /r p between J to J they present ion collection curves for zero
energy ions, which are reproduced in Figure 4.
More recently, Bernstein and Rabinowitz (12) have treated the eases of spherical
and cylindrical probes, solving the self-consistent field problem for mono-energetic
ions. Their results were obtained for a range of values of A D /r p down to about ^.
The results of their calculations for a spherical probe are reproduced in Figure 5
in which non-dimensional current is plotted versus e\V p - V m \ jkT e for the case of
A D =0.1r p . The graph indicates that an increase in ion energy decreases the current
by a small amount, which is however larger than the extremely small differences
found by Bohm et ai. in reference (10). For instance, an increase of T + /T e from
0.01 to 0.1 causes a 10% decrease in ion current. From the trend of the curves in
reference (12) it is further apparent that for smaller Debye lengths this difference
decreases in accordance with the findings of Bohm et al. which are true in the
limiting case of an extremely small Debye length.
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
FIGURE 4. Ion collection curves.
D
FIGURE 5. Ion collection curves.
Since the ion collection is found to depend on T + /T e over an important range of
A D /r p , it may be expected that the assumption of mono-energetic ions is not quite
adequate to describe the ion collection because their energy distribution is Max-
wellian in practice. Hall (13) has indicated a computational scheme to treat such
cases and Laframboise (14) of our own laboratory has independently calculated
entire probe characteristics based on Maxwellian distributions for both electrons
de leeuw: Electrostatic Plasma Probes 75
and ions at different temperatures. Some of his results will be discussed in section
2.4.
The importance of the ion collection part of the probe characteristic lies in the
facts that relatively little current is drawn from the plasma in contradistinction to
the situation near plasma potential and that in the presence of moderate magnetic
fields the ion collection will be little influenced. The practical implications of the
foregoing discussion may be summarized as follows:
(a) For very large values of A D /r p , equations (2.3.2) and (2.3.3) can be used
to give the quantity n x \/T + jm+, which when the ion temperature is known
yields n x . The results are independent of A D /r p but a test may have to be made
for this by using two different probe sizes.
(b) When A D /r??l, as indicated for instance by an ion current practically
independent of probe potential, equation (2.3.7) can be used, which means
that the charged particle density can be found when T e is measured according
to the method described in section 2.1.
(c) When the Debye length is in the range from \ to yg- of the probe radius
the ion collection depends both on T + jT e and X^jr p . Awaiting the availability
of calculations for the case of Maxwellian ion distribution functions, the curves
of Bernstein and Rabinowitz should be used. However, it will be necessary to
have additional information. For instance, if the electron temperature and
number density can be determined from other parts of the probe characteristic
or from independent measuring techniques, then the Debye length is known
and the ion collection may give an indication of ion temperature.
An alternative approach is to ignore the small differences in ion collection
as a function of T + / T e and consider the curves for zero ion energy of Allen et al.
in reference (11) as a first approximation. Their curves are given in terms of
?^" + /^"d, where
'-?^fr (2 ' 3 - 8)
which only depends on T e . The electron temperature can be obtained from
the probe characteristic and a curve of ^" + /-^" D versus -r\ — e( V p — V ao )/kT e can
be plotted. Such an experimental curve should coincide with a calculated
curve for some value of A D /r p so that A D can be determined and consequently
the charged particle density can be found.
This procedure will undoubtedly introduce some error, but the method of
determining the electron density at plasma potential suffers also from some
uncertainty. Furthermore, the measured probe current at negative potentials
can include the effects of secondary electron emission due to the incidence of
photons and metastable atoms so that the actual ion current can possess a
certain uncertainty.
At space potential the ratio of electron and ion currents is given by
However, the ratio of electron current at space potential to the ion saturation
current for cases where the latter is well defined, i.e., when r p ?A D , is considerably
smaller,
JT + 0.61 V m e V m e
76
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
09
?8
?8
01
o
V
For argon with V / m + /m e = 271, this ratio becomes ^ e0 /^" + =178, which is con-
siderably smaller than the ratio at space potential, especially if T e 5>T + . Since
under the condition r??A D the ion current does not change much with T + /T e , at
least up to T + IT e = 0.5 according to equations (2.3.5) and (2.3.6), the value of
*7~ eol^~ + should also be independent of T + j'T c over this range. In experiments
de leeuw: Electrostatic Plasma Probes 77
with single probes, this ratio should be checked as an indication of the self-
consistency of the measured probe characteristic.
2.4. EFFECTS OF LARGE ION TEMPERATURES
It was indicated in the previous section that the ion current depends only slightly
on T + /T e as long as this ratio is smaller than 0.5. French (15) pointed out that,
since the trajectories of electrons at positive potentials are kinematically similar to
those of ions at negative potentials when the temperature ratio is reversed, the
collection of electrons at positive potentials will become controlled by the ion
temperature when T + IT e > 2, leading by analogy to the expressions
/, = ?i = 0.61enJ^± (2.4.1)
and
\=*f = 0.4*n B J:
kT +
m.
(2.4.2)
for the case of small sheath thicknesses. Laframboise (14) lias undertaken calcula-
tions to shed some light on the details of the transitions that occur when T + jT e
becomes larger than unity. For this purpose he has calculated the entire probe
characteristic for a spherical probe for Maxwellian ions and electrons at arbitrary
temperatures but he assumed that the plasma is bounded by a spherical surface at
a finite distance. Some preliminary results of his as yet unpublished work are
shown in Figures 6, 7, and 8.
The potential distributions near the probe are shown in Figure 6 as a function of
non-dimensional distance from the probe for different values of the probe potential
r) = eVjkT e . The case was for an electron Debye length of -j^ probe radius and a
value of T + / T e = 0. 1 . The difference in electron sheath and ion sheath formation is
marked. The ion sheath only partly shields the probe and the penetration of the
field beyond the sheath which is responsible for the increased ion collection is very
pronounced. On the other hand the electron sheath shields the probe almost entirely
because only a small remnant of the [field is'seen to penetrate to a considerable
distance from the probe. This is explicated in Figure 7, which shows the electron and
ion density distributions for the positive probe. It is seen there that at the sheath
edge where electron and ion densities depart, the electron density is noticeably lower
than that far away. This implies that also in the case of a positive probe the
plasma supports a potential difference, but this is basically of the order of the
energy of the repelled particles and therefore small compared to the electron energy.
One may visualize this as arising from the local decrease in electron density as a
result of the removal of electrons by the probe.
The non-dimensional electron and ion currents are shown separately in Figure 8
for values of T + j T e = 1 .0 and T + / T e = 0. 1 . The electron current is non-dimensional-
ized by its value at plasma potential but the ion current for both temperatures is
normalized in terms of the value at plasma potential for the case T + /T e — 1.0. It
may be noted that the differences in ion current as a result of the different ion
temperatures are only pronounced near plasma potential. Since the probe current
there is almost equal to the electron current these differences in ion collection will
be effectively masked in a probe characteristic.
However, when T + fT e > 1 similar large changes will occur in the electron current
at potentials a little above V^ and these will show up in the probe characteristic to
give some indication of the value ofT + jT e . Situations with T + jT e >l can occur in
78
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
decaying discharges, when the electrons experience a larger cooling effect than the
ions as a result of the preferential loss of high-energy electrons in the antipolar
diffusion process as noted by Biondi (16). Similar situations will occur in extremely
hot plasmas when the electrons are mainly responsible for the radiation cooling.
In such plasmas, however, magnetic fields will be present and these will modify the
electron collection so that the above analysis will not be valid.
de leeuw: Electrostatic Pla-sma Probes
79
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80
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Another observation that may be made is that when T + /T e <l the electron
current stems basically from the incidence of the normal kinetic flux,
4 V
8kT,
on the effective sheath boundary. Conversely, when T + /T e > 1 it is to be expected
that the ion current will be determined by the analogous process.
2.5. PRESENCE OF ELECTRONEGATIVE IONS
Boyd and Thompson (17) have considered the theory of ion collection when
electronegative ions are present. They assumed that the positive ions were at rest
at infinity and that the sheath was so thin that the field could be split in a quasi-
neutral plasma and a sheath similar to the analysis by Bohm et al. (9). They found
that for ratios of electron-to-negative ion temperature T e /T _>30 and concen-
tration ratios (n_jn e ) m <2, the positive ion current in terms of the electron current
at plasma potential is unaffected by the presence of electronegative ions, i.e.,
_
= 0.66
. lULt
(2.5.1)
so that the electron concentration can be found from this relation when the electron
temperature is known, whereas no information about the negative ions is obtained.
14
12
10
rt
v
u
u
U
O
U
Pu
A /
B^
■
-20
10
10
20
30
Curve A - Probe Perpendicular to B
Curve B - Probe Parallel to B
FIGURE 9. Effect of magnetic field orientation.
de leeuw: Electrostatic Plasma Probes 81
is
For a strongly electronegative gas, i.e., w_/? e ?l, for which T + = T_, it ,?
found that the potential at the sheath edge is very close to the plasma potential
in terms of the electron energy. This fact is used in the analysis to consider that the
positive ions will arrive at the sheath edge by their random kinetic motion based
on the ion temperature T + . The problem therefore reduces to a proper choice of
the effective sheath radius and a semi-graphical process for this choice is described
in reference (17). Essentially, the quantity n + V?^, and therefore n_ VTZ, can
be determined from this procedure so that additional information about the
ion temperature is required before n + can be determined.
2.6. INFLUENCE OF MAGNETIC FIELDS
The presence of a magnetic field modifies the motion of the charged particles in
the electric field of the probe. Since the trajectories of the electrons are disturbed
at weaker magnetic fields than the ions are, the effects of magnetic fields will first
be noticed in the electron current to the probe. An experimental curve in Figure 9,
reproduced from reference (9), shows the effect of the orientation of a plane probe
with respect to the direction of a magnetic field of 1 .5 weber/m 2 in a nitrogen
plasma. It is seen that the ion collection is uninfluenced and also that the shapes of
the curves at potentials somewhat below plasma potential are similar, so that this
region most likely will yield reasonable electron temperatures. It is also clear that
for both probe orientations the electron-to-ion current ratio is much lower than that
for the case of B=0. It is also pointed out in reference (9) that as long as the
gyromagnetic radius of the ions is larger than the probe and sheath size, the ion
collection is but slightly influenced so that for this part of the characteristic the
considerations of section 2.3 apply.
For very strong magnetic fields the entire probe characteristic is influenced and
reference must be made to an appropriate theory. Very recently Bertotti (18) has
presented such an analysis. The theory is quite complicated and the reader has to
be referred to the paper itself for any application.
2.7. PROBE OPERATION AT HIGH DENSITY
All the foregoing discussion of single probe operation was valid for probes at
low density, such that the ion and electron mean free paths are larger than the
probe and sheath size. At higher densities these conditions will no longer be satis-
fied and the current to the probe will be modified as a result, because the motion of
the charged particles in the electric field will be disturbed by collisions.
When the ratio of charged to neutral particles in a partially-ionized gas is very
small these collisions will primarily involve neutral particles and in the case of
ion-neutral encounters momentum exchange as well as charge exchange events will
have to be taken into account. The cross sections for these encounters are not
accurately known at low ion energies for many gases and there is therefore some
uncertainty in determining the mean free paths. In highly- ionized gases the collisions
will primarily occur between ions and electrons.
Theories for probe operation at densities where collisions are important are
given, among others, by Zakharova, Kagan, Mustafin and Perel (19), who present
a theory for the behavior of spherical and cylindrical probes when the density is so
high that the supply of charged particles is mobility- and diffusion-controlled.
For the ion collection at large negative potentials they assumed that the field
can be split in a quasi-neutral plasma region and a well-defined sheath. In addition
they assumed that at such potentials the effect of concentration gradients is
82 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
unimportant and that the ion drift velocity is proportional to the electric field.
Only collisions with neutral particles were considered.
The ion currents are presented as follows:
, . . . , ^ + x n m T e L + 10-" /amp\
spherical probe I + = -j- = —^ — ^/^jT \ m * j ( '
,. , . , , r ^+ n x T e L + 10- 11 (272)
cylmdncal probe I + = -j- = 2 , ? ln WVp) ^--^ l ' ' '
jtf + is the ion atomic weight, L + is the ion mean free path, and x is the value of
r\r v where the quasi-neutral plasma solution indicates an infinite slope for the
electric field. The values of x are found from the following:
1 L + T e We ° e V2^7 ( 2 - 7 - 3 )
spherical probe — = b = 0.85 — ^ j
cylindrical probe lnl— — )=& (2.7.4)
where 1 = length of the cylindrical probe.
The equations essentially constitute implicit expressions for 1+ when n cc ,T e ,T + ,
and L + are known. However, when the Debye length is very much smaller than
r,? so that the sheath is thin, then z may be taken as unity and only equations
(2.7.3) and (2.7.4) need be used. It is, however, clear that estimates of L + and T e
are required for the determination of ra M .
At plasma potential the motion of the charged particles is controlled by diffusion
as a result of concentration gradients. The electron currents are found to be
(Ml
spherical probe (l e ) = jj-j; — yt.t.o)
4 L,
IcT.
w m e.
cylindrical probe (I e ) = ^— ttt (2.7.6)
i + jr-
The electron current in the retarding field region is given in approximation by
T P?
277W?
expr;,,
l+l^fJ^exvl-^ + ^xfidx
(2.7.7)
where ij J> = e(7 p -F a ,)/i2 , e
x = r/r p
y=l for cylindrical geometry
= 2 for spherical geometry
x x = oo for spherical probe
= l\r v for cylindrical probe
In the derivation of this expression both mobility and diffusion were considered
and free motion was assumed over the last mean free path near the probe. Equation
(2.7.7) shows clearly that the simple exponential nature of the electron current
de leeiiw: Electrostatic Plasma Probes 83
versus voltage curve is disturbed. Also it can be shown that the deviations become
appreciable at lower values of i\ p as the mean free path for electrons becomes
smaller. The usual analysis of the retarding field region therefore has to be con-
fined to values of r) p where equation (2.7.7) is dominated by the exponential term.
This may still be the case for potentials slightly larger than V r so that the electron
temperature can still be evaluated as long as the mean free path is not too small.
A more refined analysis of the problem which avoids the artifice of splitting the
field into a plasma region and a sheath region has more recently been presented by
Su and Lam (20). Their work is valid for small values of Ljr?. Probe characteristics
at large negative potentials are presented in their work.
Both these analyses are based on a continuum treatment. For cases where the
mean free paths are of the same order of magnitude as the probe and sheath size
the conditions for a continuum description are not fulfilled. The work of Schulz
and Brown (21) is of special interest in this area, since their experimental com-
parison of ion current drawn by probes with microwave data covers the region
where collision-free conditions prevail as well as that in which collisions just start
to become of importance. In addition, they present simplified analyses to explain
their experimental results.
2.8. EFFECTS OF PLASMA MASS MOTION
2.8.1. Collision-free Conditions
First the case will be considered in which the mean free paths are large and the
Debye length is small compared with the probe. In most flow situations, even when
the directed velocity is much larger than the random speed of the ions, the electron
random speed will still be much larger than the flow velocity. Situations like this
occur in the flight of a satellite through the upper ionosphere and they can also be
realized in the laboratory, for instance in plasma tunnels.
As far as the probing of such flows is concerned, French (15) has pointed out that
a cylindrical probe aligned with the flow direction and long enough so that end
effects can be ignored will behave as if it were in a stationary plasma. Hence, the
static plasma properties can be measured with such a probe using the methods
outlined in previous sections. Taylor, Rothman, and Morita (22) recently reported
experiments in an electromagnetic shock tube at velocities up to 8000 m/sec.
Measurements of the electron density made with cjlindrical probes were com-
pared with microwave interferometer data and a reasonably good correspondence
independent of flow velocity was obtained.
For other probe orientations and geometries, the probe characteristic will be
influenced by the flow velocity. However, since the ratio of directed to random speed
of the electrons is much smaller than unity (in argon, for instance, when the
directed velocity to random ion speed ratio is as high as 20 this ratio for electrons
is only 0.07) it is to be expected that the electron temperature can still be obtained
from the retarding field region in the manner described in section 2.1. This was
experimentally verified by French (15) at an ion speed ratio of about 2 by com-
paring the results from a cylindrical probe parallel to the flow with those from the
same probe at a perpendicular orientation.
Theoretical calculations for the ion collection of a spherical body have been
made by Davis and Harris (23). They showed that the ion current corresponds
essentially to the flux of ions that cross the frontal area of the body as a result of
the flow velocity. A small increase in the effective area over the geometric area
accounts for the influence of the electric field around the body. Meckel (24) and
84 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Clayden (25) have basically used this result in their investigation of high speed
plasma flows in the laboratory. The ion current measurements yield the product,
n x U, of number density and flow velocity.
More recently, Clayden (26) and Smetana (27) reported calculations based on
simplified models for the behavior of spherical probes in plasma flows. Medicus (28)
also treated this case for a drifting Maxwellian distribution function ignoring the
non-spherical nature of the sheath that results from the non-isotropy of the undis-
turbed distribution function. Without further experimental evidence it is difficult
to assess the validity of the assumptions made by these authors. It is very
important to have reliable theories for spherical probes because in the probing of
complicated flow fields it may be impractical to use aligned cylindrical probes
since the flow direction will not be known in advance.
At a relatively low speed ratio of about 1.5 French (15) found that the ratio of
ion current for cylindrical probes perpendicular and parallel to the flow equalled
the ratio of ions striking the probe, calculated on the basis of kinetic theory
ignoring the influence of electric fields entirely. This result is explained by French
by noting that the electron temperature in his experiment appeared to be lower
than the ion temperature, so that ion collection would be controlled by the ion
kinetic flux. Since the Debye length in his experiment was very small compared to
the probe size this can account for the fact that the electric fields had no influence.
2.8.2. Effect of Electron-Ion Collisions
Plasma conditions can also occur in which the charged particle density is so
high that the ion-electron and ion-ion mean free paths are small compared to the
probe size, whereas the electron-neutral and ion-neutral mean free paths are still
large in terms of the probe size. When this is the case the electron collection by the
probe can be significantly altered by the flow even though the speed ratio of the
electrons is negligible. The results of an experiment under these conditions are
described by French (15). Plane probes were placed perpendicular and parallel to
the flow. The experimental arrangement is given in Figure 10, which shows the
plasma source and the nozzle to provide the supersonic plasma flow. The results
for the apparent electron number density for the two probe orientations is shown in
Figure 11, which indicates that the ratio is largest at the center of the plasma jet
where the velocity is highest.
The proposed explanation for this phenomenon is as follows. When the probe is
perpendicular to the flow and at positive potential, ions are reflected back into the
flow. These reflected ions collide with oncoming ions and form an ion shock wave
which increases the ion density just in front of the probe. Since at the conditions of
the experiment, w e ~10 19 /m 3 , the sheath thickness is very small compared to the
probe and the electron density will follow the ion density increase in order to
maintain neutrality of the plasma. Consequently, the probe is drawing more elec-
trons than it does in the parallel orientation where this mechanism will be absent.
The current ratio is found to be less than the density ratio across a normal shock
wave based on a measured flow Mach number. This may possibly be explained by
the fact that the propagation speed for small disturbances in a plasma without
neutral particles is larger than that in a neutral gas at the same temperature as the
ion gas. This means that the effective Mach number should have been taken some-
what lower than the Mach number inferred from impact probe pressures, which are
essentially associated with the properties of the neutral gas. Again, much more
systematic experimentation is required to verify the proposed explanation
de leeuw: Electrostatic Plasma Probes
85
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87
2.8.3. Continuum Description
At high gas densities when all mean free paths are smaller than the probe
dimension, the supply of charged particles to a probe will be collision dominated
and a continuum description of the problem is in order. Some work has been done
on this problem under the assumption that the densities are still low enough to
ensure that recombination in the cooler gas near a probe does not occur. Talbot
(29) has analyzed the properties of the gas in the vicinity of the stagnation point of
a blunt body that is at floating potential. He suggested that a small probe buried at
the stagnation point can be used to sample the local electron density under zero
velocity conditions. Since the theory relates the electron density near the stagna-
tion point to that of the free stream, the latter can be determined. The use of
such probes was investigated by Brundin, Talbot, and Katz (30) in a plasma
tunnel by comparing the probe data with microwave interferometric electron
density measurements. The results were reasonably encouraging Pollin (37) has
studied similar probes in a shock tube and in his theoretical work he took into
account the fact that net current must exist. Lam at Princeton has recently
reported that work is in progress on the behavior of arbitrarily-shaped probes
lhis research promises to give a comprehensive theory for the entire probe
characteristic.
3. THEORY OF THE DOUBLE PROBE
The use of the single probe is predicated on the availability of a convenient
reference electrode. In some applications these are not available (for example in
the case of electrodeless discharges). For such situations the use of double probes
is indicated. The basic circuit for the use of such probes is pictured in Figure 12a
w
FIGURE 12a. Double probe circuit.
Two probes are placed in the plasma at such a separation that there is no mutual
interference, and the current is measured as a function of the potential difference
applied between the two probes. A typical current-voltage curve is shown in
Figure 12b. Johnson and Malter (31) have given a detailed account of the use of
this type of probe arrangement. The characteristic curve can be understood in
4 +
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
FIGURE 12b. Double probe characteristics for equal probe sizes.
terms of the single probe characteristic. As a result of current continuity the positive
current to one probe must be equal in magnitude to the electron current to the
other. When, as is usual, the two probes are of the same size and therefore would
have the same single probe characteristic, it is clear that the maximum electron
current is no larger than the ion saturation current. Especially when the ion
collection curve is flat, this means that as the voltage difference is increased the
potential of the electron collecting probe remains fixed while the other becomes
more and more negative. In this case the current depends little on voltage. On the
other hand, for small voltage differences both probes will approach the floating
potential of the single probes and the net current will tend to zero. The variation
of current with voltage is primarily due to the changing electron current to the
probe that is above floating potential.
A simple analysis valid for collision free operation allows the electron tempera-
ture to be determined from the probe characteristic. Using the notation of Figure
12b, it is shown in reference (31) that for equal probe sizes and the same local
plasma conditions
h F?- 1 ]--i*; F ? <31)
where I p is defined, as in Figure 12b, to be the value of the probe current at the
"break point" in the characteristic and I e = I -I p and I D = current in the circuit.
It is pointed out that any uncertainty in the determination of I PB is not too
serious since I p occurs in the expression for I e and a certain compensation of errors
takes place. I? is the ion current to probe 2 at the value of V and it will have to be
estimated from the ion saturation current at large values of V D . Johnson and
Malter describe a suitable extrapolation procedure for this purpose.
A simple formula for the calculation of T e from the probe characteristic when the
two probes are equal is based on the so-called equivalent resistance method. It
takes the form
l/' e — ft-lto-lp
(3.2)
de leetjw: Electrostatic Plasma Probes
89
where R Q =dV v ldI x> at F D = 0, and again I p is the value of the current at the
"break point" of the characteristic.
Since the value of /? is important in this simple evaluation, the electron tempera-
ture is expected to be accurate only when the break point is well defined, i.e.,
when the sheath thickness is small.
It is to be noted that only a small fraction of the electrons (those in the high-
energy tail of the distribution) contribute to the measured current with the above
methods since only electron current at potentials close to V F can be accepted, so
that the "temperature" that is measured is associated with the high-energy elec-
trons. If this is objectionable, when there is suspicion that the distribution is non-
Maxwellian, for instance, it is possible to obtain information over a larger range
of electron energies by making one of the two probes considerably larger than its
partner. Equation (3.1) will then only have to be slightly modified.
For the determination of ion densities, the ion saturation parts of the curves
can be used. Since at large voltage differences these are similar to the single probe
curves all considerations about the ion collection of the single probe apply here as
well.
A hybrid double probe circuit is described by Garscadden and Palmer (32) who
use two probes in parallel and apply to each an almost equal potential with
respect to a reference electrode. However, the difference in current as a result of
the small difference in voltage is measured. It is shown that this method allows the
deduction of the shape of the distribution function similar to the methods in
section 2.1, but with greatly improved stability of the results in the presence of
fluctuations in the plasma properties.
4. PROBE ERRORS
There are many secondary phenomena that can become sources of error. Loeb (2)
has given an extensive account of these and only a brief summary will be presented
here.
4.1. PRESENCE OF THE PROBE
The insertion of the probe in the plasma may alter the plasma properties to be
measured. To minimize this source of error small probes are preferred. Nevertheless
even small probes can draw electron currents that are appreciable in comparison
with the currents that maintain the plasma, as in low pressure discharges for
instance. When this takes place it is necessary to keep the voltage below an upper
limit that is just above the floating potential. It is one of the virtues of the double
probe that such limiting action occurs automatically. It is also possible in a very
hot plasma that the probe erodes and so produces contamination products that
seriously disturb the plasma.
On the other hand there are many situations where this first type of error is not
troublesome as can be ascertained by showing that one probe is not affected by the
presence of a second probe in its vicinity.
4.2. REFLECTION AND SECONDARY EMISSION
The interpretation of the probe characteristic rests on the assumption made in
the theories that all particles that reach the probe are collected and that no
additional charged particles are produced either at the probe wall or in the gas
Reflection, instead of collection of a charged particle when it arrives at the wall is
90 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
a possibility. If the probe field is such as to attract the particle, a reflected particle
will eventually be recaptured because its energy after reflection will be less than
that originally. So there will be no direct effect on the current. However, the
presence of reflected particles in the vicinity of the probe will alter the field
distribution in the sheath and so exert a secondary influence. If the field is such as
to repel a particle that nevertheless reaches the probe, then reflection will mean
decreased current. Langmuir and Mott-Smith (3) showed that the shape of the
electron current in the retarding field region is unchanged when the reflection
coefficient depends only on energy and the distribution is Maxwelhan. The only
effect is an overall shift of the curve and a discontinuity at plasma potential, since
at positive potentials reflected particles will be recaptured. Such discontinuities
are not noticed in probe characteristics so it is unlikely that reflection is a serious
P The presence of secondary emission of electrons at large negative potential,
however, is serious since it leads to a spurious increase in the apparent ion current.
Such emission may be due to the incidence of photons and metastable atoms on the
probe surface and also due to the bombardment of the ions themselves. The use
of multi-grid probes makes it possible to suppress the secondary emission, but in the
case of normal probes estimates of the mentioned effects on the apparent ion
current have to be made. Careful outgassing of the probe can sometimes reduce the
magnitude of the effects.
4.3. THERMAL ELECTRON EMISSION
Thermal electron emission from hot probes can completely alter the character
of the probe characteristic. Hence in cases where the probe will become too hot
when left in the plasma, the probe will have to be cooled or moved quickly so that
it does not reach an objectionable temperature. This makes it necessary to
produce an entire characteristic in a short time so that the probe has not moved
too much. .
Hot probes are sometimes used purposely to define the plasma potential, since
the current changes abruptly when the voltage of the probe swings through the
plasma potential.
4.4. EFFECTS OF CONTACT POTENTIALS
The measured value of the probe voltage will differ from the effective surface
potential by the contact potential. As long as the contact potential is uniform over
the probe surface and remains fixed in time the shape of the probe characteristic
is unchanged except for a shift along the voltage axis. This does not affect any of
the measurements except for an uncertainty in the value of the plasma potential
However Wehner and Medicus (33) have shown that changes in contact potential
can occur while the probe voltage is changed as a result of contamination of the
probe surface Furthermore, these changes can occur reproducibly so that a real
distortion of the probe characteristic can result. Wehner and Medicus also showed
that careful cleaning of the probe, by electron or ion bombardment, to red heat
under vacuum can remove contamination from the probe and that changes in
contact potential during the production of a probe curve can be minimized by
doing it quickly.
Medicus (34) has also suggested that a variation of contact potential over the
probe surface will produce distortions in the probe curve essentially by an averag-
ing process for the current over a voltage range. This will tend to round off abrupt
de leetjw: Electrostatic Plasma Probes 91
changes in the characteristic such as the ' ' break' ' in the electron current near plasma
potential.
A somewhat different difficulty is associated with the deposition of conductive
coatings on the insulators near the active probe surface. As a result, the effective
probe area may be significantly increased.
4.5. PRESENCE OF FLUCTUATIONS AND OSCILLATIONS
It is to be noted that when probe measurements are made by using a number of
steady voltages at which d-c currents are measured, quite important changes
occur in the probe characteristic in the presence of oscillations in the plasma.
When measurements are made where oscillations are expected, tests should be
made to find whether they are present or not. When fluctuations of relatively low
frequency are present it should be possible to study the fluctuation of the plasma
properties by using techniques to produce the probe characteristic within a time
short compared to a typical fluctuation period. In the case of real plasma oscillations
the frequency is likely to be too high for such a method to be applicable.
5. EXPERIMENTAL ARRANGEMENTS
A variety of probe shapes and circuits have been used. Only a few examples will
be given.
Single and double probes can be made in plane, cylindrical, or spherical forms as
indicated in Figure 1. Cylindrical probes have been made as small as 0.02 mm in
diameter. Tungsten and molybdenum are favorite materials. Plane probes can be
almost as small. Spherical probes are normally somewhat bigger since the support
should be small compared to the sphere radius.
A circuit for obtaining a probe characteristic in about one millisecond is shown
in Figure 13. Higher speeds are possible; curves have been obtained in less than
10 microseconds. At such high rates of voltage change it is, however, extremehy
important to keep the capacitance of the probe to a very small value because
otherwise spurious capacitive currents will be measured.
A plane multigrid probe for use in a satellite is described by Bourdean, Donley,
and Whipple (35). The basic structure is shown in Figure 14. Grid A is flush with
the satellite skin and electrically connected to it. Grid B is the control grid and C
represents the collector. The current to C is measured by a high sensitivity electro-
meter. When grid B is biased positively with respect to grid A all ions can be
repelled, so that only electrons can penetrate beyond B. By making the collector
slightly negative with respect to A, the electrons can reach C only when they have
enough kinetic energy at their arrival at A to overcome the potential difference
between A and C. By varying the bias on C the electron current will yield the
electron temperature in the same manner as described in section 2.1. It is also
possible to locate the plasma potential relative to the satellite potential by choosing
the value of collector bias where the electron current curve deviates from its
exponential form.
By biasing grid B negatively all electrons can be repelled and secondary emission
electrons from the collector can be suppressed. In this way the ion current can be
measured and it is possible by varying the collector potential to measure the
energy of the ions. Since the velocity of the satellite is accurately known this makes
it possible to determine the mass of the ions. Similar gridded spherical probes are
also used, as described by Boyd (36).
92
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
m
O
O
I-
de leeuw: Electrostatic Plasma Probes
93
Grid A Satellite Skin
777777777777? * [- ///?> ! Tfr77777777
Grid B.
'Collector C
<?h
FIGURE 14. Multi-electrode plane probe.
6. CONCLUDING REMARKS
The electrostatic probe is a very useful device in plasma diagnostics in spite of
the difficulties in interpretation and the many possible sources of error. Probes
can be used over an enormous dynamic range. In satellites probes have measured
electron densities as low as 10 10 /m 3 and in the laboratory densities of 10 20 /m 3 have
been determined. In addition, they are capable of making local measurements so
that even under unfavorable conditions they can indicate at least the shape of
spatial distributions. These advantages are strong incentives for the further
development of theories and for verifying experimental work applicable to those
conditions for which the probe response is at present not quantitatively known.
NOMENCLATURE
A Probe area
b Quantity defined in equation (2.7.3)
B Magnetic flux density
c Molecular velocity
d Sheath thickness
e Electron charge
/ Velocity distribution function
/ Current density
F Total current
k Boltzmann constant
I Length of cylindrical probe
L Mean free path
m Mass of Particle
M Atomic weight
n Number density of one kind of charged particle
r Radius
R Equivalent resistance
T Temperature
94 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
V Potential
x Quantity denned in equation (2.7.3)
y =1 cylindrical geometry
= 2 spherical geometry
e Permittivity of free space
77 Non-dimensional potential
A D Debye length
Subscripts
e Electrons
F Floating
p Probe
s At sheath edge
+ Positive ion
— Negative ion
Condition at plasma potential
00 Undisturbed conditions far away from probe
REFERENCES
1. Langmuir, I., and Compton, K. T., "Electric Discharges in Gases", Rev. Mod.
Phys., 3, 191 (1931).
2. Loeb, L. B., Basic Processes of Gaseous Electronics (Berkeley: University of
California Press, 1955).
3. Langmuir, I., and Mott-Smith, H., "Theory of Collectors in Gaseous Dis-
charges", Phys. Rev., 28, 727 (1926).
4. Boyd, R. L. F., "The Collection of Positive Ions by a Probe in an Electric
Discharge", Proc. Roy. Soc. A., 201, 329 (1950).
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10. Bohm, D., "Minimum Ionic Kinetic Energy for a Stable Sheath", in Charac-
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16. Biondi, M. A., ''Diffusion Cooling of Electrons in Ionized Gases", Phys. Rev.,
93, 1136 (1954).
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Electronegative Plasmas", Proc. Roy. Soc. A., 253, 102 (1959).
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Fluids, 5, 1010 (1962).
19. Zakharova, V. M., Kagan, Y. M., Mustafin, K. S., and Perel, V. I., "Probe
Measurements at Medium Pressures", Zh. Tekh. Fiz., 30, 442 (1960).
20. Su, C. H., and Lam, S. H., "The Continuum Theory of Spherical Electrostatic
Probes", Dept. of Aero. Eng. Report 605, Princeton University (1962).
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by Probes", Phys. Rev., 98, 1642 (1955).
22. Taylor, W. C, Rothman, H. S., and Morita, T., "Shocktube and Flame
Diagnostics by Ion Probes", Bull. Am. Phys. Soc. (Series 11), 8, 437 (1963).
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Atmosphere", in Rarefied Gas Dynamics (New York: Academic Press, 1961).
24. Meckel, B. B., "Experimental Study of the Interaction of a Moving Body with
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25. Clayden, W. A., "Recent Research in the ARDE Low Density Wind Tunnel
with a Plasma Jet Heater", in Rarefied Gas Dynamics.
26. Clayden, W. A., "Langmuir Probe Studies in the RARDE Plasma Jet",
Third International Symposium on Rarefied Gas Dynamics, 1962.
27. Smetena, W. O., "On the Current Collected by a Charged Circular Cylinder
Immersed in Two-Dimensional Rarefied Plasma Stream", Third International
Symposium on Rarefied Gas Dynamics, 1962.
28. Medicus, G., "Spherical Langmuir Probe in Drifting and Accelerated Max-
wellian Distribution", J. Appl. Phys., 33, 3094 (1962).
29. Talbot, L., "Theory of the Stagnation Point Langmuir Probe", Phys. Fluids, 3,
2 (1960).
30. Brundin, C. L., Talbot, L., and Katz, J. E., "A Comparison Between Langmuir
Probes and Microwave Electron Density Measurements in an Arc Heated
Low Density Supersonic Wind Tunnel", University of California Tech. Rep.
HE-150-186 (1961).
31. Johnson, E. O., and Maker, L., "A Floating Double Probe Method for Measure-
ments in Gas Discharges", Phys. Rev., 80, 58 (1950).
32. Garscadden, A., and Palmer, R. S., "Langmuir Probe Derivatives Using a
Double Probe Method", ARLS3-50, Aero. Res. Lab., U.S. Air Force, 1963.
33. Wehner, G., and Medicus, G., "Reliability of Probe Measurements in Hot
Cathode Gas Diodes", J. Appl. Phys., 23, 1035 (1952).
34. Medicus, G., "Theory of Probes with Non-Uniform Work Function", Vth
Inter. Conf. on Ionization Phen. in Gases (Amsterdam: North- Holland, 1962),
1397.
35. Bourdeau, R. E., Donley, J. L., and Whipple, E. C, "The Ionosphere Direct
Measurements Satellite", NASA TN D-414 (1962).
36. Boyd, R. L. F., "Plasma Probes on Space Vehicles", Vth Inter. Conf. on Ioniza-
tion Phen. in Gases (Amsterdam: North-Holland, 1962), 1387.
37. Pollin, I., private communication.
4*
5. Paul C. Wilber:
Experimental Investigation of
the Characteristics of a
Langmuir Probe in Ionized Low-
Density Flows
12? An experimental study of the performance of a charged circular
cylinder immersed in an essentially-uniform rarefied plasma stream is
described. Data are presented for wide ranges of speed ratio, electron
and neutral particle number densities, and electron temperature with
the collector axis oriented both parallel and transverse to the flow.
Results are discussed with respect to a theory recently developed at the
University of Southern California Engineering Center which relates
the probe measurements to local charged particle density and tempera-
ture in the flawing plasma.
INTRODUCTION
Approximately two years ago a program was begun at the University of Southern
California Engineering Center to investigate the possibility of making local measure-
ments of charged-particle number density in rarefied plasma streams. A theoretical
study was carried out by Dr. F. 0. Smetana (1) in which he was able to calculate
the flux of charged particles to a cylindrical collector immersed in the stream as a
function of its potential, relative to the plasma, for wide ranges of the flow para-
meters. His results provide a means of interpreting the measured characteristic
quantitatively in terms of the charge number density if the other parameters are
known. Since the theoretical analysis was based on several assumptions which may
or ma3 r not hold in general, an experimental study was initiated to assess the
validity of the theory. This paper discusses what has been accomplished
experimentally to date.
REVIEW OF THEORY
Since the experimental work to be discussed has the checking of a theory as one
of its principal objectives, a brief outline of that theory and its results will be
presented first. Smetana's analysis is an extension of the work of Mott-Smith and
ed. note: Mr. Wilber is with the Celestial Research Corporation, South Pasadena,
California. The research reported in this paper was conducted at the Uni-
versity of Southern California Engineering Center and was sponsored by the
Aeronautical Systems Division, Wright -Patterson Air Force Base, under
Contract AF-33(657)-7760.
97
98 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Langmuir on probes in rarefied stationary plasmas (2, 3) to the case of mass mean
motion. The basis of the method is the calculation of particle flux to the probe by
summing the distribution function over all particle velocities such that the free-
space trajectory intersects the collecting surface. A Maxwell-Boltzmann distribution
is assumed.
For the analysis of the case of a moving plasma the following assumptions were
made:
1. The plasma is composed of three species: singly-ionized positive ions,
electrons, and neutral molecules.
2. Each species is in local thermodynamic equilibrium and the ions and neutrals
have the same temperature (which may, however, differ from that of the electrons).
3. The number densities of ions and electrons are equal; the number densities
are small compared with those of the neutrals.
4. Collisions between charged particles are neglected in comparison with
collisions between charged particles and neutrals.
5. The stream is moving with a uniform velocity, U , perpendicular to the axis
of a right circular cylindrical collector.
6. The cylinder diameter is small compared with both the electron-neutral and
ion-neutral mean free path lengths.
7. The field of the cylinder does not perturb the plasma significantly beyond one
electron-neutral or ion-neutral path length. Thus the region of effective charge
collection is collisionless.
8. The nature of the field about the collector is not altered by the motion of the
stream (i.e., it remains a central force field as in the case of a stationary plasma).
Application of these assumptions resulted in the expression shown for the flux
of one of the charged species to the cylinder:
\ m } r c J_ x J_ C2max J- UoS inB (!)
x e -< m ' 2k() <<1 + <: I + < : §>dc 1 dc 2 dc3
where n — free stream number density of the species collected
r c — cylinder radius
r e = radius at which the potential on the cylinder no longer effects
collection of charge
c 1; c 2 , c 3 = components of the random thermal motion in the r, 6, and
2-directions respectively
c 2max = the maximum value of c 2 for the given value of c x for which the
particle will be collected
If we define
* = & < 2 >
s = U p (3)
^Tt (4)
V = probe potential (5)
wilber: Langmuir Probe in Low- Density Flows 99
then substituting these, and substituting for c 2max in terms of c ± and 8, and integra-
ting equation (1) twice yields
N - "-Vis* I ?. 31n . <* + v? *> ^H ( 8 cos d+r t z )
-erf(scoad-^z\\ dc x
(6)
where
Z 2 = znl(Pci+Ssm0) 2 + Vo\
K
Equation (6) cannot be integrated directly except for certain special cases. For
the case of 8=0 it yields the well-known results of Langmuir. For the general
case numerical methods are necessary; they yield the desired results provided r e is
finite. The result can be conveniently expressed as
Ji=2 W<^4°'^) (7)
Since J x is the flux of a single charged species to the cylinder; the net current to the
probe will have the form :
/ = {J 1 -J 2 )Le (8)
where ?/ 2 =flux of the oppositely charged species
L— length of collector
e = electronic charge
If one puts
(9)
"?-* el
y = y { < 10 >
/ m . \l/2
S = V l ' I = Speed ratio of the neutral species (11)
equation (8) can be rewritten
I = Kn r c VT e I ^ , ?8 0> ^ (13)
For fixed values of y, S , and rjr c , 1 is a fixed function of ij . If, in addition, we are
given a fixed probe geometry and a constant ion temperature, the probe characteris-
tic equation, equation (13), has only the charge number density as parameter
and thus becomes a convenient measure of charge density.
This analysis hinges on two basic assumptions: (1) that the probe possesses a
central force field and (2) that there is a finite radius, r e , for which the field of the
probe, in effect, terminates. The problem becomes how to insure the validity of these
assumptions. The first assumption can probably best be verified by experiment, but
a reasonable estimate of limits on the second can be obtained by solving a suitable
100
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
|0?- ■ i r
8
:: SC
LUTIONS OF THE EQUATION
!j + d!L(i)_4 sinh
r 2 dr Vr / . \ 2 n '
d
6
W"^
"- = \ d
c.
1.0
8
6
—\ —
— t —
\
t = "V~
4
i
— \—
\
0.1
V002V.02
\ \
\ 0.2
\2.0
\ 20
V200=X D 2
8
=V
V
,
"11
6
— 1
1) A
i
1
\
? 4
\
1
\
-\ —
\
1
2
.01
-1—
\
\
M-
\
h- \—
\r
8
=f
\ J^\
-\
6
~1
1 1 1
4
4
\\ t
- -
1
1 1 i
1 I .._ L_
\
2
.001
c
I
\
\ 1
).l
2
4 6
8 1.0
2 4 <
5 8 10
2
4 6
8100
FIGURE 1. Solutions of the one-dimensional Poisson equation for the cylinder with
3 = and 7 = 0.
form of the Poisson equation. This has been done for the one-dimensional case with
S = and no current drawn by the cylinder. The result is shown in Figure 1.
While the conditions assumed in obtaining a solvable form of the Poisson equa-
tion are not very realistic, it is evident from Figure 1 that considerable changes
can occur in the charge distribution near the cylinder without altering r e appreci-
ably. Thus when r e \r c > 10, the error induced in the flux calculation by the use of
the results in Figure 1 would seem to be negligible.
With the above in mind, theoretical probe characteristics have been prepared for
proposed probe geometries and conditions anticipated in the Engineering Center's
experimental facilities. The plasma was assumed to consist of electrons, nitrogen
wilber: Langmuir Probe in Low- Density Flows
FIGURE 2. Theoretical Langmuir probe characteristic for a typical case of thermal
equilibrium.
molecules, and N 2 ions. Since the Center's facilities can generate only relatively-
low enthalpy plasmas and then only such that T e >T i: T n , discussion will be
limited to such cases.
The theoretical characteristics were based on the nominal diameters of tungsten
wires which could be fabricated into satisfactory probes. Limits on the range of
charged-particle number density for which the theory could be expected to hold
were found by imposing the conditions: (1) that the region of charge collection be
collisionless with respect to electron-neutral or ion-neutral collisions, and (2) that
the value of the probe's field at the maximum allowable value for r e must always
be l/100th its value at r c . Based on Figure 1 and the desire to make the theory
applicable to values of charge density as low as possible, the maximum value for
r e was taken to be 100r c .
Figure 2 shows a theoretical probe characteristic for a typical case of thermal
equilibrium. This illustrates the effect of speed ratio on ion current even at very
low probe potentials when the electron temperature is low.
102
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
o
O
O
if)
VI
,z
5ow h
IO - ? VI
ii M VI ?.
?-i o 5
o o o
O OO
O OO
0)0.0.10.
*~ O <D<f
ro —
CVJ
'O
° u / , X (SdlflV~I)
21
O
in
o
o
ro
?
J3
-?a
eS
VI
a
o
be
C
en
b
o
>
Q.
>
— 3
2 a,
s x
"8 -
§ s
?S 3
?S.S
? z
-2
bCS
.S *
H S
- <8
?jg a>
o g
o
a-5
—
^-1 *■*
Ii
■? ?
i 5>
O _
2 J3
?fl "S
o
H?
CM
OS g
, o
H *
3 o
??&
Unfortunately the RF discharge produces plasmas which are far from being in a
state of thermal equilibrium. This means that the following temperatures were
expected in the experiments: T i =T ll x300°K, 4500°K< T e < 30,000°K. Thus
y might vary between 15 and 100 and, hence, for a given experimental configura-
tion, the probe characteristic would have both n and T e as parameters. If the
probe characteristic exhibits a strong dependence on T e throughout the ranges of
S and V available experimentally then unique determination of charge density
would depend on knowing the electron temperature. To determine if such were the
case theoretical probe characteristics were prepared for the above conditions.
Figure 3 shows the results. The electron-sheathed region is seen to be relatively
independent of electron temperature and thus provides a unique measure of charge
density. If T e and S are known the ion sheathed region also determines n uniquely.
wilbeh: Langmuir Probe in Low- Density Flows 103
EXPERIMENTAL SETUP
In an attempt to verify the above theory, an experimental program is being
carried out in the Engineering Center's low-density, Mach-6, axisymmetric test
facility sketched in Figure 4. Commercial grade liquid nitrogen provides the work-
ing gas. The stream, upon leaving the nozzle, passes through a boron nitride
constant-area heating section approximately 10 inches long. From this it exits
into a 6J-inch I.D. teflon test section having various openings for observation of the
flow. The facility is instrumented to provide plenum chamber pressure, test
station static and pitot pressures, and the approximate stagnation temperature. It
can be driven by either a large mechanical vacuum pump, a cryopump, or both.
The discharge can be produced anywhere along the boron nitride section by
suitable positioning of the external ring electrodes. Power is supplied either by a
2-kw, 10-Mc/sec generator or a 12-kw, 12.8-Mc/sec generator. Overall heating
efficiency is estimated to be not more than 20%.
The probe instrumentation is shown in Figure 5. Because of the non-equilibrium
nature of the RF plasma the entire system must be floated with respect to ground
to minimize disturbance of the plasma and to get satisfactory measurements.
Probe currents are measured with a Kay Lab model 203R microammeter. Probe
potential is measured with respect to a floating reference probe kept at a fixed
position in the stream. To insure isolation of the reference probe voltages are
measured with a Sensitive Research Electrostatic Voltmeter having an insulation
resistance > 10 15 Q. To obtain maximum resolution in the voltage measurements,
the meter is biased to the upper end of its scale by a suitable potentiometer. A
reversing switch allows measurement of probe voltages both positive and negative
with respect to the reference electrode.
The probe potential is varied with respect to the plasma by applying a voltage
between the probe and a cylindrical copper return-electrode lining the inside of the
teflon test section. Although there is considerable speculation as to how much this
technique disturbs the plasma, visual observations indicate little effect and the
distance between the probe and the reference electrode is kept as small as possible
to minimize the effects of whatever changes do occur. Surveys of various plasma
streams at the test station indicated very small gradients in the core of the flow
for the case where the probe draws no current.
Because the RF discharge in this experimental configuration appears to act like
a battery, producing voltages up to 400 volts between interior points and points
on the boundary of the plasma, a relatively high voltage potentiometer is needed
to bias the probe with respect to the plasma. The potentiometer used consists of
two variable voltage sources in series. The coarse pot has a range of to 1000 volts
while the fine pot can be varied from to 24 volts, in steps of approximately 0.2
volts. This system is connected to the probe-return-electrode combination by a
reversing switch to again provide choice of sign.
The probe itself consists of a tungsten collector welded to a No. 30 copper lead
with the combination supported in a pyrex tube of approximately 0.055-inch O.D.
and 0.035-inch I.D. The tube is bent so that the axis of the collector is perpendicular
to the axis of the support tube and centered on it. The pyrex tube is necked down
and ground off until the tungsten just passes through it. Microscopic examination
indicates maximum clearance between the collector and the pyrex to be about
0.0003 inches. The diameter of the collector is nominally either 0.003 inches or
0.0012 inches. Lengths of the cantilevered collector section equivalent to a length-
to-diameter ratio of 600 have been produced without significant droop.
104
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Q.
D
X
a
CC
(0
W
Ul
cc
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Ul
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a
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Ul
a
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IT
H
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Ul
J
Ul
z
h
Ul
a:
TO GAS SUPPLY AND
METERING SYSTEM
THRU HEAT EXCHANGER -TO
MECHANICAL PUMP AND/OR CRYOPUMP
N
00
0)
O
Ul
J
N
N
Z
(0
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5
z
Ul
(0
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o
CC
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o
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wilber: Langmuir Probe in Low-Density Flows
105
SI
Si.
PROBE
--lf^-
REF.
S2
I MICROAMMETER
V ELECTROSTATIC VOLTMETER
Pi 0-24 v FINE-DIVISION POTENTIOMETER
P2 0- lOOOv COARSE-DIVISION
POTENTIOMETER.
Z-
1 — M/W — |
300 v
FIGURE 5. Probe instrumentation schematic.
The probe support system allows the probe to traverse the plasma in a vertical
direction and to have its axis oriented at any angle with respect to the direction of
flow. Since the collector is centered on the axis of the support tube, displacement of
the probe in the plasma during a rotation is minimized.
Using this experimental system a number of measurements of probe characteris-
tics have been made for several combinations of the parameters involved.
Although the ranges of variation are not as great as were originally anticipated,
they do seem to provide some significant effects with which to study the theory.
The principal problem encountered in the work to date has been that of isolating
the probe instrumentation from the RF fields and noise associated with the
generator and discharge. Failure to properly solve this problem has limited the
measurements to a much lower upper limit on charge number density than was
originally anticipated. As a result it has not been possible to make simultaneous
independent measurements of charge density by microwave methods.
RESULTS AND DISCUSSION
A number of runs using three different probes in various flow conditions have
been made. Significant portions of probe characteristics were obtained in fourteen
cases which are described by Table I. Since an infinitely long probe oriented with
its axis parallel to the direction of flow is obviously a very good approximation to
the stationary case, most data was taken with the collector in this orientation in
order to allow interpretation by Langmuir's well established theory. In addition,
experiments showed that when placed transverse to the flow the collectors were
bent off axis by varying amounts depending upon probe geometry, flow conditions,
106
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
TABLE I.
EXPERIMENTAL CONDITIONS
Neutral particle
Dis-
number density,
Speed charge
Run
Probe
Probe axis
r c
L
n N
T?,T t
ratio
power
Mo.
location
orientation
(cm x 10 3 )
2r c
(cm" 3 )
(°K)
(So)
(Watts)
1
Centerline
Parallel
3.68
119.5
3.7 xlO 15
~300
~5
~250
2
2.52
10.7
3.5 xlO 15
~290
~5
~200
3
2xl0 16
~330
~0.5
4
6.8 xlO 15
~330
~0.5
5
,,
>'
2.6 xlO 16
~330
~0.1
6
2.52
10.7
1.9 xlO 15
~340
~5
V
7
1.52
605
8.1 xlO 15
~325
~0.05
~200
8
1.8 xlO 15
~330
~5
~100
9
^
f
3.2 x 10 15
~290
~200
10
Centerline
4.7 xlO 15
~280
11
0.55 inch below
Centerline
Parallel
4.7 x 10 15
~280
12
0.55 inch below
Centerline
Transverse
4.7 xlO 15
~280
13
Centerline
Parallel
8.0 xlO 15
~275
~200
14
Centerline
Parallel
V
V
8.0 xlO 15
~280
T
~400
voltage, and length of operation. The present theory was therefore checked by
taking a series of pairs of comparison points except for the curve obtained in run
No. 12 during which the collector's tip suffered a permanent set of 18° off axis.
Table II lists the pairs of points obtained.
TABLE II. COMPARISON POINTS INDICATIVE OF EFFECT OF ORIENTATION ON PROBE
CHARACTERISTIC AT VARIOUS CONDITIONS.
Run
Parallel
Transverse
Pair
Probe location
v P
I,
v,
h
number
number
(below centerline)
(volts)
(amps)
(volts)
(amps)
1
7
0.14"
-175
-9.56xl0" 6
-174
9.64 xlO" 6
2
7
50.2
0.907 x 10" 3
50.0
0.963 xlO" 3
3
8
-175
-3.45x 10- 5
-175
-3.40xl0" 5
4
8
63.8
3.20 xlO" 3
60.3
3.20 xlO" 3
5
9
-195
-2.48xl0" 4
-195
-2.60xl0- 4
6
9
45.2
4.96xl0- 3
42.3
4.96 xlO" 3
7
10
-201
-4.07x 10- 5
-201
-4.84x lO" 5
8
10
35.8
3.63 xlO" 3
32.6
3.60xl0- 3
9
13
-113
-3.01 x 10~ 5
-114
-3.36 xlO" 5
10
13
22.1
4.84x 10" 4
22.2
6.61 x 10~ 4
11
14
-195
-6.25x lO" 5
-195
-8.56x 10" 5
12
14
?
'
49.8
2.89 x 10" 3
46.6
2.83 x lO" 3
To aid in interpreting the results, theoretical probe characteristics corresponding
to the nominal geometries of the experimental probes and covering the range of
experimental conditions studied are presented in Figure 6. The values of I v shown
are per centimeter of collector length. Since the RF plasma was expected to be out
of equilibrium between species with temperatures as shown on page 102, most of
the experimental data was taken in the electron-collection regions of characteristics
such that the data could be compared with theory directly without first determining
T
All the theoretical curves are based on the value n = 10 9 cm -3 . The value of n
observed experimentally is obtained by multiplying 10 q by the factor corresj
iding
wilber: Langmuir Probe in Low-Density Flows
107
-10
FIGURE
tions (T,
-70 -60 -50 -40 -30 -20 -10 10 20 30 40 50 60 70
V -VOLTS
6. Theoretical probe characteristics corresponding to experimental configura-
= T K = 300°K).
to the number of decades up or down that the appropriate section of the theoretical
curve has to be shifted to make it match the observed curve. Since the probe voltage
is measured with respect to that of a floating reference electrode located at a
different position in the plasma, there is a horizontal displacement of each experi-
mental curve, relative to its corresponding theoretical characteristic, which can be
ignored. Since plasma conditions vary from run to run, the shifts in the observed
results cannot be expected to be constant.
Figures 7, 8, and 9 show the fourteen measured characteristics. The current has
been "normalized" to correspond to that of a collector whose length is 1 cm and
whose radius is either 3.81 x 10~ 3 cm (for runs 1 through 6) or 1.65 x 10~ 3 cm
(for runs 7 through 14). The scatter in the observed data is apparently due to
several factors: (1) random fluctuations in the plasma conditions, (2) insufficient
resolution of the voltmeter readings, and (3) interaction of the ammeter with the
RF field which caused shifts in the characteristics of certain input shunting resistors
during some of the runs. Lack of sufficient data to accurately define the retarding
108
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
lO
?-io' 6
<
2
-10"
4
-10"
60-50-40-30-20
10 20 30 40 50 60 70
V P ~ VOLTS
FIGURE 7. Experimental probe characteristics for runs 1 through 5.
wilber: Langmuir Probe in Low- Density Flows
109
-60-50-40-30-20 -10 10 20 30 40 50 60 70
Vp ~ VOLTS
FIGURE 8. Experimental probe characteristics for runs 6, 7, 8, 13, and 14.
110
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
\rT
—
^ <^
*
/fr
s
in 3
/
ugr
ifT(~
/7'
IMo 1
Pa
- 1 -
i .
vii
&
I
Q.
1/
- —
< -5
^ 10
<u ' w
/
in 6
RUN NO.
9
SYMBOLS
10 — m
+ in 7
— A-
?-io b
/
— ?-
<
/
*
i
Q.
I
(— |
4
H-io
-L>^=
-
=^="
: jzr-
■^cu
--
-I0 4
-7
-■ -
- —
0-6
0-5
-4
0-3
-2
.0-1
<
D 1
2
10 3
4
5
6(
Vp ~ VOLTS
FIGURE 9. Experimental probe characteristics for runs 9 through 12.
wilbee: Langmuir Probe in Low-Density Flows 111
field region in a number of the runs was primarily due to two factors: (1) random
plasma fluctuations of such period and magnitude as to make reading the current
on the more sensitive scales impossible, and (2) absorption of sufficient RF power
by the ammeter to cause failure of the resistors shunting the 10 [xa, and/or 100 (xa
scales.
Comparison of the experimental with the theoretical curves immediately suggests
that in the region of electron collection electron production processes are sufficiently
active over the entire electron-sheathed region so as to alter that section of the
observed characteristic to such an extent that alignment with the theoretical curve
is impossible. The retarding field region is always so steep that its alignment is too
inaccurate in all cases. However, all measured slopes correspond to electron
temperatures between 300°K and 75,000°K which was anticipated. Unfortunately
in all except three cases the measured temperatures lie between 11,000°K and
75,000°K and therefore alignment should be made with the missing ion-collection
sections of the non-equilibrium curves in order to determine electron number
density with best accuracy, but for the experimental results this region is defined
very inaccurately because of erratic ammeter performance in the corresponding
current range.
In the absence of the preferred method, it appears that the next best thing to do
is align the transition regions from the retarding field to the electron-sheathed
condition. If this is done comparison with the theoretical curves yields number
densities ranging from 5 x 10 7 (for run 7 where high pressure and low speed would
produce a maximum amount of recombination before reaching the probe) to
4.4 x 10 9 (for run 14 where high speed and increased discharge power would be
indicative of an increased degree of ionization at the probe).
Additional correlations between the experimental conditions and the electron
densities measured by aligning the "knees" of the curves can be made. For
example, it was noted in runs 1 and 2 that light emission from the plasma stream
reached a peak in intensity in an annular region extending from about 0.35 inches
to 0.7 inches from the centerline. To see if this was indicative of increased charge
density, runs 10 and 11 were made. The probe measurements made in these two
cases indicate that the charge density increases by a factor of about 2 in going
from the centerline out to a point 0.55 inches away.
Good temperature correlation is also observed. In those cases where the neutral-
particle number density is high and the speed is low, the electron temperature is
lower by a factor of one-half to one-fifth compared to that in runs w T here the
opposite conditions hold. For example, compare run 7 with run 12.
With respect to the pairs of comparison points verification of theory for the
stationary plasma case is provided by pairs 1 and 2. Pairs 3 through 12 apparently
all correspond to the T e ?T t case and should show little difference between the
currents collected in the parallel and transverse orientations. This is what is
observed in pairs 3 through 8 where the neutral-particle number density is appar-
ently low enough for the probe to appear free-molecular with respect to electron-
neutral and ion-neutral collisions. Points 9 through 12, however, show significant
differences between the parallel and transverse values of the ion-sheathed current.
This may be because the neutral particle number density is high enough to keep
the probe from experimentally satisfying the theoretical free-molecular condition
stated above. However, for these runs a wake was observed to extend downstream
of the probe as much as 800 diameters. This may be indicative of a highly non-
central force field which might or might not have a significant effect on current
collection. The numerical values of T e and n obtained in the experiments are
summarized in Table III.
112
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
TABLE III. EXPERIMENTAL RESULTS
le
Mot
n
Run
(ion-sheathed section)
(transition section)
number
(°K)
(cm -3 )
(cm -3 )
1
53,000
—
1.9 xlO 10
2
6,300
4.5 x 10 9
1.6 xlO 9
3
44,000
1.5 xlO 10
9.2 xlO 8
4
35,000
1.9 x 10 10
2.0 xlO 8
5
14,500
4.4 x 10 10
7.1 xlO 8
6
75,000
2.1 x 10 10
4.4 x 10 9
7
58,000
8.0 x 10 9
5.0 xlO 7
8
72,500
3.7 x 10 10
5.4 xlO 8
9
10,000
8.0 x 10 10
5.3 xlO 9
10
11,000
1.3 x 10 10
6.0 x 10 8
11
24,500
2.7 x 10 10
3.4 x 10°
12
56,000
1.7 x 10 10
4.3 x 10 9
13
10,000
1.2 xlO 10
4.5 xlO 9
14
11,000
1.1 x 10 10
4.4 x 10 9
"j" The value of n in this column is generally considered to be the less
accurate of the pair.
CONCLUSION
The principal results of the experimental program can be summarized as follows:
1. Although the probe instrumentation system lacked sufficient sophistication
to definitely establish the proposed theory and its limits of applicability, it did
display all the qualitative behavior the theory predicts and was in good enough
quantitative agreement to lead one to suspect the instrumentation rather than the
theory.
2. The electrons, although in a noisy plasma with significant RF fields, high-
concentration gradients, and complete lack of thermal equilibrium between species,
still satisfy the Maxwell energy distribution.
3. At probe potentials more than just a few volts above ( + ) the floating
potential the theory deviates significantly from reality due to secondary emission
from the collector's surface.
4. The single probe is definitely a useful experimental tool for obtaining signif-
icant local values of the electron temperature and charge density in a flowing
low-density plasma stream.
The experimental work to date has been very encouraging. However, additional
studies of the cases when the plasma is in equilibrium and where T \ > T e must be
made to complete the verification. Also the free-molecular condition should be
better satisfied experimentally than it has been to date in order to avoid any
ambiguity. This means operation at lower pressures and a more limited range of
application or else a smaller collector and much more difficult fabrication problems.
In any case further study appears justified.
REFERENCES
1. Smetana, F. O., "On the Current Collected by a Charged Circular Cylinder
Immersed in a Two-Dimensional Rarefied, Plasma Stream", Third Interna-
tional Symposium on Rarefied Gas Dynamics, Paris, France, June, 1962.
2. Mott-Smith, H. M., and Langmuir, I., "The Theory of Collectors in Gaseous
Discharges", Phys. Rev., 28, 727 (1926).
3. Langmuir, I., and Compton, K. T., "Electrical Discharges in Gases. Part II.
Fundamental Phenomena in Electrical Discharges", Revs. Mod. Phys., 3, 191
(1931).
6. Robert Betchov and Eugene B.
Turner: Measurements of MHD
Turbulence with Magnetic
Probes
l? Small magnetic probes have been used in this laboratory to make a
systematic study of MHD turbulence in a linear pinch stabilized with
an initial longitudinal magnetic field. The preserve of MHD turbulence
in such a device was first reported by Burkhardt and Lovberg (1) of
tube filM with deuterium gas by the discharge of an 85-,* capacZ
bank charged to 15 kv. The stabilizing field is 2000 gauss andZgas
pressure is typ lC ally 80 ^Hg. The small magnetic probes, unth a
frequency response up to 50 Mc, are inserted into the plasma through a
slot in the cathode and are moved radially by traversing screws The
probe signals which are proportional to B, art integrated to give B
the magnetic fieU strength. Differentiating once gives B which is a very
sensitive measure of the onset and duration of the turbulence. A com-
plete mapping f the pinch was done using the B signal to find the
onset of turbulence as a function of radius and time. The correlation
between two probe signals has been obtained as a function of the probe
separation using a technique emptying an x-y oscilloscope One
probe signal is put into the frontal amplifier and the other into the
vertical amphfier. Many shots are required to obtain a relatively
smorth pattern which has an elliptical shape with the major axis lying
at 45 to the horizontal. The correlation is a function of the ratio of
minor to major axis of an elliptical brightness contour.
INTRODUCTION
B^IZT Tf "? f ° r thlS Pr0gram was P rovided V the experimental work of
m*?^; u ix i luimoer ' lya ?- Iney ma de extensive measurements with small
Smbus S r °4 Frot S" "y?*"*** * ? ?— P-h device dTsgT^
nTZt a , data ' they were able to dedu <* the magnetic fieldT
StarftST P T Ure ^ tribUti ° nS thr °^ h0Ut the ^dr^Ttube as a
Junction of time. The probe signals at a given point were reproducible up to a time
ED ' NOTE: S??T ^ Mr - TUmer ^ ^ ^ Aer ° 8paCe <**°?*>°. E ' Segundo,
113
114
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
by joule heating. With the additional energy diwpation, the plasma app
p t:-afSSed t^f.h c :?t7?? t ?,e =^?*i ?.?.y - 7r ^
h?f^
linear pineh apparatus, similar to ^°? b ?% b ;i: ?t?^JT Pt described in
of plasma turbulence in a systematic manner. The exp "°S, ' M ? ch im .
this paper was carried out during the penod of January, 1961, to March,
DESCRIPTION OF THE APPARATUS
"stabilized pinch The ?t 8 switch the current rises sinus0 id-
4-kv capacitor bank. Alter trigge?g g ^ main digcharge 1S
ally to a maximum value in about - f>*?*? ic field pene trates the
fired. In this relatively ^^^^^^ time duration (about
7^^^?^~ ?? thickness of the copper screen is
Sr^^-n^Xlt ?* operated very reliably at ,5 k v by
heating the anode region of the tubes with infrared lamps.
f Mullite is a high temperature porcelain ceramic.
betchov and turner: Measurements of MHD Turbulence 115
i— "- . ^ . TfrmfTfT JO
VACUUM
ssms PUMP
^
o o
GROUND o o
o o
o
o
o
SOLENOID COIL -o
FOR B Z FIELD
IGNITRON SWITCHES
FIGURE 1. Schematic diagram of the linear pinch device.
The magnetic probes, described in the next section, protrude into the plasma
through a diametrical slot in the upper electrode which is at ground potential.
Two traversing screws are used to move the probes in a radial direction. One of
the probes can also be moved up and down or rotated through 360° by a gear
train located above the cathode. The discharge tube is evacuated with an MCF-60,
2-inch diffusion pump which gives an ultimate vacuum of 2 x 10 ~ 8 mm Hg.
Deuterium gas can be continuously fed into the discharge at the bottom through a
116 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
hot palladium thimble which passes only hydrogen or deuterium gas. At the same
time the tube is pumped out at the top through a small valve which can be adjusted
to give the desired pressure in the tube. The gas pressure is measured continuously
with a Pirani type vacuum gauge calibrated for deuterium.
The apparatus is equipped with a pneumatically-operated vacuum valve and
relay meters on the power supplies which automatically shut off when the proper
voltage is reached. Remote reading meters and controls are installed in the screen
room. These make it possible to fire the device every 2 minutes. Such speed is
important since it is often necessary to fire a series of 24 shots or more to obtain
sufficient data for a statistical analysis of the turbulence.
MAGNETIC PROBES
The use of small magnetic probes for the measurement of transient magnetic
fields inside a plasma discharge was first reported by Russian physicists studying
the pinch effect (3). Magnetic probes provide much valuable data about the plasma
discharge. From a knowledge of the magnetic fields inside the plasma as a function
of position and time, it is possible to determine the electrical current distribution
and the gas pressure in the plasma. A description of the magnetic probes used at
the Los Alamos Scientific Laboratories, together with some of the early results,
was reported by Karr (4). The design of our first magnetic probes was copied from
the description given by Karr.
The first magnetic probes consisted of small coils with 24 turns of no. 40 formvar
covered wire wound in three layers of 8 turns each on a 0.030-inch diameter core.
The leads from the coil were twisted and soldered to a miniature coaxial cable
connector at the other end of the probe. The probe coil and twisted leads were
enclosed in a non-magnetic stainless steel tube which was thinned to a 4-mil
wall near the coil and slotted at 90° intervals. The probes were designed to extend
4 inches into the plasma, so the last 6 inches of the probe were enclosed in a 2-mm
I.D., 3-mm O.D. fused quartz tube for electrical insulation. The total length of the
probe was 12 inches. Probes were made with the coil axis both longitudinal and
transverse so that all three components of the magnetic field could be measured.
Although this first type of probe appeared to give satisfactory results, we
endeavored to develop a technique to measure the probe sensitivity as a function
of frequency. After much difficulty a method was finally devised which gave
accurate values of the probe sensitivity over the frequency range of 1-50 Mc using
conventional electronic equipment. A Tektronix 190A signal generator, which has
a sine wave output of 10 volts peak to peak into a 50 ohm load, was used to feed
current into a small Helmholtz coil. The two individual coils had a radius of 2 cm
and a spacing of 2 cm. The Helmholtz coil produces at the center a very homo-
geneous magnetic field which can be accurately calculated. A series of four coils
with 10 turns, 4 turns, 2 turns, and 1 turn were required to adequately cover the
frequency range. The maximum frequency at which a particular Helmholtz coil
can be used should be less than approximately J the resonant frequency of the coil
so that the current in the coil is close to the measured current. The minimum
frequency is determined by the point at which the coil begins to load the oscillator.
The current input to the Helmholtz coil was measured with a Tektronix current
probe and oscilloscope which had been calibrated at frequencies of up to 50 Mc.
The magnetic probe was properly positioned in the center of the Helmholtz
coil, and the output was measured with a Boonton RF voltmeter. It was necessary
to put the RF voltmeter in a screen room with the oscillator outside to reduce
pickup. The output voltages from the probes were only a few millivolts With the
betchov and turner : Measurements of M HD Turbulence 117
probe outside the Helmholtz coil, no signal was observed. An example of probe
sensitivity as a function of frequency determined by this technique is shown in
Figure 2.
These measurements showed that the sensitivity of the first magnetic probes
fell off badly above 10-15 Mc. For this study of MHD turbulence, however, it was
desirable to have a frequency response that was fairly flat out to 40 Mc or more.
Therefore, in order to design better probes, it became necessary to investigate the
factors affecting the frequency response. At approximately this point in our
research, a paper by Segre and Allen (5) was brought to our attention. This paper
discusses the factors affecting the frequency response of magnetic probes. The
OLD PROBES WITH
24 -TURN COILS
5 -
NEW PROBES WITH
10- TURN COILS
8 10
15 20 30 .40 50
FREQUENCY, MEGACYCLES
FIGURE 2. Probe sensitivity carves.
major factor causing the falloff of sensitivity at high frequencies in the first probes
was the relatively high inductance of the probe coils. When u>L becomes com-
parable with the characteristic impedance of the coax line (50 ohms in our case),
the probe signal is partially integrated; this produces a phase shift and a reduction
in signal. The inductance was calculated to be 0.4 jxh so col = 50 ohms at 20 Mc.
It was also found that the fairly thick stainless steel wall (4 mil) surrounding the
coil for electrostatic shielding, attenuated the signal at higher frequencies —
especially for the probes with transverse coil orientations.
New magnetic probes were designed to provide, among other improvements,
good frequency response up to 50 Mc. The number of turns in the cod was reduced
to 10—2 layers of 5 turns each on a 0.042-mil diameter core. The calculated coil
inductance was thereby reduced to 0.12 jxh. The coil leads were connected directly
to a small coaxial cable instead of twisted leads. By placing the probe coil at the
end of the coaxial cable, it was possible to push the coil into quartz tubing bent into
various shapes as shown in Figure 3. The L and hook probe shapes were designed
for some of the correlation studies. The coils were electrostatically shielded with 1 mil
strips of nichrome, but we doubt that any shielding at all is required as the probes
have a quite low impedance. Frequency calibrations of the newprobes, such as shown
in Figure 2, confirmed that the frequency response was satisfactory up to 50 Mc.
118
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
J2
O
c
60
S
&
a.
a
u
hi
o
o
JS
-
The magnetic probe signal is V=NAB where B = dBjdt, N is the number of
turns in the coil and A is effective coil area. For the new probes, the value of NA
was about 1.2xl0" 5 square meter turns. The maximum signal strengths from
these probes was often greater than 100 volts. The so-called "ground potential"
was found to vary during a shot by 50 volts from the upper manifold, which is
bolted to the cathode, to the ground side of the capacitor bank. To avoid spurious
signals on the probes, it was necessary to connect a wide sheet-aluminum ground
strap from the screen room to the upper manifold where the probes were located.
The coaxial cables carrying the probe signals were then laid on the ground sheet.
To obtain signals proportional to the magnetic field, R-C passive integrators
betchov and turner: Measurements of MM D Turbulence 119
were used. Initially, a 500-ohm resistor and five 0.02- uf ceramic capacitors con-
nected in parallel were used to give an R-C time constant of 50 jisec. The capacitors
were found to have an L-C resonance at 22 Mc, so they were replaced with five
0.001-|xf capacitors with a 10K resistor. The latter were found to be satisfactory up
to 50 Mc. The passive integrating circuit and the terminating resistor were mounted
together in a brass cylinder. The terminating resistance consisted of five resistors in
parallel soldered radially from the central conductor to the shell. The 10K-
resistor was then mounted on axis followed by the five capacitors soldered radially
to the shell. This arrangement minimized parasitic inductance and thus increased
the frequency response of the circuit.
PLASMA CHARACTERISTICS
The theory of the linear pinch is given in several books on thermonuclear
research (6, 7) and will not be described here. We would like to give only a qualita-
tive description of the operation of this device, together with some experimental
observations, in order to better understand the signals produced by the magnetic
probes. When the ignitrons are triggered, the capacitor bank discharges through
the gas in the tube. Under the usual conditions of 15-kv potential on the capacitor
bank and a 2000-gauss initial longitudinal magnetic field, the duration of the first
half-cycle is about 12 ptsec and the peak value of the current is about 250,000
amperes. A typical pair of voltage and current traces is shown in Figure 4.
I5kv^
VOLTAGE
TIME, /I SEC
FIGURE 4. Current and voltage in the pinch device. Initial conditions : 15 kv, 2000 gauss
B, and 80 [xHg of deuterium.
Initially, the current begins to flow in the gas closely following the walls of the
tube. Soon, how r ever, the magnetic pressure associated with the current in the gas
pulls the plasma off the wall, and the plasma column begins to rapidly implode
toward the center. The longitudinal magnetic field is trapped inside and com-
pressed as the column contracts since the plasma is highly conducting. The change
in the diameter of the plasma column with time is shown in Figure 5. This was
5 +
120
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
calculated from probe measurements of the longitudinal magnetic field. A similar
sort of time variation of the radius was also observed with a rotating-mirror
streak camera. One sees that the radius of the plasma column oscillates with a
frequency increasing from 1 to 2 Mc until about 4 jjisec. This oscillation also shows
up in the voltage and current traces (see Figure 4). The increase of inductance
associated with a decrease in radius causes a decrease in current and an increase
in the voltage across the discharge tube. The oscillation of the plasma column also
shows up in the magnetic probe signals.
0.5
.0
1.5
RADIUS (inches)
2.0 2.5
1.0
o
co
2.0
1
I-
3.0
4.0
WALL
FIGURE 5. Radius of plasma column.
Under the assumption that the current flows in an infinitely thin layer along the
surface of a perfectly-conducting plasma, the longitudinal magnetic field can
theoretically completely stabilize the plasma column. Due to the finite conductivity
of the plasma, however, the magnetic fields can diffuse through the plasma. We
surmise that the MHD turbulence observed in the plasma column accelerates this
diffusion process. The longitudinal magnetic field trapped inside the plasma column
diffuses outwardly, and the azimuthal magnetic field outside the plasma column,
which is due to the current through the gas, diffuses inwardly. The mixing of the
two fields results in a net helical field which, in turn, results in a helical instability
of the plasma column. The behavior of the plasma column with time is shown by
the series of Kerr-cell camera photographs in Figure 6. The column appears to be
fairly stable until 5 [i.sec when the helical distortion begins to appear. This helix
expands rapidly and the plasma hits the walls after 7 |j.sec or so. Any magnetic
probe measurements which we wish to make on the "stable" plasma column are
meaningless after 5 jxsec. An "unstabilized" pinch column, produced without the
betchov axd TURNER: Measurements of MHD Turbulence
121
:S!!lli| |v ll||tliiMi|i|iMfuti!!'siSiU;
v
e
e
3
' :::;njjlh?*MiMiiM!hMinM?MM||''
fflli"!
!!fffiiff
iMIIlil,
Hfll'lli in,,,,,
illiiilliiiiiitltilllllll!
u
122
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
initial longitudinal magnetic field, reaches a smaller minimum diameter and breaks
up somewhat sooner due to other instabilities which are inhibited by the trapped
longitudinal field in the '"stabilized" case.
MAGNETIC PROBE MEASUREMENTS
Two magnetic probes were mounted in the upper manifold and extended into
the plasma a distance of about 4 inches through a diametrical slot in the cathode.
The probes could be moved radially by means of traversing screws. In addition, one
probe could be moved up and down or rotated with an external gear train. Surveys
were made with single probes aligned to measure B z , B r , and B . Also, pairs of
probes were used to measure correlation as a function of probe spacing.
Figure 7 shows oscilloscope traces obtained with B-. and B e probes inside the
plasma column. The upper trace is the direct probe signal proportional to B, while
the lower trace is the integrated probe signal, proportional to B. Four oscilloscope
— ' ' iM ^**V^Sil wC" *~*~^~ fJ% >ff f^* 1 '" ' "
—— — — '■'il\
\ ■> VZZ. * :— -
J ?
1
FIGURE 7. Four superimposed oscilloscope traces of magnetic probe signals in the
plasma column. Upper traces are li and lower traces are B. B.-signals are on the left and
B g traces are on the right. Sweep speed is 1 usee per division.
pictures have been superimposed to show the fluctuations in the magnetic field from
one shot to the next. The fluctuations, which start at about 2.5 fxsec, show up much
better in the direct probe signals than in the integrated signals since integration
sup2>resses the higher frequencies. These fluctuations have been interpreted as
evidence of MHD turbulence. The B- signal shows the compression and oscillation
of the B.. field trapped inside the plasma column. The fluctuations in B, are some-
what smaller than the periodic changes in B-, due to these oscillations. The B e
signal should, of course, be zero as long as all the current is flowing on the outside
of the plasma column. The small fluctuations in B e are evidence of local currents
inside the column. After 5 (xsec or so, the plasma column becomes unstable, and
the probe traces show large excursions.
The best indication of the onset of plasma turbulence is the second time deriva-
tive of the magnetic field. This is easily obtained by differentiating the direct
probe signal. The type of signal obtained is shown in Figure 8. Using the second
derivative, we have mapped the onset and duration of MHD turbulence as a
function of radius and time. It was found that the turbulence apparently starts on
the surface of the plasma column and spreads rapidly both inwardly and out-
wardly as shown in the diagram of Figure 9. Although the region outside the plasma
column is not luminous, there is apparently a tenuous plasma left behind which
supports the turbulence. It has been found by other investigators that there are
betchov axd Turxee : Measurement* of MHD Turbulence 123
?J.
—
-=
currents in the region between the main plasma column and the wall (4), and
substantial currents near the wall have been found to move in a direction opposite
to the main current. Kovasznay (2) has shown that MHD turbulence results in an
increase of the effective resistivity of the plasma. This, in turn, results in more
rapid diffusion of the magnetic field through the plasma and is probably responsible
for the relatively fast breakup of the so-called "stabilized" plasma.
124
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
One of the most powerful techniques used in the experimental study of turbulence
is the measurement of the correlation between signals from two measuring probes
as a function of the distance between the probes. For the short time duration and
rather high frequency of the turbulence, the best method of correlation deter-
mination appeared to be the use of an x-y oscilloscope. This method is described by
Barber (8) and has been used by several investigators, for example, A. Favre et al.
(9), for studies of turbulence. The signal from one probe is put on the horizontal
RADIUS(inches)
o
cu
CO
=1
UJ
h-
0.5
i.O 1.5 2.0 2.5
■
i ■ i rt~
RADIUS OF v s y j
CURRENT SHEET^-^ \
1.0
t
TRANSITION
\llfl\ WALL
2.0
>
1
' wvCxNa:
^^fci,
3.0
111
^^^?^
4.0
1
\\\\
lllp
FIGURE 9. Space-time diagram showing spread of turbulence.
amplifier, and the signal from the other probe is put on the vertical amplifier. For
normal distributions, the brightness contours are generally elliptical with the
major axis of the elliptical contours lying at 45° to the horizontal if the rms values
of the two signals are equal. The degree of correlation can be determined from the
shape of the ellipses. For zero correlation the contours are circular, and for a
correlation close to unity the ellipses are very thin.
Calibration patterns can be obtained by the use of two noise generators with
mixing circuits. Let the signal from one noise generator be f(t) and the signal
from the other be g(t). The rms outputs are adjusted to be equal so
Since the two signals are independent
/(%(<) =
betchoy am) tc bx er : Measurements of MHD Turbvlerux 125
Now with mixing circuits form two new signals. F(t) and G(t) such that
F(t) =f(t)+ag(t)
and
G(t) =f(t)-ag(t)
The factor " can vary between zero and unity, and represents the fractional output
of a variable attenuator on the second noise generator. The correlation. R, between
the two new signals is
K =
F(t)G(t)
\ FHKG 2 {t)
Substituting for F(t) and G(t) one finds
R =
1+rt 2
FIGURE 10. Four x-y oscilloscope calibration patterns obtained using noise generators:
degrees of correlation noted in lower right-hand corner.
126
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Thus, any value of R from zero to unity can be obtained by va^'ing the factor a
between unity and zero. A series of x-y oscilloscope patterns obtained in this
manner are shown in Figure 10. To obtain reasonably smootli x-y correlation
patterns of magnetic probe signals, traces from a large number of shots (usually
24) must be superimposed. A 65-volt positive gate signal is applied to the unblanking
terminal of the x-y oscilloscope during the period of time that the plasma exhibits
MHD turbulence. This starts at about 2.5 (xsec and stops at 5.5 [j.sec when the
plasma column begins breaking up because of helical instability. Thus the x-y
trace is recorded only during the period of MHD turbulence. High-pass filters are
used to eliminate any effect due to the gross motions of the plasma column
(particularly the "breathing" mode which has a frequency of 1-2 Mc). So far, x-y
correlation patterns have been obtained from two B, probes with varying dia-
metrical and longitudinal separations. A series of four such x-y oscilloscope
pictures using 5, probes with a diametrical separation are shown in Figure 11.
The probes were placed equal distances from the tube axis and on opposite sides
FIGURE 11. Four x-y oscilloscope patterns of B z turbulence; diametrical probe
separations, noted in lower right-hand corner, are in inches.
betchov and turner: Mea-mrements of MHD Turbulence
127
of it. At a spacing of 0.5 inches, the correlation is very high (estimated at about
0.9): at 0.75 inches, the correlation falls to about 0.7; and at 1.00 inches, it is less
than 0.5. Almost no correlation exists at a spacing of 1.5 inches.
In principle, it is possible to obtain the energy spectrum E{k) of the turbulence
as a function of a wave number, k, by taking a Fourier transform of the correlation
function. To get a reasonably good curve for E{k). however, many more points
should be obtained for correlation versus separation, and the correlation must be
obtained by a more accurate method than visual estimation.
FIGURE 12. Four x-y oscilloscope patterns of II, turbulence: longitudinal probe
separations, noted in lower right-hand corner, are in inches.
128 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Correlation patterns obtained with a z-separationf of B z probes were especially
interesting. A hook probe and a straight probe were used with the straight probe
being raised and lowered with a rack and pinion gear. The x-y oscilloscope patterns
were unusually elliptical in shape as seen in Figure 12. Oscilloscope patterns
obtained for single shots, which were a little too light for good photographic
reproduction, showed elliptical paths which appeared to be sections of Lissajous
figures. This suggested that the turbulent magnetic field fluctuations were being
propagated in the z direction with a definite velocity. An obvious explanation is
that Alfven waves are being propagated along the B z magnetic field lines which
are trapped inside the plasma column. The velocity of an Alfven wave is
B
in mks units. The Alfven wave velocity was calculated from the measured value of
B and the value of p there would be assuming all the gas is swept into the central
plasma column. This velocity calculated using this assumption was only one-half
the velocity determined from the Lissajous patterns, however. One must therefore
consider the possibility that much of the gas is left behind as the current sheath
pinches inwardly.
It was found that the presence of one probe reduces the signal picked up by a
second probe. The region of influence is elongated in the direction of the B^
magnetic field lines. The range of influence in the direction perpendicular to the
magnetic field lines was smaller than 0.5 cm, but in the direction of the field lines
the range of influence was found to be several centimeters. This is undoubtedly
due to the propagation of Alfven waves along the field lines. In view of this, the
probes should have been inserted deeper into the plasma since the cathode must
influence the turbulence for a considerable distance. Also, much care must be taken
so that one probe does not lie directly above another, i.e., on the same B z field
lines. Therefore it may have been better to have inserted the probes radially
through the tube walls rather than through the cathode as we have done.
Estimates were made of the rms values of B, B, and B by comparing these
signals with oscilloscope pictures of noise-generator signals whose rms values were
measured with a meter. The magnitude of the fluctuations in the three perpendicular
directions were equal within a factor of two. The estimated magnitudes were:
(AB) vms = 200 gauss
(AJ3) rms = 5 x 10 9 gauss/sec
(AB) rms = 1.5 xlO 17 gauss/sec 2
These values are probably accurate only to ±50% since they are visual com-
parisons. For reference, the value of B z when the plasma column is constricted is
about 16,000 gauss.
It is useful to form the following nondimensional quantity:
(AB)(AB)
(AB) 2
This quantity cannot be less than unity. For a pure sine wave it is unity, and for
random noise with a gaussian distribution it is V'S. For the values given above,
this quantity is slightly greater than unity.
■f The z-direction is parallel to the tube axis.
betchov and turnek: Measurements of MHD Turbulence 129
A study was made to find the highest frequencies present in the MHD turbulence,
i.e., the high frequency cutoff of the energy spectrum. The low frequencies were
reduced to a small value by using an R-C differentiating circuit. The resulting B
signals were displayed on a Tektronix 517 oscilloscope, which has a frequency
response of greater than 50 Mc. Frequencies of up to 20 Mc were observed. The ion
cyclotron frequency is about 12 Mc, so the high frequency cutoff is almost twice the
ion cyclotron frequency. The ion cyclotron frequency therefore appears to have no
effect on the maximum frequency of MHD turbulence.
When the survey work was being done using B signals to trace the space-time
growth of the turbulence, it became evident that there was an inherent 180°
asymmetry in the amplitude of the turbulence. Rotating the cathode and external
solenoid had no effect, so it was suspected that feeding the current at the bottom
of the tube from one side might be the cause. Furthermore, it was felt that since
the pinch discharge was very transient in nature, it would not be worthwhile to
use this device for further, more quantitative, work. For these reasons, the work
has not been continued.
ACKNOWLEDGMENTS
The authors would like to acknowledge the invaluable assistance of Professor
Leslie S. G. Kovasznay, a consultant to this laboratory. He gave us many valuable
suggestions on experimental techniques that could be applied to this problem, and
he provided much theoretical insight into the processes involved. An explanation
which he gave on the manner in which the turbulence spread through the tube
was fairly well borne out by the survey using B signals. Most of the experimental
work on this project, including much of the electronics construction, was carried
out by Mr. Ronald C. Phillips while still a student at Long Beach State College.
His excellent workmanship and dedicated efforts are gratefully acknowledged.
REFERENCES
1. Burkhardt, L. C, and Lovberg, R. H., Proc. Second U.N. Conf. on the Peaceful
Uses of Atomic Energy, 32, 29 (1958).
2. Kovasznay, Leslie S. G., Rev. Mod. Phys., 32, 815 (1960).
3. Kurchatov, I. V., Atomnaya Energiya, 1, 65 (1956); Artsimovich, L. A. et al.,
Atomnaya Energiya, 1, 76 (1956). These two papers were reprinted in J.
Nuclear Energy, II, 4 (1957), and in Nucleonics, 14 (1956).
4. Karr, Hugh J., in The Plasma in a Magnetic Field, ed. R. K. M. Landshoff
(Stanford: Stanford University Press, 1958), 40-59.
5. Segre, S. E., and Allen, J. E., "Magnetic Probes of High Frequency Response",
J. Sci. Inst., 37, 369 (1960).
6. Glasstone, S., and Lovberg, R. H., Controlled Thermonuclear Reactions (New
York: Van Nostrand, 1960).
7. Simon, Albert, An Introduction to Thermonuclear Research (New York:
Pergamon Press, 1959).
8. Barber, N. F., Experimental Correlograms and Fourier Transforms (New
York: Pergamon Press, 1961), Chapter 8.
9. Favre, A. et al., Actes du Colloque International de Mecanique, Portiers, III
(1950); also Publ. Sc. et Tech. du Ministere de I' Air, No. 251 (1950).
7. R. M. Montgomery and
R. A. Holmes: Some Experiments
in Radio-Frequency Diagnostics
of Partially-Ionized Plasmas
1<* In this work the sheath theory developed by Bohm is applied to
solve for the potential near a negatively -biased electrode in a neutral
plasma. Approximate expressions are derived for the sheath thickness
as a function of the electrode potential. The time-independent solution
is then used with a perturbation technique to solve for the high-frequency
electric field in the sheath and plasma. This field is then used to
calculate the impedance between coaxial plasma-filled electrodes.
Various portions of the impedance versus bias voltage curve and
impedance versus frequency curve are related to the plasma density
and temperature. The actual measured impedance between coaxial
cylinders is compared to that calcidated and these quantities are found
to be in good agreement.
INTRODUCTION
Radio-frequency (RF) impedance measurements on a large-area probe in a
plasma can be interpreted to find the plasma electron density and electron tem-
perature. Two common plasma diagnostic techniques, the Langmuir probe
technique and the microwave cavity method, are accomplished either at essentially
static (d-c) conditions in the first method or at frequencies well above the plasma
frequency in the second method. The RF measurements to be described, however,
are carried out at, or not too far below, the plasma frequency— the very frequency
range in which the plasma might be expected to exhibit its most interesting
behavior. Furthermore, in some plasma devices of current interest, measurements
of bulk plasma properties could be made by this technique using electrodes already
present for other purposes, eliminating the need for auxiliary probes.
The specific experiments to be analyzed and described were done with a
negatively-biased cylindrical probe electrode in a cylindrical low-pressure mercury-
arc discharge; the other electrode in the impedance measurement was a coaxial
cylinder wrapped around the discharge tube wall. This geometry is shown in
Figure 1. The net impedance from the inner cylinder to the outer one will be
composed of four parts: (1) the plasma sheath impedance (capacitive) at the inner
electrode; (2) the impedance of the spatially-varying bulk plasma (inductive,
resistive, capacitive); (3) the glass tube wall sheath impedance (capacitive and
ed. note: Mr. Montgomery and Mr. Holmes are in the Department of Electrical
Engineering at Purdue University.
131
132
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
h — 38cm. -4- — |4 cm __u_33 cm
'-I
AUXILIARY CATHODE
ANODE SPOT ANCHOR PROBE .CYLINDERS ANODE
LANGMUIR COAXIAL
7^-
k6cnr?-|
FIGURE 1. The experimental discharge tube.
practically negligible); and (4) the impedance of the glass wall (capacitive). The
organization of the results of this work logically follows this layout of the parts of
the overall impedance. First, the static behavior of the sheath at the inner electrode
is reviewed to lay the foundation for the behavior of sheath capacitance. Next, an
RF perturbation analysis is developed to find the electric fields in the sheath and
bulk plasma. Following this, the material is applied to impedance measurements
at low radio frequencies where most of the impedance is in the sheath capacitance
(the bulk plasma being a good conductor), then applied at radio frequencies in the
neighborhood of co p for the bulk plasma.
THE DC SHEATH
Before discussing time-dependent sheath phenomena, it is convenient to briefly
review the well known static sheath theory. The plasma boundary or wall under
consideration is assumed to be negatively biased to the point that the electron
current to it is a negligible fraction of the random electron current in the plasma.
(The average velocity of the electrons, u, is assumed to be zero.) The electrons are
also assumed to be near thermal equilibrium at a temperature T which is much
larger than the positive ion temperature, and the sheath thickness is taken to be
small so that no collisions occur in the sheath region.
Under these conditions the sheath theory of Bohm (1) is applicable and the
model for the sheath will be that shown in Figure 2. In this model the ions are
accelerated in the pre-sheath region and arrive at the sheath edge with a kinetic
energy equal to $kT. The derivative of the potential at the sheath edge is small
compared to its value inside the sheath.
The basic equations describing the sheath include the electron momentum
equation
= -neE-kT^
ax
the continuity and momentum equations for positive ions
E<?>
NM~ = NeE
ax
(1)
(2)
13)
Montgomery and holmes: Radio- Frequency Diagnostics 133
and Poisson's equation
_ = __ {N _ n)
(4)
where e is the charge on an electron and n is the electron density. N, M, and U are
the positive ion density, mass, and average velocity, respectively; V is the potential
and E the electric field strength; e is the permittivity of free space and k is
Boltzmann's constant.
ELECTRON DENSITY
PRE -SHEATH X
N?n
dX u
FIGURE 2. The assumed form of the potential and the electron density.
Equations (1) through (4) can be reduced to the single equation
where the normalized variables
X X
eV
"kT and * = (e kTjne 2 ) 112 ~ A
(5)
have been substituted.
For large values of ij (approximately 77 >4) this equation can be solved to obtain
where rj w is the normalized potential at the wall.
134
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
For small values of 77 (approximately 77 <5) a solution to equation (6) is obtained
by expanding ij(?) in a power series about the point where 77 = 5. Calling this point
f !, the power series for -q becomes
r,(g) = 5-1.63(f-f 1 ) + 0.147(f-? 1 ) a
-0.00345(^-^)3 + 0.000033(1- f 1 ) 4 + 0.0000275(f-f 1 ) 5 (7)
The graph of 77 versus f which is obtained from equations (6) and (7) is shown in
Figure 3 for rj? = 50. Equation (6) has been compared to and found to be in good
agreement with the experimental data obtained by Von Gierke (2).
RF ELECTRIC FIELDS IN THE PLASMA AND SHEATH
From Figure 3 it can be seen that a reasonable approximation to the electron
density at the plasma edge is a step function occurring at the point where njn s = \.
FROM EQ.(6j
FROM EQ.(7)
n/n s
50
%i
40
-.8 \
30
-.6 V
-T^-q
? n/n s
20
.4
10-
-2
. 1
X /
W*T 1 — — 1
— 1 ~
12
16
i
20
24
FIGURE 3. Variations of q and n for q w = 50.
This closely corresponds to the point where 17 = in the approximation of equation
(6). This result will be used to define the sheath thickness in calculating the
capacitance across the sheath.
If one now assumes that the wall potential, V w , has a small sinusoidal pertur-
L)?ition iiT"^
aiw niau Liie eieetron density, n, and average velocity,
Montgomery and holmbs: Radio- Frequency Diagnostics 135
are similarly perturbed, then the continuity and momentum equations for electrons
become
d , s
fa. (?0?l) = -JOtfl!
dV 1 dV
-??&
and Poisson's equation reduces to
d 2 V l en x
dX 2 ~ e
Here the variables with the subscript 1 refer to small perturbations about the
equilibrium values which have the subscript 0. Second order perturbation terms
have been neglected and, for simplicity, the electron temperature has been
assumed constant in time and space.
It is possible to eliminate % and u x from these equations to obtain
Ke 2 2 1? , 2 ? e dE 1 dV kT d 2 E x
fc—T^^ - ~7n W dT+^dX* 1 < 8 >
where E s is the perturbation electric-field strength at the wall. In the sheath region
? — and ? x ~0, implying that
dE x d 2 E x
W = ° and lx- 2 =0
and equation (8) reduces to E 1 = E S . On the other hand, in the pre-sheath and
plasma regions
dX ~
and equation (8) becomes
le m J
kTd 2 E,
For the moment, n will be assumed independent of x outside the sheath and the
following substitutions will be made:
2 n e 2 kT
e Q m wpn
The resulting equation
1 T a, 2 ! ,^ 2 m d 2 E x
Ag L a,?] Al+ kT E ° = dX 2
has the solution
E. -
- E . , a ?? r * /, ?
(9)
(10)
This solution is strictly correct only for the case when n , hence w p , is independent
of x; however, the "relaxation length",
A
[1-(">?)] 1/2
136 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
is found to be somewhat greater than the Debye length for w < w p . Thus, in a region
where ra does not vary appreciably over a Debye length, the second term in
equation (10) is negligible and E± becomes
l-K(Z)/co 2 )
Returning to equation (10) it will be noted that the second term may be written
as
Aex *[- j T D & P -T]
and for oj>co p it represents the usual "plasma wave" propagating with a wave
length
A _ 2ttA d
A - Uw*lw>)-lr a
EXPERIMENTAL MEASUREMENT OF SHEATH THICKNESS
In the preceding development it was shown that for a> considerably less than
cop the RF electric field in a plasma is given by
P - Es
^-l-KM
This indicates that for a>?w p , the field in the plasma becomes much smaller than
the field in the sheath and opposite in sign. This also means that for sufficiently
high plasma density, the RF potential difference between two electrodes in a
plasma will appear almost entirely across the plasma sheaths surrounding these
electrodes. Thus the impedance between these electrodes will be only the sheath
impedance, and hence a method for measuring sheath thickness is obtained. Of
course, the sheath edge must be reasonably well defined if this measurement is to
have any meaning. The d-c sheath theory presented previously indicates that the
sheath edge is reasonably well defined and that it is located at that value of f for
which 77 = in equation (6) or
/.*, \K2r/. \ 1/2 "ll/2
-d) [(f) H <u >
4. /.*, \l'2r/v, \ 1'2 11/2
where d is the sheath thickness.
The impedance presented by the sheath is then
_ _ ,l/2r/? \l/2 "|l/2
" jwe A 3j weo M2/ LI 2/ ^ J
where A is the area of the sheath.
Equation (12) involves two unknown parameters — the electron density, and the
electron temperature; all other quantities are either known or measurable. Thus,
the measurement of the impedance, Z s , for two different values of d-c potential,
V w , makes it possible to determine n and T from equation (12).
The validity of equation (12) was checked in the experimental discharge tube
shown in Figure 1. The impedance between the coaxial cylinders was measured
with various values of d-c bias on the inner cylinder. These measured impedances
were then corrected for the impedance of the glass tube wall and compared to
Montgomery and holmes: Radio- Frequency Diagnostics 137
those calculated with equation (12). The radius of the inner electrode was made
large compared to the sheath thickness to insure the applicability of planar sheath
theory; all calculated values of Z s were based on Langmuir probe measurements of
n and T. The results of this investigation appear in Figure 4.
250
200
| ISO
Iz
100
50-
?EXP. DATA
-THEORETICAL
(BASED ON LANGMUIR
PROBE MEASUREMENTS)
ANODE CURRENT = 2 AMP.
FREQUENCY = 50 MC/SEC.
-50 -100 -150 -200
VOLTS REL. TO ANODE
FIGURE 4. The variation of RF impedance with d-c bias.
■ .
250
RF BEHAVIOR NEAR THE PLASMA FREQUENCY
At frequencies which are near the plasma frequency the electric field in the
plasma is no longer negligible. The impedance between the concentric cylinders of
Figure 1 will now be studied for frequencies in this region. In order to simplify the
discussion the diameter of the inner cylinder and the spacing between cylinders will
be taken to be much greater than the Debye length. Furthermore, the effect of the
plasma wave represented by the second term in equation (10) will be considered
negligible. That is, the plasma may be characterized by the usual dielectric
constant
for purposes of calculating impedance. The jwv c term in this expression arises
because of the effect of collisions on the particle motions. This effect was neglected
in writing the equations of the preceding sections of this paper, but it could be
138
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
accounted for by introducing a viscous-like term in the electron momentum equa-
tion. The effects of collisions in the plasmas referred to in this paper are usually
small; however, they become very important near certain resonant frequencies.
If one considers an arrangement similar to Figure 1 with electrode length I,
inner cylinder radius a, sheath radius b, and plasma column radius c, then the Rb
electric field in the plasma is
Ei
aE,
{l-[a.?/(c a -jcov c )]}r
where E s is the field at the surface of the inner cylinder. If the electron density is
then approximated by the expression
(<x-l)?o
n(r)
C-
ab-C
b r + n ojZc
(13)
then the impedance between the cylinders becomes
CO . tuv c
17
Jt 2nj(oe l co 2 . Q)V C C — ab
In
+
2ttjcoe 1 a
A 3 ??§ '
ln- + Z a
C-b
^-?-'S
brt-
. OJV r
(14)
where o> is defined by the relation
n n e*
E m
and Z g is the impedance presented by the glass tube envelope.
The experimental conditions used to investigate equation (14) were such that
the planar d-c sheath theory is not applicable; however, the sheath thickness can
still be determined from the value of the impedance at low frequencies (w?w p ).
The following parameters are those of the discharge tube used in the experiments
described here.
Z g = -j2tt x 10 9 /o;
a = 2.31 x 10 " 3 meters
C = 1.85xl0- 2 meters
I = 6 x 10 _ 2 meters
The sheath radius was determined from the low-frequency behavior of the
impedance :
b = 3.44 x 10 ~ 3 meters
The collision frequency, v c , was determined by measurement of the high-frequency
impedance of solenoid surrounding the plasma, a technique which has been
developed by Persson (3).
Calculations were made for two values of ??? = $ which, according to the results
of Parker (4), makes equation (13) into a reasonable approximation for the
electron density in a cylindrical discharge and a = l (uniform electron density).
Montgomery and holmes: Radio- Frequency Diagnostics
139
With the preceding numerical values inserted, equation (14) becomes
Zt ~ J55 \f) J124 l/;L(///o) 2 -l-ll-j0.0261(/// )J
ln5i r (///o) 2 -l-i0-0261(/// ) 1
ta6 - 4 L(//f.)?-Hi0.0261(//f )J (15)
7 - i2fi 1M/2 1 , of (///o) 2 -JO-0261(/// o ) 1 1
for a=l and
for a = l.
(16)
Eq. (15) (a = -^-)
Eq. (I6)(a-|)
? EXPERIMENTAL
20 50 100 300 500 1000
FREQUENCY (mc/sec)
FIGURE 5. Magnitude of the experimental and theoretical impedance between coaxial
cylinders.
140
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
90
45
(DEG)
45
-90
Eq. (16) (a* I)
? EXPERIMENTAL
?I
? I
? I
J
I
I
????
Ji
4
50 100 200 400 1000
FREQUENCY (mc/sec)
FIGURE 6. Theoretical and experimental variation of impedance phase angle with
frequency.
These two equations are plotted in Figures 5 and 6 and the experimentally
measured impedance values appear as the dots on these figures.
The general appearance of these curves is briefly explained as follows : At low
frequencies the impedance asymptotically approaches the impedance of the sheath
alone as previously explained. Thus the low frequency asymptote on a log-log plot
is a straight line with a slope of minus one. At a somewhat higher frequency the
sheath capacitance and the inductance presented by the bulk of the plasma form a
series resonant circuit and there is an impedance minimum. At a still higher
frequency (the plasma frequency for the case of uniform electron density) the
inductive currents produced by the electron motion in the plasma cancel with
the displacement currents in the plasma and an impedance maximum occurs. The
magnitudes of the maximum and minimum impedance are determined by the
collision frequency. As can be seen in Figure 5, the calculated impedance minimum
is about four times smaller than the measured value and the calculated maximum
is about twice the measured value. This indicates either that the solenoidal measure-
ment of collision frequency yielded too low a value, or that there are some losses
associated with the coaxial cylinder impedance measurements which were not
present in the solenoid measurements.
The frequencies at which the impedance maxima and minima occur are in good
agreement with the calculated frequencies which are based on Langmuir probe
measurements of electron density.
Montgomery and holmes : Radio- Frequency Diagnostics 141
CONCLUSIONS
The results of the experiments performed show that high-frequency methods can
be applied to measure plasma sheath thickness directly. They also show that the
high-frequency impedance between electrodes in a plasma can be accurately
predicted and that the plasma electron density, temperature, and collision
frequency can be determined from this impedance.
REFERENCES
1. Bohm, D., "Minimum Ionic Kinetic Energy for a Stable Sheath", in Character-
istics of Electrical Discharges in Magnetic Fields, ed. A. Guthrie and R. K.
Wakerling (New York: McGraw-Hill, 1949), 77.
2. Von Gierke, G., Ott, W., and Schwirzke, F., '"Untersuchung von Plasma
Grenzschichten mit einer Electronenstrahl-Sonde", in Ionization Phenomena
in Gases, ed. H. Maecker (Amsterdam: North-Holland, 1962), 1412.
3. Persson, K. B., "A Method for Measuring the Conductivity in a High Electron
Density Plasma", J. appl. Phys., 32, 2631 (1961).
4. Parker, Jerald V., Technical Report No. 19, California Institute of Technology,
Nonr 220(13) (December, 1962).
8. W. K. McGregor: Spectroscopic
Measurements in Plasmas
12? The possible -uses of spectroscopy in the diagnostics of plasmas are
described. Brief descriptions of the methods used in measurement of
temperature are given and an attempt is made to identify the governing
energy distribution in each case. Identification with the translational
velocity distribution makes the method valid; identification with some
other distribution makes closer study necessary. Some actual data from
arc plasma jets are used to illustrate the arguments. The classical
criteria for equilibrium are re-examined briefly and some additional
limitations imposed. The influence of metastable atoms on the inter-
pretation of the spectra from low density streams is discussed and some
application to temperature measurement given.
INTRODUCTION
This paper deals with a narrow slice of a very broad subject. The title is much
too broad for the material that is to be covered. In the first place, the word
"plasma", meaning any gas that is ionized to some extent, must be narrowed in
the treatment to include only those plasmas applicable to gas dynamics studies and
to exclude gas discharge tubes, stellar atmospheres, or the high-energy plasmas
associated with fusion research. The gas dynamics realm of plasmas includes the
plasmas generated by gases flowing through electrical discharges and gases heated
in shock tubes. However, it is preferred to omit even the latter from the discussion
because the mechanism of excitation is much different, and, too, the author is
more familiar with the processes going on in plasma generators.
The concept of spectroscopy must also be narrowed for the purpose of this paper
in order to deal only with those methods and concepts which do not push the
state of the spectroscopic art. For this reason, little note will be made of the more
fundamental problems — which are, even now. not completely treated — such as the
cross sections for various excitation mechanisms and the validity of transition
probabilities.
It is also not intended that this be a review paper because (1) many review
papers exist on gas discharge phenomena and the author would not attempt to
improve upon them (1); (2) the methods of spectroscopic diagnostics have been
adequately treated in many places (2), and it is desired only to summarize them
briefly here; and (3) the applications of gas discharge phenomena and spectro-
scopic measurements in flowing systems are not yet adequately reported so that an
accumulation of material for a critical evaluation of methods and results is pre-
mature. Rather, it is hoped that this paper will serve to illuminate some of the
ed. note: Mr. McGregor is with ARO Incorporated, Tullahoma, Tennessee. The
research reported in this paper was sponsored by the U.S. Air Force under
contract AF 40(600)-1000.
143
144
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
essential mechanisms giving rise to radiation in gas-dynamic-type plasmas and to
stir some interest in solving some of the remaining problems. The theme of the
paper will be better understood if it is denned as a review of the essential mech-
anisms giving rise to the radiation and an interpretation of some of the reported
measurements.
That spectroscopy is a very powerful diagnostic tool goes without question. As
an example of the power of a single measurement, the writer recently witnessed an
experiment in which a narrow portion of the spectrum from an enclosed helium
discharge was used as the single diagnostic tool. Only three spectral lines were
employed, the 5015 and 5047 A neutral atom lines and the 5411 A ionized line.
From a single photograph, the experimenter was determining the temperature in
three different ways, and the electron density or degree of ionization in two ways,
and from these measurements calculating the pressure of the gas within the dis-
charge chamber. One might question the validity of the interpretations being
made, or perhaps the constants being used, but certainly not the methods and
principles employed. The task remaining for the researcher on diagnostics is that
of perfecting the understanding of the measurements, and to that end this paper is
dedicated.
MODEL
In order to get at the points to be emphasized, a model of a flowing plasma
generator and the supersonic plasma stream which results will be considered. The
model will possess most of the characteristics to be discussed. The device to be
considered is normally called a "plasma jet" (3), which exhausts into a low pressure
TO VACUUM
PUMPING SYSTEM -
LOW PRESSURE TEST CELL
7 _J
ARGON
GAS INLET-
1)1 I) I II llltllll I I III II Jilt 1)11 I II7TT
i ii ii ii 1 1 ii mill i
-8 KW PLASMA JET
STREAM OUTLINE
\ i ii 1 1 1 1 1 1 1 1 1 1 1 1 ii 1 1 1 1 1 1 1 1 1 1 // 1 1 1 1 ii 1 1 1 in 1 1 1 1 1 1 1 1 1 1 1 in 1 1 1 1 1 1 1 1 1
NOTE:
A. INTENSE CORE
B. LUMINOUS, HIGH VELOCITY STREAM
FIGURE 1. Apparatus schematic and plasma stream characteristics.
mcgregor: Spectroscopic Measurements in Plasmas
145
test cell; the essential features of this device are shown in Figure 1. A gas is forced
through an electrical discharge between two electrodes, and energy is added to the
gas in various forms. By far the greatest amount of energy is in the form of kinetic
energy: however, some of the energy added goes into excitation with subsequent
photon emission at prescribed wavelengths, and this is the energy to be used as a
spectral diagnostic tool. Still another portion of the energy goes into dissociating
the molecules of the gas. and another goes into ionization of some of the atoms and
produces the property which allows the gas stream that emerges from the discharge
to be called a "plasma".
In this apparatus, the electrode configuration has been illustrated as the
"Gerdien" type (4). and this configuration is used for these discussions. However.
the basic premises of the discussion will be applicable also to the more complicated
magnetically-driven spinning arcs (5) and also to the stationary arcs with their
associated gas pumping action (6). The essentials of all such apparatus is that there
is a region of electrical discharge witli a gas flowing through it which receives
kinetic and excitation energy.
The region of most interest to the gas dynamicist is the gas stream after it
leaves the discharge. At high pressure exit conditions, the definition of just where
this separation between discharge and the field free gas stream takes place has
caused some serious study and conjecture and is still a controversial subject
(7, 8). However, when the gas is expanded to a low pressure, a highly supersonic
plume is formed which can. most times, be seen by the light emitted from it. A
typical low pressure stream from a plasma jet is shown in Figure 2. The stream
appears to behave as an ordinary supersonic stream, with expected shock structure
well defined and boundaries clearlv visible.
FIGURE 2. Argon plasma jet expanding to a low pressure.
146
PHYSICO-CHEMICAL DIAGNOSTICS OK PLASMAS
SPECTRAL MEASUREMENTS
The measurements which can be made on the plasma source with the spectro-
scope shall now be considered. The emission spectrum from any point in the stream
provides a measurement of:
(1) the wavelengths of the spectral lines emitted;
(2) the intensity of the spectral lines emitted;
(3) the line intensity profile of the spectral lines emitted; and
(4) the intensity of any continuum radiation that might be present.
If a light source is now provided, the amount of radiation absorbed by the gas
stream as a function of the wavelength can be measured.
Typical spectrograms of the discharge region and the supersonic plume region of
an argon plasma are shown in Figure 3. The wavelength range is from about 3500
to 7000 A units. This spectrum was photographed with a grating instrument. A
small portion of the spectrum is shown in Figure 4. which was obtained using a
direct recording prism instrument with a photo-multiplier detector. These spectra
will be considered later.
Pressure- 0.5 mm Hg
-N 2 2nd Positive Bands
-Argon Lines
Expanded Plume
Pressure - 1 atm
-Continuum Radiation
'Argon Lines
5400 A /-Discharge Region
FIGURE 3. Spectra of argon plasma jet. (Note: The spectra were taken with spherical
gratings of different focal length.)
The application of these measurements to diagnostics of conditions within the
plasma stream involves the use of a great deal of physics. The measurements may
be put into three classes of uses: (1) identification of species; (2) thermal proper-
ties; and (3) phenomenological measurements. Application of these to the model
suggested will be made in order to demonstrate what is believed to be the proper
diagnostic attitude.
IDENTIFICATION OF SPECIES
The oldest use of spectroscopy is undoubtedly the identification of substances by
the wavelengths of the spectral lines they emit. This was, indeed, the first use to
which the spectrograph was put in the plasma diagnostics at AEDC (9). There was
considerable concern about contamination of the gas stream with electrode
material, as had been reported by other investigators using very high-energy arcs.
Such contamination would have ill effects on the experiments which were to be of a
very basic nature. The resulting spectra taken from the emission just at the orifice
exit when the plasma jet was exhausting to atmospheric pressure, or into a low
mcgregor: Spectroscopic Measurements in Plasmas
147
. — .._
— ;
;
-
S
3
ri
i— < - i
-? oo ?
Q. - *— i
— - : —9:
3> (1
* ■ A
-Zero-
Free Stream
Discharge
FIGURE 4. Illustrative spectral data from an argon plasma.
pressure cell, showed that, for devices of the 10 to 60 kw range, no appreciable
contamination could be detected from the spectra. In fact, in argon, helium, and
nitrogen, no spectral lines other than those of the gases being used could be
identified. Other investigators reported like results for similar small plasma jets,
and, thus, assurance was given that the gases heated by this method could be
considered as adequate plasma sources for many laboratory gas dynamics
experiments.
Many other qualitative conclusions can be gained by merely examining the
wavelengths of the lines emitted. Thus, the appearance of both the nitrogen mole-
cular bands and the atomic lines in a nitrogen plasma is an indication of the
dissociation of the molecule (10). This type of interpretation has been used to
locate inner zones in a nitrogen plasma where dissociation is detectably present,
and thus to establish an isotherm if the dissociation is known as a function of the
temperature. Another useful fact that can be obtained from the spectra is whether
ionization is present in any appreciable amount by the appearance of ionized lines.
Spectra taken of the discharge region in helium and argon exhibit many lines
attributable to the ionized species.
148
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
THERMAL PROPERTIES
The measurement of temperature is perhaps the most important task laid upon
the spectroscopist since the advent of the laboratory plasma. The relation of the
energy radiated by a gas to its temperature is a very old subject and one that has
been thoroughly explored in fields such as astrophysics. Only a brief summary of
the principles involved is presented because many writers have attempted to
assemble the details of these methods.
>^
ro
I 4
<
c
CD
E
c
<
'nm
\
\
o \
\
! ! ,
x A nm N n + B nm'nm N n " B mn'nm N m
N o9n
N n =-^exp(-E n /kT)
For Optically Thin Plasmas
9n N o
I = Intensity
A, B = Transition Probabilities
h = Planck's Constant
v = Frequency
g n = Statistical Weight
\ N , N n = Number Density
\
\o
E n = Energy of nth State
> U = Partition Function
\
\
\
^ o
T = 11, 600°K S
\
\
\
\
\
s
o
J_
19
20 21 22
E n (eV) - Ionized Argon
23
24
FIGURE 5. Illustration of spectral line intensity distribution methods of temperature
measurement. Example data taken from reference (12) for an argon plasma jet.
mcgregor: Spectroscopic Measurements in Plasmas
149
METHODS OF TEMPERATURE MEASUREMENT
Spectral line Intensity
The relation of the intensity of an atomic spectral line to the temperature is
given m Figure 5. Generally, methods using the intensity relation are employed
only for spectroscopically-thin sources— that is, where there is no appreciable
selfabsorption or induced emission and the equation reduces to the more simple
expression shown. At least four temperature-measuring techniques utilize this
equation. First, the absolute intensity of the line is measured by calibrating the
spectrograph with a source such as a tungsten ribbon filament lamp or a Kiel arc,
and since the constants are known, the temperature is calculated. The difficulty
here is the absolute intensity calibration. The problem is relieved somewhat by
30x10
1.0 2.0 3.0
Distance from Jet Centerline, mm
FIGURE 6. Illustration of peaking function method for measuring temperature; data
shown for an argon plasma jet using the 4158 A line.
150
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
taking the ratio of the intensities of two lines so that only a relative intensity cali-
bration at the two wavelengths is required (11). Further confidence is lent to the
latter method by using several lines and plotting log IUjvA nm versus E n ; the slope
of the resulting straight line will be \jkT as indicated in Figure 5. The data points
shown are typical of an argon discharge (12). The difficulty with this method is that
the transition probabilities, A nm , must be accurately known when actually very
few transition probabilities are known with precision. Still another method that is
applicable in some cases and avoids the necessity for calibration as well as know-
ledge of the transition probability is the "peaking function" method (13, 14, 15),
which is based on the fact that the intensity of any spectral line must reach a
maximum at some temperature, T m , which can be calculated. The method is
illustrated in Figure 6 for a particular argon spectral line, and has been used by
-t 1 — r-
Recombination + free-free
1.0 2.0 3.0
FTGTTRE 7. Illustration of peaking function method of temperature measurement using
continuum intensity; data shown for an argon plasma jet at 4150 A.
mcgregob: Spectroscopic Measurements in Plasmas 151
many investigators on both plasma generators and stationary arcs. (The data shown
were taken by the author and associates from the region just downstream of the
orifice of an argon plasma jet (16) using the 4158 A line.)
Continuous Emission
Radiation that is continuous with frequency is emitted in plasmas by the
interaction of free electrons with nuclei and also by recombination. The formulas
governing the intensity of such radiation as functions of temperature are shown in
Figure 7 (16). Here, again, measurement of the absolute intensity at a single wave-
length provides a measurement of the temperature. However, uncertainties in the
constants and in the calibration make this method somewhat doubtful. Also, it is
not clear just how much of the radiation is due to free-bound and how much to
free-free transitions. The peaking-function method may be used here, too, and this
method seems more reliable where temperatures are large enough so that it can be
applied. The peaking function is illustrated for argon in Figure 7, where the data
were taken from the continuous emission adjacent to the 4158 A line of argon used
for the data shown in Figure 6.
Molecular Band Distributions
The same basic formulas as given in Figure 5 are applicable to the vibrational
and rotational transitions which produce molecular band structure (17). Use of
such bands has been successful for a few molecules such as NO, CN, and the C 2
Swan bands, but the transition probabilities of only a few molecules are well
enough known. The advantage of using such a band is that no relative calibration
is usually required because of the small range of the spectrum covered. Dis-
advantages are that bands are generally very complicated and high resolution
instruments are required.
Planck-Kirchhoff Law
A method which has been used quite successfully for determining flame tempera-
tures in combustion has also been applied to plasmas. This method must be used in
a region of the spectrum where there is a large amount of absorption, but it has
been found useful only for wavelengths longer than about 8000 A. The method is
illustrated in Figure 8 (18). Measurement is made of the absolute intensity emitted
by a given section of plasma; then the percentage of absorption by the same
stream volume is measured and set equal to the emissivity via Kirchhoff's law
for radiators in equilibrium; temperature is then determined from the relation
Jt{T)=JI ? where J b is the blackbody radiation at a temperature T as determined
from Planck's formula. Some typical data are shown in Figure 8, also. The diffi-
culties with this method are that selfabsorption and temperature gradients are
difficult to take into account, and both these phenomena exist in plasma-jets.
Spectral Line Profile
The use of spectral line profiles, half-widths, wing structure, and peak shifts
cannot be adequately considered here. We can only attempt to separate the
mechanisms giving rise to the phenomena in order to determine whether the method
gives a measure of the electron or gas temperature. Three different phenomena give
rise to line broadening of sufficient width for measurement purposes: Doppler
broadening, collisional broadening, and Stark broadening. The first, Doppler
broadening, is related to temperature in a quite normal way through the velocity
6 +
Plasma
Monochrometer
,/ , 4 J(source)- J(plasma) ,,,. . ,. .
J(plasma) \Un,,rrp) J(black-body)
J(black-body)
J(source)
Cj, C 2 * Constants
J ? Radiancy
X ? Wave Length
T = Temperature
8X10 3
o
CD
5 4
-i — m — i — i — r~r
i i i i
CD
Q.
E
o>
oL
ii i i
I i i i ? i ? ?
0.6
0.8
1.0
1.2
1.4
Wave Length, li
FIGURE 8. Illustration of radiation emission-absorption method of temperature
measurement using Planck's and KirchhofF's laws.
mcgrbgor: Spectroscopic Measurements in Plasmas
153
distribution of the radiating atoms and, thus, provides direct measurement of the
gas temperature through the relation shown in Figure 9. Unfortunately, the amount
of Doppler broadening is quite small (less than 0.1 A for most plasma applications)
and is usually overshadowed in ionized gases by other mechanisms. Collisional
broadening is also very small at the densities currently encountered so that it is
not an important mechanism. The broadening caused by perturbing fields due to
the presence of electrons or ions near the radiating atom seems to be the chief
concern in plasmas. This is the Stark broadening which may take a variety of forms
that have been treated by many investigators. Curve fitting techniques, line half-
widths, and the wavelength shift of the peak intensity are the three methods that
are used most for the measurements. Some formulas are given in Figure 9. The
Doppler - AA 1/2 = 0. 72 x 10" 6 A VT/M (Ref. 19)
AA 1/2 = a 1 N e 2/3 (Linear Broadening Ref. 19)
AA S - a 2 T 1/6 N e (Quadratic Shift Ref. 19)
FIGURE 9. Illustration of line profile and line shift methods of temperature measure-
ment.
154 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
measurements are fairly insensitive to temperature but serve very well as a measure
of the electron density. Thus, to obtain a temperature, the electron density is put
into the Saha equations and temperature obtained in this way. [Many recent
articles exist on this subject, but for a good starting point, the reader is referred to
the work of H. Margenau (19).]
COMMON FACTOR IN ALL METHODS
It is not surprising, that in all the methods considered, a common denominator
can be found. This is the fact that the concept of a Maxwell-Boltzmann distribution
of some energy parameter has entered into each formula. It is only through such
most-probable distributions that a temperature is defined. For the spectral line
intensity formulas, the distribution was of the excited electronic states of the atom;
this distribution in turn was dependent upon the kinetic energy distribution of the
governing excitation collisions. For application of the peaking function method,
the additional requirement of chemical equilibrium was applied, which again was
dependent upon the energy distribution of the particle collision governing the
ionization of the atom. The governing collision can be identified fairly well for a
high density discharge. The frequency of electron-atom encounters is so much
greater than that of atom-atom collisions that it is clear that the electrons govern
the excitation and ionization in a discharge.
In the case of the continuous emission, the governing distribution is clearly the
free electron velocity distribution. For the molecular band intensity method, the
distribution of vibrational or rotational states is the prime factor relating to
temperature; but these in turn are maintained by collisional activity which again
brings us to a particle velocity distribution. The Planck-Kirchhoff method, how-
ever, departs from this pattern in that the underlying distribution function is of
the energy in harmonic oscillators. At first glance, this method would seem to
depend upon radiative equilibrium rather than any kinetic velocity distribution.
However, the equivalence of the method to the spectral line intensity distribution
is demonstrated in reference (18b).
The line profile method using the Doppler broadening is quite clearly related to
temperature through the velocity distribution of the emitting species. The Stark
effects, of course, are only slightly dependent upon the temperature, but the
relation to a Maxwell-Boltzmann energy distribution is obtained by going from
the electron density to temperature via the Saha equation, which, in turn, is
governed by an M-B distribution of the kinetic velocities of the colliding particles
which produce the ionizing reaction.
All this leads to the point of considering just what has been measured by the
various spectrographic methods. In each case the governing factor has been traced
to a kinetic velocity distribution. This is good because this is precisely what is
required: to measure the parameter T in the velocity distribution of the gas
particles, v 2 exp ( — mv 2 j2kT). Two difficulties appear now which must be reckoned
with if the measurements are to be understood. First, is it true that the velocity
distribution of the particles governing the excitation and radiation processes is
Maxwellian? Second, even though the distribution is Maxwellian, does it have the
same parameter T as the gas particle velocity distribution whose parameter T is
being sought?
To the first question, it is highly unlikely that any of the kinetic energy distri-
butions would not be Maxwellian (1). Observation of electron velocity distributions
are almost always reported to be Maxwellian, even in fields where the strength is
several hundred volts per centimeter, except at very low pressures. Relaxation
mcgregor: Spectroscopic Measurements in Plasmas 155
times for heavy particles may be somewhat longer but certainly no longer than a
micro-second. It is expected that the velocity distributions would be Maxwellian,
and this would also suggest that excited electronic, vibrational, and rotational
states should be distributed accordingly. It is also expected that chemical reactions
would behave in an equilibrium manner and at a temperature ascribed to the
velocity distribution of the particle governing the collision.
There is not so much confidence in the answer to the question of whether all
distributions can be described by the same temperature parameter. In order to
arrive at a meaningful answer, some actual data will be considered.
EXAMPLE OF MEASUREMENTS ON ARC PLASMA JET
Consider the plasma jet, being used as the model, exhausting into atmospheric
pressure. Certainly it is expected that all particle velocities, mean free paths, and
other particle kinetic properties will be distributed in a Maxwell-Boltzmann manner
at these high densities. The second question, that of the equality of the electron
and gas temperatures, has been answered by some investigators by the following
argument:
The value of Ejp (field strength in volts/cm divided by the pressure in mm of
Hg) is much less than one— about 0.01, in fact. Therefore, elastic collisions are
dominant. At these pressures and field strengths, terminal velocity of the
electrons is reached in a very short space. Therefore, the energy gained by the
electrons between collisions is all given up as kinetic energy in the next
collision. Thus the equation
T e -T g M effAg
T e 8m f kT e
holds. If values of the constants for argon are substituted, it is found that
T e — T g <0.02T e , and thus it has been concluded that the gas temperature is
sufficiently close to the electron temperature so that a measure of T e is
sufficient to define T g . Now a measure of temperature by any of the spectro-
scopic methods on line intensities or the continuum radiation is clearly
dependent on the distribution of velocities in the tail of the distribution
function so that the measurement is considered a valid measure of T or T
Many investigators have made measurements of temperature spectroscopically
at positions just downstream of the orifice in plasma jets. Most of the results gave
temperatures of 15,000 to 20,000°K at the center of the jet, tapered to 8000 to
10,000°K at the edges, and then dropped sharply to ambient. Although most
investigators who made simultaneous energy- balance measurements found this
temperature to be smaller by a factor of 5 or so, the usual explanation was that
gradients in the boundary layer were so steep that if an average over all the mass
were taken, the average spectroscopic temperature would be equal to the
energy balance temperature. It is proposed that this may not be an adequate
interpretation.
In the measurement program in our laboratory, measurements of temperature
using the Fowler-Milne method were made, and results similar to those reported in
Figure 6 for an argon plasma using both the 4158 A line and the adjacent con-
tinuum radiation were obtained (16). Similar results were obtained for a nitrogen
plasma (20). An attempt to locate the stream boundary showed it to be almost
identical with the radiation boundary. Then, when an enthalpy calculation across
the stream was performed by using corrected values of enthalpy as a function of
temperature, it was found that the enthalpy differed by a large factor from the
known energy input. The inescapable conclusion was then that T e ^T g .
156
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
ARC CHAMBER
GAS .
INPUT
iRIFICE ELECTRODE
INNER ELECTRODE
ARC PATHS
FIGURE 10. Illustration of the blown-arc mechanism in plasma jets having the
Gerdien electrode configuration.
The above decision was somewhat altered by later work with probes which
showed that the arc was in reality a filament of discharge moving about over the
envelope at high frequency. See Figure 10 (7). This allowed two possible inter-
pretations. First, the discharge region could have consisted of an electron gas at a
much higher temperature than the heavy particles. Second, local thermodynamic
equilibrium could have existed but only over a very small volume at any one time,
so that T e ~ T g locally but the average T g was much lower than measured spectro-
scopically. Which interpretation to use will not be discussed here, but it must be
noted that this is a case where the spectroscopic methods gave correct results but .
the wrong answers.
2 4 6 8 10"
E 2
- v cnr
N
FIGURE 11. u.JTJ versus EIN for various gas energies; condition for electron terminal
energy to be reached. (Argon used for calculation.)
mcgregor: Spectroscopic Measurements in Plasmas
157
LIMITATION OF E\p CRITERIA
This seems a good place also to discuss the reasoning leading to the above con-
clusion that T e = T g merely from the Ejp criteria and the equation. A re-examination
of that criteria (20) reveals that the original treatment did not consider the flow of
gas through the tube but dealt only with closed discharge tubes. Also, the mech-
anism of energy loss to the apparatus was not considered since the principle concern
at that time was with measurements on electron behavior. Two results of such a re-
examination are shown in Figures 1 1 and 12, where argon gas has been taken as the
test gas. In the first, it is shown that the approach of T e to T g is a function not
only of EjN, where N is the particle density per cm 3 , but also of T g itself which is
governed either by energy transfer to the walls of a container or by flow of the gas
through the discharge. Thus, at a normal field strength of 20 volts/cm and a
density of 10 19 per cm 3 , T e IT g ~2. The other facet of this re-examination introduces
the dwell time of the heavy particles in the discharge for gases that flow through
the discharge freely or are forced through. Shown in Figure 12 is a plot of the
approach of T g to T c as the gas flows through the discharge and also a plot of
the time necessary for T e = 0.982",, as a function of the pressure. For example, at a
pressure of one atmosphere, the time required is about 11 |xsec. A gas flowing at
-~IH
X
o
T
FIGURE 12a. (U-U )l(U t -U ) versus t/r, showing the approach of the molecular
energy toward the electron energy when the molecule either enters the discharge by
convection or is forced through by a pressure field.
158
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
10
10
10 J -
10
10
10
r 2
1
At-
1 1 1
16 V2 M 1
2.66o 2 7Tm Nv e
M - Mass of Atom
- 3
— Ny^
m - Mass of Electron
o- Radius of Atom ~~
N - Atomic Density
-4
—
\v - Average Electron Velocity
^^ C llu ' _L '
-5
—
^^ —
-6
1
1 1 X
0.001
0.01
0.1
1
10 atm
P - Atmospheres
FIGURE 12b. Time required for temperature of heavy particles to approach temperature
of electrons as a function of pressure ; curve shown is for argon at a temperature of
5000°K.
Mach 0.9 through a 1-inch-long orifice would remain in the discharge for about
20 [xsec, and almost complete heating would be expected. However, the Gerdien
arc, with its blown, high-frequency arc channels, does not comply with the
idealized 1-inch-long discharge considered in reference (20). The point is this: that
most of the arc discharges being used are on the borderline insofar as the
theoretical prediction of T e = T g is concerned and that some of the more exotic
forms of electrode configuration simply do not provide enough dwell time of the
heavy particle in the discharge. Therefore, on such devices one would expect the
spectroscopic temperature to be the electron temperature, and a closer look would
be required in order to say how T e differed from the gas temperature.
VALID MEASUREMENTS
The results and interpretations given above for the blown arc configuration are
not, of course, always encountered. In many cases reported, references (11) and
(18), for example, the spectroscopic measurements of the temperature of atmos-
pheric jets seemed quite reasonable and agreed with expected temperatures from
mcgregoe: Spectroscopic Measurements in Plasmas 159
energy- balance considerations. Closer examination showed that these measurements
were made under low flow operating conditions where the arc was not blown out-
side the nozzle. This mode of operation is sometimes referred to as the "laminar
mode". Thus, it appears that the prime consideration of the experimenter should
be to know something of the plasma region being measured except that it radiates
light. If the region contains a part of the discharge, then caution is in order; if it is
the field-free region, then (barring a case to be presented in the next section) good
measurements can be obtained.
PHENOMENOLOGICAL MEASUREMENTS
The spectrograph has always been employed to study occurrences in nature by a
sort of detective pattern, particularly by the chemist. A rare opportunity has
recently come to light in working with low-pressure plasma plumes. Perhaps first
the dilemma of the visibly-radiating, low-pressure plume should be explained.
Considering the plume shown in Figure 2, suppose the temperature at the exit is
of the order of 5000°K, then the static temperature in the expanded plume will
range from some 300° to 500°K upstream of the normal shock to some 1200° to
1500°K downstream of the shock. Both of these temperature ranges are much too
low to produce thermal radiation from the argon gas. Furthermore, the lifetimes of
the excited states are of the order of 10 " 8 to 10 ~ 7 seconds so that any excitation in
the arc region would radiate within about a millimeter. If recombination were the
exciting mechanism, some continuum radiation would be expected. This does not
occur, as shown in Figures 3 and 4. Also, recombination rates are such that any
recombination in argon would be expected to occur well downstream. Electron
excitation is ruled out because of the low electron temperature measured with
Langmuir probes. Therefore, the source of the radiation was at first a mystery.
MECHANISM OF RADIATION
Dr. John Dicks suggested that the radiation might be the result of metastable
atoms that are excited in the arc region, proceed downstream, and then are further
excited by collisions and radiate to the ground state (21). Spectrographs studies to
determine if this hypothesis was indeed true led L. E. Brewer of ARO, Incorporated,
into some quite interesting phenomenological evidence (22, 23). It was discovered
that the metastables were responsible for the radiation by noting the behavior of
the stream under a series of quenching experiments. It was found, for example,
that the addition of a small amount of hydrogen to the cell would effectively quench
the radiating stream, whereas helium had little effect upon it. The key experiment
was perhaps the selective excitation of the nitrogen molecule which was mixed with
the stream from the ambient gases. It was found that the second positive N 2
band always appeared in the spectrum, while bands originating from levels higher
than about 11.75 volts just did not appear. Figure 13 illustrates that this phenom-
enon is almost perfectly explicable in the light of excitation by collisions with the
metastable argon. Many other interesting excitation processes, such as production
of the CO + comet tail system when C0 2 was added, were observed.
The importance of this carrier of metastable atoms into a field-free region where
reactions with various molecules can be observed is just now being realized. Other
experimenters working at the University of Texas (24) have recently reported on
similar phenomena, using apparatus which is excited initially by RF energy.
Previous investigations of this kind have been confined to short-lived afterglow
apparatus in which the measurements had to be made in about 0.1 jisec. Here the
6*
160
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
12
10
ARGON
METASTABLE
LEVEL
FIGURE 13. Partial energy level diagram of N 2 illustrating the selective excitation of
the second positive system by collisions with argon metastables.
plasma stream might be termed a "continuous afterglow", spread out in time by
the flow process. Some worthwhile fundamental work using this apparatus is
anticipated.
MECHANISM OF EXCITATION
The next question that arose was the mechanism of the excitation of the
metastable argon, since radiation from levels as much as 3.5 eV above the meta-
stable level was detected. Three possible sources were suggested: electrons, photons,
or thermal collisions. The first was ruled out because of the low density. The second
was considered unlikely but possible. The third was intuitively discarded at first
because of the very low temperatures. In investigating the latter mechanism, a
new way of writing the distribution function for excited states was tried (25). Two
distributions were written, one with ground level at zero and the other with
ground level at the metastable energy. These were then summed to give a new
distribution function. The results were quite surprising. For example, if the density
of metastables is taken as the value that would be excited at the 15,000°K electron
temperature measured in the discharge, and if the gas temperature is assumed to
be 5000°K, the population of excited states is altered by several orders of magni-
tude. In this case, the number of metastables would be only 0.0009% of the total
particle density. This is shown by the two distributions in Figure 14. Although this
calculation seems a bit fictitious upon first glance it does indicate the tremendous
effect that a few metastables can have. The effect is also seen by the illustrative
energy distribution shown in Figure 15. Here the kinetic energy of the colliding
particles is shown, and the excitation energies of the argon levels are drawn in.
mcgregor: Spectroscopic Measurements in Plastnas
161
n =
N?
_1_
L U o
N N
m + "> pxd<E /kT)
'Vo M o u m
g n exp(-E n /kT)
N Q , N m , N n ' Number Density of gnd. State, Metastable and Excited Atoms
U , U m = Partition Function of gnd. State and Metastable Atoms
E m , E n = Energy of Metastable and Excited Levels
g n = Statistical Weight
k * Boltzmann Constant
T * Temperature
N /N
n/ o
FIGURE 14. Energy state distributions for argon showing influence of metastable
states.
162
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
MCGREGOR: Spectroscopic Measurements in Plasmas 163
At the far right, the normal excitation by collisions is illustrated. At the left, the
energy required to excite a metastable level to a higher level is shown, and the
tremendous difference in the number of such possible collisions is graphically
portrayed.
TEMPERATURE MEASUREMENT
Another unexpected result of this analysis was that the character of the ex-
ponential distribution was retained (see the equation in Figure 14). This suggested
a closer examination of the spectrum of the expanded plume to see if the distribu-
tion was actually retained. Successful verification would not only provide con-
fidence in the principle used but would also provide a temperature measurement.
Preliminary results from such measurements do indeed verify that an exponential
distribution of excited states exists and, in addition, the temperatures so measured
agree favorabfy with calculated values from energy balance and aerodynamic
calculations. It remains for more data to be obtained so as to verify unquestionably
these preliminary measurements.
CONCLUDING REMARKS
To summarize briefly the remarks on temperature measurement by spectro-
scopy, the methods which use the spectral fine intensity or the continuum intensity
formulas may be used to obtain a measurement of the excitation temperature of
plasmas which are employed for gas dynamic purposes. However, in order to relate
the excitation temperature to gas temperature it is necessary to know the mech-
anism of excitation. In arc discharge regions, excitation is almost always a result of
electron-atom collisions, and thus the measured temperature is the electron
temperature. Then other methods or analyses are required in order to ascertain if
the gas temperature and electron temperature are the same. In low pressure,
field-free regions where metastable atoms are the chief contributors to the radia-
tion, absolute intensity measurements mean little unless the formulas are modified
in the manner discussed. However, it has been shown that a relative line intensity
method is valid for the higher excited levels.
For gases containing molecules which have a band structure that is relatively
simple, the individual lines within the band are excited for the most part by mole-
cule-molecule collisions so that they provide quite a good thermometer. Unfor-
tunately, most of the molecules which can be used are impurities, such as CN or C 2 ,
or are formed under mysterious circumstances, such as NO, so that they are not of
as much use as would be thought.
The practice of using impurity metallic lines is considered by this author to be
somewhat open to question because of the proper mixing and vaporization.
Insertion of slight impurities of a vaporable metal is better but still frowned upon.
After all, one purpose of the gas dynamics facility is to provide a non- contaminated
gas stream. Then, too, it just does not seem quite right to use radiation other than
from one of the molecules present in the test gas.
The methods employing Planck's energy distribution and Kirchhoff 's laws seem
to give adequate results, but the dependence upon wavelength does not seem to be
fully explained. Another concern is with the gradient across the stream and the
complicated way in which this affects the absorption. The restriction to infrared
wavelengths is not necessarily a problem but one which needs more study.
The methods which employ Stark broadening and shift of spectral lines are very
good tools for high-temperature plasmas. The wealth of literature on this subject
attests to its value. However, at lower temperatures — 3000° to 15,000°K — the
164 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
methods are not generally applicable because of the instrument resolution problem
and the overlapping of several broadening processes. Doppler broadening, which
seems a very good technique conceptually, also suffers from the overlapping
problem, particularly by pressure broadening as the pressures of plasma jets are
continually pushed upward. Unfortunately, pressure broadening is not well
enough defined that measurement techniques can be based upon it at present.
These methods then would seem to require more study before they can be put to
work for arc-heated plasmas.
The material presented in this paper has not been aimed primarily at introducing
new methods or data for the diagnostics of plasmas. Rather, the theme has been
that of stressing the importance of proper interpretation of the results of spectral
measurements. Two concepts have been presented that are of most significance.
First, seemingly good temperature measurements using spectroscopic data, even
by two or three methods, should not be accepted without critical review of the
physical situation. Second, metastable states, which occur in all but single electron
atoms, play an important role in the radiative emission process. Still, the spectro-
scopic methods of diagnostics are the most powerful at our disposal for the
understanding of plasmas.
ACKNOWLEDGMENT
The author gratefully acknowledges the contributions to this paper by his
colleagues, Messrs. M. T. Dooley and L. E. Brewer, who have greatly influenced
the interpretations which have been presented on the spectroscopic measurement
of plasmas.
REFERENCES
1. Druyvesteyn, M. J., and Penning, F. M., "The Mechanism of Electrical
Discharges in Gases at Low Pressure", Rev. Mod. Phys., 12, No. 2, 87 (April,
1940).
2. Aller, Lawrence, H. Astrophysics (New York: Ronald Press, 1953).
3. Browning, J. A., "Techniques for Producing Plasma Jets", in Dynamics of
Conducting Gases (Evanston: Northwestern University Press, 1960), 126-138.
4. Gerdien, H., and Lotz, A., "On a Light Source of Very High Surface Bright-
ness", in Wissenshaftliche V eroffantlichungen aus den Siemens -Werken, 2, 489
(1922).
5. Reid, J. W., "High Pressure Arc Jets", ASME Paper No. 61-WA-246,
presented at Winter Annual Meeting, 1961.
6. Schoeck, P. A., and Eckert, R. G., "An Investigation of Anode Heat Transfer
in High Intensity Arcs", in Vth Inter. Conf. on Ionization Phen. in Oases
(Amsterdam: North-Holland, 1961), 1812-1829.
7. Dooley, M. T., McGregor, W. K., and Brewer, L. E., "Characteristics of the
Arc in a Gerdien-type Plasma Generator", ARS Journal, 32, 1392-1394
(1962); comments on "Characteristics of the Arc in a Gerdien-type Plasma
Generator", AIAA Journal, 1, 3, 723 (1963).
8. Harvey, J. K., Simpkins, P. G., and Adcock, B. D., "Instability of Arc
Columns", AIAA Journal, 1, 3, 714-716 (1963).
9. McGregor, W. K., Erlich, J. J., and Bratcher, J. D., "The Visible Plasma
Flame Spectra of Argon and Helium", AEDC-TN-59-134 (December, 1959).
10. Brewer, L. E., McGregor, W. K., and Dooley, M. T., "Spectral-line Intensities
from Argon and Nitrogen Plasmas", J. Am. Opt. Soc, 52, 829 (1962).
11. Winter, E. R. F., and Cremers, C. J., "Temperature Distribution in a Low Mass
Flux Argon Plasma Jet", ARL 62-3SS, University of Minnesota (July, 1962),
mcgregob: Spectroscopic Measurements in Plasmas 165
12. Shipley, K. L., "Preliminary Study of Spectrograph? Temperature Measure-
ments of an Argon Plasma Jet", Tech. Memo, of the Sandia Corp. (May, 1961).
13. Fowler, R. H., and Milne, E. A., Monthly Not. R.A.S., 83, 403 (1923); 84, 499
(1924).
14. Olsen, H. N, "Thermal and Electrical Properties of an Argon Plasma",
Phys. Fluids, 2, 6, 614-623 (1959).
15. Knopp, C. F., Gottschlich, C. F., and Cambel, A. B., "A Spectroscopic Tech-
nique for the Measurement of Temperature in Transparent Plasmas",
AF-OSR-1100, Northwestern University (July, 1961).
16. McGregor, W. K., and Dooley, M. T., "Spectroscopic Diagnostics of a Gerdien-
Type Plasma Stream Using Argon", in Temperature— Its Meas. and Cont. in
Sc. and Ind. (New York: Reinhold, 1962) 3, Part 2, 467^77.
17. Dickerman, P. J., and Morris, J. C, "Experimental Studies of the Temperature
in a Field-Free Plasma", in Optical Spectrometry Measurements of High
Temperatures (Chicago: University of Chicago Press, 1961), 170-180.
18. (a) Tourin, R. H., Temperature — Its Meas. and Cont. in Sc. and Ind. (New
York: Reinhold, 1962) 3, Part 2, 455^66; (b) Ryan, L. R., Babrov, H. J., and
Tourin, R. H., Infrared Spectra and Temperatures of Plasma Jets (New York:
Warner and Swasey Company, 1962).
19. Margenau, H., "The Structure of Spectral Lines from Plasmas", in IVth Inter.
Conf. on Ionization Phen. in Gases, Vol. II (1959), 791-807.
20. McGregor, W. K., and Brewer, L. E., "Re-examination of the Criteria for
Thermal Equilibrium in Electrical Discharges", in Vlth Inter. Conf. on
Ionization Phen. in Gases, Paper No. 11-28 (Paris, 1963).
21. Templemeyer, K. E., and Dicks, J. B., "Some Gas Dynamic Characteristics
of Argon Plasma— Application to Jet Spreading", AEDC-TDR-62-88
(July, 1962).
22. Brewer, L. E., and McGregor, W. K., "Excitation of Nitrogen by Metastable
Argon Atoms", Phys. Fluids, 5, 1485-1486 (November, 1962).
23. Brewer, L. E., and McGregor, W. K., "The Radiative Decay of Metastable
Argon Atoms in a Low-Density Argon Plasma Stream", AEDC-TDR-63-5
(January, 1963).
24. Collins, C. B., and Robertson, W. W., "Helium— Admixed Gas Reactions in a
Flow System", in Vlth Inter. Conf. on Ionization Phen. in Gases (Paris, 1963).
25. Brewer, L. E and McGregor, W. K., "The Influence of Metastable Atoms on
the Population of Excited States in a Thermal Plasma ', in Vlth Inter. Conf.
on Ionization Phen. in Gases (Paris, 1963).
168
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
CHAMBER EVACUATION LINE
RESISTIVE PAINT
CHAMBER FEED LINE
CHAMBER EVACUATION LINE
OUTER CONDUCTOR ASSY
INNER CONDUCTOR ASSY.
INDIUM SHIM
NATURAL RUBBER INSULATION
MIRROR ASSY.
BASE ASSY.
SWITCH EVACUATION LINE
SWITCH GAS FEED LINE
SECT. B-B
FIGURE 1. Test rig assembly.
One of the promising techniques for investigating plasma processes is the
monitoring, on a time-resolved basis, of their radiation by spectroscopic and
photographic means. It is the purpose of this paper to describe a preliminary
experimental program designed to reveal, principally by submicrosecond-resolved
emission spectroscopy, the types of specie excitation and induced chemical reactions
created by a hypersonically-driven arc discharge in initially quiescent, low-pressure,
elemental gases and detonable mixtures. In this case, the arc discharge is the
plasma source.
9. Kenneth M. Foreman and
Maurice E. Levy: Comparative
Spectroscopic Studies of
Electromagnetically -Driven
Hypersonic Waves in Elemental
Gases and Detonable Mixtures
\2i Time-resolved emission spectroscopy has been used to analyze
electro-magnetically driven plasmas created by arc discharges in
quiescent, low-pressure elemental gases and detonable mixtures. The
electrical energy was supplied by an R-L-C circuit in the form of an
8-ji.sec pulse. Stainless steel electrodes with a hyperbolic contour,
mounted in parallel within a cylindrical discharge chamber, created a
constant-area flow channel in which wave speeds between 8,000 and
25,000 ft /sec were recorded.
The relative excitation of hydrogen Balmer lines, the long decay
time of the 5876 A helium emission line, and the time variation of
molecular-oxygen ion emission are typical data presented (and related
to the arc-discharge-current waveform). Also presented is the emission
spectrum from a stoichiometric hydrogen-oxygen mixture.
Radiation from the H 2 + 10 2 mixture with an initial pressure
between 1 and 11 mm Hg (absolute) includes the 5126 A band attrib-
uted to OH. This data indicates that it is likely that an exothermic
chemical reaction proceeds within the order of 1 [isec downstream of the
driven hypersonic-wave field. It is believed that the reaction mechanism
can be partially attributed to photochemical processes caused by
ultraviolet radiative transfer from the intensely luminous plasma in
the arc region.
INTRODUCTION
A current part of the national space program is the effort to develop plasma
devices for the primary propulsion of aerospace vehicles or the position and
attitude control of artificial satellites. Knowledge of the composition and energy
partition of plasmas used by these devices can lead to optimum designs and
encourage more widespread application of these devices, including applications
within the earth's atmosphere (1, 2).
ed. note: Mr. Foreman and Mr. Levy are at the Republic Aviation Corporation,
107
x' arniiiigcltile, Long Island, Nc
foreman and levy : Spectroscopic Studies of Hypersonic Waves 169
DESCRIPTION OF EXPERIMENT APPARATUS
TEST STAND
The test stand has provisions for six low-inductance capacitors arranged in
parallel around a centrally-located discharge chamber. The capacitors are attached
by an equal number of tabs radiating out from two collector plates (see Figure 1).
These plates are separated by a 0.036-inch-thick, natural-rubber insulator that can
withstand 10,000 volts.
The vacuum chamber and gas-fired switch are centrally located immediately
above the collector plates. The electrode holder plates can accommodate 8-inch
diameter electrodes and are separated by a dielectric spacer made of Alumina,
fused quartz, or Mykroy. The attachment of the dielectric spacer to the perimeter
of the metal electrode holders has been successfully achieved with epoxy cement.
The gas-breakdown electrical switch is ignited by a pulse of nitrogen gas into
an initially evacuated chamber that stands off an impressed voltage. As the in-
jected gas" fills the switch chamber, the pressure increases until electrical break-
down occurs. Several resistive-paint stripes having a total resistance of 250,000
ohms are located along the dielectric spacer and electrically connect the upper and
lower electrode holders to make them, initially, of equal potential. This arrange-
ment permits the switch to be fired but limits current flow to milliamperes so that
an arc discharge is provided in the reaction- chamber gas. Three-inch-long quartz
windows in the electrodes and electrode holders permit monitoring with optical
diagnostic devices.
The cylindrical, stainless-steel electrodes mounted in the chamber have a
hyperbolic contour over the outer third of their discharge surface to present,
essentially, a constant-area flow channel for the first 1.3 inches of radial travel
inward from the periphery. Thereafter, the channel area decreases. Figure 2
shows two photographs of the test stand equipment.
With five capacitors rated at a nominal 6 /if each, a transient, damped-eurrent
waveform with an initial peak at 1.8 /xsec was produced. The other circuit para-
meters were computed from ringing-test data using Rogowski-coil pickups with
L = 4AxlO~ B h and R=5x\0~ 3 ohms. The addition of a 0.10-ohm Nichrome
resistance strip to each branch of the circuit produced a total circuit resistance of
2.5 x 10- 2 ohms and theoretically attenuated the current to less than 0.1 of the
maximum amplitude within 1.5 cycles. The initial rate of rise of current was about
3 x 10 10 amp/sec, and current amplitude was related to initial capacitor voltage m
the ratio of 16,000 amp/kV. Recorded current traces indicated essentially zero
current after 8 fisec.
PHOTOMULTIPLIER RECORDING
A Leiss, single-prism monochromator was used in conjunction with a photo-
multiplier tube for observation of the emission radiation from the plasma and its
flow field. Figure 3 is a schematic diagram of the experimental apparatus and
their relative positions. The light transmitted through the quartz window covering
slit A on top of the cylindrical discharge chamber is reflected by mirror C. The
image of slit A is formed perpendicular to the monochromator entrance slit S E .
(This arrangement permits observation of that particular part of the plasma flow
field where the slit S E intersects the slit-,4 image.) The light received at slit S E is
then dispersed in the monochromator by a quartz prism. The beam that passes
through the exit slit S x falls on the photocathode of a DuMont 6467 photomultipher
tube, the output of which is displayed as a transient trace on a Tectromx 551
170
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
FIGURE 2a. Overall view of research test stand with spectroscopic analysis equipment
in place.
FIGURE 2b. View of research test stand seen from monochromator position.
oscilloscope and is recorded with a Polaroid camera. The photomultiplier tube has
an S-ll response, a useful range between 3600 and 6000 A, and a peak response
near 4400 A. The spectral range of the monochromator is 200 m^ to 20 /x.
fobeman and levy: Spectroscopic Studies of Hypersonic Waves
171
MIRROR C
MONOCHROMATOR
SLIT S E
DISCHARGE CHAMBER
CONCAVE MIRROR COLLIMATOR-
TOP VIE* OF MONOCHROMATOR
PM COMBINATION
FIGURE 3. Schematic diagram of equipment.
The photomultiplier detector was operated at a supply voltage of 18CKJ V, and
the output voltage was in the linear region of response, thus making it possible to
compare relative intensities of emission lines after correcting for the spectral
response of the photomultiplier and the transmission of the quartz prism. The
photomultiplier circuit contained a 50-ohm output impedance to match the
impedance of the unterminated coaxial line. Extraneous electrical noise signals
were eliminated for all practical purposes by shielded enclosures around the
photomultiplier and its connecting cables and, additionally, by having the
photomultiplier about 4 feet from the discharge device.
PHOTOGRAPHIC RECORDING
A Spencer spectrometer (made by American Optical) was used for obtaining
time-integrated photographs of a wide field of the discharge spectrum. This
172
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
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instrument has a focal length of 162.5 mm. an aperture of 25.4 mm. and a relative
speed of //6.4. The accessory camera supplied with this instrument was modified
to accept a Polaroid film holder and was used to record the emission radiation on
Polaroid ASA-3000 speed film.
The positioning of the entrance slit of the Spencer spectrometer was identical to
the relative positioning of the entrance slit of the Leiss monochromator as shown
in Figure 3. The entrance slit of the Spencer spectrometer was not calibrated so
foreman and lew: Spectroscopic Studies of Hypersonic Wares
173
3WI1
E %
a
c
e
s
E s
E g
5 s
that it is not known exactly what size openings were used when photographing
emission spectra, but it is known that they were of the order of 0.5 mm. It should
be noted that despite the wide slit opening used, the /', 6.4 speed of the instrument,
and the ASA-3000 speed of the film, it was necessary to obtain about 15 superim-
posed discharge images (see Figure 4) to obtain a good photograph for any particular
set of conditions. The discharge lasted for a period of about 8 /^sec, but some
emission lines or bands persisted for a longer period of time.
174 PHYSICO-CHEMICAL DIACXOSTICS OF PLASMAS
EXPERIMENTAL PROGRAM
Preliminary to the spectroscopic observations, a high-speed, rotating-mirror
camera was used to obtain streak pictures on black and white and color film. These
pictures, typified by those of Figure 5, were an aid in guiding the interpretation of
the spectroscopic data. The streak pictures, taken through an observation slot in
the upper electrode, display the nature of the imploding hypersonic waves driven
by the accelerated plasma. The intense white illumination created by the initial arc
discharge changes, in the H 2 + |0 2 mixture, to a cherry red leading edge and deep
red flow field after the 8-/*sec current pulse is extinguished. It is particularly
noteworthy that a much less intense region of green and deep blue light can be
seen ahead of the flow field, beginning almost at the very onset of the plasma
formation and persisting for several microseconds.
The test procedure consisted of obtaining a spectrophotograph of a major
portion of the discharge spectrum in the test gas mixture and identifying the
emission lines and bands present. Lines or bands of interest subsequently were
investigated by means of photomultiplier time-resolved observations. This data
then was related to the streak photographs.
The OH emission-band head at 5126 A (3, 4) was investigated with particular
care. This band head occurs in a part of the spectrum that is relatively clear of H 2
and 2 emission and, therefore, can be isolated with comparative ease. In the
systematic identification procedure for this particular band, discharges were
induced in different nonreacting gases to find other possible contributions of
emission near the OH wavelength. Discharges in He revealed a small contribution
from metallic elements, such as Fe, Ni, and Cr, which were, presumably, from the
stainless-steel electrodes. Discharges in 2 produced spectra of the metallic oxides,
such as FeO, NiO, and CrO, as well as the 2 bands and lines. Pure H 2 also was
used for the discharges, and its Balmer series lines and molecular bands were
observed. At times, the nonreacting mixture He + ?0 2 was substituted for H 2 + 10 2
as a further check on the correct identification of the OH spectra.
The dependence of certain spectra on pressure and voltage was studied, along
with their time-resolved characteristics. It was found possible to distinguish
between two emission spectra occurring at nearly the same wavelength by means
of the distinct behavior of their time-resolved characteristics with variation of
initial pressure or voltage. Precautions were taken during these experiments to
maintain the quality of the data. The discharge chamber was filled with fresh gas
before every discharge and was evacuated to about 10 fi after each discharge to
prepare it for the next filling. The detonable (2H 2 + 2 ) mixtures were carefully
mixed and were not used for a period of time, usually of the order of weeks, to
insure complete diffusion of the component gases into each other.
The reaction chamber was filled with test gas to within + 5 per cent of the
desired pressure. Prior to initiating a discharge, the capacitor voltage was recorded
to within +2 per cent. Electrical discharge usually was initiated within one
minute after the reaction chamber was filled.
Most of the discharge observations were made at about the mid-radius of the 8-inch-
diameter reaction chamber. At this position, the imploding hypersonic wave is well
developed and starting to enter a converging channel. Some check observations
were made near the periphery of the chamber where the plasma is first formed.
All the dual-beam, oscilloscope-trace photographs display, simultaneously, the
photomultiplier output signal on the upper beam and the discharge-current signal
(integrated Rogowski-coil output) on the lower beam. The current signal triggers
the oscilloscope sweep.
fur em an and lew: Spectroscopic Studies of Hypersonic Waves
175
EXPERIMENTAL RESULTS
Photomultiplier readout traces of the H y . H?, and H ? emission lines are included
in Figure 6. The relation of this radiation to the transient current waveform
governing the discharge in the molecular hydrogen also is shown. These three
INITIAL PRESSURE
I m m Hg
INITIAL
VOLTAGE
4500 V
X s
4350 ?±35
Hg (4340A)
4500V
x =
4110/5*3.5
HM4I0IA)
4500V
2 p sec
X =
3980)U 35
H � (3970A)
UPPER TRACE- PHOTOMULTIPLIER OUTPUT
LOWER TRACE - DISCHARGE CURRENT
FIGURE 6. Time-resolved spectra of three Balmer series lines for electrical discharges in
hydrogen.
Balmer (atomic hydrogen) lines display relative amplitudes similar to those in
reference intensity tables (5). for example, hut in this case the detectable emission
persists about 6 /^sec after the cessation of current.
Several emission bands identified with molecular-oxygen ions were observed
for a similar arc discharge pulse into 2 . A typical set of oscilloscope traces is
presented in Figure 7 for various initial-pressure and capacitor-voltage conditions
176
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
\=4l50A±20(Oi2nd Negative)
SLIT WIDTH — 0.05mm INITIAL PRESSURE
0.5 mm Hg I. Omm Hg
INITIAL
VOLTAGE
0.5 v ^^^^^
-i |?-2/isec —I k-2/isec
UPPER TRACE- PHOTOMULTIPLIER OUTPUT
3000V 0.1 v-T
0.5 v -J
H K-2/Lxsec
-I 1?— 2^.s
LOWER TRACE - DISCHARCE CURRENT
2000V
O.lv
05v
—4 k— 2/JSec(Typ.) — >| -K-2/xsec
FIGURE 7. Time-resolved spectral characteristics of electrical discharges in oxygen.
at a spectral location associated with the second-negative, oxygen-ion band. The
profound effect of these relatively small perturbations in initial test conditions is
apparent from the large changes in amplitude.
The discharge in He produces excitation of the 5876 A line. The spectral profile
of this radiation is recorded in Figure 8 as a function of time. This emission persists
considerably longer (170 /xsec) than the current pulse. The 3889 A He line was
found not to be excited. Other explorations of He discharges in spectral regions
where no He lines are expected indicated that, for initial pressures less than 1 mm
Hg (absolute) electrode elements (metallic) produced significant background
radiation. For pressures greater than about 1 mm Hg (absolute) this radiation
appeared to be suppressed.
The observations described were made at a position where the imploding dis-
charge (luminous front) would have had to travel at least to the midradius of the
foreman and LEVY : Spectroscopic Studies of Hypersonic Waves
177
INITIAL PRESSURE
INITIAL
VOLTAGE
4500V
I m m Hg
O.lv
4500V
4500V
4500V
4500V
5860A ± 18
5880A± 18
5900A± 18
5930A± 18
O.lv- 1
5950A* 18
20^sec
UPPER TRACE - PHOTOMULTIPLIER OUTPUT
LOWER TRACE - DISCHARGE CURRENT
FIGURE 8. Time-resolved spectra circa
discharges in helium.
He 5876 A line resulting from electrical
discharge chamber. When H 2 or He was used, the photomultiplier trace of the
radiation displayed a dependence on initial capacitor voltage and gas pressure,
whereas with 2 there existed no such well-behaved relationship to discharge
voltage or gas pressure. This is an indication reinforced by streak photographs —
that the plasma formed in the 2 probably is irregular and asymmetric. Further-
more, with 2 . the luminous wave front did not always proceed across the point of
observation. This resulted in poor overall reproducibility of emission intensity
under otherwise identical initial conditions of discharge. When 2 emission spectra
178 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
INITIAL PRESSURE
INITIAL
VOLTAGE
O.lv
4500V
UPPER TRACE - PHOTOMULTIPLIER OUTPUT
X=3970A'-I4 (0+ 2nd negative)
-*| K-5jtysec.
O.lv-
4500V
LOWER TRACE - DISCHARGE CURRENT
FIGURE 9. Time-resolved spectra of electrical discharges in a stoichiometric hydrogen
oxygen mixture.
were monitored in mixtures containing H 2 or He. a more reproducible condition
existed (for example, see Figure 9), presumably as a result of the stabilization of
more symmetric plasma cylinders.
A comparison of spectra from discharges in He, H 2 + 10 2 . and H 2 under similar
test conditions is given by Figure 10. The discharge in He indicates that there is a
negligible metallic background emission in the 5100-5200 A bandwidth, but, in H 2 .
there is a very small amount of emission by electronic bands. The emission obtained
for discharges in H 2 + |0 2 , however, is significantly large, which strongly suggests
that the radiation is the OH band originating at 5126 A (3, 4).
Further comparisons with data of Figure 11 tend to reinforce this view. Monitor-
ing emission in the 5120-5220 A range resulting from electrical discharges in three
different gas compositions (0 2 . H 2 -f-|0 2 , and He + A0 2 ) but keeping the partial
pressure of 2 the same, there is significantly greater intensity from the H 2 + 10 2
mixture than from the other two, this, again, can be attributed to the OH emission
band. A profile survey of this radiation indicates it to be some 80 to 100 A wide
and degraded toward the red, which is in agreement with the observation of the
discoverers (6) of this visible spectrum of OH.
Corroboration of the photomultiplier data was obtained by time-integrated,
foreman a xi) lew : Spectroscopic Studies of Hypersonic Waves
179
m
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wide-spectra pictures, using the Spencer .spectrograph, previously shown by
Figure 4. A comparison of spectra for different initial gases shows that two-band
systems obtained with the H 2 -f i0 2 mixture cannot otherwise be identified with
radiation from hydrogen or oxygen species: one is at (approximately) 5126 A and
the other, of much less intensity, is between the 5460 and 5790 A mercury lines
used for calibration. The former one (5126 A) we attribute to the OH (0, 7)
emission band as a consequence of our more detailed study; the latter is similar to
the transition of the OH. either (0. 8) or (1. 9). radical shown by Herman et ah (3).
but we have not investigated it further at this time.
180
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
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The data discussed so far were obtained with reaetant mixtures at pressures
between 1 and 3 mm Hg (absolute). Tests also were conducted, however, with
reaetant pressures up to 11 mm Hg (absolute) and down to 0.2 mm Hg (absolute).
With an initial capacitor potential of 4500 V (corresponding to a peak current of
72,000 amp), it was determined (see Figure 12) that electrical discharges into
mixtures at 2^4 mm Hg (absolute) produced the largest peak-amplitude signal for
radiation at 5210 A + 40. For reaetant pressure greater than (5 mm Hg, the peak
amplitude was reduced to about 70 per cent of the 2-4 mm Hg pressure-range
F o R E M a x a x n i. e v y : Spectroxmpir StntiieA of Hyperson k Waves
181
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signal. At all pressures excejit .'5 mm Hg. the peak amplitude occurred at 2 /xsec
after current initiation; for the exception, it occurred at 2.6 /x-sec. For these times,
the streak pictures indicate the discharge to be about 1 inch away from the
position being monitored by the spectrograph. Further, this occurs from 0.2 to
0.8 /usee after the initial peak of the discharge current.
Going to the lower reactant pressure range indicated the apparent existence of an
excitation threshold at 1 mm Hg because in no case was a significant radiation
signal observed at lower pressures. Furthermore, this threshold appears to be very
critical: a reduction of but 0.05 mm Hg initial pressure from this level reduced the
182 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
photomultiplier signal trace to about 5 per cent of its higher-pressure peak
amplitude.
DISCUSSION
PLASMA PROPERTIES AND PRECURSOR EFFECTS
The work reported here represents an interplay of plasma radiation and low-
pressure chemical reactions. Considering the former, although no explicit quanti-
tative data were obtained on the thermodynamic state of the plasma, sufficient
accelerator similarities with those of McLean et al. (7) exist to warrant adoption of
their treatment for estimating plasma temperature. This treatment assumes a
pre-excitation of the gas downstream of the plasma by a radiation precursor.
Thus, assuming that the gas ahead of the driven hypersonic wave lacks internal
degrees of freedom (i.e., letting ^mv 2 = kT), the plasma temperature may be
estimated from the measured wave velocity by using strong-shock equations (7).
In the experiments considered here, the wave velocities, computed from the
streak photographs (Figure 5, for example), vary from 0.36 cm/^sec for a capacitor-
stored energy of 60 joules to 0.72 cm//xsec for 300 joules. The estimated temperature
of the driven plasma, therefore, ranges from 11,000 to 43,000°K. These values are
consistent with considerations of the stored energy and species observed.
The acceptance of the pre-excitation theory permits the consideration of a local
thermodynamic equilibrium (LTE) condition behind the wave front in shorter
times than are associated with the decay of the plasma. That is, the kinetic cross
sections of the excited gas atoms are so large that kinetic equilibrium is attained
in a negligible time period. Ionization by atom-atom collisions also will be ex-
tremely rapid because of the reduced ionization- energy requirements of these
already excited atoms. Electrons assume Maxwellian distribution in typical times
ofl0~ 10 tol0" 13 seconds and relax with the atom-ion distribution in times of the
order of the electron-ion scattering time. The electromagnetically accelerated
plasma (produced by the arc discharge) acts, then, as a thermal light source.
The pre-excitation of the "cold" gas ahead of the electromagnetically driven
hypersonic wave can be explained as being caused by absorption of vacuum
ultraviolet radiation originating in the plasma region. These photons dissociate
molecular species and raise atoms to excited states as found for H 2 (8) or pre-ionized
"cold" gas atoms as was the case for He (9) or Argon (10).
Under certain conditions, electron diffusion ahead of the shock front can play a
role in the pre-excitation process (11). A further possible effect in apparatus in
which electrodes form the flow channel and high initial voltages are applied is the
superposition of a low-current (10~ 3 amp, for example) glow discharge over the
entire channel simultaneous with the localized formation of a high current- density
arc. The glow electrons, traveling across the electrode gap well downstream of the
plasma-driven wave, collide with ground-state or excited species to create conditions
similar to the precursor effect.
These precursor effects are not too well understood; each type of experimental
setup has to be investigated separately to determine the predominant mechanisms
of pre-excitation and ionization of the "cold" gas as well as the state of the plasma.
For electromagnetically driven shock waves, precursor "conditioning" of the
"cold" gas appears to promote, in some experimental apparatus, rapid kinetic
equilibration behind the shock front and results in higher excitation temperature
than ordinarily would be predicted by strong-shock theory. Current work indicates
that these precursors also promote very fast reactions in chemically reacting
mixtures both ahead of and behind the shock-front/plasma complex.
foreman and levy: Spectroscopic Studies of Hypersonic Waves 183
QUALITATIVE ANALYSIS: ELEMENTAL GASES
The relative intensities of the Balmer-series lines of H 2 observed (H H H )
appear consistent with an equilibrium condition. (See Figure 6 ) The time'-inte
grated photograph of the H 2 discharge spectrum (Figure 4), however, although
exhibiting the H, hnef, does not show the H a line that one might expect to be of
the greatest intensity. Additionally, photographs of the He discharge spectrum
Figure 4, for example) show the He 5876 A line but fail to disclose the He 3889 A
line which should have the same intensity in an equilibrium condition This
evidence supports the conclusion that an equilibrium distribution might not have
been established in our apparatus in spite of the apparent precursor conditioning
and excitation of the "cold" gas (see Figures 5 and 6) by photolytic or electron
impact processes.
The strong emission identifiable with OJ (see Figure 9) downstream of the
discharge may be attributed to collisional processes with glow-discharge electrons
Not excluded, however, is the possibility that strong emission in the vacuum
ultraviolet from the oxygen or oxy-hydrogen plasma could cause photoionization
of the molecule. Energy absorption of about 12.5 ev is necessary to ionize the
molecule, and this could be supplied by photons in the 1000 A portion of the
spectrum. The spectral quality of this radiation is produced by 01 and H species
(Lyman spectra) in arc discharges (12). The exploratory scope of this research
program precludes a more quantitative analysis.
QUALITATIVE ANALYSIS: GAS MIXTURES
It long has been recognized (13, 14, 15) that irradiation of oxygen-hydrogen
mixtures by ultraviolet light affects its explosion limits and provokes rapid
reactions at very low pressures. These various investigators (13, 15) consider the
reaction process to be:
2 +hv->20 (!)
+ H 2 -*OH + H (2 )
0H + H 2 ->H 2 + H (3)
It is interesting that previous investigators have used the 3064-3090 A system of
OH almost exclusively for monitoring the reaction kinetics.
Photolysis of water vapor by ultraviolet radiation (16) has been examined and
shown to yield only small fractions of gaseous molecular-oxygen and hydrogen
products. All observations of the hydroxyl-band system at 5126 A (3 4 6) on the
other hand, have resulted from low-current glow discharges in low-pressure
water-vapor environments. This excited state of the OH radical has been attrib-
uted to electronic dissociation of H 2 and the subsequent recombination of
atomic hydrogen and excited atomic oxygen; the role of radiation absorption is
considered to be secondary (3).
It is significant that no other investigators have reported observing the green
emission bands of OH from a stoichiometric mixture of the combustible reactants
furthermore, the advances in photomultiplier detection and recording since 1954
(15) have improved the temporal discrimination of this reaction by at least one
order of magnitude, so that we now can determine that the reaction proceeds
within less than 0.2 M sec after the initiation of the arc discharge.
enough to bo H pk^5pS Were ° bSerVed Wkh a ph0t ° mUlti P lier detect - ^t were not intense
184 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
The maximum 5126 A system emission was observed at 3 mm Hg initial pressure.
For this condition, the peak emission output is found to be proportional to the
peak discharge-current magnitude. Comparison with lower reactant pressure
indicates that the emission intensity is slightly less than proportional to initial
pressure, and, at the lower initial pressure, is not proportional to the current.
With this background data and the apparent reaction threshold at 1 mm Hg the
presence of OH is tentatively indicated as resulting from a primary photochemical
and a secondary electron-impact process. The former is due to precursor radiation
from the plasma and the latter is from the free electrons of the glow discharge.
Although it is possible to speculate on various reaction mechanisms and con-
current processes, it is preferable to defer more detailed discussion until additional
data from our continuing research program becomes available.
CONCLUSIONS
A preliminary emission spectrographs investigation has been conducted of
electromagnetically-driven hypersonic waves into elemental gases and detonable
mixtures. The role of precursor radiation from the plasma in affecting gas properties
significantly downstream of the plasma/shock- wave field has been observed.
The reported spectroscopic data does not support the conclusion of other
researchers that rapid, local kinetic equilibrium is promoted in the wave structure
as a result of precursor conditioning of the downstream gas. This evidence, how-
ever, is not viewed as being in conflict with other work, but, rather, emphasizes
the variation of plasma properties and excitation mechanisms between seemingly
similar plasma accelerators and the need for separate evaluation of the
characteristics of each device.
The rapid formation of an excited state of the OH radical, not observed in
flames, has been detected by emission in the 5126 A and 5534 A band systems. This
radiation ahead of the plasma commences within 0.2 ^sec after initiation of the
electric arc discharge (plasma formation) and persists about 6 M sec after extinction
of the arc.
A reaction-product threshold has been observed for an initial pressure ot 1 mm
Hg. Above this pressure level, a reproducible, positive indication is measured up to
at least 11 mm Hg, and the maximum radiation signal occurs at 3 mm Hg.
The nature of the present results, reflected against the background of previously
reported work, suggests that the OH formation mechanism is associated with
plasma precursor radiation excitation of the "cold" gas downstream of the
hypersonic wave front. This leads to very fast chemical reactions involving
energetic atoms, which produce OH radicals. Secondary electron-impact processes,
arising from a glow discharge along the entire flow channel concurrent with the
arc, probably combine with the initial photochemical one to excite the unusual OH
radiation spectrum reported.
REFERENCES
1 Foreman, K. M., "The Electromagnetic Detonation Concept", PPL-TR-61-10,
Republic' Aviation Corp., Farmingdale, L. I., N.Y. (Also available as ARS
Preprint 1702-61 and AFOSR Document 564.)
2. Foreman, K. M., "Terrestrial Hypersonic Flight Propulsion", AIAA Paper
63110, presented at the AIAA-ASME Hypersonic Ramjet Conference, White
Oak, Md., April 23-25, 1963.
3. Herman, L., Felenbok, P., and Herman, R., "Emission Spectra of the OH
ana uu xvauiuais , u . inysiquz et n?i?Kt/H, *, o?j \iaiji).
foreman and levy : Spectroscopic Studies of Hypersonic Waves 185
4. Benoist, S., "Contribution to the Study of the Spectra of the OH Molecule",
Ann. Physique, 10, 363 (1955).
5. Harrison, G. E., MIT Wavelength Tables (New York: Wiley, 1939).
6. Schuler, H., and Woeldike, A., "Uber den Anregungsmechanismus im H 2 —
Molekiil auf Grand der Befunde an seinem Emissionsspektrum im Sichtbaren",
Physikalische Zeritschrift, 44, 355 (1943).
7. McLean, E. A., Faneuff, C. E., Kolb, A. C, and Griem, H. A., "Spectroscopic
Study of Helium Plasmas Produced by Magnetically-Driven Shock Waves",
Phys. Fluids, 3, 6 (November-December, 1960).
8. Wiese, W., Berg, H. F., and Griem, H. R., "Measurements of Temperatures
and Densities in Shock-Heated Hydrogen and Helium Plasmas". Phys. Rev.,
120, 4 (November 15, 1960).
9. McLean, G. A., Kolb, A. C, and Griem, H. R., "Visible Precursor Radiation in
an Electromagnetic Shock Tube", Phys. Fluids, 4, 8 (August, 1961).
10. Groenig, H., "Precursor Photoionization and Electrons", Phys. Fluids, 6, 1
(January, 1963).
11. Weyman, H. D., "Electron Diffusion Ahead of Shock Waves in Argon",
Phys. Fluids, 3, 545 (1960).
12. Handbook of Chemistry and Physics (Cleveland: Chemical Rubber Publishing
Co., 1961).
13. Semenov, N. N., Some Problems in Chemical Kinetics and Reactivity (Princeton:
Princeton University Press, 1959), II.
14. Kaufman, F., "Reactions of Oxygen Atoms", in Progress in Reaction Kinetics,
ed. G. Porter (New York: Pergamon Press, 1961), I.
15. Norrish, R. G., Porter, G., and Thrush, B. A., "Kinetic Studies of Gaseous
Explosions", in Fifth Symposium on Combustion (New York: Reinhold
Publishing Co.. 1955).
16. Chen, M. C, and Taylor, H. A., "Photolysis of Water Vapor". J. Chem. Phys.,
27, 4, 857 (1957).
10. Robert B. Spiers, Jr., and
Charles Husson: Development of
a Rocketborne Spectroradiometer
to Measure the Radiation
Environment of a Reentry
Vehicle
12? A flight spectroradiometer has been developed for measuring the
ultraviolet and visible spectral steradiancy of the hot-gas plasma of a
supercircular velocity reentry vehicle. It has a spectral range from 2500
A to 6000 A and a dynamic range from 10 ~ 7 to 10~ 3 watts/cm 2 -
steradian-micron. The experimental parameters and vehicle character-
istics affecting the spectroradiometer design is presented with a
description of the optical window, spectroradiometer design, and
calibration procedures. Finally, the flight performance is discussed.
INTRODUCTION
A flight spectroradiometer has been developed as a reentry payload sensor for
the Langley Research Center's Five-Stage Scout Reentry Project. The purpose of the
sensor is to measure the spectral and total intensity of the luminescent air in the
shock-induced flow field produced by the vehicle reentering the earth's atmosphere
at a velocity of approximately 28,000 ft/sec. At this velocity the radiative heat
transfer to a vehicle due to the luminescent air is insignificant compared to the
convective heat transfer. However, the magnitude of the hot-air radiation should
be great enough to detect and measure. Due to the absence of flight data of this
type, a radiative heat-transfer experiment was selected as one in a series of reentry
experiments to be performed. There are no flight-tested spectroradiometers for
use in such experiments, so the development and evaluation of a rocketborne
spectroradiometer was taken as an additional objective of the radiative
heat-transfer experiment.
The Scout vehicle used to perform these experiments is shown in Figure 1. For
the radiative heat-transfer experiment the vehicle is launched from Wallops
Island, Virginia, with a trajectory as shown in Figure 2. After launch the vehicle
goes through a series of staging events which cause the fifth-stage payload to
reenter approximately 275 nautical miles south of Bermuda. A tracking station on
Bermuda and one on a ship records the reentry data in real time and delayed time.
ed. note: Mr. Spiers and Mr. Husson are with the NASA Langley Research Center,
Langley Station, Hampton, Virginia.
187
188
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
-5TH STAGE
-4TH STAGE
-3RD STAGE
/*-2ND STAGE
11 \
ST STAGE
FIGURE 1. Five-stage Scout rocket.
The delayed-time data are provided by an on-board tape recorder in case radio
blackout is experienced during the prime data period. A telemeter transmitter in
the fifth-stage payload transmits the data to the tracking stations. The payload
shown in Figure 3 has a beryllium nose with an optical window on its axis to
transfer the radiant energy to the spectroradiometer sensor. There the quantities
to be measured are converted into electric signals and fed into the telemetry module
for transmission to the tracking stations. The 17-inch-diameter spherical rocket
motor boosts the payload to its final reentry velocity. No attempt is made to
recover the payload.
The nose window and spectroradiometer part of the fifth stage is discussed in
this paper. Their final design and construction resulted from factors peculiar to the
radiative heat-transfer experiment and the rocket vehicle used.
DESIGN CONSIDERATIONS
EXPERIMENTAL
As stated before, the experimental quantities to be measured are the spectral
and total intensity of the shock-induced, flow-field radiation. An analysis of the
spiers and husson: Rocketborne Spectroradiometer
189
1st I.G.
B.O.
2nd I.G.
B.O.
3rd I.G.
B.O.
4th I.G.
B.O.
5th I.G.
B.O.
BERMUDA
o
D
■
o
?
v
T
?
FIGURE 2. Trajectory for the reentry radiative heat-transfer experiment.
BERYLLIUM NOSE
AND WINDOW
TELEMETRY
MODULE
-SPECTROR AD IOMETER
SENSOR
'.17 INCH DIA. SPHERICAL
ROCKET MOTOR
FIGURE 3. Scout fifth-stage payload.
expected hot-air radiation was made in order to determine the required sensor
range, sensitivity, frequency response, and resolution. The analysis was made using
a theory of hot-air radiation (1) which was derived from laboratory measurements.
This theory gives sufficient indications of the spectral emission of gases at the
temperatures and densities of interest. The expected flow-field gas temperatures
and densities were taken from normal shock data (2) which applies to the hyper-
velocity reentry trajectory. An altitude-versus- velocity curve for the experiment is
190
PHYSICO-CHEMICAL DIAGNOSTICS OB" PLASMAS
360
320
2801-
240
ALTITUDE,
FTxIO" 3 200
160
120
80-
40
5TH STAGE BURNOUT-
BERYLLIUM NOSE MELTS-
_L
4 8 12 16 20 24 28
VELOCITY, FT/SEC x I0~ 3
FIGURE 4. Altitude versus velocity.
32
shown in Figure 4. Radiation from hot air in the altitude range from 350,000 to
150,000 feet was taken as the region of primary interest. Calculations of the spectral
radiation from several of the most intense air constituents were made for the
various temperatures and densities throughout this altitude range. One set of
spectra is shown in Figure 5 for an intermediate altitude. The peaks and inflections
in the upper curve indicate the spectral features due to the ionized nitrogen
molecule's first negative band system. The lower curves are due to two nitric oxide,
NO, band systems. The expected dynamic range of radiant energies is shown in
Figure 6. This curve shows the change in specific intensity, or steradiancy, over the
reentry period for the 3900 A radiation of the NJ(1 — ) band system. The stera-
diancy increases by approximately 7 decades during a 25-sec data period. This
analysis of the flow-field radiation suggests the following sensor design character-
istics. The sensor should provide a spectrum over the wavelength range from 2000
to 6000 A and a total radiation measurement over as wide a wavelength range as
the window transmits. The spectral part of the sensor should have a resolution of
75 A to resolve the expected molecular band spectra. It should record the spectrum
in approximately ^th of a second if a spectrum is to be obtained which does not
change in intensity significantly during the scan. It should be able to detect a
minimum steradiancy of 10 ~ 8 watt/cm 2 -steradian-micron and have a dynamic
range covering 7 decades of radiant energy. In addition to these characteristics,
spiers and h us son: Rocketborne Spedroradiometer
191
ALTITUDE = 280,000 FT ; VELOCITY = 28,500 FT/SEC
GAS TEMPERATURE = 6400 K°
10"
SPECIFIC INTENSITY
WATTS
CM 2 - STERADI AN -MICRON
2000 3000 4000 5000 6000
WAVELENGTH (ANGSTROMS)
FIGURE 5. Specific intensity versus wavelength.
SPECIFIC INTENSITY, 10
WATTS
CM 2 - STE RADIAN-MICRON
10 -
10 -5 10 20 30
TIME AFTER MOTOR BURN OUT (SECS)
i ■ i ■ i i i
400K 300K 20OK IOOK
ALTITUDE-(FEET)
FIGURE 6. Specific intensity versus time and altitude.
7*
192
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
the vehicle configuration suggests the sensor be packaged in a cylindrical volume
no larger than 10 inches in diameter and 6 inches deep. It should not weigh more
than 10 lb.
ENVIRONMENTAL
The environment in which the sensor must operate also affects its design. The
maximum vibrations and accelerations are listed in Table I. The temperature will
vary from 75° to 130°F and the pressure will vary from 1 atmosphere to the
vacuum of space. During the period of reentry the optical window must efficiently
transfer the radiation to the spectroradiometer while being subjected to a peak heat
pulse of 800 Btu/ft 2 -sec.
TABLE I. ENVIRONMENTAL TEST
MAXIMUM LEVELS
TYPE
LEVEL
FREQUENCY
DURATION
DIRECTION -
VIBRATION
1. SINUSOIDAL
2. RANDOM
9 G rms
8 1/2 G rms
500-2000 CPS
15-2000 CPS
105 SECS
110 SECS
LONGITUDINAL
LONGITUDINAL
ACCELERATION
(STEADY STATE)
60 G
6 G
3 MIN
3 MIN
LONGITUDINAL
TRANSVERSE
SHOCK
22 G
5-15 MSECS
LONGITUDINAL
DESCRIPTION OF SENSOR
GENERAL
A sketch of the sensor designed to meet the above requirement is shown in
Figure 7. It consists of a vehicle nose window, an optical monochromator, a
thermistor system, and a photoelectric system. These components are combined
into a single unit which forms the nose section of the fifth-stage rocket.
The hot-gas radiation in the stagnation-point region of the nose passes through a
fused quartz window, the internal surface of which is used as the entrance slit of a
modified Ebert type scanning monochromator (3). The radiation passes through
the monochromator as shown forming a spectrum at the exit slit. The spectrum is
scanned across the exit slit by oscillating the diffraction grating with an electric
motor. The narrow spectral band of radiation that passes through the exit slit
excites the phototube which provides a voltage output to one channel of the tele-
metry system. Part of the radiation passing through the nose window illuminates
the total radiation thermistor detector. This radiation is chopped by a motor-
driven, squirrel-cage chopper. The total range of wavelengths that is transmitted
by the window excites the detector which supplies a voltage output to another
channel of the telemetry system.
NOSE WINDOW
dow is a fused-quartz light pipe 0.020 inch wide, 0.75 incli high, and
spiers and hussos: Rocketborne Spectroradwmeter
193
REFRASIL
CONCAVE MIRRORS
BERYLLIUM
THERMISTOR
a CHOPPER
j DIFFRACTION
GRATING
PHOTOTUBE
-D.C. MOTOR
FIGURE 7. Nose-sensor assembly.
2 inches thick. It is heat sink immersed in a beryllium nose. It is so designed to
survive the extreme heat generated at the nose and to efficiently transfer radiation
to the scanning monochromator and thermistor. It transmits radiation from 2000
to 30,000 A, has a melting point higher than that of beryllium, and excellent
thermal shock characteristics. The 0.020-inch width of the window serves as the
entrance slit width of the monochroniator.
SCANNING MONOCHROMATOR
The scanning monochromator has an//3.3 spherical concave collimating mirror.
The plane reflection diffraction grating has 600 grooves per millimeter and is
blazed for the 3000-A wavelength. The grating is oscillated sinusoidally by a
28-volt d-c electric motor. The grating oscillates at 2.5 cycles/sec, causing the
spectrum to scan across the 0.020-inch exit slit five times per second. The halfpeak
band width of the radiation that passes through the exit slit to the photodetector
is 75 A wide.
PHOTOMULTIPLIER DETECTION SYSTEM
The photoelectric detector used to record the spectral radiation is a photo-
multiplier type 1P28. The electronics used are designed to cover approximately
5 decades of radiant energy. This essentially covers the sensitivity range of the
1P28 from a so-called "wide open" gain condition to maximum attenuation. The
gain or attenuation of the photomultiplier is achieved by electronic feedback
control of the high voltage applied to the photomultiplier. This is a technique
employed in conventional devices to achieve a logarithmic energy response with
194
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
the photomultiplier. However, all functions are achieved with solid-state devices.
A block diagram of the photomultiplier system is shown in Figure 8a. The amplifier
fed by the 1P28 controls the amplitude of the high voltage applied to the 1P28.
In this manner, optimum operating points for the photomultiplier and amplifier
may be chosen. At zero signal condition, 1000 volts are applied to the photo-
multiplier and the applied voltage is related to the energy level of the radiation
input. The output is recorded by monitoring the high voltage through a voltage
divider.
THERMISTOR DETECTION SYSTEM
The thermistor detector is essentially a photoresistive bridge device. Adequate
compression of the output signal, which covers 5 decades of radiant energy, is
achieved by utilizing saturating operational amplifiers. Five operational amplifiers
are cascaded and their outputs are divided by 10 to reduce the voltage; they are
then summed. Logarithmic compression is achieved by permitting each stage to
saturate at an equivalent decade of energy. The last stage saturates at an input
of 0.0001 volt and the first stage saturates at an input of 1 volt, indicating all
states are saturated. Saturated output for each stage is 10 volts. Dividing by 10
and summing each stage, the maximum output for maximum input is 5 volts.
This system was developed as an all-solid-state device. A block diagram of the
system is shown in Figure 8b.
IP28
PHOTOMULTIPLIER
SIGNAL
OUTPUT
AMPLIFIE
200-1000 VOLTS
HIGH VOLTAGE
POWER SUPPLY
(a ) PHOTOMULTIPLIER SYSTEM
THERMISTOR
kj(J>-r— xi?>-T— XI0>^ XO>— r- XI0>
- - - ri
[T ip dp EjQ
SUM ALL INPUTS
(b) THERMISTOR SYSTEM
FIGURE 8. Detector electronics.
SIGNAL
OUTPUT'
H^'Y?^ 0-5 VOLTS
FINAL CONFIGURATION
The spectroradiometer-nose assembly is shown in an assembled and exploded
view in Figure 9. The spectroradiometer is housed in an airtight can which is
purged with dry nitrogen to approximately 20 lb/in 2 pressure to eliminate any
low-pressure problems that might occur in the vacuum of space. All metal parts
spiers axd hussox: Rocketborne. Spectroradwmder
195
EXPLODED VIEW
Uta_
^ ■ -■ ' ■ . * : . ; : -
ASSEMBLE VIEW
FIGURE 9. Flight spectroradiometer.
196
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
fc-
X
13
a.
a.
<8
S
O
w
P
<cro
oujcc
OQ- =
o?5
are anodized or painted black to eliminate as much stray light as possible. Light-
weight metals such as aluminum and magnesium are used where possible to cut
down on the weight of the instrument. The final weight of the spectroradiometer is
10 lb. It is housed in a can 7 inches in diameter and 6 inches deep. The electrical
requirements to operate the spectroradiometer are 28 volts, 250 milliamps, d-c.
spiers and nvssom: Rocketborne Spectroradiometer
197
SENSOR CALIBRATION
CALIBRATION APPARATUS
The spectroradiometer is calibrated with an NBS Standard of Spectral Radiance
(4). This is a ribbon filament tungsten lamp which operates at 6 volts and 35
amperes and is calibrated for spectral steradiancy over the wavelength range from
2500 to 26,000 A. Neutral density niters of the wire screen type and the partially
aluminized quartz type are used to attenuate the standard lamp by known amounts.
The spectral transmission of these neutral density filters was measured with a
spectrophotometer over the wavelength range. The spectral calibration apparatus
is shown in Figure 10.
ENERGY
Figure 11 shows the calibration curve for the spectroradiometer. The voltage
output versus radiant energy input is shown for three different wavelengths of
radiation. There is a change in calibration with wavelength due to nonlinear spectral
response of the spectroradiometer. The minimum energy detectable for the
5r
SENSOR
OUTPUT
(VOLTS)
4358 A
3663 A
10-8
' i i mill Ll ' i null | i i i mil | | I I I llll I I llllll
10-7
10-6
STERADIANCY INPUT
IO"5 |0" 4 I0" 3
WATTS \
\CM 2 - STE RADIAN - MICRON ,
FIGURE 11. Spectroradiometer calibration curve.
spectral detector is approximately 10 " 7 watt/cm 2 -steradian-micron. The 0-5 volt
output represents approximately 4 decades of radiant energy input. The total
radiation thermistor detects a minimum energy of approximately 10 ~ 3 watt/
cm 2 -steradian. Due to the less sensitive thermistor which has no radiation-
collecting optics, the total radiation detector does not begin to record radiation
until the photomultiplier saturates. The thermistor was calibrated using the same
NBS standard by integrating the energy under the spectral steradiancy curve
from 2500 to 30,000 A.
198
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
WAVELENGTH
The wavelength calibration is made for the spectroradiometer by recording a
spectrum of a mercury discharge lamp. A spectrum of the mercury lines is shown in
Figure 12 as recorded by the spectroradiometer during a rocket prelaunch system
SENSOR
OUTPUT
(VOLTS)
6000 4000 2000 2000 4000 6000
WAVELENGTH (ANGSTROMS)
0.1
0.2
0.3
SPECTRAL SCAN PERIOD - SECONDS
FIGURE 12. Hg spectrum as recorded by the spectroradiometer.
check while on the launching pad. This record shows a forward and reverse scan of
the mercury spectrum. The square waves are voltage calibrate pulses at the red
end of each spectral scan. The saw-toothed pulse shown by the dotted line is a
radiant energy calibrate pulse generated by flashing a small tungsten lamp
momentarily at the ultraviolet end of the spectral scan. The voltage and energy
calibrate pulses serve to check the integrity of the system during flight. The dotted
line shows the zero radiant energy input to the spectroradiometer. The approxi-
mately 0.2-volt level is due to instrument noise. The shark-fin appearance of the
intense 2537-A line is due to insufficient frequency response of the system. A
radio-frequency filter was added late in the program to eliminate radio-frequency
noise in the sensor. This, unfortunately, reduced the sensor frequency response
causing the erroneous wave form.
FLIGHT PERFORMANCE
The flight spectroradiometer was launched in the early hours on the morning of
August 23, 1962. The vehicle's third stage malfunctioned causing the fifth-stage
payload to go into a flat, spinning attitude. Consequently, it reentered the earth's
atmosphere at a velocity much lower than predicted. Although the radiative heat-
transfer-measurement objectives of the experiment were not obtained, the flight
evaluation of the spectroradiometer was quite successful. Telemetry records
indicate thai the spectroradiometer operated properly throughout the flight. The
spiers and husson: Rocketborne Spectroradiometer
199
velocity of reentry was not determined but an analysis of the flight records showed
the velocity could not have been greater than 10,000 ft/sec. Therefore, the probable
2000°-3000°K hot-air radiation could not have been detected with the on-board
spectroradiometer. Nevertheless, the ablation of vehicle materials did provide
radiation the sensor could detect. One hundred and eighty-one scans of spectral
radiation were measured during a 31 -sec period. One such recorded spectrum is
shown in Figure 13. This spectrum came from a hydrocarbon flame. Most likely it
came from charring ablator material (refrasil) used on part of the beryllium nose.
An oxy-acetylene flame spectrum is shown with the flight record to show the
similarity. The peaks recorded are the carbon, C 2 Swan, band system, and the CH
molecular band system . The relative intensities of the two band systems are different
for the two records and are due to the different modes of excitation.
FLIGHT RECORD
SPECTRUM
OXY-ACETYLENE
FLAME SPECTRUM
SPECTRAL
STERADIANCY
mm m ro
<? (Dio 1
to m *t ro
C 2 SWAN CH
6000 4000 2000 2000 4000 6000
WAVELENGTH, (A)
FIGURE 13. Comparison of a flight record spectrum with an oxy-acetylene flame
spectrum. (Two adjacent scans of the same spectrum are shown.)
CONCLUSIONS
The flight spectroradiometer sensor performed as expected, recording the
radiations it detected with good fidelity. Not all the design characteristics strived
for in the sensor development were obtained. The spectral resolution was finally
100 A instead of 75 A due to the reduced frequency response. Although the sensor
could detect a wavelength range from 2000 to 6000 A, the energy calibration
below 2500 A was very poor due to insufficient radiation standards below 2500 A.
The final dynamic range of the sensor covered 4 decades of radiant energy instead
of 5. Due to the rocket malfunction, the nose- window design was not tested. The
200 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
window survival problem for hypervelocity reentry radiative transfer measure-
ments is very difficult to solve because no ground facilities are available to re-
produce the heating rates that occur during reentry. There was hope this flight
would provide window survival data for use on future reentry experiments.
The final accuracy in measuring wavelength and radiant energy is as expected.
Wavelength can be measured to +50 A on a final record. The radiant energy
measurements have an uncertainty due to several instrument errors. The calibra-
tion standard lamp has a maximum uncertainty of + 5 per cent. The spectroradio-
meter sensor calibration procedure results in a maximum uncertainty of + 25
per cent. Another error in measuring the voltage output of the spectroradiometer
through the telemetry system is + 2 per cent of the full-scale reading. The maximum
overall uncertainty in measuring the hot-gas steradiancy from a telemetry record
is approximately + 35 per cent.
REFERENCES
1. Keck, James C, Camm, John C, Kivel, Bennett, and Wentink, Tunis, "Radia-
tion From Hot Air. II. Shock Tube Study of Absolute Intensities", Ann.
Phys., 7, 1, 1-38 (1959).
2. Hochstim, A. R., "Gas Properties Behind Shocks at Hypersonic Velocities. I.
Normal Shocks in Air", Convair, Rep. No. ZPh(GP)-002 (January 30, 1957).
3. Foster, W. G., "I. A Small Grating Monochromator, and II. Image Forming
Properties of the Ebert Monochromator", Opt. Soc. Amer., 42, 9 (September,
1952).
■4. Stair, R., Johnston, R. G., and Halbach, E. W., "Standard of Spectral Radi-
ance for the Region of 0.25 to 2.6 Microns", Jour. Res. Nat. Bur. Standards,
64A, 4, 291-296 (1960).
11. M. R. Denison and R. W. Ziemer:
Investigation of the Phenomena
in Crossed-Field Plasma
Accelerators
12? The acceleration of a plasma by means oj a crossed-field accel-
erator is beset by problems which as yet do not have adequate explanations.
The experimentally observed effects include: the sudden drop in thrust
ivith increasing magnetic field strength, extremely unsymmetrical
electrode heating, and lack of acceleration in some closed-channel
accelerators. These problems also have their counterparts in MHD
generators.
In order to obtain a better understanding of the physical phenomena
associated with J x B acceleration, an analytical and experimental
diagnostic study urns undertaken. A primary objective was to determine
and understand the current density distribution in the discharge region.
A theoretical description of the current density distribution in a
constant area J x B channel was developed, including the effects of
both Hall currents and ion slip. Computer solutions for several values
of the Hall parameter
1 + CO^eOi^i
were obtained which exhibited the physically observed characteristics of
high-current density concentrations at the upstream edge of the cathode
and the downstream edge of the anode.
An experimental investigation of the phenomena occurring in a
crossed-field accelerator was conducted using a confined jet-type
accelerator, specifically designed and built for this basic study. The
accelerator employed electrodes which were segmented transversely and
longitudinally to the flow. These segments were electrically insulated,
but at the same potential, and the current through each of the cathode
and anode segments was individually measured.
In addition, electrode side wall potential measurements were made.
Reproducible data were obtained which indicate the magnitude and
distribution of the electric field in the core of the plasma as well as the
ed. note: This work was performed at Electro-Optical Systems, Inc., Pasadena, Cali-
fornia, under sponsorship of the Air Force Office of Scientific Research,
Contract AF 49(638)-1063.
201
202 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
sheath potential drop on each electrode. Physical interpretations and
evaluation of the observed phenomena are given and specific needs for
more detailed diagnostic information are outlined.
INTRODUCTION
The purpose of the program of research discussed in this paper is to obtain a
better understanding of the physical phenomena associated with magnetodynamic
acceleration. Specifically, both the experiments and the analysis pertain to the
phenomena which occur in a steady-state, crossed-field accelerator of uniform cross
section. Pioneering work with such accelerators was carried out by Wood and
Carter (15), and Demetriades and Ziemer (16). Since that time the number of such
accelerators in this country has been steadily growing. It therefore appears that a
closer look at the fundamental process is desirable. Presumably, when the nature
of the interaction between the electromagnetic fields and the plasma is understood
in detail some of the results will be applicable to other types of accelerators (or to
generators), but in particular some of the difficulties encountered with crossed-field
accelerators can be explained. These difficulties include electrode heating, thrust
drop-off at high magnetic fields, and lack of acceleration in some closed-channel
accelerators.
Most of these difficulties are linked to the current density distribution. For
example, it is usually observed that the upstream end of the cathode and the down-
stream end of the anode glow brighter than other spots during the experiments and
that damage due to heating occurs at these spots. Concentration of current might
explain the heating. Furthermore, the general direction of the current is that which
would be caused by the Hall effect. The resultant force vector due to the Hall
effect is therefore at an angle to the direction of the channel. In addition, it is often
argued that at high magnetic field the current density tries to seek a path of lower
back EMF either by going through the boundary layer or by popping out of the
magnetic field which is finite in extent.
In order to obtain some quantitative information on the current density distri-
bution and other phenomena, a systematic series of experiments has been initiated
using a crossed-field accelerator. The diagnostic techniques employed in the first
series of experiments are relatively simple. However, these give very important
information as to the overall problem and pinpoint specific needs for more
sophisticated diagnostics in later experiments.
This paper contains a summary of the first series of experiments which have
been carried out in less than a one-year period. One technique employed for
obtaining information on the current density distribution consists of dividing both
cathode and anode into nine segments. The nine segments are at the same potential
but electrically isolated so that the current through each one can be measured
independently. Another technique consists of side-wall potential measurements.
These experiments are interpreted in light of a "weak interaction theory" which is
summarized in this paper.
EXPERIMENTAL APPARATUS
A low-power, crossed-field (J x B) accelerator was designed for the experimental
study of the phenomena occuring during continuous electromagnetic plasma
acceleration. The system consists of an arc jet plasma source followed by a 1-inch
denison and ziEMER : Crossed- Field Plasma Accelerators
203
square channel in which the plasma is accelerated by perpendicular electric and
magnetic fields. Two water-cooled electrodes with a 1-inch square surface area are
used to pass a current through the plasma normal to the flow direction and normal
to a magnetic field generated by an electromagnet. A schematic diagram of the
apparatus is shown in Figure 1. The arc jet and accelerator system is suspended
-TANK DOOR
VACUUM TANK
MAGNET COIL
ACCELERATOR ANODE
MAGNET YOKE
FIGURE 1. Schematic diagram of crossed-field accelerator experimental apparatus.
from a force measuring balance and is entirely enclosed within a vacuum tank.
The accelerator magnet is mounted to the balance and the arc jet is, in turn,
mounted to the magnet. Attached to the arc jet is a supersonic nozzle followed by
the accelerator channel and electrodes. The nozzle and channel walls are made of
boron nitride and are cooled by radiation. The arc jet mount contains a traversing
mechanism so that the arc jet and accelerator as a unit can be moved back and
forth with respect to the magnet. This feature permits the study of the effect of
204
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
magnetic field symmetry on the discharge phenomena. In addition, the ends of the
magnet polepieces are replaceable so that various magnetic field distributions can
be generated.
As indicated in the Introduction, the apparatus was designed for diagnostic
studies. Current density distributions on the surfaces of the cathode and anode in
longitudinal and transverse directions are measured by using electrodes which are
divided into a number of segments. Each segment is electrically insulated from the
others but is at the same potential. Therefore, by measuring the current through
each segment, a current distribution is obtained. The accelerator electrodes were
divided into nine segments as shown in Figure 2. (More finely divided segments can
be used if greater resolution is desired in future experiments.) A divided electrode
assembly is shown in Figure 3. Each segment is individually water-cooled. The
water tubes conduct the current through each segment and also serve as a current-
measuring shunt. The general experimental arrangement is shown in Figvire 4, and
a rear view of the entire apparatus is shown in Figure 5.
CATHODE
/ '? / a / 9
/
' 4 / 5 / e
/
/ / / 3 / J
ANODE
FIGURE 2. Arrangement and identification of divided electrode segments.
Incorporated into one side wall of the accelerator was an array of nineteen tung-
sten pins for the measurement of the potential distribution. Each pin was 0.040
inches in diameter and was set into a counterbored hole so that electrode material
deposited on the side wall would not contact the pins and disturb the electrical
measurement. The potential was measured with an oscilloscope through a motorized
stepping switch which sampled the voltages at a rate of 20 per second.
In addition to the above measurements, direct measurements of the total
momentum of the system were made. By measuring thrust and gas mass flow,
measurement of effective exhaust velocity can be made. Direct visual and photog-
raphic observations also have been made by use of a mirror placed below the
exhaust jet.
The arc jet is of rather conventional design and can be operated without a
magnetic field to rotate the arc. This is required to avoid interference with the
magnetic field of the accelerator. To increase the range of operating conditions of
,tne arc jet, iu is designed
with an anode nozzle throat section which can be readily
dekisox axi) ziemer: Crossed- Field Plasma Accelerators
205
FIGURE 3. Divided electrode assembly.
replaced. This permits variation of the stagnation pressure and the nozzle area
ratio. The arc jet is designed for a power input of up to 40 kw and a mass flow rate
of 0.1 to 1 grains sec.
To test for any magnetic interaction giving extraneous forces, the arc jet and
accelerator electrodes were short circuited. Then the maximum currents were run
through the arc jet. the accelerator, and the magnet, and the balance output was
observed. A small net force from the arc jet current was observed but its magnitude
was only 1 gram at 300 amps and 0.5 grams at 150 amps which is small for the
thrust forces being imposed on the balance under normal operating conditions.
In addition, the arc jet current is normally held constant for a series of tests. No
206
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
< ->
appreciable force was observed from either the accelerator current or the
electromagnet.
The general experimental procedure when thrust measurements were made was
to first select the arc jet power level, mass flow rate, and vacuum tank ambient
pressure. (The tank pressure was usually set at the level which yielded slight
underexpansion of the flow, normally about 0.8 torr.) The arc jet was then operated
at these conditions and measurements taken of current, voltage, and thrust. Next
the accelerator current was turned on and measurements were taken of accelerator
current, voltage, and thrust. Then, holding the accelerator current constant, the
den iso x am) ziemee : Crossed- Field Plasma 'Accelerators 207
FIGURE 5. Rear view of accelerator and thrust balance mounted on vacuum tank door.
magnetic field was incrementally increased and measurements again taken at each
magnetic field level. Measurements of all variables are observed on panel meters
during the test and simultaneously recorded on a 36 channel high-speed oscillo-
graphic chart recorder for later reduction and evaluation. The frequency response
of the recorder is from 150 to 8000 cps depending upon the particular galvanometers
being used.
SUMMARY OF "WEAK INTERACTION THEORY
In order to attempt interpretation of data it is necessary to have some sort of
theoretical model and description of the process. Much of the early theoretical
work was carried out because it was easy to solve, rather than because it aided in
understanding experiments. Some insight into the performance can be obtained by
means of one-dimensional analysis (1, 2). However, it has not been possible to
apply these treatments to the correlation of experimental data. With respect to
the erossed-field accelerator, the one-dimensional approach is deficient largely
because of fringing electromagnetic fields and the Hall effect.
A striking experimental observation which cannot be explained by means of
one-dimensional analysis is the tendency of the current to concentrate at the
upstream end of the cathode and downstream end of the anode as shown by visual
observation (if bright spots. It appears that at least two-dimensional calculations
are necessary- before proper correlation between theory and experiment can be
obtained.
208 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
An attempt has been made to develop a two-dimensional analysis for accelerators
in reference (3). The analysis developed is specifically for the crossed-field accel-
erator although extension to other geometries is straightforward. It is in the category
of a "weak interaction theory" because it is assumed that the interactions of the
electromagnetic field with the gas through the Lorentz force and the power
addition are both weak. Hence, constant gas properties can be assumed. It is
shown that for constant plasma properties, small magnetic Reynolds number, and
induced field small compared to applied field, the solution of Maxwell's equations
and Ohm's law is reduced to the solution of Laplace's equation for the induced
magnetic field.
The solution of this problem has been obtained in three ways: analytically,
numerically, and approximately. The analytical solution is similar to the work of
Sutton et al. (4, 5) developed for generators. However, the present analysis is for
magnetic field geometries and plasma properties different from those studied
previously. The numerical finite difference method was carried out because it is a
first step toward development of a method for computing a "strong interaction
theory" in which plasma properties vary. The importance of variable properties
has been pointed out by Rosa (5).
ANALYSIS
The generalized expression of Ohm's law (7, 8) which was used is as follows:
j = a [E + qxB]—^jxB+ e °± l jxBxB (1)
This is a somewhat simplified version but it contains the important features of
electron spiraling and ion slip.
Another simplification is to restrict attention to two dimensions. In the case of
the crossed-field accelerator this corresponds to flow between infinite parallel
plates with the direction of the entering fluid in the x direction. Let both the induced
and the applied magnetic fields be in the z direction, perpendicular to the flow
direction. In this way variations in the z direction can be neglected so that
?=; 3 = * 3 = *, = o
In order for the plasma properties to be constant, it is necessary to restrict
attention to the inviscid core of the gas. Even with weak interactions plasma
properties vary across the viscous boundary layers and sheaths adjacent to the
surface.
In the absence of surface currents the magnetic field is continuous across
boundaries. The electric field, however, is not continuous because of surface
charges in the sheaths. For these conditions the boundary conditions for the
electric and magnetic fields are shown as follows:
B = B, | - | B = B,
2
where
_ w = -qxB 1
E x =
E + x = -qxB 2
-oo = -Bi
E x =
B + a> = B 2
B = B, | + |
B = B 2
B x = B n + ^, B 2 -
= B n
denison and ziemer: Crossed- Field Plasma Accelerators 209
The components of Maxwell's equations and Ohm's law in two dimensions are
; -L d J*l i - -±^ (2)
h Mo by J ? Mo ex K)
?*JEx = (3)
i)y 'dx
B x =B y = (4)
bjx = o[E x +vBJ-qj, (5)
bj y = o[E s -uB,]+aj x (6)
where a = u> e r e , 6 = 1 + w i T t uj e T e .
In order to solve these equations, the electric field is eliminated from equations
(5) and (6) by means of equation (3) and the normalized induced magnetic field is
defined as:
B 2(B Z -B )
If the induced magnetic field is small, /x / r /fio2k< 1 , and if the magnetic Reynolds
number is small, i? m =a/i M 1 Z?l, the resulting expression can be reduced to
Laplace's equation for the induced magnetic field:
V 2 B = (7)
The boundary conditions on the electrodes can be obtained from equation (5) when
it is noted that the normal component of velocity is zero on all walls:
8B ? 8B ~ w e r e /e .
— = C -r- where C = - (°)
dy dx 1 + WiT t (u e T e
Once the induced magnetic field is obtained the potential difference can be
determined by means of Gauss's theorem. If the volume is chosen such that the
electrodes are the upper and lower surfaces and the cross section in the x-y plane
is rectangular, then
a
^dydx= -(* + -*_)(* a -*i) (9)
Let x x = -x 2 to make use of the symmetry. Then it can be shown by use of
equation (6) that
(<P + -<J>_) = uB h + — I T B F(C) (10)
n,e
where
F(C) - th LC S{ -~ x * g) dg+c G 2 **? 0) H
- x y
210
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
denison and ziemer: Crossed- Field Plasma Accelerators
211
As mentioned previously, the advantage of the finite difference method is that it
can later be extended to include variable properties and large induced fields since
the character of the equations remains elliptic. Experience in overcoming numerical
difficulties has been gained with this method, and a considerable number of cases
for various values of the parameter C were run.
A typical induced field pattern computed by this method is shown in Figure 6.
Current concentration at the upstream end of the cathode and the downstream
end of the anode even at this modest value of C is evident, in agreement with
experimental observations. It can be shown that when C->oo the solution reduces
to a source and sink at those locations. Note also that throughout much of the
region the current path is straight at an angle given by the electrode boundary
conditions. This suggests a possible approximate solution.
The approximate solution was obtained by assuming that equation (8) holds not
only at the electrodes but in the entire region between the electrodes with the
exception of the points on the electrodes where the gradients become steep. This
is equivalent to assuming the electric field is uniform and is in the y direction over
most of the region between the electrodes. The boundary conditions on the
10'
"T I — I I MM
"1 1 — 1 M!l|
"I I I I II I
ARGON
100 1000 10,000
B (GAUSS)
FIGURE 7. Effect of magnetic field strength on the parameter C for argon at several
temperatures.
212
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
insulator were satisfied at the diagonally opposite corners of the electrodes which
do not have steep gradients. The result is
2(x+Cy)
5=1-
l + Ch
(11)
where I is the electrode length and h is the gap. This approximate solution is very
convenient for estimating the influence of the parameter C on measurable quantities
such as voltage and current density distribution.
HALL PARAMETERS IN ARGON
The Hall parameters ?i e T e jB and w^^B can be obtained from expressions given
by Cann (8, 9) to yield approximately the following:
B = ± e \8m e KT e ) [ 2 +n °*")
~B~ = 4 e \8m (J KTj
(n a + n e ) 2 q ia
(12)
(13)
Cross sections were computed by Ziemer and Cann (10) assuming equilibrium.
From this data the parameter C which is involved in the boundary conditions on
the electrodes can be computed. The results for a pressure of 10 " 3 atmos, which is
approximately the channel pressure used, are shown in Figure 7. At low field
strengths C increases proportionally with respect to the magnetic field. The peak is
3
2
1
1
?
2
3
c =
"e^
-MACHINE COMPUTATION
I3/I-
-- APPROXIMATE
I, /I T , I?/I
2 /i T
I +o) ^T e w i ^"i
FIGURE 8. Distribution of current among electrode segments as a function of the
parameter C.
denison and ziemer : Crossed- Field 'Plasma Accelerators
213
reached when w e T e cancels out and V is inversely proportional to B. Thus the
current should spread out on the electrodes at high magnetic fields. This occurs at
field strengths in the range of the experimental equipment. Although ion-slip
controls in this region it does not follow that the ions do much spiraling; co^tj is
only of the order of 10 -1 . Non-equilibrium effects will shift the peaks because of
the change in the collision time for electrons. It is of interest to determine whether
this spreading out of the current is observed experimentally.
CURRENT DENSITY AND VOLTAGE CALCULATIONS
For comparison with the divided electrode experiments, consider electrodes which
are divided into three parts in the direction of flow with all parts at the same
potential. The current distribution predicted for each segment as a function of the
parameter C as calculated by the numerical analysis is shown in Figure 8. It can be
seen that the approximate solution is rather good. Within the assumptions that
have been made the distribution depends upon C only.
6 r
— MACHINE COMPUTATION
-APPROXIMATE
,_ L± cl
C (l+C)
i/h=l
C =
^e T e
i+ojjTjOvr,
FIGURE 9. Variation of the potential function F(C) with the Hall parameter C.
214
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
TEMPERATURE x 10 , (°K)
FIGURE 10. Hall coefficient for argon as a function of plasma temperature.
The influence of the current density distribution on the voltage is reflected in
the function F(C) of equation (10). Computation of F(C) for various values of x 2
is a check on the numerical calculations since the results should be independent of
x 2 . This was found to be true. A plot of F(C) is given in Figure 9. It can be seen that
again the approximate solution compares well with the machine computations.
Note that at values of C greater than unity F(C) itself approaches unity. Thus the
only dependence of the potential difference on plasma properties is through the
term \jn e e. This quantity is a strong function of temperature if equilibrium condi-
tions occur as Sue
. ill X it
10. At low values of C, F(C) is inverselv nronortional
denison and ziemer: Crossed- Field Plasma Accelerators
215
to C so that the magnetic field cancels out of the second term or the right-hand side
of equation (10). At low field strength under these conditions this term represents
the scalar resistance of the plasma. These results will be referred to later when side-
wall potential measurements are discussed.
EXPERIMENTAL RESULTS
PERFORMANCE
To aid in the interpretation of the current density and side- wall potential
measurements and relate them to the accelerator operating conditions, the gross
performance characteristics of the arc jet and accelerator should be known. In
particular, it is important to know the effective plasma velocity and the velocity
increment imposed by the accelerator.
Measurements were made of thrust with the force balance from which the
apparatus was suspended and of the gas mass flow rate. In order to accurately
determine the plasma velocity, measurement was also made of the channel exit
and vacuum tank static pressures, and the velocity was computed from the
relation
T = mu 2 +(P 2 -P 3 )A 2
in which subscript 2 refers to the channel exit and 3 refers to the ambient conditions.
The results are shown in Figure 11 for the standard operating conditions of the
arc jet.
From this data at various tank pressures with the arc jet alone operating and
the accelerator channel present, the average exhaust velocity was determined. It
was found to be 1000 to 1250 meters/sec, depending upon the mass flow rate and
"*-,.
i 1
?
? ""^w^
40
m = 325 GM/SEC
1=250 AMPS
W 30
o
-
<n
| 2
-
-
10
^""-"-^I i
1.0 2.0 3.0
TANK PRESSURE, T0RR
FIGURE II. Measured thrust of arc jet with accelerator channel in place as a function
of vacuum tank pressure.
8 +
216 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
power input. The higher figure corresponds to the conditions of the diagnostic
experiments.
Measurements were also made of the velocity increment resulting from the
J x B acceleration at conditions close to those for the subsequent studies. At an
argon mass flow rate of 0.147 gm/sec and an arc jet power input of 3 kw, an arc
jet thrust of 15.7 gm was obtained. Then operating the accelerator, a thrust ratio
of up to 2.6 was obtained for a current of 62 amps and a magnetic field strength of
3450 gauss.
In later tests when the prime objective was current distribution or wall potential
measurements, thrust measurements were not repeated in order to simplify the
experiment. In this series of runs, the standard operating conditions for the arc
jet were:
Gas Argon
Mass Flow Rate 0.325 gm/sec
Power Input 5 kw
Total Pressure 145 mm Hg
Throat Area ~ 0.11 in 2
Channel Pressure 1 .0 mm Hg
Gas Velocity 1250 m/sec (from thrust)
DIVIDED ELECTRODES
A pair of divided electrodes was constructed for use in the crossed-field accel-
erator to measure the current distribution over the cathode and anode surfaces ; each
electrode was divided into nine segments. All segments of an electrode were at the
same potential but electrically isolated so that the current through each segment
could be measured independently. One of the divided electrode assemblies is shown
in Figure 3. The segments used in these first tests were water-cooled copper,
insulated by an epoxy potting material. The numbering system for the segments
used in describing the test data was shown in Figure 2.
The plasma source (arc jet) for these tests was run at a constant mass flow rate
of argon of 0.325 gm/sec with a power input of about 5 kw yielding an average
velocity of 1250 meters/sec. The accelerator was operated at a constant current of
50, 100, and 150 amps, and the applied magnetic field strength was varied
incrementally from zero to 3400 gauss.
CATHODE DISTRIBUTION
The observed current distributions in general were unstable and sometimes
oscillatory. More specifically, with no applied magnetic field, the cathode current
was carried entirely by one segment, indicating a concentrated cathode attachment
point. However, the cathode segment which carried the entire current was not
always the same. The attachment point would be on one segment and then
"instantaneously" jump to another segment, remain there for several tenths of a
second or longer and jump to another segment. On some runs, the current would
remain on one segment and not move for the duration of the test run. As the
magnetic field was increased above 500 gauss, secondary discharges began to
appear on other segments for durations of about 0.01 seconds, but still with the
intermittent migration of the primary discharge region. At about 3000 gauss, the
current became distributed over as many as four or five segments but still with
short periods during which one segment carried the total current. In addition, the
amplitude of the current waveform for each participating segment appeared to take
denison and ziemer: Crossed- Field Plasma Accelerators
217
on the character of a random fluctuation. At these higher field strengths, there was
a tendency for the cathode spots to confine their migration to the upstream seg-
ments. The general appearance of the discharge was considerably more steady with
a magnetic field than without one.
The reasons for the observed current density distribution are as yet unknown. It
is believed that the cathode distribution may be controlled by the cathode emission
mechanism and that its behavior and cause is similar to that for other d-c arc
cathode spots (without transverse flow and an applied magnetic field); this
phenomenon is still not fully understood. One explanation for cathode spot migra-
tion is that the deposit or formation of a low work function material on the
cathode surface such as an oxide occurs and the cathode spot moves to this region.
Very rapidly this film is removed or destroyed and the cathode spot moves to a
new portion of the film. This phenomenon occurs at a rate such that the cathode
spot migrates over the cathode surface in a rapid and apparently random manner.
Future tests will be run with tungsten electrodes instead of the copper ones used in
these tests to determine if any effect can be attributed to the electrode material.
ANODE DISTRIBUTION
The character of the current distribution on the anode was quite different from
that of the cathode. In general, the distribution measured on the anode was stable
and more consistent among several runs. With no magnetic field, the current was
carried predominantly by the trailing edge segments, 3, 6, and 9, but with some
transverse asymmetry. There were a few runs, however, in which the current was
carried largely by the center and upstream segments. As the magnetic field was
increased, the current tended to concentrate on the three trailing edge segments as
to 4
THEORETICAL- NO ION SLIP
THEORETICAL— WITH ION SLIP
? EXPERIMENTAL 1= 20- 155 AMP
_L
1000 2000
APPLIED MAGNETIC FIELD, (gauss)
3000
FIGURE 12. Comparison of theory and experiment for the fraction of current carried by
the downstream third of the anode as a function of applied magnetic field strength.
218 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
predicted by theory. Above 700 gauss, the current was carried entirely by the
trailing edge segments and the distribution among these three was uniform. Only
very rarely was there observed any instability in the anode current distribution.
When it did occur, the duration was about 0.05 to 0.2 seconds and then the previous
stable distribution was re-established.
The anode current carried by the trailing third of the electrode, / 3 //r> i s compared
with theoretical predictions in Figure 12. The theoretical predictions make use of
the machine calculations for I 3 jI T as a function of C (presented previously in
Figure 8) as well as equilibrium values of C for argon (which were presented in
Figure 7). For the curves labeled "no ion slip" it was assumed that the cross section
for ion-atom collision is sufficiently large to eliminate ion slip effects. Of all the cross
sections used for the equilibrium calculations, this one is the least reliable. It can
be seen from Figure 12 that the data agrees qualitatively with the predictions for
"no ion slip" but with erratic behavior superimposed. No evidence was obtained
of the current spreading out at high magnetic fields. This may be due to a faulty
cross section for ion-atom collisions, or it may be that non-equilibrium conditions
control. Independent measurement of plasma properties such as electron number
density, electron temperature, and gas temperatures would shed some light on this
question.
Much remains to be done with divided electrode measurements themselves. So
far there is little data between 1000 and 3400 gauss. It is planned to carry out
additional experiments in this region with tungsten electrodes instead of the copper
ones used in these experiments. Hopefully, more reproducible data, which may
permit more conclusive interpretation, can be obtained with such electrodes.
WALL POTENTIAL MEASUREMENTS
In order to obtain further correlation with theory, and in order to gain insight
as to the behavior of the plasma, the potential distribution on the accelerator
side wall was measured. If no appreciable current flows normal to the insulator
side wall, the wall potential is indicative of the local plasma potential. This
technique is similar to that employed by Louis et al. (11) for the generator.
A set of 19 tungsten pins was imbedded in one side wall of the accelerator, flush
with the inner surface. The arrangement is shown in Figure 13. The pins were
connected through a 2 pole stepping switch to a 502 Tektronix oscilloscope with a
10 megohm input impedance for voltage readout. With this system, the potential
of the various pins was sampled and displayed two at a time with a sampling speed
of 20 pairs per second. The oscilloscope display of two complete cycles was recorded
photographically.
The first experiment to obtain the wall potential distribution was run with
solid (not divided) water-cooled copper electrodes. After several series of tests, it
was discovered that copper sputtered from the electrodes was depositing on the
wall and was electrically interconnecting the pins. This resulted in very strange
potential profiles. Even attempts to clean the wall after each test point failed to be
adequate.
In order to eliminate this effect, two changes were made. First, the copper
electrode surfaces were capped with a sheet of tungsten 0.060-inch thick to reduce
the amount of material sputtered on to the wall; tungsten has a very low sputtering
rate compared to copper. Secondly, the wall was counterbored at each pin so that
the pin would not be in contact with the inner surface of the wall. If metal deposi-
tion did occur, the film could not easily bridge across to the tungsten pin insert.
denison and ziemeh: Crossed- Field 'Plasma Accelerators
219
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The above modifications proved successful and consistent measurements were
obtained in subsequent tests.
The arc jet was operated at 5.2 kw input with an argon flow rate of 0.325 gm/sec.
The accelerator was run at a constant current of 25, 50, and 100 amps with the
magnetic field varied from zero to 5000 gauss. The measured wall potential for the
50-amp runs are plotted in Figures 14 to 16 as a function of the applied magnetic
field strength for the distribution in the direction of the applied electric field at the
upstream, middle, and downstream regions. The distribution normal to applied
electric field is plotted for regions near the cathode (upper set), the mid-plane, and
near the anode (lower set) in Figures 17 to 19. The effect of varying the current is
indicated in Figure 20.
220
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
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FIGURE 17. Measured potential distribution along plane near cathode, / = 50 amps.
ELECTRIC FIELD IN INVISCID CORE
The electric field in the inviscid core can be estimated from the slope in the
central portion of the date presented in Figures 14 to 16. This is presented in
Figure 21. It can be seen that there is no systematic variation in the data from
leading edge to trailing edge. Furthermore, there is no systematic variation with
applied current. Although there is scatter in the data, the reproducibility is very
good. An average curve (almost a straight line) is plotted. The value of E/B from
this line is approximately 6400 m/sec. Data from the total electrode potential is
shown for comparison in which the field strength is determined by subtracting a
constant electrode voltage drop of 20 volts and dividing by the electrode spacing.
This data gives an equivalent value of E/B which is still higher. The difference is
due to the effect of the magnetic field on the boundary layer or sheath potential
drops which will be discussed later.
8?
224
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
MIDDLE SET
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FIGURE 18. Measured potential distribution along middle plane, I = 50 amps.
From thrust measurements with pressure correction made with the arc jet
connected to the accelerator section but with no second discharge, the velocity at
the accelerator entrance, u , is 1250 m/sec. The average velocity in the accelerator
can be expressed as
BIh
if all of the Lorentz force is imparted to the gas. This is equivalent to a velocity of
2080 m/sec at 4000 gauss. Even with this correction, the velocity is far below that
corresponding to the indicated value of EjB.
An additional increase in core velocity due to boundary layer effects can be
introduced. It can be shown that for a square channel the thrust with the pressure
correction divided by the mass flow is
T' /, 40\
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denison and ziemer: Crossed- Field Plasma Accelerators
225
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FIGURE 19. Measured potential distribution along plane near anode, / = 50 amps.
TRAILING EDGE
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current, but constant magnetic field strength.
226
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
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APPLIED MAGNETIC FIELD ,{ gauss)
FIGURE 21. Measured electric field strength as a function of applied magnetic field.
where u c is the core velocity, h is the electrode gap, and 9 is the boundary layer
momentum thickness. It can be seen that if the momentum thickness becomes as
large as 10° of the gap, an error of close to a factor of two in estimating the
velocity is possible when total thrust and mass flow are used.
An estimate of the momentum thickness can be obtained from hypersonic
boundary layer theory from which
9 0.664
x Be 112
This has the same form as the incompressible relation but the Reynolds number
should be based on core properties. .For a length, x, of 2 inches and a viscosity for
denison and ziemer : Crossed- Field Plasma Accelerators 227
equilibrium argon (12) at about 8000°K, the Reynolds number turns out to be
about 100. Hence, a value of on the order of a tenth of an inch is reasonable. The
core velocity could then be increased by a factor of 1.7.
An alternate method of estimating the velocity in the accelerator section is from
the power input to the arc jet and the mass flow. Under the conditions mentioned
previously for these tests, and an estimated efficiency of 30%, the power into the
gas represents a total enthalpy of h T IRT — 85. The corresponding measured total
pressure is P r ^0.19 atmos. Under these conditions the equilibrium degree of
ionization in the chamber is only 1%. Therefore, modest supersonic Mach numbers,
and a vacuum velocity of about 3000 m/sec, would be achieved. Use of the measured
pressure in the accelerator section of 1 mm Hg with the measured total pressure
leads to an accelerator inlet Mach number of 4.3. The area ratio would give the
same results if the channel area were reduced by a displacement thickness of 6%
for each side. This is not an unreasonable value of 8* for a highly cooled boundary
layer. This method, therefore, leads to velocities considerably closer to EjB.
However, due to the nature of the arc column and the geometry of the arc head,
the stagnation conditions are not accurately known.
The remaining portion of EjB may be explained by the resistance of the plasma
including the influence of the Hall effect. In the analysis it was shown [equation
(10)] that
— = u + — Tg F(C) (note that I T = Ijk)
For the Hall parameter C greater than unity, F(C) is approximately unity. For a
current of 50 amps at a gas temperature of 8500°K the second term would be as
high as 4000 m/see if the gas were in equilibrium, or as low as 450 m/sec if fully
ionized. Such a temperature is not unreasonable considering the energy input to
both arcs.
It is interesting to note that in spite of considerable thermal and kinetic energy
addition, there was no detectable variation in the electric field from the leading
edge to the trailing edge of the electrodes. It is possible, of course, that a significant
fraction of the current is shunted around this portion of the core through the
electrode boundary layers. This would reduce the value oil in the above expression
so that the same value of the second term would correspond to a lower value of n e .
The lack of a strong variation with applied current would seem to indicate non-
equilibrium conditions if the electric fields observed are due to plasma resistance.
Under equilibrium conditions the variations of l/n e e are exponential (Figure 10)
with the changes in temperature which would result from changes in power input.
In order to obtain a more complete understanding of the data, it is obvious that
further measurements are required. Direct measurement of velocity, temperature,
and electron number density in the accelerator is desirable. In addition, non-
equilibrium calculations along the lines of Kerrebrock's analysis (13) or that of
Russell et al. (14) may help to explain the results. However, quantitative compar-
ison cannot be expected since these theories are still not valid to closer than a
factor of 10.
ELECTRODE VOLTAGE DROPS
From the wall potential measurements, the voltage drops near the surface of the
cathode and anode can be determined. These voltage drops, which are due to
electrode surface, electrode sheath, and cold boundary layer phenomena, are
observed as regions of high electric field between the plasma core (where the electric
field is constant) and the electrode surface.
228
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
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denison and ziemeb: Crossed- Field Plasma Accelerators
229
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230 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
From Figures 17 and 19 it can be seen that, except for a few anomalous points,
the potential along the electrodes is relatively constant. Thus the condition imposed
in the analysis that for the inviscid region the potential is uniform along the
electrodes appears to be justified, especially along the cathode.
It is observed that, with no magnetic field, the cathode drop is about 8 volts and
the anode drop about 12 volts. As the magnetic field is increased, the electrode
drops increase in the manner shown in Figures 22 and 23. At 5000 gauss, the cathode
drop is about 25 volts and the anode drop is 50 volts.
Another interesting effect can be seen in Figures 14, 15, and 16. The thickness of
the cathode drop region is constant. However, the anode sheath and boundary
layer thickness increases at the center and trailing edge planes at about 2000 gauss
and above. One possible explanation for this effect is that the Hall component of
the Lorentz force, which is in the direction normal to the flow and the applied
magnetic field, forces the gas away from the anode and towards the cathode. This
pressure gradient across the stream would tend to compress the boundary layer
on the cathode and thicken it on the anode. The voltage drop is further increased
by a reduction of effective electrical conductivity in the boundary layer due to the
Hall effect which can become very large in the cooler gas. Hence, the voltage drop
across the boundary layer would tend to increase with increasing magnetic field
strength.
The existence of these large electrode drops, particularly at the higher magnetic
field strengths, represents a very large loss mechanism which is very detrimental to
the overall accelerator efficiency.
CONCLUSIONS
The simple diagnostic techniques employed in these experiments have yielded
interesting information about the behavior of the accelerator and qualitative
correlation with theory.
Current concentration at the leading edge of the cathode and the trailing edge
of the anode was confirmed with the divided electrodes in agreement with theory
and visual observation. There was no evidence of the current spreading out at high
magnetic fields as would occur if ion slip controls.
Reproducible data were obtained from side wall potential measurements. The
magnitude of the electric field in the core cannot be explained by the back EMF
alone. The resistance of the plasma appears to have a significant effect on the
observed potential. The electric field was observed to be uniform from the leading
edge to the trailing edge of the electrodes. Variation of the applied current by a
factor of four had little effect on the core electric field. The anode sheath potential
drops, on the other hand, increased with current but this was compensated by a
reduction in cathode sheath drop. The magnitude of the sheath or boundary layer
potential increased significantly with magnetic field. The potential along the
electrodes at the edge of the boundary layer was relatively constant.
Although a considerable amount of information has been obtained with these
simple diagnostic methods, and much remains to be done with these and similar
techniques, the need for more sophisticated diagnostic tools has been demon-
strated. Detailed information on electron density, electron temperature, gas
temperature, and gas velocity would be very helpful in explaining the results. It
appears that the phenomena which occur in such accelerators are sufficiently
complex that a combination of diagnostic tools along with a realistic theory are
required in order to obtain quantitative correlation and more complete under-
standing of the physical processes.
denison and ziemeb: Crossed- Field Plasma Accelerators 231
NOMENCLATURE
a
Hall parameter, defined in equation (6)
b
Hall parameter, defined in equation (6)
B
Magnetic field strength
Bo
Applied magnetic field
B
Dimensionless induced magnetic field
C
Hall parameter, defined in equation (8)
e
Electronic charge
E
Electric field strength
h
Channel height
It
Total current per unit height
3
Current density
K
Boltzmann's constant
I
Electrode length
m e
Mass of electron
?"(
Mass of ion
n a
Number density of atoms
n e
Number density of electrons
P
Pressure
q
Velocity
tfea
Electron-atom cross section
9ei
Electron-ion cross section
?io
Ion-atom cross section
T e
Electron temperature
T t
Ion temperature
U
x component of velocity
V
y component of velocity
w
s component of velocity
X
Distance along channel
y
Distance across channel in direction of electrodes
z
Distance across channel in direction of normal to electrodes
Mo
Permeability of free space
p
Density
a
Electrical conductivity
Te
Mean free time for electrons
T i
Mean free time for ions
<}>
Electrical potential
">e
Gyration frequency for electrons
a>;
Gyration frequency for ions
ACKNOWLEDGMENTS
The authors would like to thank Professor E. Zukoski of the California Institute
of Technology for many valuable discussions.
REFERENCES
1. Resler, E. L., and Sears, W. R., "The Prospects for Magnetoaerodynamics",
J. Aero. 8c, 25, 4, 235 (1958).
2. Kerrebrock, J. L., and Marble, F. E., "Constant Temperature Magnetogas-
dynamic Channel Flow", Reader's Forum, J. Aero j Space Sci., 25, 1, 78 (1960).
232 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
3. Denison, M. R., "A Two Dimensional Weak Interaction Theory for Crossed
Field Accelerators", Electro-Optical Systems RN-12 (April, 1963).
4. Sutton, G. W., "End Losses in Magnetohydrodynamic Channels with Tensor
Electrical Conductivity and Segmented Electrodes", J. Appl. Phys., 34, 2, 396
(1963).
5. Hurwitz, H., Kibb, R. W., and Sutton, G. W., "Influence of Tensor Conduc-
tivity on Current Distribution in a MHD Generator", J. Appl. Phys., 32,
2, 205 (1961).
6. Rosa, R. J., "Hall and Ion-Slip Effects in a Non-uniform Gas", Phys. Fluids,
5, 1081 (1962).
7. Cowling, T. G., Magnetohydrodynamics (New York: Interscience, 1957).
8. Cann, G. L., "Energy Transfer Processes in a Partially Ionized Gas", Cali-
fornia Institute of Technology — Hypersonic Research Memorandum No. 61
(June 15, 1961).
9. Cann, G. L., Teem, J. M., Buhler, R. D., and Branson, L. K., "Magnetogas-
dynamic Accelerator Techniques", AEDC-TR-62-145 (July, 1962).
10. Ziemer, R. W., and Cann, G. L., "A Steady State Hall Current Accelerator",
First Quarterly Progress Report, Electro-Optical Systems Report 3160-1Q
(September 15, 1962).
11. Louis, J. F., Lothrop, J., and Brogan, T. R., "Studies of Fluid Mechanics
using a Large Combustion Driven MHD Generator", RR 145, AV CO -Everett
Research Laboratory (March, 1963).
12. Baum, E., "Transport Properties of Argon" (unpublished).
13. Kerrebrock, J. L., "Non-Equilibrium Effects on Conductivity and Electrode
Heat Transfer in Ionized Gases", California Institute of Technology —
Guggenheim Jet Propulsion Center TN No. 4 (November, 1960).
14. Russell, G. R., Byron, S., and Bortz, P. I., "Performance and Analysis of a
Crossed-Field Accelerator", paper presented at AIAA Electric Propulsion
Conference, Colorado Springs, Colorado (March 11-13, 1963), AIAA preprint
63-005.
15. Wood, G. P., and Carter, A. F., "Consideration in the Design of a Steady DC
Plasma Accelerator", in Dynamics of Conducting Gases (Evanston: North-
western University Press, 1960).
16. Demetriades, S. T., and Ziemer, R. W., "Energy Transfer to Plasmas by
Continuous Lorentz Forces", in Magnetohydrodynamics, Proc. of the Fourth
Biennial Gas Dynamics Symposium (Evanston: Northwestern University
Press, 1960).
12. Alan F. Klein: A Survey of
Optical Interferometry as
Applied to Plasma Diagnostics
12 The principles and techniques involved in the application of
optical interferometry to plasma studies are reviewed. The assumptions
and accuracy of the theoretical calculations art summarized. Experi-
ments to date in the field are reviewed, and recent experiments at
Aerospace Corporation are described in which monochromatic inter -
ferograms about two-dimensional, sharp and blunted bodies have been
obtained using an image converter camera and an exploding voire light
source. Resolution times down to 20 nanoseconds have been obtained
while maintaining a conventional field of view. Using the multiple
frames provided by the image converter camera, the flow fields have
been studied as a function of time. White-light color interferograms of
these flows have also been obtained at exposure times of 50 nanoseconds
using a recently developed Kerr cell.
INTRODUCTION
The technique of optical interferometry has long been used in fluid mechanics
and gas dynamics to measure gas density in nonionized flows in wind tunnels and
shock tubes (1). However, not until the experiments of Alpher and White (2, 3, 4)
was it successfully demonstrated that interferometry at optical wavelengths could
be used to measure electron densities in plasmas.
Optical interferometry, as considered here, depends upon changes in the index
of refraction of the test gas. In previous applications, when there were no changes
in the chemical composition of the gas, the change in the index of refraction was
just due to changes in the gas density. In the present application to plasma
diagnostics, the change in the index of refraction is due to both neutral and
charged particle-density changes. It will be seen that, usually, the only charged
particle of importance in determining the index of refraction of the test gas is the
electron. Under most conditions the interferograms reflect contributions due to
both the neutral particles as well as the electrons, and additional techniques are
required for separating the relative contributions. However, under some conditions,
the changes in the index of refraction due to all but the electrons are negligible and
the resulting interferograms then represent a direct mapping of the electron
density in the flow field.
ed. note: Mr. Klein is with the Aerospace Corporation, El Sequndo, California. This
work was sponsored by the U.S. Air Force under contract No. AF04(695)-
269.
233
234
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
The essential features of the optical system typically used in this work are
indicated in Figure 1. The interferometer is of the Mach-Zehnder type, consisting
of two fully-silvered mirrors, denoted by M, and two half-silvered mirrors, known
as beam splitters, and denoted by S. Light from the light source is collimated by the
lens L 1; and the parallel beam of light enters the interferometer and is divided into
TEST SECTION
COMPENSATING
CHAMBER
FIGURE 1. Schematic of optics.
two beams of equal amplitude by the first beam splitter. One beam passes through
the test section and the other through a compensating chamber which compensates
for the optical thickness of the test section windows and for the gas initially in the
test section. At the second beam splitter the beams are recombined. The recom-
bined beams are then focused onto the film plane of the camera by the lens L 2 .
Details of the construction and operation of such an interferometer are presented
in reference (1).
Consider now the situation in which the collimated beam of light is a mono-
chromatic beam of wavelength A. If the optical lengths of the two beams are the
same, and if the mirrors and beam splitters are all parallel, then the two beams will
be in phase over the whole field when they recombine, and they will interfere
constructively to produce a uniformly bright field. If the mirrors and beam splitters
remain parallel, but the optical length of one beam is increased or decreased by
A/2 with respect to the other beam, then they will interfere destructively upon
recombining and the field will be uniformly dark. If the optical lengths of the paths
are the same, and one of the mirrors is rotated slightly, a linearly- changing path
difference will be introduced across one beam relative to the other and, upon
recombining, there will be alternate constructive and destructive interference,
resulting in what is referred to as the initial or undisturbed fringe pattern. If a
plasma is now introduced into the test section, further phase differences are
introduced between the test and reference beams, causing fringe shifts relative to
the undisturbed fringe pattern. These fringe shifts are just proportional to the
change in index of refraction due to the presence of the plasma.
As is evident from Figure 1, changes in the index of refraction will be integrated
across the width of the test section, and if local flow properties are to be obtained,
it is necessary that properties be constant in this direction. Axisymmetric flows
can also be treated, but the data reduction then involves an integral transformation.
In addition, boundary layers, through which the test beam passes, are developed
klein : Optical Interferometer Plasma Studies 235
at the walls and, under some conditions, these boundary layers can produce
nonneghgible effects. Notice, too, that at the second beam splitter half of the
recombmed beam passes vertically out of the interferometer. This beam is generally
not used, although in principle it could be.
THEORETICAL DISCUSSION
The theoretical aspects of both monochromatic and white-light interferometry
have been discussed in detail in the literature (3, 4, 5). Aspects of the theory of
monochromatic interferometry are summarized in this section, with recent addi-
tions to the theoretical picture included. Differences between monochromatic and
white-light interferometry are discussed in a later section. Emphasis is placed on
the case of shock-heated hydrogen, as this is particularly germane to the experiments
that will be described in the next section.
The shift, S (in units of fringe spacing), of a fringe with respect to an undisturbed
fringe is given by
S = A(n-l)LIX (1)
where n is the index of refraction (the velocity of light in vacuo divided by the
velocity of light in the test gas), L is the thickness of test gas traversed, and A is the
monochromatic observing wavelength. The quantity (?- 1) is the refractivity, and
the fringe shift is proportional to A(ra - 1), or the change in refractivity with respect
to some reference value.
If one considers the situation where a test section is initially filled with an
undisturbed gas at room temperature and at some ambient pressure, and, at some
later time, is filled with a plasma (for example, produced by the passage of a strong
shock wave), then the fringe shift will be given by
? = [(?-1U??-(i?-1)o]?/A (2)
where the subscript refers to the gas initially in the test section.
The plasma refractivity can be made up of several components,
(?-l)plasma = (?~ Va + (?~ 1) M + (? — 1), + (w- l) e + ? ? ? (3)
The subscripts A, M, and / refer to atoms, molecules, and ions, respectively, in the
ground state, and e refers to electrons. In addition, there may be contributions
from such things as excited states. Any contribution from excited states will be
neglected here; the justification is given in the next paragraph. In the following
paragraphs each of the contributors to the plasma refractivity in equation (3) is
considered briefly; its significance in particular examples is alsodiscussed.
For atoms and molecules, the refractivity is given by
( n ~ 1 )a.u = 2nN AM a AM (4)
where N is the number density of the molecular or atomic species and a is its
polarizability. The polarizability is related to the separation between bound charges
or the dipole moment, which can be induced in the atom or molecule per unit
applied electric field. The larger the induced dipole moment, the more the test
beam is retarded in passing through the medium, and the larger the phase difference
between the test and reference beams when they are recombined. The polariz-
ability is a function of wavelength, but in most cases there is little difference between
the polarizability at optical wavelengths and the d-c or infinite wavelength
polarizability. This is because optical frequencies are still small compared to the
natural atomic frequencies. Table I contains values of the refractivity for molecular
236
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
hydrogen at standard temperature and pressure (S.T.P.) for several wavelengths (6).
The results of some recent calculations of the refractivity of atomic hydrogen in
the ground state (7) are also tabulated. Although the polarizability of an excited
state of an atom, molecule, or ion is expected to be larger than the corresponding
species in the ground state, the number density of particles in these excited states
is generally so low that the contribution of these particles to the plasma refractivity
can be neglected.
TABLE I. HYDROGEN REFRACTIVITIES
Refractivity
Wavelength (A)
oo 5870 5401
(n-l) H2 xlO*
(n-l) H xl0 4
1.358 1.388
1.132 1.173
1.392
1.179
Due to the lack of accurate values, most experimenters have assumed that, for
hydrogen, the molecular and atomic refractivities are equal. Table I indicates
there may be nonnegligible differences. Further experimental work is necessary to
establish the validity of these differences. Infinite-wavelength polarizabilities for
many atomic and molecular gases of interest are tabulated on page 86 of Allen (6).
The refractivity of the free electrons is calculated from dispersion theory. For
an electron gas in which the electron-heavy particle collision frequency is much less
than the observing frequency, the index of refraction is given by
?i z = l-
lh
(5)
where to 2 , = 4^ ' e e\M e is the square of the plasma frequency, and is the observing
frequency. N e is the number density of free electrons, c the electronic charge, and
M e the electron mass. Since a^/a> 2 ?l for optical frequencies and for the electron
density range of 10 15 to 10 18 cm -3 , one can write
(n-l)e
-27rN e e 2
(6)
Putting in the appropriate constants,
(?-l), = -4.46x10 ""A 2 iV e (7)
From equation (7), the contribution to the plasma refractivity of the free electrons
is seen to depend only upon the wavelength and the electron number density,
independent of the ambient gas. At a wavelength of 5461 A, with a test-section
thickness of 7.6 cm., from equations (1) and (7) it is seen that a shift of 0.1 fringe
widths, due to electrons, corresponds to an electron density of 5.4 x 10 15 cm -3 .
Since a fringe shift of 0.1 fringe is considered a reasonable lower limit on the
sensitivity of the technique, this places a lower limit of approximately 10 15 cm" 3
on the electron number density that can be measured with optical interferometry.
It is possible to increase the sensitivity to 0.01 fringes and measure still lower
electron densities (8).
For the case of the ions, both calculations and experiments are more difficult.
It can be generalized that calculations and experiments are more difficult any time
the state of the gas requires high temperature (e.g., ions and dissociated molecules).
For argon, the ratio of the polarizability (hence the ratio of refractivities) of the
kleix : Optical, Interferometer Plasma Studies 237
argon ion to the argon atom has been calculated by approximate quantum
mechanical techniques, yielding a calculated value of 0.7 (3, 5). The accuracy of
this value is questionable, but it is the best available. Since the value is of the same
order as the atom value, the usual practice has been to set them equal.
Since the fringe shift is proportional to the number density and since the electron
refractivity, per particle, is generally much larger than the atom and ion refrac-
tivity, setting the ion polarizability equal to the atom polarizability results in
no significant error, because the electron number density is always at least as
large as the ion number density. In the case of hydrogen this uncertainty does not
exist. The hydrogen ion, being a proton, is treated as an electron with a positive
charge and a different mass. From equation (6), the electron refractivity is inversely
proportional to the mass, so the ratio of electron refractivity to ion refractivity will
be equal in magnitude to the ratio of proton mass to electron mass (approximately
10 3 ). The hydrogen ion refractivity is therefore completely negligible, since a free
electron is always created with each ion.
Returning to the fringe shift equation (2) and inserting the appropriate expres-
sions, one obtains
[(2 27^-4.46 x 10-"A 2 iO -2^ a | j
S= \lZ^ZTTlV l a;—i.'MixW- l *X' i N_l — 9*7V-?-\- (8)
where the subscript i refers to the uh atomic, molecular, or ionic species in the
plasma. The second term on the right of equation (8) is the free electron refrac-
tivity; the third term represents the refractivity of the reference gas (subscript 0).
The density of free electrons in the reference gas is assumed to be negligible.
Consider now the case realized in the experiments to be described in later
sections, where the undisturbed gas is room-temperature molecular hydrogen, and
the plasma is generated by the passage of a strong shock wave. The plasma will
then consist of free electrons, protons, and atomic hydrogen. It is assumed that
the shock waves are strong enough to fully dissociate the hydrogen molecules.
Using the infinite wavelength refractivity values of Table I, equation (8) becomes
S = -? [(4.21 x 10- 25 A t h-4.46 x 10 ""^A 8 )- 5.06 x 10~ 25 N H2 ] (9)
where the protons have been neglected. The relaxation time for dissociation is
much shorter than that for ionization, and short enough that dissociation appears
as a discontinuity, so that immediately behind the shock front the gas will be
fully dissociated, and N e will be approximately zero. In addition, the gas will have
been compressed by the shock. At this stage the fringe shift S will be given by the
difference between the first and third terms of equation (9), and will be in the
direction of increasing refractivity, inversely proportional to the observing wave-
length. Behind the shock front, ionization will start and there will be a shift in the
fringes in the direction of decreasing refractivity due to the second term in equation
(9). The fringe shift due to the electrons is proportional to the wavelength, so that if
the neutral particle density is also changing, one can separate the relative contribu-
tions to the net fringe shift by taking interferograms at two wavelengths. For a
detailed discussion of this point see Alpher and White (4).
Since the fringe shift is proportional to the density N, conditions can be achieved
where the ambient density is so low that, for the strongest shock waves, the fringe
shift due to the compression and dissociation of the gas is less than 0.1 fringes.
Under these conditions the interferograms represent a direct mapping of the electron
density in the plasma.
238
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
TECHNIQUES
When optical interferometry was used mainly with steady-state devices such as
wind tunnels, the light source/camera requirements posed few problems as one
could use a long exposure time to photograph a comparatively large field of view,
the extent of which was usually determined by the size of the interferometer
optics. Many light sources of sufficient intensity and spectral distribution were
available. For pulsed devices, such as shock tubes, one had to use an exposure
time that was short enough to "stop" the motion of the shock wave. A brighter
light source was thus required to expose films in these short exposure times.
Shuttering was provided by either a fast mechanical shutter or, more commonly,
the duration of the pulse from the light source itself. However, for application to
many devices of interest today, the natural duration of these light pulses are too
long to "stop" the motion and the light pulses are not bright enough to expose
films in the extremely short times required. One way of circumventing these
problems, as well as studying the time history of transient phenomena, is to use
the technique of streak interferometry. In streak interferometry an image of the
fringe pattern is swept across a film by a mirror rotating at high speed. However,
instead of photographing a relatively large field of view as with conventional
interferometry, only a very narrow strip of the test section is viewed. With this
technique the effective resolution time is determined by the width of the strip of
test section being viewed and by the speed at which the image is swept across the
film. Typically, resolution times of ~ 0.1 [xsec. are obtained. One now can use a
long-duration pulsed light source of moderate intensity, and no shutter is neces-
sary. The technique of streak interferometry was first reported by Bennett, Shear,
and Burden, applying it to the study of axisymmetric, exploding-wire pheno-
mena (9). Their white light work is mentioned again in the next section.
Most of the work that has been reported to date, applying optical interferometry
to plasma diagnostics, has utilized the technique of streak interferometry (10-14).
These experiments have involved electron density measurements in both two-
dimensional and axisymmetric flows. Perhaps the most interesting of these are the
experiments of Ramsden and McLean (12, 13) in which an attempt was made to
compare the electron densities measured interferometrically with those measured
TABLE II. COMPARISON WITH SPECTROSCOPICALLY DETERMINED ELECTRON
CONCENTRATIONS
1. Incident Shock Experiments
Interferometer
x 10 16 cm -3
Continuum
x 10 16 cm -3
Line Width
x 10 16 cm -3
4.5 ±0.4
A5200
A4530
H,
H Y
5.6±0.7
5.4 ±0.7
4.3±0.6
4.8 ±0.7
2. Reflected Shock Experiments
Interferometer
x 10 17 cm" 3
Continuum
x 10 17 cm" 3
Hg Line Width
x 10 17 cm" 3
2.9±0.11
2.28
2.44
klein : Optical Interferometer Plasma Studies 239
by spectroscopic techniques. Table II summarizes their results. In the first
experiments, using an electromagnetic shock tube of the T type, with hydrogen as
the test gas, electron densities were measured with the interferometer. The
densities were also measured spectroscopically both by the absolute intensity of the
continuum plasma emission at two different wavelengths and by the widths of
Stark-broadened hydrogen Balmer lines. In the second experiments, working with
the higher electron density gas behind the reflected shock wave in the same device,
the interferometrically-determined electron densities were again compared with the
spectroscopic values. Much better agreement, which the authors attribute mainly
to the higher electron densities and hence the larger fringe shifts, was obtained in
the second experiments.
If one is interested in studying, for example, the electron density distributions
about bodies, or in the wakes of bodies, it then becomes necessary to photograph
the whole test section, and not just a narrow strip. Hence, streak interferometry
becomes unacceptable. In addition, for application to some of the devices of
interest today, resolution times are required that are not attainable with streak
interferometry.
Towards these ends, techniques have recently been developed at the Plasma
Research Laboratory, Aerospace Corporation, for obtaining significantly better
time resolution, at the same time maintaining a conventional field of view (15).
Both monochromatic and color, white-light experiments have been conducted.
The white-light experiments are discussed in the next section. In both the mono-
chromatic and white-light experiments the plasma was generated in a conical-
driver electromagnetic shock tube (16) using hydrogen as the working gas. This
type of shock tube operates typically over the shock Mach number range of 20
to 60, at pressures from 5 microns to a few millimeters Hg. In all of the experiments
an exploding tungsten wire was used as the interferometer light source. This light
source was developed as part of the experimental program to provide a light pulse
that was intense enough to enable one to expose conventional films in exposure
times of ~0.01 /isec. The light source consists of a 5-mil tungsten wire, supplied by
a 6000 joule capacitor bank, charged to 18 kV. Following a 6-/j.sec rise time, the
resulting light pulse decays slowly back to zero over approximately 100 /isec. The
light pulse is extremely bright and consists almost entirely of continuum radiation.
The intensity is fairly uniform over most of the visible spectrum. The fight source
is thus suitable for both monochromatic and white-light interferometry. For the
monochromatic experiments, a narrow pass-band interference filter is inserted in
the light path. In the monochromatic experiments, the interferograms were
photographed with a Space Technology Laboratories image converter camera.
This camera provides three separate exposures per run, with individual frame
exposure times down to 0.01 /xsec, and any desired interval between each exposure.
Figure 2 is an overall view of the apparatus. In the left foreground is the conical
discharge tube. The shock tube runs to the right, across the picture. Behind the
interferometer, in the left background, the exploding wire light source and its
associated optics can be seen. As shown in Figure 2, the wire itself is enclosed in
the cylindrical can. This deflects the shock wave, which accompanies the explosion
of the wire, away from the interferometer. The interferometer, visible in the center
of the picture, has 6-inch diameter mirrors and beam splitters which can be
adjusted remotely.
Figure 3 is a photograph of the test section as seen looking in through the
interferometer. The aluminum shock tube has a 3-inch-by-3-inch cross section, and
the diameter of the test section windows is 6 inches. A cylindrical model is shown
in the photograph. Both a |-inch diameter cylindrical model and a 30° half-angle
240
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
a.
p.
s
p
as
wedge were used in these experiments. The models are supported by holes in the
test section windows.
Figures 4 and 5 are monochromatic interferograms of the flow about the f-inch
cylinder at 5461 A, with both vertical and horizontal fringes. Figure 6 is a mono-
chromatic interferogram, also at 5461 A, with vertical fringes, of the flow about the
30° wedge. In each case the initial pressure of hydrogen is indicated in the picture.
The arrow indicates the direction of flow in each of the frames. The time interval
between successive frames, is indicated in microseconds by the time scale in each
photograph; the exposure time of each frame is also indicated in microseconds.
Notice that in the interferogram of the flow about the wedge the exposure time of
each frame is 0.02 /usee. In each of the photographs the shock Mach number, at the
test section, was approximately 20 to 30.
KLEIN : Optical Interferometer Plasma Studies
241
PS
Little attempt has been made in these experiments to reduce the interferograms
to give a point-by-point mapping of the electron density distribution in the flow
field, although this could be done. The interferograms have only been analyzed
qualitatively. This is due to the fact that the emphasis in die work to date has been
on the development of the techniques. Also, the plasma generated in this type of
shock tube is highly non-uniform and far from two-dimensional, so that the
measured electron densities are not local properties of the flow field, but rather
averages across the thickness of the test section.
WHITE LIGHT INTERFEROMETRY
While a monochromatic fringe pattern is made up of many fringes, indistin-
guishable from one another, a white-light fringe pattern consists of approximately
242
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
FIGURE 4. Monochromatic interferogram about | -inch-diameter cylinder at 5461 A
with vertical fringes.
10-20 fringes, each having its own color and, hence, distinguishable from the
others. This property of the white-light fringes is of particular significance when
there is a discontinuous shift in the fringe pattern, such as across a shock wave
propagating into a non-ionized gas. In such a situation one cannot usually follow
an individual fringe, in a continuous manner, through the shock. If the fringe shift
is more than one full fringe width, an error of an integral number of fringe widths
can result in the determination of the total fringe shift. However, this is not a
problem when working with a white-light fringe pattern. The fringes are labeled
by their color and the fringe shift is measured by connecting a fringe of a particular
color with its counterpart on the other side of the shock.
As discussed by Alpher and White (4), there are several essential considerations
that distinguish white-light interferometry from monochromatic interferometry.
It now becomes necessary to distinguish between the phase index of refraction and
the group index of refraction, and, hence, between the phase and group refrac-
tivities. The phase index of refraction, n p , is the velocity of light in vacuo divided
by the phase velocity in the medium, and the group index of refraction, n g , is the
velocity of light in vacuo divided by the group velocity of light in the medium.
The shift of an individual fringe in either a monochromatic or white-light inter-
ferogram is determined by the phase refractivity, while the change in location of
klein : Optical Interferometer Plasma Studies
243
FIGURE 5. Monochromatic interferogram about § -inch-diameter cylinder at 5461 A with
horizontal fringes.
FIGURE 6. Monochromatic interferogram about 30 half-angle wedge at 5461 A with
vertical fringes.
the center of contrast of the white-light fringe pattern is determined by the group
refraetivity (see Alpher and White [4]. p. 163). The center of contrast of a white-
light interference pattern is where the monochromatic fringe patterns of all the
244 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
individual wavelengths making up the white light are in phase. When calculating
the shift of the center of contrast by equation (1), A is now a mean wavelength over
the visible spectrum. The phase and group refractive indexes are related by
A dn P
~~d\~
(10)
at a wavelength A. As illustrated by Alpher and White (3-5), for the non-ionized
case there is usually a negligible difference between n p and n g , and there is then no
observable difference between the shift of the center of contrast and the shift of
the individual fringe. This is the property that allows one to follow the white-light
fringes through a discontinuity. However, for electrons, the phase and group
refractivities are equal in magnitude but opposite in sign. Hence, for the case of
the ionized gas, where the free electrons have been seen to be the dominant species,
the individual fringe shifts in one direction and the center of contrast shifts in the
opposite direction by an equal amount.
Another aspect of white-light interferometry which has been used extensively by
Bennett is known as single-fringe interferometry (11). In this case the spacing
between fringes of the initial fringe pattern is increased until one fringe fills the
entire test section. The fringe pattern that results from the presence of the plasma
then represents lines of constant electron density. In the color, white-light work of
Bennett (11), as in the monochromatic case, the technique of streak interferometry
was used. Until now, no other color, white-light interferometry has been reported.
This is due to the lack of a high-speed shutter that would transmit most of the
visible spectrum without dispersion. Also adding to the difficulty has been the
slow speed of color films and the lack of a suitable light source.
The recent development of a new Kerr cell, employing a fluid known as
Kerrmax 17 instead of the usual nitrobenzene, coupled with the intensity of the
exploding-wire light source and the fastest color films available has made possible
color, white-light interferometry of the same flow fields which were described in
the monochromatic section, with time resolution of 0.05 jusec.
Figures 7, 8, and 9 are typical color, white-light interferograms of the flow field
with no model, the flow about the f-inch cylinder, and the flow about the 30°
wedge, respectively. In each case the initial pressure was 0.5 mm Hg of hydrogen.
As discussed earlier, this initial pressure is low enough so that the fringe shift due
to the compression and dissociation of the hydrogen at the shock front will be too
small to be resolved (less than 0.1 fringe), and the interferograms are a direct
mapping of the electron density distribution. Since the fringe shift is only reflecting
the presence of electrons, under these conditions one expects the center of contrast
to shift in the opposite direction by an equal amount. This can readily be observed
in Figure 7. The center of contrast is approximately the darkest of the three
purple fringes in the undisturbed region of the flow (adjacent to the "whitest"
bright fringe). Behind the shock front the fringes shift upwards, corresponding to a
decrease in refractivity, while the dark purple coloring, characteristic of the center
of contrast, shifts downward by an equal amount. (Note that in Figure 9 a shift
upwards corresponds to an increase in refractivity.) The peak electron density is
~5xl0 16 cm -3 . In each of the color interferograms the exposure time was
0.05 fisec. The film used was Ansco Type FPC-132.
SUMMARY
The principles and techniques involved in the application of optical interfero-
metry to plasma studies have been reviewed and summarized. Recent experiments
?
o
"— .
.a
*
;?.
e
fa
u
M
C
13
?-
c
o
c
o
N
5
i-
&>
C
-s
■S
a
,?
o
s
-0
i
5
D.
U
c
o
c
u
fc.
J5
a.
Wi
Q
s
"C
t
0/
s
5
.*-
s
sr.
■^*
JC
t)
c?
-rt
JZ
?
.
a.
t-
3
fa
C
s
<:
5
-;
O
J=
fa X
FIGURE 8. White-light interferogram of flow about % -inch-diameter cylinder with hori-
zontal fringes. Flow is from left to right. An upward shift of the fringes corresponds to a
decrease in refractivity.
FIGURE 9. White-light interferogram of the flow about 30° half-angle wedge with hori-
zontal fringes. Flow is from left to right. An upward shift of the fringes corresponds to an
increase in refractivity.
klein: Optical Interferometer Plasma Studies 245
at Aerospace Corporation have been described in which monochromatic interfero-
grams have been obtained with significantly better time resolution than was
previously available, while at the same time maintaining a conventional field of
view. Techniques have been described by which it is possible to obtain color, white-
light interferograms of entire flow fields, with good time resolution. The same
color techniques could be applied to obtaining single-fringe interferograms of
entire flow fields.
The technique of optical interferometry has been seen to provide measurements
of the electron density in two-dimensional and axisymmetric, high electron density
plasmas (10 15 -10 18 cm -3 ). In a particular case, the electron densities obtained by
spectroscopic techniques have been seen to agree quite well with the interfero-
metrically-determined values.
ACKNOWLEDGMENT
The author would like to gratefully acknowledge the major contribution to the
early stages of the research described in this paper, and the continuing support
throughout the program, of Dr. Richard M. Head, Consultant, Aerospace
Corporation.
REFERENCES
1. Ladenburg, R., Physical Measurements in Gas Dynamics and Combustion
(Princeton: Princeton University Press, 1954).
2. Alpher, R., and White, D., "Interferometric Measurement of Electron Con-
centrations in Plasmas", Phys. Fluids, 1, 452 (1958).
3. Alpher, R., and White, D., "Optical Refractivity of High-Temperature Gases,
I. Effects Resulting from Dissociation of Diatomic Gases", Phys. Fluids, 2,
153 (1959).
4. Alpher, R., and White, D., "Optical Refractivity of High-Temperature Gases.
II. Effects Resulting from Ionization of Monatomic Gases", Phys. Fluids, 2,
162 (1959).
5. Ascoli-Bartoli, U., De Angelis, A., and Martellucci, S., 'Wavelength Depend-
ence of the Refractive Index of a Plasma in the Optical Region", II Nuovo
Cimento, 18, 1116 (1960).
6. Allen, C, Astrophysical Quantities (London: The Athlone Press, 1955).
7. Marlow, W., Ill, "Measurement of the Ground State Polarizability of Atomic
Hydrogen", Ph.D. thesis, Stanford University, 1963, and Bull. Am. Phys.
Soc., 8, 362 (1963).
8. Shukhtin, A., " Interferon! etric Method for the Determination of the Gas
Density and Electron Concentration in Plasma", Optics and Spectroscopy, 10,
222 (1961).
9. Bennett, F., Shear, D., and Burden, H., "Streak Interferometry", J. Opt. Soc.
Amer., 50, 212 (1960).
10. Medford, R., Powell, A., Hunt, A., and Wright, J., "Interferometric Measure-
ments of Electron Density in Deuterium Plasma", Proc. Vth. Inter. Conf. on
loniz. Phen. in Oases. 2, 2000 (1961).
11. Bennett, F., "Shock-Producing Mechanisms for Exploding Wires", Phys.
Fluids, 5, 891 (1962).
12. Ramsden, S., and McLean, E., "Optical Refractivity of Free Electrons",
Nature, 194, 761 (1962).
246 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
13. Ramsden, S., and McLean, E., "Optical Interferometric Measurement of
Electron Density in an Electromagnetic Shock Tube", Bull. Am. Phys. Soc,
7, 157 (1962).
14. Klein, A., "Some Results Using Optical Interferometry for Plasma Diag-
nostics", Phys. Fluids, 6, 310 (1963).
15. Klein, A., and Head, R., "Optical Interferometric Measurements about Bodies
in a Hydrogen Plasma", Bull. Am. Phys. Soc, 8, 167 (1963).
16. Josephson, V., and Hales, R., "Parametric Study of the Conical Shock Tube",
Phys. Fluids, 4, 373 (1961).
17. Courtesy of Kappa Scientific Company, Sierra Madre, California.
13. Koichi Oshima: Microwave
Diagnosis of a Partly-Ionized
Flow in the Presence of a
Magnetic Field
12? Starting with the conventional expression of tensor conductivity of
a plasma, the interaction between a plane-polarized microwave and
the plasma in the presence of a magnetic field is expressed analytically.
Especially, this expression can give the angular dependence of the
received power to the polarization plane. K-band and X-band micro-
wave systems with a rotatable receiving horn to measure this angular
dependence were developed and the measurements were carried out
with supersonic flows of argon and nitrogen gas through a small wind
tunnel.
The results with the K-band system were analyzed successfully by
this analytical expression, but the analysis of the data with the X-band
system was not conclusive. However, the measured angular dependence
of the phase shift and attenuation showed qualitative agreement with
the calculations.
INTRODUCTION
The application of microwave interferometry to plasma diagnostics, while it
commands several technical advantages in principle, is somewhat limited in
practice by the relatively narrow ranges of electron density and collision frequency
in which any device of a given frequency can make effective measurements. For
example, a 24-Gc interferometer, traversing a plasma 5 cm thick, can respond to
electron densities between about 5xl0 10 and 2xl0 12 cm" 3 . The possibility of
extending the range of sensitivity of an interferometer through the introduction
of an additional parameter — the electron cylotron frequency — would seem to be
desirable and warrants specific assessment. Such an investigation would also have
bearing on the problem of radio communication through the ionized gas surround-
ing a reentry vehicle.
In conventional microwave interferometry, two quantities are measured, phase
shift and attenuation, which are related to two physical parameters in the plasma,
ed. note: Dr. Oshima is now at the Aeronautical Research Institute, University of Tokyo,
Komaba-Meguro-Ku, Tokyo, Japan.
The research reported in this paper was sponsored in part by the Aeronautical
Systems Division, Wright-Patterson Air Force Base, under Contract No. AF 33
(657) -7760, and the Air Force Office of Scientific Research under Grant AF-AFOSR
55-63.
9+ 247
248 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
the plasma frequency (hence electron density) and electron- heavy particle collision
frequency (hence electron temperature). While it yields no new information about
the plasma, the presence of a magnetic field (which renders the plasma conductivity
a tensor) does add a dimension of versatility and redundancy in the interfero-
metric techniques. The present investigation is an attempt at assessing the practi-
cality of such an approach to microwave diagnostics.
Two principal results are obtained, one from analysis and the other from
experiments, which indicate severe limitations on the application of the magnetic-
field technique to microwave interferometry. The theoretical study of the inter-
action of a plasma slab of finite depth with a microwave field having a magnetic
field reveals a non-linear behavior with respect to the plasma thickness. The
experimental study reveals that the properties of a plasma may be significantly
altered by the presence of the magnetic field (beyond simply introducing gyration
in the electrons) in ways that cannot be predicted by theory, thus rendering the
diagnostic results ambiguous as to electron density and temperature.
MICROWAVE FIELD IN A PLASMA
We begin with the conductivity tensor a of a plasma in a magnetic field as
follows:
I L i M \
(1)
The z-axis is taken as the direction of the magnetic field, and, in the present
experiment, is also the direction of the microwave propagation ; w is the angular
frequency of the microwave; and
< - fcf
jS = V -> y = - c (2)
w a)
w p , v, and w c are plasma frequency, electron collision frequency, and electron
cyclotron frequency, respectively.
= Infill = 3 18>< 1()9 ((rad / sec) 2 ) ^ cm 3j
m
(3)
= c|Bo| = 1.76 x 10 7 |B | (rad/sec, gauss)
mc
where m, n e , and e are electron mass, its number density, and its charge, respec-
tively; |B | is the strength of applied field, and c is the speed of light. The
Gaussian unit system is used.
To solve for the field in the plasma, one eliminates the terms involving the mag-
netic flux from the Maxwell equations to obtain
VxVxE + ^ + ^- = (4)
Time dependence of the electric field is e~ ,mt . For a plane wave propagating in the
c-direction, the space dependence is e' k2 , and the z-component of the field E, E 2 ,
o shim a: Microwave Diagnostics 249
is zero. Using the above expression of a, the x- and ^-component equations of E,
which are expressed as E x e~ ii,at -' cz '' and E y e' Kwt - kl: \ are
jp_i_ ( i _, L) ^ -z_ vMEy =
From the secular equation of these, two values of k are determined
(5)
which correspond to the ordinary and extraordinary waves, respectively. The
electric field components E z , E y , at a point where the microwave penetrates a
plasma slab to depth z, may then be expressed as
E x = .E+exp (jk x z) + E_exp (jk 2 z) E y = j? + exp (jk 1 z)-jE_exp (jk^) (7)
where E + and E_ correspond to the ordinary and extraordinary waves, respec-
tively, and are determined by the incident condition.
Introducing the complex refractive index, n, and expressing the real and
imaginary parts of k and n by a prime and double prime, respectively, we obtain
h d+rh H 1/2
L 1 (l+y) 2 +/? 2 JJ
?' _ ? 4 ' _ _l rfh t 1 -^ r, r ft rv ;2 w
" 2 " " " 2 " V2 Lil 1 (l-y) 2 +H + L(l- y ) 2 +jS 2 J J
+ L (l-y) 2 +|8 2 JJ
n ?- e k ?- 1 rf[i d-rh I 2 . T ft 1 2 V /2
" 2 " ? ta " V2 III (i -y) 2 +H + l(i-y) 2 +H }
f, d-yh 11 ia
L (l-y) 2 +/J 2 JJ
where the subscripts 1 and 2 represent the ordinary and extraordinary waves,
respectively. Values of n' and n" are shown for < 77 < 5 in Figure 1 for the case of
y8 = 0.25 and y = 0.6, 0.4, 0.2, and 0. In Figure 2 n is expressed in a complex plane,
which may be useful for a general view of its character; that is, n 2 is much larger
than n" for large values of rj and y, so the extraordinary wave decays rapidly in
this case; and n\ is nearly constant for n> 1, so that the phase shift is independent
of 17.
Using equations (7) and (8), we obtain
E z = E + exp {jn 1 z) + E_ exp (jn 2 z) E y = jE + exp (jntf-jE. exp (jn 2 z) (9)
250
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
FIGURE 1. Values of n' u n\, n' 2 , n" 2 at ? = 0.25.
where z is a non-dimensionalized plasma depth defined as
z = c s = T s
and A is the wavelength of the microwave in vacuum.
(10)
PHASE SHIFT AND ATTENUATION DUE TO A PLASMA SLAB OF
FINITE DEPTH
The incident, reflected, and transmitted waves through a plasma slab bounded
by quartz slabs (of the same thickness as the plasma) are depicted in Figure 3.
Rigorously, one should consider the five-slab configuration, since, unless the
o shim a: Microwave Diagnostics
251
"0.5 1.0
FIGURE 2. Values of n l and n 2 on a complex plane at /3 = 0.25.
microwave system is imbedded in the quartz, the quartz slabs are bounded by air
(or vacuum). However, it has been found from experience (1) that a five-slab
analysis introduces no significant alterations to the three-slab analysis, and thus
does not warrant the significantly increased amount of algebra involved. With the
amplitude E known, the other quantities, A, B,C, and D, can be determined by
the boundary condition that the electric field strength and its space derivative
must be continuous at the boundary. From this one obtains
B = E
4nn exp [— j(n Q — n)d]
(n + n ) 2 — (n — n ) 2 exp (2jnd)
(11)
252
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
QUARTZ
no
E-?xp(-jwt +jn z )
PLASMA
n
A-exp(-jwt + jnz )
QUARTZ
no
B-exp(-jwt + jn ?)
D-exp(-jwt-jn z)
C-exp(-jwt-jnz)
*■ Z
FIGURE 3. Propagation through a bounded plasma.
In the absence of the plasma, the value of B, denoted by B , is
4w exp[-j(w -l)d]
B = E
(l+w ) 2 -(l-? ) 2 exp(2jrf)
Thus the relative phase shift, (in radians), and attenuation, A (in nepers),
between two paths of the microwave, one through the plasma and the other through
vacuum, can be expressed as
/ -^ ? B (l+? ) 2 -(l— w ) 2 exp (2jd) r .,, .-:, , 1C1 .
exv(-jQ-A) = — = V °; ; f ^-^ f nex V [-j(l-n)d] (12)
-Do (n + n o y~ (n — n ) 2 exp (2jnd)
Introducing an "effective refractive index", N, and Re and Im for the real and
imaginary parts of the coefficient of the exponential term in equation (12), we
obtain
exp[-j(l-N)d] = (Re + Im) exp [-j(l-w)rf]
From equation (13)
N = M, + i [Iln(fle 2 + /n? 3 )+jtan- 1 ^
jd L2 -? e
and
(l-N')d or 9 = - = 1-A T '
d
(13)
(14)
(15)
A = N"d or a = 4 = N"
(16)
where N' and N" are the real and imaginary parts, respectively, of N; and 6 and
a are normalized shift and attenuation, respectively.
oshima: Microwave Diagnostics
253
FIGURE 4. First-order terms in phase shift and attenuation.
In the presence of a magnetic field the polarization of a plane-polarized incident
wave undergoes a rotation. If the receiving horn on the far side of the plasma is
placed parallel to x, which is also the direction of polarization of the incident
wave, then
J = \ (exp t-i(l -iVJdRexp [-j(\ -N 2 )d]}
254
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
0.3
-0.3
tan"'{tanh ^(nf-ng) tan ^{n^-ni )}
0.3
T^n{"r cosn ^ n | /_n 2^ + Y cos ^ n i'~ n 2^}
FIGURE 5. Zero-order, nonlinear terms in phase shift and attenuation.
and the resultant phase shift and attenuation are
= l-^^ + ,tan-
1 tanh
N'1-NZ
d ■ tan
N\-N'
m+N* i 1n
2 2d
[^ cosh (N'l-Nl)d + )^ cos (iV'j-iV^dl
(17)
(18)
The terms (N\ + N' 2 )j2 and (N'l + N'^fi represent first-order terms in the phase
shift and attenuation, while the other terms indicate the nonlinear behavior.
Assuming N = n (which implies tj < 1, as will be seen later), typical values of the
first-order terms are shown in Figure 4; and, assuming further that d = \, the
nonlinear terms are shown in Figure 5. It is seen from Figure 4 that the first-
order term (valid for -q < 1), always results in increased attenuation witu increasing
OSHIM a: Microwave Diagnostics 255
magnetic field, while the nonlinear term (Figure 5) tends to decrease the attenua-
tion. In general, it is clear that the overall behavior in 6 and a is a very compli-
cated function of d as well as ij, /?, and y.
Small 7j Approximation
If t] < 1 equation (18) simplifies to
n> - 1 l (1+ ^
2(l + y) 2 +/J 2
? ! fa
2(l+y) 2 + 2
B2 ~ 1 2(l- y ) 2 + | 8 2
(19)
2 (l- y )2 + j3 2
Further, if ij < 1, n < 1, so that equation (14) can be expanded in a power series
in (?— 1)
tf = w + ( fie '+j/m') (B _ 1) + ot(B _ 1)2] (20)
where
P * _ _ (1— w 4 ) ain g d-Kl— rag)??sindco8rf
4?g+(l-?g) 2 sin 2 5
Im , = 2w (l - ?.g) sin d cos rf+ (1 -Wq^m.q - (1 + ? ) 2 sin 2 d]d
4k 2 , + (1- re 2 ,) 2 sin 2 d
If we retain only the zero order term in (n — 1) we obtain
N = ? (21)
If the first order term in (?— 1) is retained,
2V = n' + ^r- ( n '-l)+- = - n"
d d
Ar ? , Re' Im' .
from which ? can be deduced from measured values of N' and N", equations (15)
and (16), as
?' = l + P(N'-l)+QN" n" = Q(N'-l) + P(N") (22)
where
Im'jd (Re'\ 1
P = Im'jd = //^\ _
(l+/m7d) 2 + (/?e7d) 2 ' I d J (1
(l+/i?7d) a + (Jte'/d) 2 ' \ rf / (l+Im'jd) 2 + (Re'ld) 2
P and Q are shown in Figure 6. It is seen that the dependence of P and Q, and,
consequently, of n, on d is quite complex. The values of d corresponding to a
plasma thickness of 1 cm and with microwave at X-band and .ff-band are indicated
in the figure. From these it is seen that X-band would be a poor choice, while at
/if -band the nonlinear effects are negligible.
9*
256
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
0.4
0.2
-0.2
-0.4
X-BAND
K-BAND
2 4
i" ^ 27T
6 6
0.3
0.2
0.1
-0.1
-0.2
X-BAND
K-BAND.
3
-7T TT JTT -|tT 2tT
FIGURE 6. First-order, nonlinear effects in phase shift and attenuation.
EXPERIMENTAL STUDY
The experimental study is carried out with a plasma produced in a small super-
sonic wind tunnel (test section 16 mm in ^-direction and 13 mm in z-direction) by
the discharge from a 13-megacycle field imposed across the flow in the ^-direction.
The plasma is thus a nonequilibrium cold plasma. The static pressure in the flow
(of nitrogen gas) is typically around 10 mm Hg, and the Mach number about 2.
The magnetic field is produced by a pair of solenoids straddling the flow. The
microwave propagates through the holes m the centers oi tue SGienoiuS. DCnernaiic
o shim a: Microwave Diagnostics
257
.
MAGNETIC
FIELD COIL
MAGNETIC
FIELD COIL
MAGNETIC FIELD
1
1
,
,
"
1
/
■0-
WIND
50
lin
{%— ?■ MICROWAVf
o
TUNNEL
\
_
TRANSMITTING
1 unDM
1
|
1 RECEIVING
- 13 ?-
*" rn - rm11 22.5X10.5 9.2KMC
OPENING AREA ^ 40 24KMC
\
?m OD
-m "? c
unit:mm
i *j
- - 40 ??
FIGURE 7. Wind tunnel and solenoids.
THIS PART IS MOUNTED ON
THE ROTATING STAND
CRYSTAL
I
TERMINATION
MAGIC
TEE
HORN ?-
ATTENUATOR
KLYSTRON - TUNER - UNILINE - DIRECTIONAL — MAGIC - TERMINATION
COUPLER
FREQUENCY
METER
crystal f- M j|g C -Crystal]
<— ATTENUATOR - ATTENUATOR -
FIGURE 8. Microwave interferometer.
diagrams of the wind tunnel-solenoid combination and the microwave inter-
ferometer are shown in Figures 7 and 8. Figure 9 shows a photograph of the experi-
mental set-up. Detailed descriptions of the experiments may be found in Oshima
(1) and Pass (2).
In the experiments both K-b&nd and X-band interferometers are used. The
results with X-band, at a wavelength of 3 cm which is larger than the depth of the
plasma, are quite unsatisfactory. The if-band results, with a wavelength of 1.2 cm,
are deemed acceptable in the absence of the magnetic field. The slab height of
16 mm was shown in Oshima (1) to be an adequate approximation of an infinite
258
PHYSICO-CHEMICAL DIAGNOSTICS OK PLASMAS
FIGURE 9. Experimental set-up.
slab. In Oshima (1) microwave measurements, utilizing the .same apparatus as in
the present work, with polystyrene sheets 30 cm x 30 showed results which were
the same as those obtained with small sheets cut to fit the interior of the small
wind tunnel test section. Typical results for zero magnetic field are shown in
Table I. The notation "Heating Power" refers to the power in the 13-Mc exciting
TABLE I. ELECTRON DENSITY AND COLLISION FREQUENCY IN NITROGEN FLOW
Stagnation
Pressure
(cm Hg)
Heating
Power
a
"a
V
5
High
0.075
0.014
10.7 x ion
2.9 x 10i°
5
Low
0.043
6.2 x ion
10
10
High
Low-
0.083
0.054
0.028
12.2 x 10"
7.9 x 10 11
5.1 x 10i°
15
15
High
Low
0.075
0.040
0.035
10.7 x 10"
5.7 x 10"
7.1 x 10i°
o
field. At low power the attenuation is not detectable because of the fact that the
plasma thickness is only about equal to the wavelength. The calculations leading
to n e and v are based on equations (19) and (21), since -q < 1.
o shim a: Microwave Diagnostics
259
In the measurements with magnetic field, results are quite inconclusive, for the
following reasons:
At low magnetic field (less than 1 kilogauss) the measured values of phase shift
and attenuation differ from those measured in the absence of the magnetic field
with the same flow conditions and the 13-Mc input by very little, being of the order
of the experimental scatter. At higher magnetic field (greater than 1 kilogauss) the
conditions of the plasma are clearly affected by the presence of the magnetic
field so that it is not possible to draw meaningful conclusions. Visually, the color
of the plasma changes when the magnetic field is increased, and the highly luminous
part of the plasma extends closer to the tunnel walls. Quantitatively, the static
pressure in the flow, which increases when the 13-Mc power is turned on (due to
the heating of the gas by the discharge), decreases when the magnetic field is
increased, resulting in an apparent increase in the flow Mach number. This effect
is shown by the data presented in Table II.
TABLE II.
CHARACTERISTICS
OF NITROGEN FLOW WITH MAGNETIC FIELD
Stagnation
Pressure
(cm Hg)
Static
Pressure
(mm Hg)
Magnetic
Field
(k/gauss)
Inputf
(kW)
M
5
5.5
2.096
5
10
1.6
1.444
5
9
1.2
1.6
1.549
10
8
2.300
10
11
1.75
1.912
10
10
1.2
1.75
2.023
10
8
2.300
10
15.5
2.0
1.546
10
14.5
1.2
2.0
1.616
15
10
2.416
15
15
2.0
1.913
15
14
1.2
2.0
1.991
■f Energy input to the 13-Mc power tubes = plate current x plate voltage
An explanation for the observed effect of the magnetic field may lie in the fact
that the electron cyclotron radius for the experimental conditions is comparable
to the electron mean free path (with respect to collisions with heavy particles),
so that the presence of the magnetic field tends to reduce the collision frequency,
which, in turn, reduces the decay rate in the nonequilibrium plasma used in the
experiment. That this postulated mechanism is plausible is surmised from the
decrease in the static pressure. Thus, the basic properties of the medium, with
regard to density and temperature, are altered by the presence of the magnetic
field, so that any apparent changes in propagation characteristics cannot be
attributed to the magnetic field alone.
260 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
CONCLUSIONS
It is shown by analysis that the presence of a magnetic field in a plasma renders
the effect of the thickness of the latter nonlinear with respect to the propagation
of microwaves.
The changes in phase shift and attenuation due to the presence of the magnetic
field are not monotonic with respect to the strength of the magnetic field, because
of the nonlinear effect of the plasma thickness.
The properties of a plasma, especially a nonequilibrium plasma, may be so
altered by the presence of a magnetic field as to render very difficult the interpre-
tation of the measured results with a microwave interferometer.
REFERENCES
1. Oshima, K., "Microwave Measurements of Plasma Flow in a Supersonic
Wind Tunnel", USCEC Rept. No. 83-208, AFOSR 1556, September, 1961.
2. Pass, H. R., "iT-Band Microwave Interferometer Description and Initial
Experiments in a Pilot-Model of the USC Low-Density Wind Tunnel",
USCEC Rept. No. 56-217, AFOSR TN 60-1087, August, 1960.
14. Charles E. Shepard and Velvin
R. Watson : Performance of a
Constricted-Arc Discharge in a
Supersonic Nozzle
12? The application of the wall-constricted electric arc to the heating of
gas flowing through a DeLaval nozzle is discussed. It is shown that a
direct-current arc can be maintained through the nozzle throat without
disrupting the supersonic flow. High enthalpies are obtained by
elongating the throat to form a constrictor tube. The behavior of the
device can be described by the arc-column analysis of Stine and Watson
in which radial conduction is assumed to be the only heat-loss mecha-
nism. The measured radial and longitudinal enthalpy profiles are
similar to those predicted by the theory.
INTRODUCTION
A new plasma generator has been developed at the Ames Research Center which
produces a supersonic flow of gas at very high enthalpies. The design, based on the
analysis of the constricted arc by Stine and Watson (1), has been successfully
tested with mixtures of nitrogen and air and mixtures of nitrogen and carbon
dioxide. The generator produces a steady supersonic gas stream, but the total
enthalpy has a large gradient in the radial direction. With nitrogen, the aver-
age enthalpy of the stream is approximately 30,000 Btu/lb, whereas the center-
line enthalpy was estimated to be 80,000 Btu/lb.
The purposes of this paper are to describe the new plasma generator, to present
the experimental results obtained during recent testing, to compare the results
with the theoretical analysis of Stine and Watson (1), and to discuss the pertinent
arc-column scaling laws.
APPARATUS
The new plasma generator developed at Ames, called the constricted-arc super-
sonic jet, is shown schematically in Figure la. A conventional plasma generator
for wind-tunnel use is shown for comparison in Figure lb. In the conventional
plasma generator, the gas is heated prior to entering the supersonic nozzle, but
much of it bypasses the hot arc and remains cold. If the gas is allowed to reach a
uniform temperature in a plenum chamber, additional heat is lost to the plenum
chamber walls, and the energy of the gas in the test section is always far less than
ed. note: Mr. Shepard and Mr. Watson are with the Ames Research Center, National
Aeronautics and Space Administration, Moffett Field, California.
261
262
PHYSICO-CHEMICAL DIAGNOSTICS OF TLASMAS
SUPERSONIC
NOZZLE
ELECTRODES ■
FIGURE la. Arc-heated supersonic jet, constricted arc.
STAGNATION
CHAMBER
_GAS INJECTOR
/—SUPERSONIC
/ NOZZLE
■ ,
J
^^-^
>--
VACUUM
^_^EXHAUST
\
\
^^-^^^
\ /
|
ELECTRODES -
-PLENUM CHAMBER
FIGURE lb. Arc-heated supersonic jet, conventional arc.
the energy of the gas within or near the arc column. In the constricted-arc super-
sonic jet, however, the arc is forced completely through the nozzle, thus providing
continuous heating of the gas up to the test section. All of the gas thus passes
through or very near the arc column. Therefore, the energy of the gas in the test
section of the constricted-arc supersonic plasma jet is much nearer the high energy
of the gas within the arc column.
Two sizes of the constricted- arc supersonic jet were tested. The first had a
|-inch-diameter throat and is shown in Figure 2a, and the second had a |-inch-
diameter throat and is shown in Figure 2b. The three basic components of both
units are the supersonic nozzle, the cathode at the upstream, or subsonic, end of the
nozzle, and the anode at the supersonic end of the nozzle.
The nozzle has an extended throat to constrict the arc and provide high heating
at relatively low arc currents. The throat must withstand the high heating rates
developed at the edge of a constricted-arc column and must, at the same time,
support the voltage gradient impressed along the arc. To meet the requirements
for good thermal conductivity in the radial direction and good electrical insulation
in the axial direction, the nozzle consists of water-cooled copper disks separated
by boron nitride insulating wafers.
The cathode must be capable of carrying large currents without contaminating
the test gas. A pointed, thoriated tungsten cathode, shielded by nitrogen, provides
a steady attachment point for the arc column with negligible contamination.
(If one is interested in heating air, oxygen-rich air can be added at the gas inlet to
shepabd and watson: Constricted -Arc Discharge
263
UPSTREAM ELECTRODE DOWNSTREAM ELECTRODE
(CATHODE AND PILOT ARC) SUPERSONIC (ANODE)
n NOZZLE
40 kw 1WIND0W
PLASMA-JET _t
SHIELD GAS
INLET
(NITROGEN)
HEAT
EXCHAN-
GER
c+> TYPICAL 1.0 Ohm
WATER-COOLED
BALLAST RESISTOR
FIGURE 2a. Schematic diagram of constricted-arc supersonic jet, | -inch-diameter
throat.
THORIATED
TUNGSTEN
CATHODE
UPSTREAM ELECTRODE
(CATHODE AND PILOT ARC)
80 kw SUPERSONIC NOZZLE
PLASMA- CONSTANT AREA
JET-, THROAT SECTION
DOWNSTREAM ELECTRODE
(MULTIPLE ANODE)
SUPERSONIC
SECTION
SHIELD GAS
INLET (NITROGEN)
TYPICAL 2 Ohm BALLAST
RESISTOR (WATER- COOLED)-tJ
COOLING WATER SUPPLY MANIFOLD
AND COMMON ANODE BUS
FIGURE 2b. Schematic diagram of constricted-arc supersonic jet, i-inch-diameter
throat.
TO
VACUUM-
SYSTEM
-TYPICAL
ANODE
ELEMENT
(WATER-
COOLED
COPPER
SLUG)
produce the proper mixture in the test section.) A commercially available plasma
torch is used in each unit as the cathode and shield.
The anode is in the low-pressure, supersonic end of the nozzle, so the arc attach-
ment to the anode is diffuse. The anode can, therefore, withstand large currents
with long lifetimes without a need for magnetically moving the arc attachment
point. To assure a symmetric current distribution, the anode is segmented circum-
ferentially, and each segment is connected to the power supply by means of a
ballast resistance. In the J-inch-diameter unit, the segmented anode consists of
six water-cooled loops of copper tubing placed downstream of the nozzle. In the
^-inch-diameter unit, the anode consists of 24 water-cooled copper blocks attached
directly to the end of the nozzle. (See Figure 2*.)
264
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
RESULTS
The results of the recent experimental testing of the plasma jets verified that the
arc can be passed through the nozzle without disrupting the supersonic flow, and
that very high enthalpies can be reached. Shock diamonds emerged from the
nozzle as the current was increased from a very low value to the design current,
indicating that the flow was supersonic. High-speed photographs indicated that the
flow was very steady. Selected frames are shown in Figure 3.
Conventional steady-state instrumentation was used to measure current, voltage,
cooling- water flow rates and temperature rises, gas flow rate, and plenum chamber
2>ressure for the two units. Calculations of the power released to the gas and
calculations of the power loss were carried out from the measurements of current,
voltage, and cooling water flow and temperature-rise.
.a
o
a.
e
o
3
er
>
o
S 5?
3 s
S I
H .2
N T3
shepard and watson: Constricted-Arc Discharge
265
o
o
tr
o
o
a.
< m
x
<
r-
o
UJ
o
<
tr
32XI0 3
28
24
J 20
16
- 0.4 atm\ \
PRESS ?
0240
* i>240
\ C\2I0 \ PRESS ? 0.7 atm
?210
\o \
v i83 \ 210 \G207
Ol32\ \ \ Y
,3 a° l35 o\ ?IS K 141
III I32\p ^\ \ PRESS w 0.6 atm
'108
(114 .
\I08 \ H3
% I08\ PRESS " °- 5 Qtm
LEGEND: NUMBERS NEAR DATA POINTS INDICATE
ARC CURRENT
APPROXIMATE STAGNATION PRESSURE— atm
1 1 1 1 1 J _ 4
2 4 6 8 10 12x10
MASS FLOW RATE, W, lb/sec
FIGURE 4. Average total enthalpy at the end of the constant area throat section in the
J-inch constricted-arc supersonic jet as a function of nitrogen flow rate for various
currents.
An average total enthalpy at the end of the constant-area throat section was
determined by dividing the gas flow rate into the net power remaining in the gas
at that location. Figure 4 shows enthalpy as a function of gas flow rate for various
currents, together with the approximate plenum chamber pressure. Average
total enthalpies in excess of 30,000 Btu/lb were obtained for the J-inch-diameter
unit at about i atmosphere of pressure. The average total enthalpy for a few runs
30xl0 3 r
>-
<
UJ
28 -
24
? 20
uj w
ox
<
ac
UJ
3
<
o
o
16 -
SUPERSONIC
SECTION
FLOW RATE,
lb/sec
5.3 xlO -4
CURRENT,
amp
240
210
183
207
183
.24
.04 .08 .12 .16 .20
AXIAL DISTANCE, Z , feet
FIGURE 5. Throat section average total enthalpy versus axial distance for various arc
currents and nitrogen flow rates.
266
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
was also determined in the test section of the J-inch-diameter unit from the power
balance described above and the power absorbed in a tube and shell heat exchanger.
It was found that the enthalpies obtained from the two methods agree within 12
per cent. The test section enthalpy was generally somewhat higher than the con-
strictor outlet enthalpy given in Figure 4.
Detailed measurements were made of the voltage drop between the cathode
and the various constrictor-nozzle disks and of the power absorbed by each of the
disks for the |- inch-diameter unit. Calculations were then made of the longitudinal
distribution of power released to the gas, heat flux to the walls, and average total
enthalpy. The buildup of average total enthalpy with longitudinal distance is
shown in Figure 5 for several values of current and flow rate. The enthalpy level
and the rate at which it increases is a function of the current and flow rate. The
enthalpy rises more quickly at low flow rates and in some cases reaches an asymp-
totic value in the throat section. A further increase in enthalpy takes place as the
gas leaves the constant-area section and enters the divergent (supersonic) region
of the nozzle.
Profiles of impact pressure and stagnation heating rate to a ^-inch-diameter,
flat-faced calorimeter probe were measured in the test section of the f-inch unit.
In order to deduce the enthalpy profile shown in Figure 6, it was assumed that the
heat flux was proportional to the first power of enthalpy and to the square root
of impact pressure. There was no region in the test section for which the enthalpy
gradient was small; the center-line enthalpy was estimated to be 2.7 times the
radially-averaged enthalpy of the test stream. Although the generator does not
Ld
ID
q /q ? q
M S H S,f H s, t
H/H t ;H t =
38,000 ^T
lb
0.2 0.4 0.6 0.8 1.0
<
EC
r/r.
exit
FIGURE 6. Typical radial profiles of impact pressure and stagnation-point heat transfer
to a ^-inch-diameter, flat-faced calorimeter probe and derived total enthalpy profile
(f-inch unit).
provide a uniform stream for testing large models, it does provide high heating
rates for small models. The gas used for most of the tests was nitrogen, but a few
tests with air indicated that results were nearly the same for both gases. Both
units were also operated with carbon dioxide (with a small amount of nitrogen
shielding the cathode), and there was little change in the operating characteristics
of the units; in other words, the flow was steady and supersonic.
shbpard and watson: Constricted-Arc Discharge
267
COMPARING EXPERIMENT WITH THEORY
One of the features of the arrangement of the supersonic-arc plasma jet is that the
gas heating process in the throat is amenable to analysis. In fact, the two plasma
jets tested were designed with the aid of the theoretical analysis of the constricted-
arc by Stine and Watson. Most of the heating takes place in the throat where the
cross-section area is small; the simplified mathematical model of the arc column
analyzed by Stine and Watson may be used to represent the arc column in the
throat. The theoretical analysis presents the distribution of enthalpy and current
in an axisymmetric arc column in which the dominant mechanism of energy loss
from the column is radial conduction, and for which the specific mass flow, pu,
is constant. The relations between the state properties, enthalpy, electrical
conductivity, and thermal conductivity potential, are linearized. The remaining
characteristics of the column, such as voltage and heat flux, can be determined
from the known enthalpy and current distributions.
To determine the degree to which the linear analysis can describe the arc-
column characteristics, a series of comparisons was made between the experi-
mental measurements and the predictions of the analysis.
Heat Flux
The analysis of Stine and Watson predicts that the heat flux to the elongated
throat will be a function of enthalpy and will be independent of gas-flow rate.
Figure 7 shows the experimental measurements of heat flux as a function of the
average total enthalpy. The flow rates are also shown beside each data point.
From this figure it can be seen that the heat flux is insensitive to the flow rate,
but does correlate reasonably well with enthalpy, as predicted by the analysis. A
straight line fitted to the data indicates that radiation is not important.
o
a>
3
x
3
<
X
<
z
O
H-
O
UJ
V)
\-
<
o
(E
X
20
rXlO 2
NOTE:
NUMBERS
INDICATE FLOW RATE, W x I0 4 lb/sec
16
70° /
,XJ ~S^ O 5.3
^(553
59/ O
12
4.4.lf3^03., 070 ° 31
8
J&& 4-4
3.7
4
i i i i i i
8 12 16 20 24 28 32xl0 3
LOCAL TOTAL ENTHALPY, H, Btu/lb
FIGURE 7. Throat section wall heat flux versus local average total enthalpy for various
nitrogen flow rates; 2 = 0.14 feet (J-inch unit).
268
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Voltage Gradient
The analysis also predicts that the voltage gradient will approach an asymptotic
value as the gas-flow rate is decreased. The measured voltage gradient, shown in
Figure 8, appears to approach an asymptotic value of about 500 volts/ft. Since the
data are for a range of enthalpies, it appears that the voltage gradient is independent
of enthalpy as predicted by the theory of Stine and Watson.
> 2 4 6
MASS FLOW RATE, W X 10? lb/sec
FIGURE 8. Voltage gradient as a function of nitrogen flow rate for the J-inch-diameter
constricted-arc supersonic jet; 2 = 0.15 feet, 7 = 183_amperes.
Enthalpy Distribution
The analysis predicts that the increase of enthalpy with axial distance will be
given by the equation,
A* = A*..(l-e-"- Bs ' s o)i?
where
h F ? = 4.08x10"
W i,2 )(J
and 2 = — p
77 k
and the constants cjk and A represent the slopes of the straight-line approxima-
tions to the relationships between h and <1> and between a and O, respectively;
/ is the current, r e is the column radius, and w is the mass flow rate. The values
of k and A are not known accurately, and, therefore, accurate predictions of
enthalpy cannot be made from purely theoretical calculations. Furthermore, the
relationships between h and and between a and <1> may be — in fact, probably
are — nonlinear, so that the linear approximations will introduce further inaccuracy
into the analysis. These relationships can be estimated from the theoretically-
computed values of thermodynamic and transport properties, and electrical
conductivity. The estimates shown in Figures 9 and 10 for air and nitrogen use
the thermodynamic and transport properties from calculations by Hansen (2),
and Ahtye (3), and electrical conductivity from calculations by Viegas and Peng
(4), and Yos (5). The location of the straight line which best approximates each of
these relationships is not obvious, and, unfortunately, a small change in the
location of the line appreciably affects the value of the enthalpy predicted by the
oriDlrcic \T oirortnolooa r\v?c?
rlnrlv
shepard and w atson : Constricted- Arc Discharge
269
60XI0 3
-APPROXIMATE SLOPE, C p /k,
FROM EXPERIMENTAL DATA
(1/4-INCH CONSTRICTED-ARC
/ / PLASMA-JET)
4 8 12 16 20
<f> =/ kdt, Btu/ft.sec
FIGURE 9. Enthalpy as a function of thermal conductivity potential for air and nitrogen
at 1 atmosphere.
2400
APPROXIMATE SLOPE, A, FROM EXPERIMENTAL
DATA (1/4 INCH DIAMETER CONSTRICTED-ARC
SUPERSONIC JET)
4 8 12 16 20
<^=/kdT(Btu/ft-sec °R)
FIGURE 10. Electrical conductivity as a function of thermal conductivity potential for
air and nitrogen at 1 atmosphere.
in Figures 7 and 8; in particular, a line drawn through the data in Figure 7 deter-
mines the line in Figure 9, and the value of E (of Figure 8) at zero mass flow
determines the line in Figure 10. The prediction based on these deduced values of
c p jk and A is shown in Figure 11, and the experimental measurements are shown
for comparison. The use of the values of c p jk and A deduced from measurements
made in the J-inch unit influences the agreement of the asymptotic enthalpy and
the length required for the enthalpy to approach the asymptotic value for the
270
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
H F r/I
BtU X ft
lb x amp
OPEN SYMBOLS: 1/4 inch UNIT
SOLID SYMBOLS: 1/2 inch UNIT
.04
.08
.12
.20
.16
z/z
FIGURE 11. Comparison with theory (1) of experimentally
parameter, H E rjl, versus dimensionless axial distance, zjz .
24 .28
.32
determined enthalpy
|-inch unit. However, the shape of the theoretical curve is not prescribed by the
use of these values; the data therefore verify that the analysis predicts qualitatively
the rate of increase of enthalpy with axial distance. Furthermore, the experimental
data for the |-inch unit agree with this curve, so it appears that once the values of
c p jk and A are determined experimentally, the analysis predicts quantitatively
the enthalpy for constrictors of all sizes.
Radial Enthalpy Profile
The analysis predicts that the radial profile of enthalpy in the constrictor will
be a Bessel function of the first kind and of zero order. The ratio of center-line
enthalpy to radially-averaged enthalpy would then be 2.3. The estimated ratio
of center-line enthalpy to average enthalpy based on measurements at the end of
the nozzle was 2.7 (see Figure 6). Therefore the enthalpy profile appears to be
more peaked than the analysis predicts.
SCALING LAWS
Laws for scaling the constricted-arc supersonic jet can be deduced from the
analysis for the range of throat sizes and pressures for which the flow remains
laminar and for which the conduction heat loss is much larger than the radiation
loss. The sizes and pressures for which the flow becomes turbulent are not known;
however, theoretical calculations indicate that radiation losses become important
in the |-inch unit at pressures over 10 atmospheres. Stine and Watson treat the
scaling laws in detail, but we shall here present only the more interesting results.
Length and Flow Rate
The throat length and the mass flow rate do not affect the enthalpy independ-
ently. Only the ratio of z\w appears in the solution. Therefore, an increase in
length is equivalent to a decrease in flow rate. For this reason, the dimensionless
length, zjz , where z a = wc p jnk, is used hereafter.
shepard and watson : Constricted- Arc Discharge 271
Enthalpy
The radially averaged enthalpy is given by
where
f(l\ = (i_ e -ii-5^o)i?
For constant z/z , the enthalpy increases as the first power of current and increases
with the inverse of the throat diameter.
Voltage Gradient
The voltage gradient is given by
E oc l
and is independent of current.
Heat Flux
The heat flux to the throat wall is given by
q oc
or
D* f \z )
h F
'"J
For a given enthalpy, the heat flux decreases with increasing diameter. Therefore,
assuming a given throat-cooling capability, the highest enthalpies should be
obtained at the largest diameter for which the flow remains laminar and for which
the radiation loss can be neglected.
CONCLUSIONS
We conclude, therefore, that an arc can be passed through a supersonic nozzle
without disrupting the flow, that much higher enthalpies can be achieved by this
process than from the more conventional plasma generator arrangements, and that
the qualitative characteristics of the constricted-arc supersonic jet can be predicted
from the analysis of Stine and Watson.
NOMENCLATURE
A Parameter of the approximation a = A<f> used by Stine and Watson
mho-sec/Btu
c p Specific heat at constant pressure, Btu/lb °F
D Diameter
E Voltage gradient, volt/ft
H Local total enthalpy, Btu/lb (defined as zero at 530°R)
H B Mass average total enthalpy, Btu/lb (defined as zero at 530°R)
h E Radially averaged enthalpy, Btu/lb (defined as -3500 at 0°R)
272 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
/ Current, amperes
k Thermal conductivity, Btu/ft °R sec
p Pressure, atmospheres
p t Impact pressure, mm Hg
q Heat flux, Btu/ft 2 sec
q s Stagnation-point heat flux, Btu/ft 2 sec
r c Radius of the current-carrying cylinder, ft
ib Gas mass flow rate, lb/sec
z Axial distance along the column (1), ft
2 wCpInk (1), ft
d> Conductivity function, jk dT, Btu/sec ft (defined as -0.3 at 0°R)
Subscripts
( )? Value at large z/z
( ) c Downstream end of constrictor
( )(j Center-line value
REFERENCES
1. Stine, Howard A., and Watson, Velvin R., "The Theoretical Enthalpy
Distribution of Air in Steady Flow Along the Axis of a Direct-Current Electric
Arc", NASA TN D-1331, 1962.
2. Hansen, C. Frederick, "Approximations for the Thermodynamic and Transport
Properties of High-Temperature Air", NASA TR R-50, 1959.
3. Ahtye, Warren F., and Peng, Tzy-Cheng, "Approximations for the Thermo-
dynamic and Transport Properties of High-Temperature Nitrogen with
Shock-Tube Applications", NASA TN D-1303, 1962.
4. Viegas, John R., and Peng, Tzy-Cheng: "Electrical Conductivity of Ionized
Air in Thermodynamic Equilibrium", ARS Journal, 31, 5, 654 (1961).
5. Yos, Jerrold M., "Transport Properties of Nitrogen, Hydrogen, Oxygen, and
Air to 30,000°K", AVCO Corporation Technical Memorandum RAD-TM-63-7,
March, 1963.
1 5 . Philip Brockman, Robert V. Hess,
and Richard Weinstein:
Measurements and Theoretical
Interpretation of Hall Currents
for Steady Axial Discharges in
Radial Magnetic Fields
12? Experiments for a Hall-ion accelerator are presented using axial
electric fields and radial magnetic fields. Measurements of the variation
of Hall currents with magnetic field for various constant axial currents
are presented together with voltage variations. The pressures in the
experiments vary from 15 to 40 [L, the magnetic fields from to 500
gauss, and the currents from 1 to 40 amperes. The Hall currents first
increase with magnetic field and then decrease again as the magnetic
field is increased. The variation can be interpreted in terms of Joule-
and ion-slip losses for the partially-ionized plasma used in the
experiments. The effect of transition to turbulence is also evaluated and
the present state of the theory for turbulent conduction is discussed.
Preliminary experiments for preionization and for the heating of
ring-shaped cathodes to thermionic emission are discussed.
INTRODUCTION
The research on acceleration of plasmas or ions in plasmas using azimuthal Hall
currents and radial magnetic-field components has grown considerably since the
early work on Hall current plasma accelerators at the NASA Langley Research
Center (1), and the subsequent description of an added ion acceleration mechanism
for improvement of a traveling wave accelerator by AVCO Everett Research
Laboratory (2). The final grouping of the latter mechanism of ion acceleration under
the principle of Hall-ion acceleration is based on the efforts of many research
laboratories: Electro-Optics, General Electric, the Lewis and Langley Research
Centers of NASA, and United Aircraft. A history of the development of Hall
ed. note: Mr. Brockman, Mr. Hess, and Mr. Weinstein are with the NASA Langley
Research Center, Langley Station, Hampton, Va. The research for this
paper was performed in the Plasma Physics Section of the Magnetoplasma-
dynamics Branch. Part of the material in this paper has been presented by
Mr. Brockman as a thesis in partial fulfillment of the requirements for the
degree of Master of Arts at the College of William and Mary.
273
274 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
current accelerators is given in reference (3) in the section "Acceleration Using
Hall Currents". (Note: one of the earliest contributions published in this field, ref-
erence (17), was omitted in this review.) The reason for the interest in Hall current
accelerators is that they offer the possibility of magnetic containment, increased
uniformity of discharges, reduction in electrode erosion, and operation over a very
wide range of density and specific impulse.
There are several reasons for measuring Hall currents. One more or less obvious
reason is that it gives an independent check of the thrust, which can be compared
with direct thrust measurements. In this connection it should be noted that the
total voltage drop must overcome the losses as well as accelerate the ions, so that
this voltage drop is only a true measure of the acceleration of the ions if the losses
are small.
The present measurements of Hall currents differ from those previously per-
formed at the Langley Research Laboratory (4, 5), in that a much greater number of
measurements were made at various axial currents and magnetic fields. By cross-
plotting the results to indicate variation of Hall currents with magnetic field at a
variety of constant axial currents, it was possible to establish more definite trends
which were only suggested by the experiments in reference (5). Simultaneous
measurements of the variation of axial voltage drop with magnetic field Mere also
performed. In the present experiments measurements were also made over a wide
current range for considerably lower pressures than previously reported by us.
A special effort has been made to evaluate up to what point the novel effects can be
interpreted through conventional loss mechanisms rather than through the popular
field of plasma turbulence.
Finally, it should be pointed out that the Hall current apparently can provide
vital information on certain anomalous or "turbulent" conduction effects which
have recently received considerable attention. In the first (to our knowledge)
study of instabilities and turbulent conduction effects in a Hall current accelerator
which was conducted at the Langley Research Center (6), probes which were
placed in the azimuthal direction of the Hall current indicated that although coaxial
symmetry was imposed by the electrodes and the magnetic-field distribution, the
plasma did not maintain symmetry under all conditions. At the same meeting
Dr. Buneman independently emphasized in the Round Table Discussion, the
importance of checking for plasma asymmetries in geometrically symmetric
experimental arrangements. The azimuthal Hall current could be especially
sensitive to deviations from symmetry and thus could offer a clue to the transition
from conventional to turbulent conduction. Preliminary application of these
concepts to the Hall-ion accelerator are discussed in the preprint with more details
to be presented in the talk.
Experiments for the preionizer and the thermionically heated cathodes have to
date been made in a separate test apparatus. The preionizer was designed and
operated by J. Burlock and T. Collier, and the heated cathode by 0. Jarrett.
Details are given in Appendices B and C.
An experimental study of the influence of preionizers and heated cathodes on
Hall currents, electric fields, and oscillations is being undertaken.
The major purpose of this paper is to gain an understanding of the acceleration
mechanisms in a low-pressure Hall current accelerator. From a more fundamental
viewpoint it is the aim to obtain an understanding of the mechanism of electric-
conduction across a magnetic field in the presence of ion motion.
Hall currents also have been measured for a high-power, high-pressure plasma
Hall accelerator, and a Hall-ion accelerator operating in this range also has been
constructed. Also note studies made at Electro-Optics (7).
brockman, hess, and weinstein: HaU Currents
275
APPARATUS
A schematic of the apparatus is given in Figure 1. The electrodes are 7.3-cm
I.D. inserts within water-cooled holders. The inserts are copper at the anode and
aluminum at the cathode in the experiments reported here, but these may be
easily replaced by any other material. The edges of the electrodes and the glass
are protected from the discharge by boron nitride insulators; these insulators leave
2.54 cm of the electrodes exposed to the discharge. The center glass is 7.3-cm I.D.
and the discharge length is 22.86 cm. On either side of the discharge the electrode
holders are connected to glass crosses. These crosses contain Hastings thermocouple
vacuum gauges. The anode cross is connected to the gas input and the cathode cross
leads to the vacuum system. The cathode cross also contains a cantilever support
for a bakelite rod which, in turn, supports an iron bar in the center of the discharge.
The iron bar is centered under the magnet and is 22.9 cm long, the bar is 3.16 cm
O.D. and has a 1.27-cm hole through the center. This hole contains a teflon rod
which is screwed to a boron nitride insulator at the anode end and to the bakelite
rod at the cathode end. The iron bar is covered by a 38-cm pyrex tube. This
cantilever arrangement was designed so that the accelerator can be mated with
any type of preionizer at the anode and without changing the configuration or
interfering with the flow from the preionizer. The magnet solenoid is 2.8 cm long
and its center is 10.16 cm from the anode and 12.7 cm from the cathode. It is a
450-turn coil and is powered by ten 6- volt batteries; it is current controlled by
means of a variable resistor. A search coil is mounted 4 J cm from the center of the
magnet on the cathode side. This is a 100-turn coil and is connected in series with
a ballistic galvanometer. The arc power supply is a 700- volt, 1400-ampere motor-
generator set and is connected to the electrodes through a 10.37-ohm ballast
resistor. The pumping system consists of a cold trap, a 14-inch diffusion pump, and
a Stokes vacuum pump. Figure 2 is a diagram of the magnetic field configuration
for an average radial field of 100 gauss — a rapid increase of axial field strength occurs
above 500 gauss due to saturation of the iron bar.
The investigations reported here are a study of the basic mechanisms of the
discharge. The pumping system at this time is not adequate to remove the mass
flow due to high ion currents. As a consequence, during operation there is a pressure
rise at the pump entrance and a pressure drop at the gas inlet. This results in
O-KINO VACUUM .SEAL
:con COBZ
COIL
cathode:
,— VACUUM
-FLOWMETER
CtHTI LEVER
.SUPPORT
FIGURE 1. Schematic of apparatus.
276
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
a flow of neutral particles from cathode to anode. The back flow or circulation
of neutrals permits the maintenance of high ion currents. A larger vacuum
system (four 35-inch diffusion pumps) is now under construction, to be used for
experiments at high specific impulse.
OPERATION OF DISCHARGE AND MEASUREMENTS
As the solenoid is in the center of the discharge, the radial magnetic field reverses
direction from the anode side to the cathode side of the discharge. This will also
reverse the direction of the Hall current and of any gas rotation as these are
functions of v x B. However, the forces will remain in the same direction as these,
in turn, are functions of (v x B) x B. Thus, the reversing magnetic field has the
advantage of tending to destroy any gas rotation which may build up on one side
,. /.,
m.mm-
.-— iE/ECH COIL
CATHODZ
tMS^IlMI
?o uc 55 60 70 80 90 60
50 60 80 90 100 120 HO 120 Q
1.0 80 115 120 lW 160 ISO 160 Meters ',
10 1 *
" " I g=
BAKELITE
50 ^5 ^ 55 20 10 5 ItO
W 50 25 15 10 5 ;'
50 20 15 10
15
Br av. ^ 100
"
? * e ?l
FIGURE 2. Schematic of magnetic field configuration.
of the magnet. On the cathode side of the discharge the gas will enter with any
rotation that has built up; on the anode side the rotating force will then be reversed
and the average rotation on the cathode side should be close to zero.
The discharge for these experiments was operated with no preionizer. Thus, all
ionization was supplied by the electric field. Starting ionization was supplied by a
Tesla coil, but this was turned off before any measurements were taken. Voltage
and current were monitored on standard meters and also recorded on a Consoli-
dated Electric Co. oscillograph. Pressure was monitored on two Hastings thermo-
couple gages and also recorded on the oscillograph. Hall current was measured by
means of a 100-turn search coil and ballistic galvanometer. The discharge was
turned off and the collapsing magnetic field of the Hall current induced an EMF
in +V?o ?porpVi pru'l Trip sporpVi noil was pn.rmpnt.pn 1 in QpripQ tn the ballistip ornlvn.rm-
brockman, hess, asd weixstein: Hall Currents 277
meter through a 15-ohm resistance; the current through this circuit was integrated
by the ballistic galvanometer giving the total charge. This charge is proportional
to the original Hall current. The ballistic galvanometer was calibrated by placing
two 80-turn coils in place of the Hall current. These coils were 5.3 cm in diameter
and 7 cm in length. The ballistic galvanometer was calibrated by running various
currents through the coils. The direction of current was reversed in the two coils to
represent the Hall current. When the current was turned off, the reading on the
galvanometer was taken. The calibration was retaken at several magnetic field
strengths in order to see if any saturation of the iron bar was affecting the readings.
A slight drop in reading was noted at 550 gauss but this drop was within reading
error. However, the sudden increase of the axial field at saturation may explain
the sharp dropoff in Hall current. This effect is negligible below 550 gauss. The
ballistic galvanometer was calibrated in amperes and the area of the Hall current
was estimated at 17.79 cm 2 . According to visual observation the discharge area
did not vary much above a magnetic field of ~ 10 gauss. The current was multiplied
by 10 4 /17.79 to give amperes/m 2 . The axial current was multiplied by 10 4 /30.59 to
give amperes/m 2 and the arc voltage multiplied by 100/22.86 to give volts/meter.
Mass flow was measured by a tri-flat flow tube and a standard pressure meter.
Magnetic field was calibrated versus current in magnet by a gauss meter. Magnet
current was set with a standard ammeter.
In operating the discharge, pressure was set using a variable leak; the voltage
across the electrodes and the magnetic field were preset. The discharge was started
with the Tesla coil and when voltage and current oscillations as observed on the
meters had settled out, the oscillograph was started and the switch controlling
the ballistic galvanometer was depressed. The discharge was then turned off and the
reading on the ballistic galvanometer taken by hand. Ideal operation would have
been to operate the discharge at constant current for various magnetic-field
strengths. However, as the power supply was not current controlled it was both
difficult and time consuming to adjust the current during each run. At each
magnetic-field strength the discharge was started at various voltages; the running
voltage and current were allowed to adjust themselves. After preliminary data
reduction, more data were taken in regions of interest. In order to extend the
range of currents at high magnetic-field strengths, it was sometimes necessary to
start the discharge and then decrease the voltage. Data were taken at 15, 30, and
40 microns and these data are presented in the form of arc voltage in volts/meter
and Hall current in amperes/m 2 plotted versus arc current in amperes/m 2 for
various magnetic-field strengths.
The data were then cross-plotted to give arc voltage and Hall current versus
magnetic-field strength for various arc currents. These curves are presented in
Figures 3 through 6.
The primary purpose of this study was to measure the Hall currents. Making a
survey of any parameter is time consuming and thus several measurements which
are needed for a complete analysis have not yet been made. A program has been
active for some time to measure local voltage drop with floating probes and to make
some measurements of ion density and electron temperature with Langmuir
probes and double probes. The floating probe errors should cancel if the probes are
close together so that the plasma conditions are equal at both probes. However,
the magnetic field will influence the electron temperature and ion density measure-
ments to some extent (8). The variation of these parameters should be comparable
at any constant magnetic-field strength, but there is some question in comparing
measurements taken at different magnetic-field strengths. An attempt will also
be made to measure velocities and forces in the accelerator.
278
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
//
if
I- *.,
ft
4'°
(?) v . 1' n ".:■
(t>) p-JOiiffi.
/"??
/A
/■ft.
M--
_.:■ ' --~-t—
(c) p . to jiHi.
FIGURE 3. Hall current density versus axial current density for various magnetic
flux densities.
A few basic measurements of oscillations in the discharge have been made with a
simple metal plate capacitively coupled to the discharge through the glass. A
survey of oscillations with probes placed in the plasma will be reported.
INTERPRETATION OF RESULTS
The most striking result found is the increase, peaking, and decrease of Hall
current with increase of magnetic field at constant axial current. The initial
increase of the Hall current with increasing axial current at constant magnetic
field and the form of the arc voltage versus axiai current curves at constant
brockman. HESS. AND weinstein: Hall Currents
279
^1
1
, J, UeberaV
.?
.06
(O j - 20 * ife.
72ld
— 1585
■ — ?930
--- 527^
Mnene-.ic fiux ijeoslty, 1. Iktwn^
FIGURE 4. Hall current density versus magnetic flux densities for various axial current
densities.
magnetic field has been previously reported (4). The shape of the curves of arc
voltage versus magnetic-field strength are different in certain regions than those
normally reported in, for example, references (9) and (10), but this may be due to
the inherent errors in measuring total arc voltage rather than local electric field,
or it may be due simply to our particular operating conditions.
Since the experiments are concerned with a partially ionized-plasma in a
magnetic field and include the motion of ions with respect to neutrals, it is of
interest to see to what extent the experiments can be interpreted in terms of the
conventional generalized Ohm's law including ion slip. The influence of turbulence
is discussed in a later section.
10+
280
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
-■S-o..?*-.--o
o c>
/ Ac
* ?
D e-e-
(?) P - ^ H Kg.
--G - - <* O t
(M p - JO ? H ? .
(c) p -i.0 m Hg.
FIGURE 5. Electric field versus axial current density for various magnetic flux densities.
Repeating equation (A4) from Appendix A, which is the complete equation for
j e including motion of ions and neutrals but not turbulence,
-je = ^Ajz-n e ev x )
(1)
The inclusion of 2co t T i a> e T e in the term
W =
1+2,
COpT.CO.-Tj
gives the influence of ion slip. The ion slip term will increase W and, therefore,
decrease^ at constant magnetic field. However, solving equation (A2) for E' x ,
l + W* j x B v x B
W n e e W
The effect of ion slip on E' x is more complicated than on j g . The term
1 + W 2 1
W
rp+IF =
■ +
1+2,
CO^T.CO.T,-
1 + Za) e T e CU,Ti U) e T e
(2)
(31
brockman, hess, and weinstein : Hall Currents
281
/ H
5275
-K . j .<* .&
^70
CO r - ~ 1. He
FIGURE 6. Electric field versus magnetic field strength for various axial current
densities.
Thus for TF?1 an increase in cujTj will decrease E' x (through an increase in ion
current) but for Wy>\ an increase in ca i r i will increase E' z (neglecting v e ). For
constant j x the increase then decrease of —j g is due either to variations of W, v z
or n e with B. At the particular conditions that we operate n e is probably small and
v z the average (or center- of- mass) plasma velocity is limited, as pointed out in the
section on apparatus. It, therefore, seems that the effect of n e ev x can be neglected,
for the present case.
A simple explanation of the variation of Hall current with magnetic field can be
based on the variation of W with magnetic field. The following assumptions were
made: first, that n e ev z was negligible compared to j x , and, second, that r e and r t
282
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
were constant for j x constant. This second assumption is based on the condition
that r e and t { are not explicit functions of E' x or B. The calculated values of
(x> e T e jB and w^r^B in the literature usually depend on the equivalency of electron
and ion temperatures; we know that our low-pressure operation does not justify
this assumption. In order to generate some theoretical curves for j g versus B,
equation (1) is rewritten in the form
W =
-Je
(4)
and then for a particular experimental curve a calculation is made of the minimum
value of W, as W mln = jj - j e . mAX - The values of u) e T e /B and ojjTj/B, at j e , max ,
were then calculated for this case using equations (All) and (A12).
These values were then divided by the magnetic-field strength at the maximum
j e point. The resultant values of o> e T,, and ajjTj were used with equation (A7) to
calculate W as a function of B. Typical plots of 1/W versus B and (1 + W 2 )jW
are given in Figure 7. Equation (4) was then used to calculate theoretical values of
j e versus B. Equation (2) was used to calculate values of n e eE' x versus B. The
sheath voltage was assumed to be equal to the experimental voltage at B = 0, and
.01
05
.02 .03 .04
Magnetic flux density, B, Webers/m 2
1 1 + W 2
FIGURE 7. Variation of — and — ttt — with magnetic flux density.
W W
brockmais', hess, and WEINSTEIK : Hall Currents
283
it was also assumed that n e was constant; for constant j x a value of n e was chosen
so that the highest point of the experimental and theoretical E' x versus B curves
would match and the assumed sheath voltage was added to the theoretical curves
so that the bottom points would also match. Thus, only the shape of these
curves can be compared. The method of calculating W mia , of course, forces the
experimental and theoretical Hall current curves to match at j e , m ax- I* 1 Figure 8
experimental and theoretical curves of j e versus B are compared for ^ = 3930,
5240, and 9170 amp/m 2 ; at j I = 3930 amp/m 2 , 1^=0.2, 5=0.015 web/m 2 ,
oi e T e /B=668, <u i T i /B=3.32; at ^ = 5240, JF mln = 0.1158, 5=0.015 web/m 2 ,
w e r e IB = 112, co i T i /B = 2.9; at j x = 9170, JF mln =0.1274, 5=0.0125, <o e T e /5=1256,
exio 1 * -
. Experiment
Theory
CM
.6
c
p = JO (I Hg.
I
.01 .02 .05 .04
Ifegnetic flux density, B, Vfebers/m^
?05
.06
FIGURE 8. Comparison of theory and experiment (Hall current density versus magnetic
flux density).
284
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
2800 r-
2ltfX>
Ox ~ f'S'tO amp lv?
2000
1600 —
1200 ■-
800 —
U00
.01
? 05
.06
?02 .03 .01+
Magnetic flux density, b, Webers/ra 2
FIGURE 9. Comparison of theory and experiment (electric field versus magnetic flux
density).
co j T i /fi = 2.55. In Figure 9 the theoretical and experimental curves of E' z versus B
are compared for j x = 5240 at 30 microns Hg. We added 247 volts/m to the the-
oretical curve to account for sheath voltage at B = 0; for curve matching n e was
adjusted to be 2.67 x 10 18 particles/m 3 . This corresponds to a very reasonable low
percentage ionization. The values of oijTj/5 show good agreement with theory if
the cross sections, Q in _ ex , for resonant charge exchange (18) are used in the expression
for t ( = A in /c = ^-l{n n Q inez c). The mean free path A jn is at least of an order of magni-
tude smaller than the length of each accelerating section so that sufficient collisions
of ions with neutrals can take place to develop friction between the two species
characteristic of the ion-slip concept. This should even be true when the directed
ion velocities exceed c. Detailed calculations of aijTj depending on random (tempera-
ture), or directed-ion energies, neutral temperatures, and densities will be presented
elsewhere. Ion-wall collisions must also be considered at pressures slightly below
those reported here. Calculations for oj e T e jB for a variety of electron temperatures
bbockman, hess, and wbinstein: Hall Currents 285
considerably in excess of ion temperatures and for various charged-particle concen-
trations also show good agreement. The Hall current curves match quite well and
seem off by only a slight rotation. This can be due to the error involved in neglecting
various effects when calculating W^n- The E' x does not match as well except at the
low- and high-magnetic-field strengths, where the general curvature is the same.
In matching theory with experiments, one must also be reminded that the values
for E' x in Figures 5 and 6 are based on averaging the voltage drop over the length of
the apparatus including sheath drop. Only isolated measurements have been made
so far of the voltage distribution in the accelerator. A complete survey is, however,
necessary to obtain a more detailed account of the contribution in sheath drop
with varying magnetic field. One should also be reminded that the electric field
appearing in the equations is given by E' x = E x — v e B where E z is the measured
quantity.
Although special care has been taken to reverse B in the acceleration process, a
certain amount of rotation will exist. The effect of rotation can also reduce j e lj x , but
it appears unlikely that it would be the sole effect since the drop in j e begins at
values of tOjTj (which approximately equals Aj/r Lj ) considerably below unity and
the center-of-mass velocity is small. Prehminary observations of the rotational
speed of the discharge also indicate that it is low.
Before it can be stated with assurance that ion slip is the main contributor, and
not turbulence (see next section), several additional measurements are necessary.
These include measurements of n e , v x , local measurements of E x , and measurements
of turbulent effects. Also, measurements of electron and gas temperatures would be
helpful in directly calculating values of t? and t ( .
COMPARISON WITH OTHER THEORETICAL APPROACHES
NEGLECT OF ION SLIP AND LOSS-FREE CASE
For negligible values of u> e T e <o i T t the ion-slip losses can be neglected and equation
(A4) in Appendix A changes from
<O e T e .
~Je = TTo Oi-'W
l+2tt> e T e CO,T,
to
/, n.ev x \
-Je = Jz<?ere\l y-j (5)
where the center of mass velocity v x in equation (5) does not include the motion of
neutrals. For small values of ion flow, equation (5) assumes the familiar form
~ j j = ?.T. (6)
Jz
Equation (A2) for j x changes for negligible ion slip from
l+2w e r e <o i T i E' x , ?
Jz = n e e ■
1 [ / l+2ai e T e cu i T i \
\ <"e-r e I
I n e e E'\
Jz = [n e ev x + ^
to
/ n e e E'\[ 1
1 = I -n Oil -I i I
(7)
1 +
(— )
286 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Solving equation (7) for v x and substituting into equation (5) for j B gives
E' i
-Je = n e e^-J±- (8)
Equation (1) indicates that the inclusion of ion motion will reduce the value
°f jelji below w e r e and equation (8) shows that with increasing co e T e
-Jo->n e e^ (9)
Noting that for large w e T e values j x in equation (7)
j x -> n e ev x (10)
the limiting value for j e lj x is
-i'-*§! (ii)
3x B v x
Since for the loss-free case the ions are electrostatically accelerated,
l2eV
Assuming E' x l = V,
Equation (12) shows how much j e /j x will be reduced below the increasing w e r e
as the losses decrease with increasing B, if an increase in the flow of ions is allowed.
The transition to smaller losses as B increases beyond the Hall current peak in
Figure 4 is, however, most unlikely in the present experiment.
Another possibility for a decrease in j B jj z with B after the peak, for a constant
j x , can be explained from equation (8) in terms of a decrease in r e or a decrease in n e
with increasing B (assuming that E' X }B is constant or increases). Since
_ A _ 1 1
Te ~ a ~ 2 nQ c
a decrease in i- e , barring an increase in n e (which would also decrease j e ), would
require an increase in the collision cross section. The possibility of such a decrease
will depend very much on T e and the degree of ionization, which help to determine
whether elastic collisions of electrons with neutrals, or with ions (Coulomb colli-
sions) predominate. Of course, a check has to be performed if such changes in r e and
n e could agree with the experimental variation of E' x with B for high values of
j x = constant, when ion-slip losses become negligible. The neglect of ion-slip losses
applies when the friction force, Jwijj/j^j — v n ), between ions and neutrals is small.
See equations of motion in reference (6). This is true for dense plasmas with low
percentage ionization and slow acceleration where v n differs little from v t , as well as
for fully-ionized plasmas where with vanishing of neutrals the collision frequency
i>j, between ions and neutrals, approaches zero. Neglect of ion-slip losses may also
apply to the acceleration of very low-density plasmas in the Hall accelerator, when
collisions between (approximately) axially moving ions and neutrals are scarce, but
the collisions of electrons, moving in a spiral path, with ions or neutrals, are more
frequent. Experiments using accelerators with length below A,? will be useful in
?U^ol?^*? +U~ ,?*.;?i^ w ??i :
beockmax, hess, and weinstein : Hall Currents 287
In looking for simple effects the influence of rotation also has to be considered.
For the neglect of ion slip the rotation appears only in the term E' x = E x — v e B. It
must be remembered again that E x is the measured quantity so that v e B could
reduce j e with increasing B. The effect of rotation alone, however, does not seem
well suited to explain the pronounced increase and decrease of j $ with B. Integra-
tion of the simultaneous equations of motion for the ions, electrons, and neutrals
is in progress to check if there exists a density range where rotation must be
considered. Experiments with plasmas for which the ion slip is known to be small
will be performed using injection of low-density, highly-ionized plasmas.
EFFECT OF TURBULENT CONDUCTION MEANING OF LINEAR
VARIATION OF E' z VERSUS B FOR TURBULENT AND
CONVENTIONAL CONDUCTION
In the theory for turbulent conduction (11) adapted to the present case in
references (9) and (3), two basic assumptions are made. One is that the ions are
assumed at rest, and, second, the influence of turbulence on j g and the possibility
of polarization of the oscillations is not taken into account. The neglect of ion
motion limits the theory to high-frequency oscillations with frequency larger than
the ion cyclotron frequency. The applicability of this restricted theory to the
interpretation of comparatively low frequencies at high magnetic fields (9) thus
must be examined in detail. Recently the theory developed in reference (11) has
been extended in reference (12) to include ion motion, and the result was obtained
that ion motion greatly reduces the effect of turbulent conduction. This result
seems in contrast to the discussion of the growth of other instabilities of plasmas
in magnetic fields in reference (12) and of the relevant stabilities discussed in
references (6), (13), (19), and to one unpublished discussion of instability of hollow
cathode discharges by D. L. Morse of M.I.T. where the presence of ion motion is
essential for such growth. Detailed measurements have to be performed to under-
stand to what extent the ions influence the turbulent conduction process and to
decide which instability has the greatest effect in producing the turbulent state.
Also, a careful separation has to be made between the effects of ion slip and turbu-
lence since both may reduce j e jj x .
Next, the influence of turbulence on the azimuthal Hall current j e is evaluated.
For this purpose, the basis for the development of the theory for turbulent con-
duction in reference (11) has to be briefly discussed. The theory deals in essence
with turbulent conduction and diffusion assuming isotropic turbulence. It can be
regarded as a limiting case for small random non-uniformities of the theories of
conduction in plasmas with distributed non-uniformities in the presence of Hall
effects; these theories were independently developed (6, 14). Since non-uniformities
affect the Hall current it appears proper to include their influence also in a theory
for turbulent conduction, especially since it was shown experimentally (6, 19), that
the instabilities have their origin in azimuthal phenomena.
Since the effect of turbulence on the Hall current has not been considered in the
literature, an attempt is made here to introduce it formally in analogy to the effects
of turbulence on the axial current. (Note that in this attempt we have avoided the
inclusion of the important ion oscillations which may even affect v x .)
E'
j x = an e e-jZ + n e ev x (13)
10*
288 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
where a under the neglect of ion motion is given by
Comparison with equation (7) for the fully-ionized case indicates that w e T e has
been replaced by a constant 1/a. The quantity a is assumed to be about yV in
references (11) and (9). The possibility also must be considered that the reduction of
j g with B could be influenced by transition to turbulent conduction. Experiments
for a highly-ionized plasma, using a pre-ionizer, should help to emphasize the
turbulent effects by keeping ion slip small.
The turbulent losses could be introduced into j g in formal analogy with equations
(5) and (8) for the fully ionized case, with the result
-je^j.-ll-^f 2 ) (14)
? \ 3x1
and
-jo = n e e-^-aj t (15)
While such a theory would indicate a reduction in j g from the non-turbulent case,
an increase in a with B would be necessary to explain the decrease in j g /j x .
Since an increase in a with B would also influence the E' x versus B relation in
equation (13), the important question also arises as to whether the turbulence
differs in the axial and azimuthal direction, that is, is polarized in the magnetic
field rather than isotropic. The possibilities that the oscillations may not develop
into fully-turbulent flow because of finite dimensions or that the oscillations can
cause an increase in resistivity without changing the proportionality of E x to B 2
(19) must be considered also.
Finally, a brief evaluation of the influence of turbulent conduction on the
variation of E' z versus B is made. In the absence of ion motion the conventional
conduction across B changed from [see equation (7)]
to [see equation (13)]
_ n e e E' x n e m e 1
■?* _ T7T ~b = —^ ~?2 A * ( lb )
jx = <xn e e -^ (17)
Assuming constant values for n e , r e , a, and j x , for conventional conduction
E' x oc B 2 (18)
while for turbulent conduction
E' x oc B (19)
It should be noted in this connection that some curves in Figure 6 representing
the variation of E' x versus B could, with a little imagination, be interpreted as show-
ing transition from square to linear dependence for the higher currents. This
transition seems to occur approximately for values of B where the Hall current
begins to drop in Figure 4. As noted before, however, since the drop in Hall current
does not seem to fit into existing turbulent theory, excluding the influence on j g ,
the possibility of polarization and the effect of ion motion would have to be studied
to evaluate what could be very important effects in turbulence. The effect of ion
brockman, hess, and weinstein: Hail Currents 289
motion has also a very simple influence for n e ev x = constant, since as v x increases
n e is decreased, which in turn can change the term an e eE' x jB and thus the variation
of E' x with B.
Hence, the importance of obtaining a better theory and more measurements for
turbulent conduction, including ion motion across B in the presence of neutrals,
and for turbulence in the azimuthal direction of the Hall current is very evident.
Before such advances are made, the influence of turbulence is difficult to assess,
except with many more careful measurements. This, of course, does not mean that
means for delaying transition to turbulence may not be found before turbulence is
fully understood. Theoretical reasoning (3) and experiments and theory for other
discharge-magnetic-field instabilities (15) suggest that preionization, with resulting
reduction in E' x , should give such a delay. Proof must wait for experimental results.
The question also arises as to whether the change from square to linear depen-
dence of E' x on B can be explained by mechanisms other than the transition
from conventional to turbulent conduction. A deviation from the parabolic
characteristic can also be interpreted in terms of ion slip, since the latter is a loss
which reduces the impedance due to high Hall currents alone, which is the basis
for the parabolic characteristic. This reduction in impedance occurs, in essence, for
^i^t — 1, since for ojji-j > 1 a related increase in impedance as occurred originally due
to w e T e > 1 sets in, with resulting tendency again toward E' x ccB 2 . (Note that v e B,
due to rotation, can modify the effect.) Since most of the experiments performed so
far in the Hall accelerator are in the range of cojTj^I, the change from square
dependency and even a transition to approximately linear dependency could be
possible, especially if the possibility of variations in r e , T? and n e are also included.
The question also arises as to what extent a linear variation of E with B could be
explained through ionization and diffusion. The various possibilities of influencing
the conduction across a magnetic field for partially-ionized plasmas, with pre-
dominance of electron-neutral collisions or electron-ion collisions are discussed in
reference (20). In accordance with equation (16), if n e JT e azB, j x azE' x IB, or for
j x = constant, then E' x ccB. Experiments with high-density plasmas where oscilla-
tions and ion-slip losses are small showed EccB, meaning that effects other than
oscillations can cause EccB. The calculation of the variation of the ionization with
B requires the use of the energy equation. Preliminary studies of the energy balance
were reported in reference (16). A detailed study of the energy balance including
non-equilibrium effects (since J , c ?T j ) and radiation was in progress at the time of
the publication of reference (20), and will be reported elsewhere. Finally, it would
be of great interest to study the effect of random non-uniformities or turbulence on
non-equilibrium ionization.
Appendix A
EQUATIONS FROM OHM'S LAW
Ohm's law in the presence of a magnetic field can be written (6, 7) in the following
manner where the factor 2 with the term 2to c x e co i T j is included in t ( (7):
(w e T e ) 2 +(i+2<o e T e a> i T i r v ???""■'" b
290 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
In the linear Hall accelerator E r , E?, v r , B x , and B g are all taken as zero. Noting that
ct _ n e e
and defining
w _ l+2co e T e aj iTi 1
<O e T e (V?T,
The expressions for j x and j B are
n ° e 1 + W 2
E'
(A2)
B Wv *
-je = n e e 1+}y2 (A3)
We use —j e since the Lorentz force in the axial direction is -j e B r . Three other
expressions for -j? can be found by eliminating E' x , v x , and n e from the above
equations:
-3b = fj?Ux-n e ev x ) (A4)
W
~B~
F"
-3e = n e e-^-Wj x (A5)
§-Wv x
~3e = p jx (A6)
W^ + v x
If f° r 3x constant, r e and t ( are also assumed constant, W will be a function of B
only,
1 9.pt.
(A7)
and
1
?PT
w
e -^B
m e
+
m i
'-B
dW
1
2e
dB
e
T?B 2
tn e
d 2 W
=
2
dB 2
e
T e
B 6
m e
(A8)
(A9)
Thus IF will have a minimum value at
m, m.
LGi.T-tli^T,
= 1 (Mm
bkockman, hess, and weinstein : Hali Currents 291
and at this minimum value
W mla = — (All)
and
2w,t, = — (A12)
°>e T e W = min
Appendix B
METHODS OF PREIONIZATION
REASONS FOR PREIONIZATION
As pointed out in the discussion of turbulent conduction in the body of the
paper, the effect of preionization is not only to increase the number of ions being
accelerated over the full length, its function is also to delay the onset of instabilities
and transition to turbulent conduction by reduction of the voltage which provides
energy for the growth of instabilities and turbulence. Two methods of preionization
will be discussed. One makes use of a coaxial preionizer with magnetic field which
injects a plasma stream into the accelerator. Such a preionizer has been designed and
operated. The second method of preionization is actually a method for supplemen-
tary ionization in the accelerator region itself. Such an approach has been tried for
delaying the onset of instabilities of an arc column in an axial magnetic field (15)
and will be applied to the present Hall-ion accelerator.
DESIGN AND OPERATION OF ARC PREIONIZER
J. Burlock and T. Collier
Method and Design
Most preionizers for the low-density plasma accelerators consist of some form of
PIG discharge with externally-heated, thermionically-emitting cathodes. In order
to obtain a highly-ionized plasma, the use of high currents in the preionizer becomes
desirable; for that purpose it has to operate in the arc mode. For injection into the
Hall-ion accelerator with a center core it is, furthermore, desirable to produce a
plasma stream which is concentrated, more or less, in a cylindrical annulus.
These various requirements suggested the use of a tungsten disk cathode self-
heated by the arc discharge inside a ring anode. The design is shown in Figure 10.
The arc discharge establishes itself mainly in the space between the edges of the
disk and the anode and is blown into the accelerator. The edges of the disk can act
as an electric field concentrator and facilitate the starting and act to maintain the
discharge in this position. The magnetic field can be purely axial or somewhat
slanted giving the effect of a Hall current plasma accelerator. The disk cathode was
supported by a center sting with much smaller diameter, which resulted in uniform
heating of the cathode disk, since only a small ( J-inch) spot was cooled by presence
of the rod. The major mechanism for removal of heat from the disk was radiation.
292
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
FIGURE 10. Arc preionizer.
Operation
A high- voltage, low-current glow discharge produces the initial heating. A rapid
shift to high-current operation follows as the cathode reaches emitting temperature.
The cathode disk appears uniformly heated except for the central region, where the
supporting rod is welded. Operation appeared quite smooth except for the occasional
appearance of anode spots. (Operation in this instance was in argon at 30 microns
pressure, and 15 to 18 amperes at several hundred volts in a magnetic field of
5000 gauss.)
METHODS FOR SUPPLEMENTARY IONIZATION
IN ACCELERATOR
The basic requirement for any technique of ionization enhancement is that the
Hall current accelerator mechanism should not be disturbed. Several possible
techniques for obtaining the desired ionization will be discussed briefly.
Electrostatic coupling of high-frequency energy directed radially along the flux
lines could be used. For frequencies much below plasma frequency, it would be
necessary to minimize the impedance of any dielectric intervening between the
electrodes and plasma because of the relatively low impedance of a highly over-
dense plasma. However, if leads through the structure are permissible, the electrode
could be placed inside, and the dielectric problem would not occur. Electrode
cooling in this case would also protect the glass wall.
Inductive coupling of high-frequency energy by means of a solenoid has been
used to increase ionization and reduce the axial electric field. The presence of the
radial magnetic field of the Hall accelerator transverse to the induced azimuthal
electric field hinders the coupling of energy, and relatively high powers are required
brockmax. hess. and welnsteix: Hall Currents
293
to produce appreciable changes in conductivity and axia] electric field. Operation
at electron cyclotron resonance frequency would provide an important coupling
enhancement. For this operation the magnetic fields of interest for the acceleration
process, with intensities of hundreds of gauss and higher, would call for power at
frequencies to the order of hundreds to several thousand megacycles. A reasonable
upper limit for the resonance technique could be at between one and two thousand
gauss, where high power at the corresponding cyclotron resonant frequencies (in
the kilomegacycle range) is still reasonably available. Since the electron motion is
bidirectional, it should probably not interfere with the undireetional fields and
current flows of the accelerating process. It could perhaps provide additional
stabilization (3).
One other possible means of enhancing ionization would be the use of electron
ionizing beams, which have proved successful in generating plasmas of reasonably
high densities (20) and hollow cathode plasma injection.
Appendix {'
DESIGN AND OPERATION OF AN EXTERNALLY-HEATED RING
CATHODE
Olin Jarrett
Most designs for externallydieated cathodes for thermionic emission use either a
tungsten filament heated b\- Joule losses due to resistance or a tungsten disk
heated by electron bombardment. Since in the Hall accelerator the use of axiallv-
symmetrie cathode shapes, especially ring cathodes, is highly desirable, another
method of cathode heating was tried which ideally seems to suit this purpose. This
method of heating also avoids the necessitv of vacuum seals for hot external leads.
FIGURE 11. Inductivelv-heated cathode.
294 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
A RF-heated ring cathode has been constructed and tested. The heated cathode
(Figure 11) consists of a tungsten ring placed inside of a boron nitride holder which
fits into a vycore or quartz tube, inside of which the low pressure is maintained.
A connection to the direct-current power supply for operation of the Hall-ion
accelerator is provided.
Tests of this device showed that the cathode is uniformly heated to thermionic
emission temperature. Since a 20-kw, 450-kc power supply has been available to
us, the heating is done with power to spare. The cathode has been installed in an
accelerator and the effect on the discharge characteristics will be tested in the near
future. Various methods of avoiding possible disturbances of Hall current measure-
ment during such heating have been considered, such as choking the Hall current
diagnostic coil, or providing a cathode thick enough to provide sufficient heat
capacity for the duration of the Hall current measurement.
The use of a RF-heated cathode should also prove very useful in preionizers or
axially symmetric plasma accelerators in general.
Tests are also in progress with thick, resistance-heated ring filaments, such as
those used in induction furnaces.
NOMENCLATURE
B
Magnetic flux density
c
Mean thermal velocity
e
Charge on singly-ionized ion
E
Electric field strength
— > -> — *. — >
E'
E'=E + vxB
— >
3
Current density
I
Length
m e , m t
Mass of electron and ion
m
Meter
n
Particle density
P
Pressure
Q
Collision cross section
r L
Larmor radius
t
Time
T
Temperature
V
Center of mass velocity
V
Voltage
w
W _ (l+2tU e T e <O t T,)
<?eTe
a
Quantity defined in equation (13)
A
Mean free path
H-
Microns
V
Collision frequency
11 6 T
Conductivity in the absence of a magnetic field, a = — — -
Mean free time between particle collisions
Cyclotron frequency, w e = — > w t = —
beockman, hess, and weinstein : Hall Currents 295
Subscripts
e Electron
i Ion
n Neutral
r, 0, x Refer to cylindrical coordinate system
Superscript
( ) Vector quantity
REFERENCES
1. Hess, R. V., "Experiments and Theory for Continuous Steady Acceleration of
Low Density Plasmas", in Proc. XI Internatl. Astronautical Congress, August
1960 (Vienna: Springer Verlag, 1961), I, 404-411.
2. Bratenahl, A., Janes, G. S., and Kantrowitz, A. R., "Plasma Acceleration in
the Electromagnetic Region II", Bull. Amer. Phys. Soc., Series II, 6, 4, 379
(1961).
3. Hess, R. V., "Fundamentals of Plasma Interaction with Electric and Magnetic
Fields", NASA-University Conference on the Science and Technology of Space
Exploration, 2, Paper 59, Chicago (November, 1962).
4. Rigby, R. N., "Some Physical Properties of an Axial Electric Arc in a Radial
Magnetic Field" (M.A. thesis, The College of William and Mary, August, 1962).
5. Hess, R. V., Rigby, R. N., and Weinstein, R. H., "Observation of Hall Currents
for a D-C Axial-Arc Discharge in a Radial Magnetic Field", Bull. Amer. Phys.
Soc., Series II, 8, 2, 168 (1963).
6. Hess, R. V., Burlock, J., Sevier, J. R., and Brockman, P., "Theory and
Experiments for the Role of Space Charge in Plasma Acceleration", Sym-
posium on Electromagnetics and Fluid Dynamics of Gaseous Plasma, April,
1961; published in Microwave Res. Inst. Symposia Ser. (Brooklyn: Brooklyn
Polytechnic Press, 1962), XI, 269-305.
7. Cann, G. L., Ziemer, R. W., and Marlotte, G. L., "The Hall Current Plasma
Accelerator", presented at the ARS Electric Propulsion Conference, Colorado
Springs, Colorado (March, 1963).
8. Chen, F. F., "A Time Resolved Probe Method", MATT 62, Plasma Physics
Lab., Princeton University (February, 1961).
9. Janes, G. S., Dotson, J., and Wilson, T., "Electrostatic Acceleration of Neutral
Plasmas. Momentum Transfer Through Magnetic Fields", Avco-Everett Res.
Lab. AMP 88 (September, 1962).
10. Salz, F., Meyerand, R. G., Jr., and Lary, E. C, "Ion Acceleration in a Gyro-
Dominated Neutral Plasma Experiment", Bull. Amer. Phys. Soc., Series II, 7,
7, 441 (1962).
11. Yoshikawa, S., and Rose, D. J., "Anomalous Diffusion of a Plasma Across a
Magnetic Field", Phys. Fluids, 5, 10, 1272 (1962).
12. Kadomtsev, B. B., "Turbulent Plasma in a Strong Magnetic Field", J. Nuclear
Energy, Part C (Plasma Physics), 5, 31-36 (1963).
13. Velikhov, E. P. "Hall Instability of Current Carrying Slightly Ionized
Plasmas", Symposium on Magnetoplasmadynamic Electrical Power Genera-
tion, Newcastle, England, September, 1962.
14. Rosa, R. J., "Hall and Ion-Slip Effects in a Nonuniform Gas", Phys. Fluids, 5,
9, 1081-1090 (1962).
296 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
15. Gierke, G., and Wohler, K. H., "On the Diffusion in the Positive Column in a
Longitudinal Magnetic Field", Nuclear Fusion Journal of Plasma Physics and
Thermonuclear Fusion, 1962 Supplement, Part 1, 47-53 (1962).
16. Chubb, D. L., "Hall Current Ion Accelerator", Fourth Symposium on the
Engineering Aspects of Magnetohydrodynamics (10-minute paper, only oral
presentation), April, 1963.
17. Haines, M. G., "A Mechanism for the Acceleration of Positive Ions in a Pinched
Plasma", Conference on Plasma Physics and Controlled Nuclear Fusion
Research, Salzburg (September 4-9, 1961).
18. Hasted, J. B., "Charge Changing Collisions", Vth Inter. Conf. on Ionization
Phen. in Gases, Munich (August 28-September 1, 1961).
19. Lary, E. C, Meyerand, R. G., and Salz, F., "Fluctuations in Gyrodominated
Plasma", Vlth Inter. Conf. on Ionization Phen. in Gases, Paris (July 8-13,
1963).
20. Smullin, L. D., and Getty, W. D., "Generation of a Hot, Dense Plasma by a
Collective Beam-Plasma Interaction", Phys. Rev. Letters, 9, 1 (July 1, 1962).
16. Sterge T. Demetriades:
Momentum Transfer to Plasmas
by Lorentz Forces
"Entia non sunt multiplicands, praeter neeessitatem"
(Occam's Razor, William of Occam, ca. 1340 a.d.)
|?J A theoretical and experimental study of momentum transfer to
plasmas by Lorentz forces is described. A generalized Ohm's law is
used to predict changes in the direction and magnitude of the momen-
tum of a stream of plasma and other observable macroscopic effects in a
crossed-field accelerator in terms of species temperatures and con-
centrations and other plasma parameters. The, assumption of local
thermal equilibrium is not required in this approach. Measurements of
momentum change and other effects are presented that are substantially
in agreement with theory. Gross mean estimates of the plasma para-
meters in the cross-arc region are obtained from the measured
momentum changes and power input.
INTRODUCTION
A large number of laboratories are engaged in research and development of
plasma accelerators using a wide variety of devices to accelerate a plasma by
Lorentz forces. One of the most popular of these devices appears to be the d-c linear
shunt plasma accelerator. It operates by the application of an externally-supplied
current across a usually preionized gas stream in a region where an external
magnetic field can be applied in a direction which is, more or less, perpendicular
to both the discharge and the flow direction. This type of accelerator is usually
called a crossed-field plasma accelerator. At last count, these devices were in use in
at least nine industrial organizations and three government laboratories. Needless
to say, the author finds this situation very flattering.
Progress in understanding the processes of the conduction of electric current in
a plasma in the presence of electric and magnetic fields (1-8) has yielded valuable
insight into the operation of crossed-field accelerators (8-19).
Since the most important results of the most promising projects are not yet
openly available, it is rather difficult to carry out a comparative evaluation of the
various programs at this time. However, the author has carried out experiments
with multiple-electrode accelerators with each electrode pair powered by a
separate power supply. Three-, four-, and seven-electrode-pair accelerators were
built and tested. The four-electrode-pair accelerators were tested with uncooled
as well as water-cooled electrodes. Power levels of approximately 750 kw have
ed. note: Mr. Demetriades is with Rocket Power, Inc., Pasadena, California. This
work was supported by the U.S. Air Force through the Propulsion Division,
Directorate of Engineering Sciences, Office of Aerospace Research, Air
Force Office of Scientific Research, under Contract AF 49(638)-1160.
297
298 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
been attained at flow rates for argon as low as 1.5 gm/sec. Velocities of approxi-
mately 8 x 10 3 m/sec have been achieved with air. Large accelerators ( > 10 Mw) for
wind-tunnel application are under development (20, 21, 22). Most of the power
supplied to these accelerators goes into the gas.
Early continuous, crossed-field accelerators suffered from considerable side-wall
and electrode erosion. Experiments by the author have shown that side-wall
insulator erosion can be effectively stopped under certain conditions by the use of a
metal stud side-wall design similar to the peg side-wall used in AVCO's MHD
power generators (20). In the author's segmented (stud or peg) side-wall design,
each water-cooled segment is made of metal (copper) and is insulated electrically
from the other segments. This "mosaic" of water-cooled segments is mounted
firmly on a transite slab and the interstices (0.15 to 0.50 cm wide) between the
segments are filled with a slurry of alumina or zirconia insulator. The slurry is
baked to give a firm matrix. However, the insulator matrix does not carry any
stress since the copper segments are firmly mounted on the transite slab. The
surface of the copper studs or segments (approximately 1 cm x 1 cm to 1.5 cm x 5 cm)
is exposed to the plasma. The cooling-water connections are on the other side of
the slab facing the magnet poles. These side- walls can remove between 1 and 4 kw
per cm 2 of surface. Under certain circumstances these side-wall losses can be
unacceptable and other methods of containment (e.g., magnetic or cold-gas) may
be necessary. The electrode erosion and melting problems were solved by using
multiple electrodes powered by separate power supplies (i.e., by passing only a
fraction of the total current through each electrode) and by proper design of the
electrode cooling passages so that wiping speeds in excess of 6 m/sec and high
cooling rates (>5 kw/cm 2 ) can be achieved. Accelerator electrodes can now be
operated for long periods of time ( > 1 hr) with very little erosion.
Sufficient progress has been made on component development during the last
year at Northrop Plasma Laboratories and elsewhere to ensure that crossed-field
accelerators of high performance and long life for wind-tunnel, enthalpy booster,
space propulsion, and many other applications will be available soon if the present
rate of progress is not interrupted.
The space propulsion applications of these relatively low- voltage accelerators
will have to meet very tough competition from other devices (notably the high-
voltage electrostatic accelerators and low-pressure electrothermal engines) that
are more advanced in development and are presently favored despite the power-
conditioning problems imposed by the required high voltages. In any case, the
deplorable lack of vision and progress in planning and developing suitable power
supplies for space applications such as electric propulsion will certainly effect a
delay, perhaps fatal, in the use of crossed-field accelerators for space propulsion.
Thus, it appears that the major engineering problems involved in crossed-field
accelerators for conventional applications are not only well understood, but also
well on the way to solution. Despite these formidable problems, the crossed-field
accelerator is the first plasma accelerator to be put into practical use, as for reentry
simulation (17, 20, 22).
The questions now become: What are the possibilities of crossed-field accelerators
for less conventional applications? If enthalpies of the order of 10 9 joules/kg can be
achieved in these devices with such relative ease and on a continuous basis, why
not hope for enthalpy levels of 10 12 or 10 14 joules/kg through further development
of these machines? Can these devices be used as radiation sources? If strong
Lorentz forces can be developed by the applied-current, applied-magnetic-field
technique, why not use the same technique for the containment of the dense and
y hot plasmas that these devices appear capable of generating?
dbmbtkiades: Momentum Transfer to Plasmas 299
To answer these questions will require considerably more understanding of the
detailed processes that take place in these accelerators, including electrode
emission, electrode fall, ionization, radiation, chemical reaction, transport and
thermodynamic processes in the presence of electric and magnetic fields, energy
and momentum transfer by Lorentz forces, and many other important phenomena.
These are essentially scientific problems that require additional effort.
Engineering progress in crossed-field accelerators is thus stimulating scientific
investigations that may lead to the answer of many important scientific problems
in plasma physics, and this in turn may lead into accelerated engineering progress
in plasma technology.
To illustrate, we shall consider some experiments on the momentum transfer to
plasmas by Lorentz forces carried out in the course of the engineering development
of crossed-field plasma accelerators and their effect on our understanding of the
processes governing the transport of electric charge (generalized Ohm's law) in a
plasma in the presence of electric and magnetic fields.
Another objective of this study will be to measure macroscopic momentum-
change effects and to relate them to those microscopic plasma properties that are
significant in momentum exchange processes in a plasma; and conversely, to relate
microscopic plasma parameters to measurable macroscopic momentum changes.
In this investigation, measurements are obtained of changes in the direction and
magnitude of the momentum of a stream of plasma in a crossed-field accelerator
with increasing magnetic induction at different power levels by mounting the
entire accelerator assembly on a sensitive balance and observing (1) the forces due
to interaction between the applied fields and the plasma stream, and (2) the deflec-
tion of the jet of plasma. The accelerator is operated in the free-jet mode in order
to simplify the analysis. The close agreement between free-jet and fully-confined
experiments has been confirmed by Burkhard et al. at AVCO/RAD (16, 17).
THEORY
To compute the momentum transfer to a plasma by Lorentz forces, one needs to
know the force per unit volume F v acting on the plasma. The local magnitude of
this force is given by the relation
F v = JxB (1)
where J is the local current density and B is the local magnetic induction. When the
magnetic induction is externally applied and the induced magnetic field is relatively
small (as is usually the case in crossed-field accelerators), the local value of B can be
estimated with considerable precision. Thus, the problem of computing F v reduces
to the problem of determining J.
For low-frequency oscillations and therefore also for a quiet or non-turbulent
plasma where the local small-scale density fluctuation can be neglected, it can be
shown (1) that the generalized Ohm's law in the first approximation (i.e., neglecting
viscosity) has the form
E' = Tj^T+J^p^Vpt + frVVT
+ W 2) J+ 2 ft/ 2) ViV + & 2 ^T] x B (2)
+ [ij (3) ( 1 x B) + 2 /V 3, ( Yp, x B) + 0?(VT x 2?)] x ~B
300 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
In equation (2) E' = E +U x B, E = applied electric field, TJ — plasma streaming
velocity, T = plasma temperature, p u = partial pressure of species fx, and the
coefficients rf°, /9 (1) , and (F* are functions of species concentrations, charge of each
component, collision cross-sections for momentum transfer between components,
temperature of each component, mass of each component, thermal diffusion
coefficients, etc., as defined by Polovin and Cherkasova (1). Strictly speaking,
equation (2) is valid for a multicomponent plasma where all the components are at
the same temperature, 1 '. However, when the temperature gradients can be
neglected, it can be shown that equation (2) is also valid for a two-temperature
plasma where the electron temperature T e is different from the atom or ion
temperature T a =T t , provided the electron drift velocity v d is small compared to
the electron random thermal velocity in the plasma, v e (2). Assuming that the
current is carried by the electrons only, the inequality v d ?v e is satisfied when
v* = JK en e) = 6.25 x 10 18 J/? C ? 6.2 x 10 3 T e 1/2 = v e (3)
where J = amp/m 2 , ra c = electrons/m 3 , T e = °K, and the velocities are given in
m/sec. Thus, for n e = 10 21 electrons/m 3 and T e = 10 4 C K, the current density must be
considerably less than 10 8 amps/m 2 in order that equation (2) may be used for a
two-temperature plasma with negligible temperature gradients. When the tem-
perature gradients cannot be neglected, it can be shown that equation (2) is still
valid provided m e T e lm a ?T a <T e . In both cases all magnitudes in equation (2),
except r ia , should be determined at T e . The modifications of equation (2) required
when these conditions are not fulfilled are beyond the scope of this paper. Yoshi-
kawa and Rose (3) and several other authors have shown that when the tempera-
ture gradients are negligible, local small-scale plasma turbulence leads to different
values of the coefficients ^ <f) and /? (i) . Their work confirms the "anomalous diffu-
sion" theory proposed by Bohm (4). However, since anomalous diffusion takes
place when the pressure is low (p < 100 [j. Hg, n < 10 20 particles/m 3 ) and the mag-
netic field is high (a> e T e ?l, T e = r ea T ei j{T ei + r ea )), the values of the coefficients rj it}
and /3 (i) given by Polovin and Cherkasova (1) apply in the experiments described
here where w>10 20 particles/m 3 and w e T e <lQ. It can be shown that the general
form of Ohm's law given by equation (2) leads to the special cases derived by
Cowling (5), Schliiter (6), Lehnert (7), and Liubimov (2). Thus, when the plasma
consists of electrons (e), one species of singly charged ions (i), and one species of
neutrals (a), and temperature gradients and space charge concentrations are
negligible (n e = n t ), while the inequality ^m i q ia v ia = eBI(2co i T ia n a )?m e q ea v ea =
eBj(uy e T ea n a ) is valid, equation (2) reduces to
t , = ^±^ T+ ± {{7x ^_ Vpe)
(4)
+ i^2^ [V(ft+ ' d -S VA - (7x:3 > ]x:s
where \ ea = m e q ea v ea , X ei = m e q el v ei , \ ia = \m i q ia v ia , m e = electron mass, w, = ion
mass; v ea , v ei , v ia = relative velocities between electrons and atoms, electrons and
ions, and ions and atoms, respectively; q ea , q ei , q ia = collision cross-sections for
momentum transfer between electrons and atoms, electrons and ions, and ions and
atoms, respectively; n e , n a = electron and atom concentrations, respectively;
e = electronic charge, w e = e.B\m e , w i = tB\m i ; T ea , r ei , r ja = inverse of collision
frequencies for collisions between electrons and atoms, electrons and ions, and ions
demetriades : Momentum Transfer to Phsmas 301
and atoms, respectively. For r ea ?r ei (i.e., w i A ei ? W(1 A eo ), equation (4) reduces
further to
E" = —T+ x (Jx B) - ^( J x B) x B (5)
°o
where
and
E" = E' +x \ Pe + l fi^ v Pa - V(j?.+p,)] xB
(6)
X = —><P = e - v e 2 a/ and <x = l^Iii (7)
Equation (5) can also be written
7=VE" (8)
Equation (4) is identical with Liubimov's version of the generalized Ohm's law (2)
and is equivalent to the Cowling-Schliiter version (5, 6), with the additional terms
Vpi and - (? e /? a )Vp a . The coefficients of the terms J, 7 x B, Vp e , and (7x B) x 1?
of these authors, including Lehnert (7), are identical with the coefficients derived
by Polovin and Cherkasova (1) even when A eo and r ei are not negligibly small
compared with A io and r ea , respectively. The work of all these authors leads to a
generalized Ohm's law similar to equation (5). Finally, the components of the
tensor V of equation (8), the equivalent of equation (5), were given by Demetriades
(8, 9).
The assumptions leading to equations (2) and (4) are enumerated and discussed
by Polovin and Cherkasova (1), and Liubimov (2).
As shown in an earlier publication (10), equation (2) or equation (4) can be used
in an attempt to relate the magnitude of the components of the current density
(and also the components of the conductivity tensor and therefore the collision
cross-sections for momentum transfer between electron, ion, and neutral gases as
well as other plasma parameters) to the observable changes in magnitude and
direction of the momentum of a stream of plasma in the Mark II (8, 9) crossed-field
plasma accelerator operating in the free-jet mode. The changes in the momentum
of the stream of plasma due to the Lorentz force per unit volume, J x J3, can be
measured by mounting the entire accelerator assembly on a sensitive balance in a
vacuum tank and observing the thrust (or drag) and the angle of deflection, <f>, of
the jet. It should be stressed that the results of this approach can be as precise as
the analysis is sophisticated. However, in order to make the analysis tractable, it
will be necessary to make simplifying assumptions that may introduce an error of
as much as a factor of 3 or 4 in the mean values of some of the plasma parameters,
temperatures, and concentrations obtainable by this method.
The assumptions made in the derivation of equation (4) limit its applicability to
experiments where boundary layer and transition layer effects are negligible.
These conditions are most nearly satisfied in the core of the cross-arc of the Mark II
plasma accelerator when it is operated in the free-jet mode. The phenomena
associated with the cross-arc of this accelerator were described in an earlier
publication (11).
Since the distribution of the magnetic induction B can be established and J can
be obtained from equation (5), precise expressions forthe forces acting onthe plasma
in the x and y directions can be computed in principle. If, in order to simplify the
302 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
computation, it is assumed that E' = (E' X , E' y , 0), B = (0, 0, B z ), and U=(U X , 0, 0),
the current density components in the region of influence of the magnetic field are
given by
O0 Hl + ^B i )E' x -a 1 BE' y \ , Q)
lx ~ {X + iliB^f + ^Bf
and
g0 [(i + ngg')^+Q 1 fl^] (10)
ly ~ (l + n 2 2 B 2 f + (^iB) 2
where
and
Of = eWJm* = olx* (11)
Q| = 2e 2 T ia T ej (l-a) 2 /m e m j = a >/i (12)
The ohmic heat dissipated per unit volume is
JE = J x E x +J y K y - (l + n 2 B2) 2 + (niB) 2 - [ aQ \ J W
The total electrical power per unit volume of plasma in the accelerator is given by
E -T= ( * + °f o Bl ) ( J2 + J ') + ( W?? -TzVyB*) ( 14 )
When E' x = E 0x + U y B-, = 0, B, = B, the total power supplied to the plasma per unit
volume is given by
and when J x = ("staggered" electrodes), the total power supplied to the plasma
per unit volume is given by
E 0y J a = (l±^?*)j*+U x BJ y (14b)
When E 0x = ( ie -> "symmetrical" electrode positions, long electrodes, no end
effects), equation (14) becomes
E 0y J y = - (1 +a^B 2 )Jl- x B z J y J x + V x B z J y (14c)
CT o
since
E' x = - {(l+^V.+M^)
and
E' y = - {(l+o tB*)J y -(o oX )J x }
Note that J x in equation (14c) is negative. The first term on the right-hand side of
equations (14a), (14b), and (14c) is the ohmic heating term and the other terms on
the right-hand side are the acceleration power. Note that equations (14b) and (14c)
demeteiades: Momentum Transfer to Plasmas 303
yield lower values of E 0y than equation (14a) for the same values of J y , U x , ct , tf>,
and B. Note also that as the degree of ionization approaches unity, <ji approaches
zero and the ohmic heating decreases.
Equations (13) to (14c) demonstrate the need to know the magnitude of the
quantities % and i/> (or O x and Q 2 ) in order to determine accelerator performance.
When single electrodes (one anode and one cathode) are used in a symmetrical
configuration (i.e., no stagger; their centerlines on the same line normal to the flow
direction), the axial electric field E' x is negligible because the increase of conductivity
with axial distance x is equivalent to longer electrodes with constant conductivity
and therefore E 0x x0 and U y B z xO over most of the interaction region as shown
by Denison (19) and Hurwitz et al. (27). Thus it can be assumed that the plasma is
at approximately the same potential at the inlet and at the exit of the inter-
electrode region ("shorted axially") and E' x =0. Then the current density com-
ponents in the region of influence of the magnetic field where the electric field is
E' ly become (9)
11 (l + QlB^-MQifl) 2 K '
and
<T Q E' ly (i+ntB*)
ly (l + CllBtf + i^Bf ( '
If, in addition, it is assumed (1) that the magnetic field in the accelerator is
constant in the region between the electrodes and zero elsewhere, (2) that the
current density is constant with x in the region between the electrodes while it is
zero upstream of the electrodes and of some undefined form in the region down-
stream of the electrodes, and (3) that (when the applied current is kept constant)
the electric field in the plasma between the electrodes with the magnetic field on,
E' ly = E — U X B Z , is equal to the applied electric field at zero magnetic induction
(E Q ) B = , it can be shown (9) that the components of the forces acting on the plasma
(equal and opposite to the thrust on the accelerator) are given by
<=> f T R JV hBI 0c (l+W 2 B 2 )
where h = electrode gap, I 0c = total applied current, and V= volume.
To determine the validity of equations (9) to (18) and, consequently, the validity
of the generalized Ohm's law, equation (5), it is necessary to devise some tests of
these equations on the basis of easy-to-observe macroscopic effects and simple
measurements. In particular, it was decided to perform critical experiments to
determine whether, for example, the deflection of the jet of plasma by the action of
J x B forces was due to the "blowing-out" of the discharge as a result of the high
plasma velocity (i.e., due to a more pronounced skewness or "distortion" of the
discharge in the accelerator resulting from higher plasma velocities) or due to a
higher Hall current (i.e., to higher values of the axial current resulting from the
higher magnetic field).
304
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Note that a simple momentum-vector diagram for the deflection angle <j> gives
tan <f> = . _f? n
(19)
where ml) \ is the rate at which momentum enters the inlet of the accelerator
(called inlet momentum in the following text). The quantities tan <f>, & x , and
rhU 1 can be easily measured (8-12). The geometry of this analysis is shown in
Figure 1.
FIGURE 1. Schematic diagram of one electrode-pair Mark II- A JxB accelerator
showing dimensions and coordinates.
Now equations (9) to (19) predict the following effects:
1. If the polarity (direction) and magnitude of the total applied current is
kept constant while the polarity of the magnetic field is reversed (B z = — B),
equations (17), (18), and (19) predict that:
1.1 The jet deflection remains in the same direction (i.e., tan rf> does not
change sign).
1.2. The deflection angle <f> increases:
1.2.1. By a small amount if wf7 1 ?0 I ,
1.2.2. By a large factor if rhU 1 is only slightly larger than Q x .
This is shown schematically in Figure 2a.
2. If the polarity of both the applied B and applied I 0c are reversed, the angle
<f> changes sign (i.e., the deflection is in the opposite direction). This is shown
in Figures 2a and 2b.
3. An increase of inlet momentum (mil x ) while all other parameters remain
constant decreases the magnitude of tan <$>.
4. An increase of the degree of ionization by increasing the power (energy
content) of the plasma jet entering the inlet of the accelerator (e.g., by an
increase of arc jet power) brings about a decrease of the magnitude of tan <j>.
This is due to the decrease of the Hall coefficient (which is proportional to
l/w e ) and therefore of J z and Q y . Note that an increase in arc jet power
increases ZJ-, and decreases t and therefore the observed decr^ a se of
demetriades : Momentum Transfer to Plasmas
305
b z posmvr
J POSITIVE
mil,
B z NEGATIVE
I POSITIVE
ml),
mD. ?
1 x
- e
- e
mU,
rhU. ~ e
1 x
FIGURE 2a. Effect of magnetic field polarity on deflection angle <f> when mU 1 ?Q 2 and
fnt\ > & z (J = J y , B = B Z and J =./?, B = - B z ).
tan <f> by the combined effects should be more than that predicted for each
effect alone. This is shown in Figure 3 where the experimental and theoretical
results of the jet deflection angle <j> are presented as a function of the arc jet
power input. The theoretical curve was computed assuming I 0c = constant,
B = constant, and
?j, = QJ1+ 1 | tan <f, = constant
in equation (19). Thus
(20)
(21)
tan <j> =
mU 1 + Q x
306
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
+ y
Z
+z
+ J
- J
B POSITIVE
z
J NEGATIVE
y
+ y
*JL
+ X
e ,u
- e
- j.
B NEGATIVE
z
J NEGATIVE
mU
mU
- 9
FIGURE 2b. Effect of electric and magnetic field polarity on deflection angle $
(J=-J y , B=B 2 a,ndJ = -J y , B = -B z ).
where the subscript min denotes evaluation of the term in the brackets at
the minimum arc jet power point on the experimental curve. However,
from equations (17), (18), and (19), it follows that
9H 1+ -er) w = I+
Qi-B
(22)
tan J> = -=- — ^-rr q — _??? I oc — (23)
Y Q I + mU 1 L 1 + Q1-B 2 \ n e y '
where
1 .76x10" & Z B
1 + D.IB 2
constant
(24)
Note that the experimental tan </>, when compared with the theoretical
curves computed by the increase in the rhU 1 alone, appears to decrease
faster for argon than it does for helium. This is due to a comparatively
smaller decrease in T ei for helium with increasing arc jet power.
demeteiades: Momentum Transfer to Plasmas
307
0.30
0.20
r
0.10 _
O Argon,
X Helium,
= 1.36 gm/sec
m = 0.57 gm/sec
P = A. 7 mm Hg
B = 0.045 weber/m
0.56 newtons
I = 400 amps
P = .4.7 mm Hg
B - 0.035 weber/m
I = 300 amps
e\_ = 0.33 newtons
P =
B =
I =
y
8 =
4.8 mm Hg
0.035 weber/i
300 amps
0.36 newtons
P = 3.1 mm Hg
B = 0.045 weber/m^
I = 400 amps
y
8 = 0.75 newtons
10
20
30 40
Arc Jet Power kw
50
60
70
FIGURE 3. Experimental and theoretical results of jet deflection angle ^asa function
of arc-jet power input. Dashed lines represent computations of tan <j> from equation (21)
under assumption of constant Q y .
5. At moderate values of B (0<JS<0.2 weber/m 2 ), an increase in B (the
applied magnetic field) brings about an increase in the deflection angle.
Note that from equations (17), (18), and (19),
6.
. , = O. x B 2 hI 0c
(25)
The quantity QJ Q z = Q x Bj{ 1 + Q*B 2 ) = [1 + (m UJQJ] tan j> is proportional
to B as ?->0. At the same time at B = 0, d(Q y l& z )/dB=Q 1 , tan <f> = 0, and
d(t&n<l>)ldB = Q. Moreover, as B^0, tan <j> becomes proportional to B 2 ,
d(t&n<f>)jdB becomes proportional to B, and [l + (mU 1 l@ z )] becomes
proportional to \jB.
7. An increase of the accelerator power at constant B decreases the magnitude
of tan ^ as a result of:
7.1. An increase of I 0c and consequently I7
7.2. An increase of n e and consequently a decrease in y .
8. A decrease of pressure (or density) in the plasma jet at constant I 0c and B
brings about an increase in the magnitude of tan <f> as a result of an increase
in r ei .
An increase in B while I 0c remains constant brings about a decrease of the
transverse conductivity o y and an increase in the total power required to
push the current 7 0c through the plasma.
Staggering the electrodes by an appropriate amount so as to introduce an
axial electric field eliminates the axial (Hall) current, J x = in equation (9),
and the jet deflection. It also decreases the accelerator power required to
drive the same current I 0c across the electrode gap at any given magnetic
field. In other words, the required voltage (electric field) for a given applied
current at a given applied magnetic induction is substantially reduced and
the efficiency of the accelerator is improved.
9.
10.
308
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
11. The required stagger, J x = in equation (9), is such that the anode should be
placed upstream of the cathode at a distance d = ho xBJ y l[(l + o <JiB 2 )J y +
UBo ]xhQ, 1 BI(l+Q.%B 2 ), where h is the electrode gap along the y-axis and
U is an average velocity.
12. At constant B, an increase of the applied current I Qc brings about an
increase in the transverse conductivity a y (since n e increases and O x and Q. 2
decrease). Moreover, the transverse conductivity initially increases rather
rapidly with increasing applied current (or increasing cross-arc power) as
both O x and Q 2 decrease. The rate of increase of a y decreases as the power
level increases, and when O x and Q 2 both become negligible, a y levels out.
As the power level increases, a y changes at a rate specified by the electron
temperature.
13. As the cross-arc power level increases, the electron concentration n e also
increases. Therefore, the value of r ei decreases.
14. Since the currents in the accelerator will tend to avoid regions of (a) low
conductivity, (b) high back EMF, (c) high magnetic field, (d) low pressure or
density, and (e) high velocity (where the static pressure drops and the back
EMF increases simultaneously), it is clear that a magnetic plug (i.e., a local
maximum of the magnetic field in a region of decreasing pressure) can be
LOW IMPEDANCE PATH
j"x~B = NEGATIVE
~0 GAUSS
LOW IMPEDANCE PATH
7 xlT = NEGATIVE
FIGURE 4. Schematic of thrust-configuration plasma accelerator operating in the
decelerating mode. Magnetic field normal to page and directed from page to reader.
demetriades: Mo mentu m Transfer to Plasmas 309
made to divert the current in such a manner that an accelerator in the thrust
configuration (thrust-producing polarity of J and B) can be made to produce
drag by passing most of the current from one electrode to the other in a
negative (decelerating) direction as shown schematically in Figure 4 by the
dashed arrows.
15. At low B (B<0.2 weber/m 2 ), the magnitude of the reduced thrust & z jhl 0c
should be proportional to B. As B increases, @ x /hl 0c goes through a maximum
and then begins to decrease.
16. The power dissipation (ohmic heating) in the plasma should be given by
equation (13). The power dissipation at high magnetic inductions and
constant applied current (equal to the difference between the total power
into the accelerator and the sum of the power going into acceleration and the
power going into the electrodes and confining walls) should be proportional
to B 2 when Q 2 remains constant with increasing B.
17. When there is no applied current and E Ox = E Ou = 0, the current density
components are given by J^Xooiil^U.BjA andJ ly x-a (l + ?l?,B 2 )U x B/A
where A = (I + Q 2 2 B 2 ) 2 + (Q^) 2 and B=B Z . Then for V x x l\ = constant,
O x Z -o (l + a%B a )U 1 B a hlA and V ? -a^Q^U^hlA
Since these induced currents will be usually small, there will be only a slight
slowing-down and a slight downward deflection of the jet when the electrodes
are shorted externally. These effects will manifest themselves in a decrease
of the diameter of the supersonic jet in the region between the pole pieces
and a slight exhaust jet deflection. When there are no electrodes, the jet will
still deflect — perhaps in a complicated way — because the current loops will
have to close within the plasma. Note the dependence of @? on 2? 3 . The
deflection angle, in this case, changes sign with B. This effect is the opposite
of the effect described in item 1 (Figure 2a) and was observed by Warder
(24). Note also that the induced electric field (back EMF) is sufficient to
cause electron heating and a non-linear Ohm's law even in the absence of
applied electric fields.
18. At high pressures (p a >l atmos) and low degrees of ionization in the pre-
ionized gas stream [a = n e l(n e + n a )<0.01], n e X ei ?.n a X ea and equation (4)
reduces to J = [n e e 2 l(n a m a q ea v ea )]E' . Then the conductivity of the gas at the
accelerator inlet will be of the order of 100 mhos/m and the high particle
density would prevent the electrons from picking up enough energy between
collisions in the cross-arc to cause a large increase in ion pairs more or less
uniformly over the entire region between the electrodes. The electron
temperature will increase only slightly above the ion and atom temperatures
(T e >T a =T i ). The combined effect of non- equilibrium ionization and
elevated electron temperature will still cause the Ohm's law in the plasma
to be non-linear. However transition region, boundary layer, and other
aerodynamic phenomena are no longer negligible, and the simple theory
outlined above would not apply. At high pressure, relatively "cold" gas
flow (low n e ), and relatively low applied currents (< 10,000 amps), the
discharge will tend to be of the thin filament type investigated by Thiene,
Chambers, and Jaskowsky (23), and it would tend to blow out by aero-
dynamic forces. The discharge would then be unstable. It would ignite close
to the leading edge of the electrodes, and would be blown downstream to the
trailing edge where it would bulge out until it became extinguished, only to
re-ignite at the leading edge. The application of the magnetic field would
310 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
not significantly alter these events, although it might increase their frequency
and regularity. The bulging-out of the discharge would be enhanced by the
magnetic field of the proper polarity and the increased discharge length
would drive up the required voltage with increasing B, perhaps at a rate
faster than that demanded by the increase in the induced electric field UB.
The bulging current paths would then react with the magnetic field to smear
out the jet instead of simply deflecting it in a well-collimated beam.
Other observable effects could be predicted by this simple treatment [equations
(15) to (19)] if sufficient control is possible in designing and performing the experi-
ments. For example, if the expellant is changed while the electron concentration
and collision cross sections remain the same, one should expect the magnetic field
B at which the reduced thrust ? x jhl 0c reaches a maximum to be roughly propor-
tional to To; 3 ' 4 and ( @ x lhI 0c ) meiX to be proportional to wij" 1 ' 4 .
Since the observable effects will give a good estimate of the magnitude of the
components of the tensor conductivity, it is possible, in principle, to obtain
estimates of the values of some of the parameters of the plasma in the region of the
interaction of the cross-arc with the magnetic field. These parameters include the
electron, ion, and atom concentrations, temperatures, and partial pressures, and
the electron-ion and ion-atom collision cross sections. Gross mean values of these
parameters can be obtained from the following set of equations (in mks units) :
p e = n e kT e (26)
Pa = n a kT a (27)
Pi = n t kT { , T a = T f , n e = n t (28)
P=Pe+Pa+Pi (29)
m = (n e m e + n a m a + n i m a )A ej U ei , m { = m a (30)
q ei = 5.85xlO- 10 T e - 2 lnA (31)
A = 1.23xl0 7 T e 3/2 M e " 1,z (32)
/oA P = (l + Qg? a )x7.7xlO- 3 7'. 3 ' a (lnA)- 1
° y V ep A ep (l + n^f + ^Bf [6 *>
q ei = 2.84xl0 7 (n e Q 1 )- 1 T e - 1 i 2 (34)
9ia (n e + n a ) 2 m, i ll2 (8kT i ) li mi ( '
where
and
Q x
= [ 1+ !^]W(i + ngg) (36)
2 dB
while A ei ■ = effective jet cross-sectional area, U ei : = effective jet velocity, h ep =
effective discharge length, V ep = effective voltage drop in plasma, A ed = effective
discharge cross-sectional area, and w = flow rate at accelerator inlet. In principle,
the magnitude of these effective quantities can be obtained by determining the
distribution of current density, electric field, flow velocity, etc., in the cross arc.
demetbiades: Momentum Transfer to Plasmas 311
Then the simultaneous solution of equations (26) to (37) would yield values of
Pe> P^ Pt> n e, n a , T e , 5T,, q ei , q ia , ?2 1; and ?1 2 in terms of tan <?, @ x , B, mU^ m u and
these effective quantities.
EXPERIMENTAL INVESTIGATION
This work is a continuation of earlier experiments (8, 10, 22). The apparatus
used has been described in detail in earlier publications (8-14, 22). In the experi-
ments reported here, the Mark II- A accelerator (shown in Figure 1) was operated
in the free- jet mode (8). Some ambient gas entrainment occurred and the accel-
erator inlet momentum mU 1 used in equation (19) should, strictly speaking, be
measured in a manner such as to include the increase in inlet momentum due to the
suction generated by the operation of the accelerator. The flow rate m in equation
(30) should likewise be corrected for entrainment. The increase of the inlet momen-
tum with the accelerator on was measured by means of static pressure, total pres-
sure, and vane-deflection measurements at various places in the inlet. These
measurements proved that the increase in inlet momentum due to accelerator-
induced entrainment was negligible as long as the accelerator operated at I <2.5
newtons and the geometry was essentially as described in reference (8) (i.e., the
inlet was within a few mm of the arc-jet exit).
Plasmas of argon and helium were used and measurements were made of the
deflection angle </>, the axial thrust X , the plasma generator flow rate m, the inlet
momentum rhU^ the magnetic field B, the current- voltage characteristics of the
cross-arc discharge with and without magnetic field, the tank pressure p, the
plasma generator (arc- jet) power input, the power absorbed by the arc- jet coolant,
the power added to the argon and helium plasmas by the plasma accelerator, etc.
The axis of the luminous jet was found to coincide with the flow axis in all cases.
In the course of these experiments, all the predicted effects (1 to 17, listed in the
previous section), with the exception of item 18, were observed. No experiments
were performed a,t pxl atmos. Experiments concerned with item 17 were recently
also performed by Warder (24). The experimental results presented in Figures 2a
to 20 indicate that the description of momentum transfer to plasmas in these
experiments given by the above analysis includes all major effects. Experimental
verification of most of the theoretical predictions instills a measure of confidence
in the use of the generalized Ohm's law given by references (1) through (7) and
increases the probability that the momentum-change technique, with further
elaboration, can be made to yield valuable information on basic plasma properties.
It is left to the readers to explain how, in spite of the numerous assumptions,
reasonable answers were obtained.
Additional work is required to examine in detail the magnitude and effect of the
coefficients /3* and ff- n , to formulate an energy balance that allows for ionization
and recombination and provides information on the current density, electric field,
velocity, species concentration, pressure, and temperature distributions.
Figures 2a and 2b show qualitatively the predicted deflection of the jet (identi-
fied as the resultant) with various combinations of magnetic field and applied
current polarity for mU 1 ?<d x and mU{> % x . These deflections (items 1 and 2 of
the theoretical discussion in the last section) were indeed observed. Observations
of the discharge were described in reference (11).
Figure 3 shows the experimental results obtained for tan <j> as a function of arc-
jet power at constant I 0c and B for helium and argon. The results of Figure 3
confirm the predictions of items 3 and 4 of the theoretical section. The theoretical
curves for constant 0? were obtained in the manner discussed (item 4). The
11 +
312 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
decrease of tan <f> with increase in gas enthalpy is not as marked for helium as it is
for argon because the degree of ionization (electron concentration) increases faster
for argon than for helium at these enthalpy levels. The ratio of the temperature
increase of argon over the temperature increase of helium is approximately equal
to (mC p ) He /(mC p ) A s;4, where C p = specific heat at constant pressure. The power
into the gas at the arc jet can be estimated from Figure 5. It shows the power into
the arc-jet coolant as a function of total arc-jet power for helium and argon. The
heat input to the arc-jet coolant is determined by measuring the flow rate and
temperature rise of the water coolant flowing through the plasma generator
cooling jacket.
60
u 40
30
20
10
i 1 1 r
X Argon, in = 1.36 gm/sec
Q Helium, m= 0.57 gm/sec
10 20 30 40 50 60 70 80 90
Arc-jet Power input kw
FIGURE 5. Arc-jet power absorbed by coolant as a function of total power input.
Figure 6 shows the axial thrust increment obtained for argon and helium plasmas
as a function of magnetic flux density for constant cross-arc current and three
arc-jet total inputs of 24, 32, and 40 kw. The results were corrected for magnetic
interference by careful calibration of the thrust balance. The data indicate that
within the region covered by these experiments the recorded thrust is independent
of the arc-jet power level and the type of plasma used. The data agree with the
theoretically-predicted values to within a few per cent.
Figure 7 shows the accelerator inlet momentum mU 1 for argon and helium
plasma jets as a function of arc -jet power input. The measurements were made by
mounting a flat steel plate on a negligible-displacement pendulum balance. The
flat steel plate was perpendicular to the arc-jet flow axis. Great care was exercised
to have the normal to the plate correctly aligned with the plasma jet axis. The
plate was placed approximately where the accelerator electrodes were normally
located (~14 cm downstream of the arc-jet exit). Running time was also found to
be an important factor. In order to prevent the hot plasma from deforming the
2.5-cm-thick steel plate and from moving the center of mass of the Dendulum
demetriades: Momentum Transfer to Plasmas
313
2.0
1.6 _
1.2 _
0.4
Theoretical thrust 9 * hBI -
400 flips y
h = 0.036 ■
O Argon
A = 1.36 gn/sec
P = 5.6 ± .2 m. Hg
X Helium
■ * 0.57 gn/sec
F = 5.3 ± .5 m, Hg
0.02
0.04
0.06
0.08
0.12
B webers/n (peak value)
0.14
FIGURE 6. Argon and helium axial-thrust increment as a function of magnetic flux
density.
40
-
1
1
1
~^o—§ — °
1
-. Areon
m =
1
1.36
gm/sec
-
1
i
i
Helium
i
m =
0.57
1
gra/sec
60 80
Arc Jet Power Input kv
FIGURE 7. Argon and helium inlet momentum as a function of arc-jet power input.
314
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
0.5
0.4
0.3
0.2 U
0.5
0.4 -
0.3
0.2
1 1 1 1 r~
Arc Jet Power 24 kw
— 1—
1 - 1 -■" 1 1
- Arc Jet Power 32 kw
1 1 -
e 9^
*sT
^^
~ ? M
s — ?
? X
" *JL
,y$>
.3?
j*i
-
s* *
-
,
—*r i i i
i i
1 r i i i
■■' 1
1 1 i
i i.
Arc Jet Power
Argon
24 kw^.
- Arc Jet Power 40 kw
-
- m = 1.36 gm/sec
I = 400 amps
/32 kw.
P = 5.6 ± .2 mm Hg
*^%
./C^^O kw
eft^o
- 5^^
"
aJn
Jt*
- s'y? // ^
-
^r*T L 1 1 1—
1
J 1
0.02 0.04 0.06 0.08 0.10 0.12 0.02 0.04 0.06 0.08 0.10 0.12 0.14
2
B webers/m (peak value)
FIGURE 8. Argon jet deflection angle as a function of magnetic flux density and arc-jet
power input.
B webers/m (peak value)
FIGURE 9. Helium jet deflection angle as a function of magnetic flux density and arc-jet
power input.
demetriades: Momentum Transfer to Plasmas
315
system (by expansion), each run was limited to a few seconds, and only those runs
where the balance returned exactly to the null point were retained. A recalibration
of the thrust balance immediately after each run was also performed.
Figures 8 and 9 show the jet deflection angle for argon and helium, respectively,
as a function of the magnetic flux density for constant cross-arc current and for
three different arc-jet power levels. The deflection angle was determined by double-
exposure pictures of the deflected and undeflected jet. The results are in agreement
with the qualitative theoretical predictions discussed earlier (items 4 through 7 in
the theoretical discussion). Examples of the double exposure pictures obtained
were given in references (8) and (25).
O Argon
n = J..36 gm/sec
I = 400 amps
= 5.6 ± .2 mm Hg
Arc Jet Power
O 24 kw
D 32 kw
A 40 kw
1
0.02
0.04
0.06
0.10
0.12
0.14
B webers/m (peak value)
FIGURE 10. Gross-arc power input into argon and helium plasma as a function of
magnetic flux density at constant cross-arc current.
Figure 10 shows the cross-arc input power required to pass a given amount of
current across argon and helium plasma streams for three different arc-jet power
levels with increasing magnetic flux density. The data seem to indicate that the
cross-arc power is independent of the arc-jet power level. This is generally not true.
However, the difference in static enthalpy of the plasma stream between the three
arc-jet power levels used in our experiments is not large enough to produce any
appreciable difference in the results.
Figure 11 shows the dependence of v /0 J = [l + (rnC r 1 /0 I )] tan <f> for argon and
helium on the magnetic induction as computed from the data presented in Figures
6 to 9 for three different arc-jet power levels. It is of interest to note that the Hall
thrust, and therefore the Hall current, may well exceed the axial thrust and the
transverse current respectively.
316
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
1.4
h.
1.0
.6
0.4
.Arc Jet Power
I I
Hel ium
m = 0.57 gm/sec
I ~ 400 amps
5 mm Hg
Argon
= 1.36 gm/sec
I = 400 amps
- 5.6 +. .2 mm Hg
0.04 0.06 C
2
B webers/m (peak value)
0.10
FIGURE 1 1 . Ratio of Hall-thrust to axial-thrust increment for argon and helium as a
function of magnetic flux density and arc-jet power [values from equation (19)].
Figure 12 shows the apparent efficiency, 7/ app = {[??+ 0J]/2m+ #1 ?J/fo + 7r m )
where ir e = electrical power input to the cross-arc and n m = power to the magnet, of
the unconfined accelerator operating with argon and helium plasmas as a function
of the magnetic induction and three arc-jet power levels. These results were
computed from the data presented in Figures 6 to 10, and they indicate an increase
in efficiency with increasing arc-jet power. Figure 13 shows the total apparent
specific impulse [&y + (Q I + rhU 1 ) 2 ] ll2 lmg c of the unconfined accelerator operating
with argon and helium plasmas as a function of the magnetic induction and three
arc-jet power levels. These results were computed from the data presented in
Figures 6 to 9, and they indicate an increase in specific impulse with increasing
arc-jet power level. The flow rate m used in these computations was the arc-jet
flow rate and gr c = 9.81 newtons/kg.
During these experiments, it was observed that a decrease of tank pressure at
constant I 0c and B brought about an increase in the magnitude of tan <f>, while an
increase in R (when 7 0c and the pressure remained constant) brought about an
demetkiades: Momentum Transfer to Plasmas
317
15
o 10
9- 5 _
Argon
m = 1.36 gra/sec
1 ~ 400 amps
y
P = 5.6 ± .2 mm Hg
Arc Jet Bower
0.02 0.04 0.06 0.08 0.10 0.12 0.14
2
B webers/m (peak value)
FIGURE 12. Apparent efficiency of an unconfined accelerator as a function of magnetic
flux density and arc-jet power.
600
500
M " 400 _
JB 200 _
1 1 1
1 1 !
Helium
-
m - 0.57 gn/sec
I = 400 amps
?y
-
P = 5.3 ± .5 mm Hg
Argon
m = 1.36 gm/sec
\ \\_ *° kw
I = 400 amps
V
\ \ 32 kw r Arc Jet Power
P = 5.6 ± .2 mm Hg
' 24 kw
1 1 1
1 1 1
0.02 0.04 0.06 0.08 0.10 0.12 0.14
2
B webers/m (peak value)
FIGURE 13. Apparent specific impulse as a function of magnetic flux density and arc-jet
power.
318
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
increase in the total power required to push the current I 0c through the plasma
(i.e., an increase in the applied voltage). The effects described by items 8 and 9 of
the theoretical discussion were thus observed to occur (8, 9, 11, 13, 14). The
electrode stagger effect predicted by items 10 and 11 of the theoretical discussion
was also observed as described in references (8), (11), (13), and (14). The effects
described by items 12 to 17 were also observed to occur and are described in
references (9), (11), (14), and (18). In particular, an accelerator with a field geometry
approximately as depicted in Figure 4 was built and the drag effects described by
item 14 were observed. At constant B, the quantity dV jdI 0c , where V is the
applied voltage, is proportional to l/o-^. This quantity was found to behave as
described by item 12 (9, 14, 18). The cross-arc power increases as either I 0c or B,
or both, increases. In that case, the quantity x (Hall coefficient) was found to
decrease, and therefore n e increased while T ei decreased (14), as described by item
13. This effect is also shown in Figure 14, where typical values of ?2 X [given by
equation (36)] are plotted as a function of B for argon and helium. The effect
predicted by item 15 was observed as already described in reference (9). The effect
described by item 16 was also observed and may be obtained from the data
presented in Figures 10 and 12, together with the electrode power losses presented
in references (9), (13), and (14). Note that Q 2 , as obtained from equation (37), is
indeed nearly constant with B for argon (Figure 15), and that Q x decreases mark-
edly for helium but only slightly for argon as B increases. This behavior of D x
appears to indicate that the argon is already highly ionized by the application of
the cross arc at B = 0, and an increase of B (and of cross-arc power, see Figure 10)
brings about a small increase in n e . For helium, however, an increase of B (and of
cross-arc power) brings about a significant increase of the degree of ionization.
50
40
10
Helium
m = 0. 57 gm/sec
I = 400 amps
Arc-Jet Power
24 kw
32 kw
40 kw
Arc -Jet Power
24 kw
Z3TT: 32 kw
40 kw
Argon.
rfi - 1.36 gm/sec
400 amps
5. 6 ± . 2 mm Hg
I = 400 amps
y
p
_L
J_
I
_l_
0.02
0. 04
0. 06
0. 10
0.12 0.14
B webers/m {peak value)
FIGURE 14. The value of Q. x for argon and helium as a function of magnetic flux density
demeteiades: Momentum Transfer to Plasmas
319
The corresponding behavior of typical values of Q 2 is shown in Figure 15. The
values of Q 2 decrease slightly with increasing B for argon, while they first increase
and then decrease for helium. Since, in mks units,
m 3/2
Q x = Oox = 4.84 xlO 16 ,' ,
n? In A
and
D| = o^ = 2.6 x 10 9
r e 3/ X
ne^ + n^q^T^^tn^ln. A
(38)
(39)
the initial increase of Q 2 for helium cannot be easily explained on theoretical
grounds. It is possible that the scatter in the observed values of ? x and tan <f> at
low values of B do not permit an accurate determination of Q 2 from equation (37)
for helium. The effect described by item 17 was also observed by Warder (24).
The values of Q 1 and Q 2 plotted in Figures 14 and 15 were obtained by assuming
a uniform current density distribution.
Figures 16 to 18 are presented lest we forget that some very crude assumptions
are made in the analyses given here.
Figure 16 presents two photographs of the argon spectrum in the interelectrode
region. In both exposures, the top of the figure represents the upstream edge of the
region observed. Approximately 5 cm along the axis of the jet of plasma was
focused onto the spectrograph slit to produce these spectra. The electrode axis
coincided with the center of the 5-cm length focused on the slit and the electrodes
were equidistant from the jet axis. The top exposure presents the spectrum of the
20
16
12 _
1 i
Arc-Jet Power
- 24 kw
1 1 1 1
Helium
m = 0. 57 gm/?ec
I = 400 ampt
-
32 ky^ ^^^>
. P = 5. 3 ± . 5 mm Hg
/ 40 l?/
— /
Arc-Jet Power
-
~~ ~ __ . 2 * kw
—
Argon 40 kw
' 1
m = 1. 36 gm/sec
I = 400 amps
P = 5. 6 ± . 2 mm Hg
... 1. 1 1 1
-
4 _
0.02 0.04 0.06 0.08 0.10 0.12 0.14
B webers/m (peak value)
FIGURE 15. The value of Q 2 for argon and helium as a function of magnetic flux
density and arc-jet power.
11*
320
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
4300.1 I 4181.9 I 4044.4 I
FIGURE 16a. Argon spectrum: arc-jet power = 32 kw; no cross-arc power; no magnetic
field.
4345.2 I 4300.1 I
4181.9 1
4044.4 I
3914.4 N?
FIGURE 16b. Argon spectrum: arc-jet power = 32 kw; cross-arc power = 16.5 kw;
magnetic induction B = 0.033 weber/m 2 .
plasma stream generated by the arc jet in the absence of a cross arc and with no
magnetic field. The bottom picture is the spectrum of the same region with the
cross-arc power on (16.5 kw) and a magnetic field of 0.033 weber/m 2 applied. In
the upper exposure, only atomic lines are observed, and this suggests that the
radiation might be the result of metastable atoms that are excited in the arc region
of the plasma generator. The ions have to a large extent recombined by the time
demeteiades: Momentum Transfer to Plasmas
321
they reach the region in focus. The atomic radiation shown in the upper exposure
is augmented in the lower exposure by many lines from singly-ionized atoms
(e.g., 4383 A, II) and additional neutral atom lines. Some neutral lines have
disappeared almost completely (4300.1 A, I). It is important also to note that in the
lower exposure the atom lines get stronger in the interelectrode region where a
high cross-arc current density is present. Similarly, the ion radiation is weak in the
upstream (top edge) and downstream (bottom edge) of the figure but increases in
the space between the electrodes (center of lower picture). Thus, in the inter-
electrode region, an increase in either the ion and electron concentrations or the
electron temperature, or both, appears to take place. Finally, the presence of
10
E
<4
c
a
Q
*j
c
V
u
u
a
U
Tj = 10, 000"K
2 -
10"
T x = 9000"K
_L
I
0. 5
1.0
1. 5
2.
2. 5
x = Axial Distance x 10 (meters)
FIGURE 17. Theoretical transverse current density distribution in argon for three inlet
temperatures, T lt obtained by Lenn (14) using an analysis that allows for variable
conductivity but assumes local thermal equilibrium (L.T.E.). Discharge characteristics
are: J r Oc = 1000 amperes, 5 = 0.1 weber/m 2 , electrode length = ? = 0.025 m, electrode
width = W = 0.025 m, discharge cross-section = W L.
322
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
N 2 bands indicates strong deviations from local thermal equilibrium, but does not
positively rule out equilibrium ionization and excitation at the electron tempera-
ture, despite the effect of the electric field.
Figure 17 is a theoretical computation of the current density as a function of
electrode length for a geometry similar to Figure 1. This computation was carried
out by Lenn (14). It appears to indicate that the current density increases towards
the trailing edge of the electrodes. This increase becomes more pronounced for low
inlet temperatures. Figure 18 presents the current-voltage characteristics for an
electrical discharge across preheated (and preionized) argon and helium supersonic
jets at B = 0. These cross-arc characteristics indicate that the transverse conduc-
tivity a y = dI 0c ldV of helium is considerably lower than that of argon. The
observed behavior of the current- voltage cross-arc characteristics with B = at
low applied current is not easy to explain. These jets of argon and helium plasma
were produced by the equipment described in references (9), (11), and (22).
50
A5
40
o
>
m
ao
- 35
o
>
13
a
a.
<
1 r
Electrode Gap, h =
" Length L =
" Width, w =
-3
B ?s 10 weber/m
T
T
0.036 m
0.025 in
0.025 m
H e 1 ium
m = 0. 57 gm/sec
P ? 2.5 mm Hg
x 10 ergs/gm
30
25
1.36 gm/sec
3 mm Hg
in 10 /
10 ergs/gm
20
200
400
600
800
1000
1200
Applied Current Amps
FIGURE 18. Current-voltage characteristics for an electrical discharge across a
preheated plasma stream.
demeteiades: Momentum Transfer to Plasmas
323
Typical values of the gross mean plasma parameters obtained by using these
experimental results to solve the system of equations (26) to (37) are (for argon):
T e x 12,000 to 29,500°K, r a = T,s7000 to 4000°K, w e s6xl0 20 to 8.6 xlO 20
electrons/m 3 , ? a x:7xl0 21 to 6.2 x 10 21 atoms/m 3 , and, using the values corres-
ponding to the highest T e , p e x2.65 mm Hg, p a x2.6 mm Hg, p t xOM mm Hg,
,k6.7x 10 3 m/sec,
0.007, ^s 0.016
S5.7xl0" 7
sec,
g ej s5.2xl0- 18 m 2 , g ja ^1.9 x 10" la m a _
<7 ?5100 mhos/m, ^XillOO mhos/m, T ei x2.l x 10" 10 sec,
(o e T ei z2, co t T ia x0.01. Typical values of the same quantities for helium are given
by: r e xl9,500 o K, T a = 2 , i x20O0°K, n e x2.8x 10 20 electrons/m 3 , w o x2.4xl0 22
atoms/m 3 . p e x0.55 mm Hg, p^O.05 mm Hg, p a s4.64 mm Hg, q ei Xl.2 x 10" 17
m 2 , q ia x2.5xl0- 19 m 2 , ? d s2xl0 4 m/sec, x ~0<>2, >jiX0.05, a ~2700 mhos/m,
a v s;400 mhos/m, t?,s3.4x 10" 10 sec, Tia s5xl0- 8 see, <u e T ei s;3, UjT^xO.OOe.
324
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
These values were obtained at B = 0.05 weber/m 2 , I Qc = 400 amps, arc- jet power = 32
kw (for argon — 4.7 kw into kinetic energy, 4.1 kw into static enthalpy, remainder
into coolant; for helium — 2.5 kw into kinetic energy, 6.8 kw into static enthalpy,
remainder into coolant), cross-arc power = 20 kw for argon (2.3 kw into kinetic
energy, 7.1 kw into static enthalpy, 10.6 kw into coolant) and 42.5 kw for helium
(3.4 kw into kinetic energy 21.1 kw into static enthalpy, and 18.0 kw into coolant);
total static enthalpy into gas = 8.2 x 10 6 joules/kg for argon and 4.9 x 10 7 joules/kg
for helium, m=1.36xl0- 3 kg/sec for argon and 0.57 xlO" 3 kg/sec for helium,
X = O.7O newtons, 0?=O.43 newtons for argon and 0.75 newtons for helium,
demetriades: Momentum Transfer to Plasmas 325
K = 50 volts for argon and 106 volts for helium, and thU 1 = 3.56 newtons for
argon and 1.7 newtons for helium. A linear current-density distribution was
assumed in these computations and the evaluation of the various parameters
was carried out at the point x where \I 0c = I J y wdx. Note that the degree of
ionization for helium is low enough to make n a A ea = 5.2 x 10 8 only slightly smaller
than w e A el = 27 x 10 8 . Note also that it takes a minimum of 51.2 kw to ionize
1.36 x 10 -3 kg/sec of argon and a minimum of 335 kw to ionize 0.57 x 10 ~ 3 kg/sec
of helium. It appears that the static enthalpy for argon measured calorimetrically
is in good agreement with the static enthalpy (including ionization) obtained by
the momentum-change technique. The agreement is not so good for helium. It is
entirely possible, however, that the probable error in the helium static-enthalpy
estimate obtained from the scant calorimetric data available on helium can account
for the discrepancy. In any case, the assumptions made in obtaining these
estimates of species temperatures, concentrations, and collision cross sections do not
justify expectations of accuracy better than within a factor of two or three. Some
refinements of the theory have recently been carried out by Kontaratos (26).
The information obtained in these and previous experiments (8-18, 22),
notably the early results of Demetriades (22) and the more recent results of
Burkhard et al. (16, 17), were used to design a crossed-field plasma accelerator for
wind-tunnel applications (Figures 19 and 20). The objective of this accelerator was
to produce a stream of air with a velocity of approximately 8 x 10 3 m/sec and a
static pressure of 1 to 10 mm Hg. The design and testing of accelerator Mark
CA-1 was carried out under subcontract from MHD Research, Inc., for NASA/
Ames Research Center, Contract No. NAS 2-1170.
CONCLUSIONS
Momentum transfer to plasmas by Lorentz forces away from boundary and
transition regions can be described quantitatively by means of a generalized
Ohm's law for multicomponent, two-temperature plasmas expressed in terms of the
plasma properties and species temperatures and concentrations. The assumption
of local thermal equilibrium is not required in this approach.
Observations and measurements of momentum change and other effects are
reported that are substantially in agreement with theory. This experimental
verification of the theoretical predictions instills confidence in the use of the
generalized Ohm's law to describe the conduction of electrical current through
plasmas in the presence of magnetic fields and appears to justify most of the
assumptions made in this crude analysis.
The measurement of momentum change effects brought about by the interaction
of the cross arc with the magnetic field yields valuable information on plasma
properties and species temperatures and concentrations in the absence of local
thermal equilibrium.
Preliminary independent measurements of some of these parameters appear to
be in agreement with the results obtained by momentum-change techniques.
Refinement of the theory is required to improve the accuracy of these measurement
techniques.
ACKNOWLEDGMENTS
I want to thank the Air Force Office of Scientific Research for making funds
available for this study under Contract AF 49(638)-1160 at the Plasma Labora-
tories of Northrop Corporation. I also want to thank Dr. A. N. Kontaratos, who
326 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
helped perform the experiments and reduce the data; the laboratory technicians
J. Superata and L. Goltra, who helped assemble, maintain, and operate the
apparatus known as accelerators Mark I, II, and II-A, Mark III, and Mark CA-1
in tanks "A", "B", and "C", respectively, at the Plasma Laboratories of Northrop
Corporation; Mr. C. F. Knopp and Mr. L. R. Dawson, who assembled the spectro-
scopic equipment and obtained useful spectroscopic data; and the other members
of the staff of the Plasma Laboratories of Northrop Corporation, including Dr. J. R.
Bodoia, Dr. P. D. Lenn, Dr. C. L. Maldonado, Dr. J. J. McClure, Dr. H. N. Olsen,
Dr. J. B. Wilkinson, Mr. G. L. Hamilton, and Mr. D. Ward, for their comments.
Finally, I want to thank Professor A. B. Cambel and Mr. R. W. Springer for
making the presentation of this paper possible.
REFERENCES
1. Polovin, R. V., and Cherkasova, K. P., "Magnetohydrodynamic Description of
a Plasma", Zhurnal Tekhnicheskoi Fiziki, 32, 6, 649-656 (June, 1962) [trans-
lation in Soviet Physics — Technical Physics, 7, 6, 475-479 (December, 1962)].
2. Liubimov, G. A., "On the Form of Ohm's Law in Magnetohydrodynamics",
Prikladnoi Matematika i Mekhanika, 25, 4, 611-622 (July, 1961) [translation
in Soviet Mathematics: Applied Mathematics and Mechanics, 25, 4, 913-929
(February, 1962)].
3. Yoshikawa, S., and Rose, D. J., "Anomalous Diffusion of a Plasma Across a
Magnetic Field", Phys. Fluids, 5, 3, 334-340 (March, 1962).
4. Bohm, D., Chapter 3 in The Characteristics of Electrical Discharges in Magnetic
Fields, ed. A. Guthrie and R. K. Wakerling (New York: McGraw-Hill, 1949).
5. Cowling, T. G., Magnetohydrodynamics (New York: Interscience Publishers,
1957); also, "The Electrical Conductivity of an Ionized Gas with Applications
to the Solar Atmosphere", Proc. Boy. Soc. {London) A., 183, 453^78 (1945).
6. Schluter, A., "Dynamik des Plasmas I", Z. Naturforschung, 5a, 72 (1950);
6a, 73-78 (1951).
7. Lehnert, B., "Plasma Physics on Cosmical and Laboratory Scale", Suppl.
Nuovo Cimento, Series 10, 13, 1, 59-110 (1959).
8. Demetriades, S. T., "Experiments with a High Specific Impulse Crossed-Field
Accelerator", NSL-62-130, Northrop Space Labs, Northrop Corp., Hawthorne,
California; presented at Third Symposium on Engineering Aspects of Magneto-
hydrodynamics, University of Rochester, March 28-30, 1962 (to be published
by Gordon and Breach Science Publishers, Inc.).
9. Demetriades, S. T., Hamilton, G. L., Ziemer, R. W., Jarl, R. W., and Lenn,
P. D., "Three-Fluid Non-Equilibrium Plasma Accelerators, Part I", ABS
Preprint No. 2375-62, ARS Electric Propulsion Conference, Berkeley, Cali-
fornia, March 14-16, 1962; published in Progress in Astronautics and, Aero-
nautics, ed. E. Stuhlinger ["AIAA Series" (New York: Academic Press, Inc.,
1963)], 9, 461-511.
10. Demetriades, S. T., "Novel Method of Measurement of Plasma Properties by
Momentum-Change Techniques", Phys. Fluids, 4, 12, 1569-1570 (December,
1961).
11. Demetriades, S. T., and Lenn, P. D., "Electrical Discharge Across a Super-
sonic Jet of Plasma in Transverse Magnetic Field", AIAA Journal, 1, 1,
234-236 (January, 1963).
12. Demetriades, S. T., and Ziemer, R. W., "Energy Transfer to Plasmas by
Cnntinnmis T.nrpnt^ TTnrpoa" A J?1 J3^.? mv ^t onno Rl TV+I. r;???;?i p?r.
demetriades: Momentum Transfer to Plasmas 327
Dynamics Symposium, Northwestern University, Evanston, Illinois (August
23-25, 1961); published in Magnetohydrodynamics, eds. A. B. Cambel, T. P.
Anderson, and M. M. Slawsky (Evanston: Northwestern University Press,
1962), 185-205.
13. Lenn, P. D., Bodoia, J. R., Ward, D. L., Hamilton, G. L., and Demetriades,
S. T., "Three-Fluid Non- Equilibrium Plasma Accelerators, Part II", AIAA
Preprint No. 63047, AIAA Electric Propulsion Conference, Colorado Springs,
Colorado, March 11-13, 1963 (to be published).
14. Demetriades, S. T., et al., "Experimental and Analytical Investigations of
Crossed-Field Plasma Accelerators", NSL-62— 113-10, Northrop Space Labs.,
Northrop Corporation, Hawthorne, California (June, 1963).
15. Blackman, V. H., and Sunderland, R. J., "The Experimental Performance of a
Crossed-Field Plasma Accelerator", ARS Preprint No. 2633-62, ARS 17th
Annual Meeting and Space Flight Exposition, Los Angeles, California,
November 13-18, 1962.
16. Burkhard, K., Devine, R., Hogan, W. T., and Kessler, R., "Experimental
Investigation of a Crossed-Field Accelerator for High-Enthalpy Re-entry
Simulation", IVth Symposium on Engineering Aspects of Magnetohydro-
dynamics, University of California, Berkeley, California, April 10-11, 1963.
17. Burkhard, K., Devine, R., Hogan, W. T., and Kessler, R., "A Continuous
Crossed-Field Gas Heater for Re-entry Simulation", AIAA Preprint No.
63-203, AIAA Summer Meeting, Los Angeles, California, June 17-20, 1963.
18. Russel, G. R., Byron, S., and Bortz, P. I., "Performance and Analysis of a
Crossed-Field Accelerator", AIAA Preprint No. 63-005, AIAA Electric
Propulsion Conference, Colorado Springs, Colorado, March 11-13, 1963.
19. Denison, M. R., "A Two-Dimensional Weak Interaction Theory for Crossed-
Field Accelerators", Research Note RN-12, Electro-Optical Systems, Inc.,
Pasadena, California (April, 1963); also "Physical Phenomena Associated with
Magnetogasdynamic Acceleration", co-author R. W. Ziemer, AFOSR Contract
No. AF 49(638)-1063, presented at Sixth Annual AFOSR Contractors'
Meeting on Ion and Plasma Acceleration, Northwestern University, Evanston,
Illinois, March 14-15, 1963.
20. Kantrowitz, A., AVCO-Everett Research Laboratory, Everett, Massachusetts,
private communication.
21. Wood, G. P., NASA/Langley Research Center, Langley, Virginia, private
communication.
22. Demetriades, S. T., "Experimental Magnetogasdynamic Engine for Argon,
Nitrogen and Air", Second Symposium on Engineering Aspects of Magneto-
hydrodynamics, Philadelphia, Pa., March 9-10, 1961; Engineering Aspects of
Magnetohydrodynamics, eds. C. Mannal and N. W. Mather (New York:
Columbia University Press, 1962), 19-44.
23. Thiene, P. G., Chambers, J. E., and Jaskowsky, W., "Experimental Investiga-
tion of the Behavior of an Arc Positive Column in the Presence of Forced
Convection", Report No. T-4TN031-334, AFOSR-682, Contract No. AF
49(638)-334, ASTIA Document No. AD-260648, Plasmadyne Corp., Santa
Ana, California (April 29, 1961).
24. Warder, R. C, Jr., Northwestern University, Evanston, Illinois, private
communication, also "Microwave Diagnostics of Arc Heated Argon Plasma
Flows" (Ph. D. thesis, Northwestern University, April, 1963), NU-GDL
Report No. B-l-63.
25. Demetriades, S. T., "Plasma Propulsion, Parts I and II", Astronautics, 7,
3 and 4, 21 and 40 (March and April, 1962).
328 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
26. Kontaratos, A. N., Rocket Power, Inc., Research Laboratories, Pasadena,
California, private communication.
27. Hurwitz, H. Jr., Kilb, R. W. and Sutton, G. W., "Influence of Tensor Con-
ductivity on Current Distribution in a MHD Generator", J. App. Phys,, 32,
2, 205-216 (February, 1961).
17. L. J. Krzycki, H. M. Larsen,
and W. M. Byrne, Jr. :
Magnetohydrodynamic Power
Generation from a Supersonic
Rocket Exhaust
12? A theoretical and experimental feasibility investigation of an
MHD electrical power generator using a supersonic rocket exhaust
(Mach 2.3, 2160 mjsec) as the working fluid was conducted at the
Naval Ordnance Test Station, China Lake, California. Theoretical
calculations of thermal ionization and gas conductivity, using a
digital computer, indicated that a supersonic gas source had definite
advantages over a subsonic one. Experimental firings of a liquid
rocket-MHD power generator proved the feasibility of the concept and
indicated areas of developmental difficulty.
INTRODUCTION
Theoretical and experimental studies have indicated that the MHD generator,
in which electrical power is generated without the use of moving parts from the
magnetohydrodynamic interaction of a partially-ionized gas and an external
magnetic field, is one of the few systems potentially capable of satisfying the unique
power requirements of present and future weapons systems (1). Further study
indicated that supersonic MHD power generation using a solid-fuel plasma source
would be an ideal method of generating large amounts of electrical energy for
short periods of time. MHD power generation systems were envisioned which had
high power densities, long shelf life, and rapid start capabilities.
At the time the project reported herein was initiated, little theoretical, and no
experimental, work had been reported on MHD power generation from a supersonic
gas stream. It was deemed advisable, therefore, to determine by means of a
theoretical and experimental program at least some of the difficulties associated
with supersonic MHD power generation.
THEORY
MHD POWER GENERATION
The mechanism of MHD power generation is similar to that of conventional
rotating generators, in that an electrical conductor is moved across a magnetic
field and a potential difference is induced along the conductor. In the conventional
mechanical generator, an external power source causes a metallic conductor to
ed. note: Mr. Krzycki, Mr. Larsen, and Mr. Byrne, are with the Propulsion Devel-
opment Department, U.S. Naval Ordnance Test Station, China Lake,
California.
329
330
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
rotate in a magnetic field. In the MHD generator the metallic conductor is replaced
by an ionized gas and the external power source by a pressure differential. The gas
flows through a region which is subjected to a strong magnetic field perpendicular
to both the gas flow and to electrodes in contact with the moving, ionized gas. An
external load connected to the electrodes draws energy from the gas stream which
in turn suffers a reduction of enthalpy as a result of the power extraction. Figure 1
shows a simplified rocket-MHD (RMHD) generator in which a chemical rocket
engine furnishes the partially-ionized gas to the MHD power channel.
MAGNETIC FIELD
v ROCKET MOTOR
FIGURE 1. Schematic diagram of RMHD generator.
The equations describing the operation of MHD power generators are well
documented; see (2), for example. For initial engineering calculations, the following
equations can be used (2).
(a) V oc = uBW
(b) /? = ouBDL (1)
(c)
n =
l B 2
The electrical conductivity of the gas, a, is a function of both pressure and
temperature for a given chemical composition. The electrical conductivity of
seeded equilibrium combustion gases rapidly reaches a maximum on the order of
tens of mhos per meter. The magnetic field, B, is a separate variable which, in
most cases, can be varied independently of the gas. (As we shall see later, the
strength of the magnetic field can affect the gas conductivity.) The velocity of the
fluid may be widely varied depending upon whether the flow is subsonic or super-
sonic. The dependence of the maximum generated power density on the term u 2
means that a reduced electrical conductivity due to the expansion of the gas can
be more than compensated for by the increased gas velocity associated with that
expansion. For this reason, MHD power generation using a supersonic combustion
gas is very attractive from the point of high generated power density.
THERMAL IONIZATION
To obtain the functional dependence of a on the thermodynamic variables and
constitution of the gas, it was first assumed that the electric current in the gas
was due to the motion of free electrons under the influence of the electric field ,
kezycki, laesen, and byese: MHD Power Generation 331
and further, that these electrons were produced by thermal ionization of seed gas
atoms. An expression was required which related the equilibrium number density
of electrons to the neutral particle number density, in terms of the thermodynamic
variables of the gas. The equilibrium degree of thermal ionization of a gaseous
species is given by the Saha equation (3, 4)
where x is the degree of ionization, P is the gas pressure in atmospheres, <f> is the
ionization potential of the species, and T is the Kelvin temperature. The constants
g h g e , and g , refer to the multiplicity of energy states of the ion, electron, and
neutral atom, respectively. Suitability arguments have been formulated which
justify the application of the Saha equation to a complex system such as a com-
bustion product gas. In the temperature and density regime typical of chemical
rocket engines, the degree of ionization of the gas is relatively low; however, with
the addition of a small amount of an alkali metal or its salt, the number density
of electrons can be greatly increased. In this case, the Saha equation can be written
ln T ^ = ^ + 2.5]nT-]nP s + k 2 =r 1 (3)
where ^=—1.1616^x10*, fc 2 =— 14.946, and P s is the partial pressure of the
monatomic form of the seed gas in atmospheres. For the case of macroscopic
electrical neutrality, equation (3) can be solved for the degree of ionization of the
alkali metal seed
n> s = (e-"+l)- 1/2 = x (4)
where n s is the number density of seed atoms initially present in the gas mixture.
The particle density of species j is related to its partial pressure by
?, = P#T (5)
where k is the Boltzmann constant. Implicit in equation (5) is the assumption
of a Maxwellian velocity distribution — a valid assumption for the collision-dom-
inant case of ordinary chemical rocket processes. If the molar concentration of
species j is denoted by X t , equation (5) can be rewritten as
n,. = k z X,jT (6)
where k 3 takes the constant value 1.013(AAA) x 10 5 /k. (AAA) is a conversion
factor for molar concentration to partial pressure and is printed on the output
sheets of the NOTS Propellant Evaluation Program (5)f. Equations (4) and (6),
when combined, give the free electron density of the gas as
n e = xk 3 XJT (7)
where X s is the molar concentration of monatomic seed material.
ELECTRICAL CONDUCTIVITY
The d-c electrical conductivity, a, of a gaseous mixture can be written as (6, 7)
4.5xl0" 12 ? e /Q .
"" T^In jQi (8)
j
t The NOTS Propellant Evaluation Program is a computer program (IBM 7090) used to
determine the thermodynamic parameters of a propellant combination. The temperature,
enthalpy, entropy, ratio of specific heats, molecular weight, and gram-moles of the constituents
at equilibrium are calculated for both the combustion chamber and the exhaust. The expansion
process assumes shifting equilibrium and dissociation of the combustion products.
332 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
where Q } is the elastic scattering cross section of species j with electrons. The
various terms involved in the summation refer to the interaction of electrons with
electrons, ions, seed atoms, and typical combustion-product molecules. For a
macroscopically neutral plasma, equation (8) can be rewritten with the aid of
equations (4) and (5) as
= 4.5 x 10-* 2
° T^(Q e +Q i + Q s lx+PQ lxP s ) K >
where the subscripts e, i, s, and refer respectively to electrons, ions, seed atoms,
and typical combustion molecules.
The electron-electron cross section as given by Fay (7) is
[1 24 x 10 7 7' 3/2 1
Using equation (7) this may be written as
[1 '>4x
1.24 xlO 7 ?' 5 ' 2
3-^s
(11)
The electron-ion cross section (8) can be written in c.g.s. units as
Q t = 8.16 2 In (h/b) (12)
where h is the Debye lengtht and b is the impact parameter for 90° scattering^.
By the same method as was used to obtain equation (11), and converting to
m.k.s. units, the cross section can be written as
Q t = 1.25xl0-i°r- 2 ln [ L54 J^ 14r4 ] (13)
The d-c electrical conductivity of seeded rocket exhaust gases is given by
equation (9) in terms of the thermodynamic variables of the gas. The interaction
terms, Q e and Q t , are given in terms of the thermodynamic variables of the gas by
equations (11) and (13). Terms Q s and Q are constants. For the electron energy
range involved, a value of 4xl0~ 18 square meters may be assumed for Q s (9)
while a representative value of Q would be 2 x 10 _19 square meters (7).
MAGNETIC FIELD EFFECTS
The design of MHD generators using strong magnetic fields is complicated by the
fact that the electrical conductivity is not merely a scalar function of the tempera-
ture and pressure, but is also a tensor function of the magnetic field. This tensor
quality reduces a in a direction perpendicular to the magnetic field (10) as
where w is the gyromagnetic frequency of the electron (a function of B only) and
t is the electron collision period (a function of the thermodynamic variables of the
gas). In addition, the current density in the gas is no longer parallel to the electric
field (Hall effect), but has a component along the axis of the generator channel.
t ;j = (fc2 , /47rn e ? 2 ) 1 ' 2
t h = fi 2 /3itT
EXHAUST.
CHAMBER '
fuel:
0XIDI2
seed:
0/F R
TOTAL
ER:
ATio:
PRESSURE:
ST PRESSURE
METHANOL
GASEOUS OXYGEN
CESIUM CARBONATE
1.5
294 PSIA
22 PSIA
EXHAU
SEEDING RATE,% TOTAL FLOW
FIGURE 3. Variation of molecular weight with seeding rate.
a?
020
CH
AMBER S EXHI
?UST\
0.10
FUEL:
OXIDIZER:
SEED:
0/F RATIO
TOTAL PRESSU
EXHAUST PRES
METH
GASEC
CESIU
1.5
RE: 294 P
SURE: 22 PS
ANOL
US OXYGEN
M CARBONATE
SIA
IA
2 10
SEEDING RATE, % TOTAL FLOW
FIGURE 4. Molar concentration of monatomic cesium for various seeding rates.
krzycki, larsen, and byrne: M II D Power Generation
333
The value of cot is given by
cot = 1.3xl0 3 (5/P)(7 7 ) 1,:
(15)
The derivation of this relationship is given in Appendix A. A constant value for
the gas-particle collision cross section of 3xl0~ 19 square meters (6) has been
chosen for the energy range and species appropriate to the systems under
consideration.
MICROWAVE DIAGNOSTICS
For an experimental verification of the programmed conductivity expression,
a series of microwave experiments was performed to determine the electron density
in the supersonic exhaust of the rocket engine which was used in the power genera-
tion experiments. The results of this study, which indicated good agreement with
the electron densities predicted by the programmed expression, are presented in
(11).
THEORETICAL CALCULATIONS
The equations describing the thermal ionization and electrical conductivity
of seeded combustion products were programmed for digital computer (IBM
7090) solution. Figures 2 through 9 show the variation of some of the parameters
and equations discussed under THEORY. These figures were theoretically deter-
mined using conditions that were typical of those used in the experimental inves-
tigation. Figures 2 through 9 are all plotted against a common abscissa which
indicates a wide range of cesium carbonate seed rates. Figures 10 and 11 are plots
of the electron density and electrical conductivity at the entrance of the MHD
channel for conditions of interest other than those actually used in the power-
generator experiments. A sample calculation of the thermal ionization and
electrical conductivity in a'rocket engine exhaust is presented in Appendix B.
3,200
2,800
2,400
2,000
1,600
CHAMBER^
.EXHAUST
^
Fl
0>
EL:
IDIZER :
ED:
F RATIO :
TAL PRESSURE
<HAUST PRESSU
METHA*
GASE0U
CESIUM
1.5
294 PS
RE: 22 PSIA
0L
S OXYGEN
SE
0/
TC
E
CARBONATE
IA
'
10 20 30 40
SEEDING RATE, % TOTAL FLOW
FIGURE 2. Variation of gas temperature with seeding rate.
20 30
SEEDING RATE, % TOTAL FLOW
FIGURE 5. Per cent ionization of monatomic cesium for various seeding rates.
10
/ FUEL
0X10
SEE!
0/F
TOTA
FVH?
METHANOt
IZER: GASEOUS
> : CESIUM C
RATIO: 1.5
L PRESSURE 294 PSIA
UST PRESSURE 22 PSIA
OXYGEN \
ARBONATE \
25
10 20 30 4
SEEDING RATE, % TOTAL FLOW
FIGURE 6. Electron density versus seeding rate.
33(5
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
EXHAUST^
CHAMBER v
y
FUEL: METHANOL
OXIDIZER: GASEOUS OXYGEN
SEED: CESIUM CARBONATE
O/F RATIO: 15
TOTAL PRESSURE: 294 PSIA
EXHAUST PRESSURE: 22 PSIA
20 30
SEEDING RATE, % TOTAL FLOW
FIGURE 7. Electron-electron collision cross-section versus seeding rate.
FUEL:
ER:
ATIO:
PRESSURE:
ST PRESSURE
METHANOL
GASEOUS 0X1
CESIUM CAR
1.5
294 PSIA
22 PSIA
gen :
BONATE /
0X1012
SEED:
O/F R
TOTAL
EXHAL
CHAMBER.
* EXHAUST
10
40
50
20 30
SEEOING RATE, % TOTAL FLOW
FIGURE 8. Electron-ion collision cross-section versus seeding rate.
20 30
SEEDING RATE, % TOTAL FLO*
FIGURE 9. Electrical conductivity versus seeding rate.
P,= 66PSIA
$:|40PSIA
■1=210 PSIA
FUEL : METHANOL
OXIDIZER: GASEOUS OXYGEN
SEED: CESIUM CARBONATE
EXHAUST PRESSURE: 1.5 ATM
0/F RATIO: 1.5
2 4 6 g 10
SEEDING RATE, % TOTAL FLOW
FIGURE 10. Electron density at nozzle exit versus seeding rate for various chamber
pressures.
338
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
FUEL METHANOL
OXIDIZER: GASEOUS OXYGEN
SEED. CESIUM CARBONATE
TOTAL PRESSURE ?IO PSIA
EXHAUST PRESSURE 14 7 PSIA
SEEDING RATE ( % TOTAL FLO* BY WEIGHT)
13 14 15 16 IT 18
O/F RATIO
FIGURE 11. Electrical conductivity at nozzle exit versus o/f ratio for various seeding
rates.
POWER GENERATION APPARATUS
LIQUID-FUEL ROCKET ENGINE
The NOTS rocket-MHD experiments utilized a small research rocket engine
which burned gaseous oxygen and methyl alcohol. Seed material was caesium
carbonate which was dissolved in the alcohol prior to the experiment. The NOTS
Propellant Evaluation Program (5) was used to calculate the thermodynamic
properties of the rocket combustion process.
The nozzle exit Mach number (the MHD channel entrance Mach number) was
selected on the basis of an optimization study employing the NOTS Propellant
Evaluation Program and the NOTS Electrical Conductivity Program. The results
of this optimization study are shown in Figures 12 and 13. The goal of the study
was to determine the channel Mach number and seeding rate which would give
the highest generated electrical power density based on equation (lc). The Mach
number thus chosen was 2.3 and the seeding rate was eight per cent cesium
carbonate by weight of the total propellant and seed flow through the generator.
The initial design of the RMHD rocket engine (design "A") used a nozzle with a
22-degree expansion half-angle. This abnormally large angle was necessary because
of the fabrication technique used in the construction of the square-throat, rectan-
gular-exit nozzle. Flow separation and extreme erosion of the power- channel -
insulating side plates were experienced with this nozzle. However, numerous
tests were conducted and electrical power was generated through its use. This
engine was also used in the microwave diagnostics study (11).
Because of the flow separation and channel erosion experienced with engine
design "A", an advanced design was formulated (design "B") using a different
fabrication and assembly technique which reduced the expansion half-angle of the
nozzle to 10 degrees. A constant -area, water-cooled, flow-straightener section,
1 in/>h 1<-?t-i?-t nroo
J- AA.AU.1.A. 1VUK ) ?? %M*J
r\rr +V??a flrmr iirf/"\ a -naT* Q 11°l
- :gL uaav nu it AA.il/vr w kiwi uiixva
krzycki, larsen, and BYRNE: M H D Power Generation
339
50 i-
45 -
*
e
40
*
o
o. 35
2
2
90
1.25
1.50
FUEL:
OXIDIZER:
SEED:
SEED HATE:
0/F RATIO:
METHANOL
GASEOUS OXYGEN
CESIUM CARBONATE
8% TOTAL FLOW BY WEIGHT
1.5
EXHAUST PRESSURE: 22 PSIA
MAGNETIC FIELD: I WEBER/METER 2
2.25
2.50
1.75 2.00
MACH NUMBER
FIGURE 12. Maximum generated power density versus Mach number.
fuel:
oxioizer
SEED:
TOTAL PRESSURE:
EXHAUST PRESSURE:
MACH NUMBER:
MAGNETIC FIELD:
METHANOL
GASEOUS OXYGEN
CESIUM CARBONATE
294 PSIA
22 PSIA
2.3
' I WEBER/METER'
5 10 15 20 25
SEEDINS RATE, % TOTAL FLOW BY WEIGHT
FIGURE 13. Maximum generated power density versus seeding rate.
340 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
stream. A nozzle-exit pressure line for measurement of the static pressure immedi-
ately upstream of the power channel entrance was attached to the flow straightener
section. This engine design resulted in improved flow characteristics and reduced
the erosion problem of the channel-insulating side wall.
Specifications and operating parameters for the water-cooled copper rocket
engine were:
Sonic throat 0.50 x 0.50 inches (square)
Nozzle exit 0.50 x 1.35 inches (rectangular)
Combustion chamber pressure 294 psia
Combustion chamber temperature 3159°K (8 per cent seed rate)
Nozzle exit pressure 22 psia
Nozzle exit temperature 2550°K
Nozzle exit Mach number 2.3 (2160 m/sec)
Total propellant flow 0.42 lb/sec
Cooling water flow 2-3 lb/sec
Energy loss to coolant 60 kilowatts
The injector used for all RMHD rocket engine operations was of the impinging-
stream type with nine triplet combinations. Injector and combustion chamber
lifetimes were normally measured in terms of hours of actual firing time.
POWER CHANNEL
The NOTS RMHD generator used a constant-area supersonic power-extraction
channel. This structure presented a great number of material and operational
problems. Both continuous and segmented electrode configurations were used.
The experimental results discussed in this report are from the continuous electrode
configuration only. Several designs of segmented electrodes were tried. Each
design was rejected after hot firings because of failure to maintain either electrical
or structural integrity over even a short time period.
The RMHD power channel consisted of two water-cooled, non-magnetic stainless-
steel, backing plates supporting the electrically-insulating material. This assembly
formed the walls of the channel normal to the applied magnetic field. The electrodes,
which were fitted between the side walls, were water-cooled copper. The electrode
surface exposed to the hot gas flow was knurled to break up the boundary layer;
it was hoped that this would permit better contact between the electrode and the
ionized gas. The electrode area was 0.50 x 4.2 inches. The short generator length
was determined by the length of the magnet-pole pieces and did not represent any
appreciable fraction of the total generator length that might have been used had a
more suitable magnet been available to the project. Immediately downstream
of the power generating section the flow was rapidly expanded to lower its conduc-
tivity and reduce end losses. Electrode- cooling water was dumped into the
hot exhaust at the end of the power channel. Electrical connections to the elec-
trodes were made through the electrode water coolant lines. The channel was
assembled with nonmagnetic stainless- steel cap screws and micarta insulating
sleeves. Epoxy resins and Sauereinsen high-temperature cements proved helpful
in channel component assembly and sealing, and appeared to endure the operational
environment well.
Magnesium oxide (MgO) in two different grades and Vycor glass in rolled form
were used with partial success as materials for the insulating side walls of the
power channel. These walls were required to have electrical resistance orders of
magnitude greater than the ionized gas resistance yet they were directly exposed
to the hot (2550°KV hi>h-velocitv (2160 m/sec^ gas stream.
krzycki. larsex. and byrxe: 31 H D Power Generati
341
=
S
S
c
5.
it
3
>
X
pi
Norton Magnorite fused MgO in |- and ^-inch-thick slab form and Lofero HM
MgO brick (cut and ground to the required size for use in the power channel) in
^-inch-thick slab form were the two MgO materials used. In the initial experiments
the J-inch-thick Magnorite plates were used but this thickness was found difficult
to handle in assembling the power channel because of its brittleness. Thereafter,
all MgO insulating plate thicknesses were J-inch. The Lofero HM brick was
342
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
97 per cent MgO with small amounts of other oxides. Results from the power
generation runs indicated that the fused MgO was able to endure the hot, high-
velocity gas stream better than the 97 per cent MgO.
Both J- and J-inch-thick Corning Vycor glass plates were used in the generator
experiments. Again, because of assembly difficulties with the |-inch thickness in
o
kkzycki, larses, and byrne: M H D Power Generation 343
the initial experiments, all succeeding runs were made with the J-ineh thickness.
The Vycor glass had a tendency to flow during the experiment and after a firing
of 30 or more seconds about half of the ?-inch-thiek plate would be gone. Figure 14
is a photograph of the RMHD power channel attached to engine design "B"
after a power generation run of 41 seconds. Vycor glass was used as the insulating
material and the roughened surface and flow of glass is noticeable in the photo.
FLOW VISUALIZATION
The flow pattern occurring within the power channel of the RMHD generator
was of interest because of the possibility of shocks due to the supersonic gas stream.
Subsonic-flow MHD power generators are not subject to this phenomenon,
although flow patterns through them also are important. Spark shadowgraph
photographs were taken of a gaseous nitrogen flow through transparent-walled
devices which duplicated in dimension and configuration the RMHD power
channel with continous electrodes. In the cold flow studies the continuous electrode
configuration was used with one electrode surface knurled while the other remained
a smooth, machined surface. Nitrogen plenum conditions were adjusted so that
the channel static pressure matched that experienced in the hot-fired experiments.
The cold flow channel Mach number was 2.5, while the hot flow case was 2.3.
Figure 15 is a composite of three spark shadowgraph photographs indicating the
shock structure in the RMHD channel with engine design "B". The knurled
electrode surface clearly perturbs the flow and yields the desired mixing action.
Comparison of the cold-flow shock locations and the erosion pattern observed on
the MgO and Vycor insulating plates which had been subjected to hot firings
indicated a striking similarity. The conclusion to be made from the flow- visuali-
zation studies is that contoured nozzles designed to give shock-free and parallel
flow at the nozzle exit are required for acceptable flow in a supersonic MHD power
channel.
MAGNET
An uncooled d-c laboratory magnet with adjustable pole gap was used in the
NOTS RMHD experiment. The limitations imposed because of the small field
volume of the magnet were many. Foremost was the influence on power channel
design. When the |-inch-thiek insulating plates were used in channel fabrication,
it was possible, by operating the magnet at overload conditions, to maintain a
10,000-gauss field across the power channel. However, when the J-inch-thick
plates were used, this field was reduced to 5700 gauss.
LOAD ELEMENT
The load element for the RMHD generator was an air-cooled, 16-ohm, manually-
operated rheostat. The potential across it and the current through it were recorded
on an optical galvanometer oscillograph. A wattmeter was used to determine the
maximum power point for the generator when it was under load.
POWER GENERATION EXPERIMENTS
TEST ARRANGEMENT
The RMHD experiments were performed in the magnetofluids experimental
bay at the Applied Research Laboratory, NOTS.
12 +
344
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Gaseous oxygen was regulated by remotely-loaded dome regulators. The flow
was controlled by two remotely-operated ball valves; flow rate was measured with
an ASME thin-plate orifice. Differential pressure was measured by a high-pressure
manometer.
Methyl alcohol and cesium carbonate seed were premixed before the experiment
and then stored in a high-pressure, stainless-steel fuel tank. The fuel was pressurized
by gaseous nitrogen regulated by remotely-loaded dome regulators. Fuel flow
rate was measured with an ASME thin- plate orifice and a mercury manometer.
An empirical calibration curve was used for the liquid fuel flow (with seed material),
while flow curves were calculated for the gaseous oxidizer. All pertinent differential
and line pressures were photographically recorded from a gauge panel. All dome
handloaders and valve controls were located in one console in full view of the
gauge panel, so that chamber pressure and oxidizer-fuel ratio could be monitored
— and controlled — during a run.
Ignition of the primary propellants was accomplished by heating a carbon rod
to incandescence in an oxygen and propane flame inside the chamber. When the
rod was incandescent, the primary propellant flow was initiated. The hot carbon
rod ignited the propellants and was then blown from the engine by the exhaust.
The rocket engine test stand was an integral unit which also contained a support
for the MHD power channel. An over-head view of this experimental arrangement
is shown in Figure 16.
FIGURE 16. RMHD generator and magnet.
EXPERIMENTAL PROCEDURE
The usual operating procedure for an RMHD power generation run follows.
With all facility equipment and recording apparatus operational, the cooling water
flow for the rocket engine, the backing plates, and the electrodes was started.
KRZYCKI, LAKSEST, AND BYRNE: 3JHD Power Generation
345
The magnet current was gradually increased to operating value while, simulta-
neously, the pilot flows of propane and oxygen were ignited and the carbon rod heated
to incandescence. The oscillograph was started and the primary propellants were
injected into the combustion chamber. After primary-propellant ignition the cham-
ber pressure would build smoothly to the desired value in about four .seconds.
During this initial phase only the open-circuit voltage was being recorded. Small
changes were made in the propellant flow rates to bring chamber pressure and
oxidizer-fuel ratio to design values. At this point the RMHD generator was
alternately switched from the open-circuit condition to the short-circuit condition.
Then the load resistor was cycled through its full range to obtain a voltage- current
characteristic. When maximum power conditions were obtained (as indicated by
a wattmeter) the motor-generator powering the magnet was cut and the magnet
current allowed to slowly decrease. This entire test procedure was repeated for the
duration of the firing. When the run was terminated an automatic nitrogen flush
system purged the rocket engine and power channel. A photograph of the RMHI.)
generator during a hot tiring is shown in Figure 17.
FIGURE 17. RMHD generator in operation.
EXPERIMENTAL RESULTS
Experimentally measured voltage and current and the computed power for the
seven successful firings of the RMHD generator (April through December of 1962)
are tabulated in Table I. The theoretical values for the first two firings are approxi-
mations due to the rocket engine operating far from desired conditions (due to the
short run time); conductivity daia was lacking in this regime. All values in the
rows marked "Per cent Theoretical" refer to the measured percentage of
346
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
TABLE I. STTMMABY OF EXPERIMENTAL BMHD GENERATOR RESULTS
Experiment Number
1
2
3
4
5
6
7
Open-circuit voltage
Measured (volts)
Per cent theoretical
34.9
47.2
29.0
40
31.8
44
18.2
43
28.1
66.4
17
40
13.6
32.3
Short-circuit current
Measured (amperes)
Per cent theoretical
3.4
4.6
6.3
9
3.6
4.2
2.5
5.4
2.9
6
2.34
5
2.53
5.5
Maximum Power
Measured (watts)
Per cent theoretical
3.5
0.26
6.1
0.48
18.2
1.2
9.1
1.9
23.7
4.7
12.8
2.6
5.38
1.1
Seeding rate (per cent)
4
8
8
8
8
4
8
Magnetic field (gauss)
10,000
9800
9800
5700
5700
5700
5700
Gas conductivity (mhos/meter)
[see equation (14)]
25.4
24.5
30
27.8
28.7
27.8
27.7
Experiment duration
(seconds)
7.2
32.3
7.1
41.4
83.8
253
244
the theoretical maximum predicted under the operating conditions at the time the
experimental measurement was made. The MHD channel equations given by
equation (1) were used in calculating the theoretical maximums. The gas conduc-
tivity was obtained from the programmed electrical conductivity expression and
corrected for the effect of the magnetic field, equation (14). Appendix C presents
a sample calculation of the MHD generator characteristics.
Figures 18 and 19 contain the external characteristics and power curves for two
of the RMHD generator firings. For the run represented by Figure 18 Vycor glass
insulating side plates were used and the cesium carbonate seed rate was 8 per
cent. For the run represented by Figure 19 fused MgO insulating plates were used
and the seeding rate was 4 per cent. The curves indicate that the same general
trends apply to both runs.
The data for Figure 18 were taken in a 14-second elapsed time interval beginning
23 seconds after engine ignition by varying the load rheostat from open to short
circuit. The voltage decreased linearly from the open- circuit to the short-circuit
condition. The power curve indicates that the maximum point occurred at a current
of 1.6 amperes and a potential of 13.5 volts. The load resistance under these condi-
tions is 8.4 ohms. From simplified theory (7) maximum power is drawn when
the external and internal resistances of the generator are matched. Therefore, the
effective internal resistance of the generator is 8.4 ohms.
The data for Figure 19 were taken in a 7-second elapsed time interval beginning
15 seconds after engine ignition. Desired flow rates and stable engine operation
were achieved 13 seconds after engine ignition. The voltage decreased almost
linearly from the open-circuit to the short-circuit condition. A slight decrease in
dVjdl appeared as the current increased. The open-circuit voltage maximum
changed 9.3 per cent during the 7-second recording interval. The power curve
indicates that the maximum power point occurred at a current of 0.9 amperes and
krzycki, laesen, and byrne: MHD Power Generation
347
c 16
w
*
o |2
8% SEED
VYCOR
VOLTAC
E
a
*v
\ #
A
i
\
S V
1.5 Z.O
CURRENT, AMPS
2.5 3.0 35
FIGURE 18. Performance characteristics of RMHD generator.
a potential of 9 volts. The load resistance is therefore 10 ohms. In a similar measure-
ment, taken 165 seconds after ignition, the resistance was calculated as 9.4 ohms.
Since the internal and external resistances are the same at the maximum power
point, the voltage drop is the same and, therefore, the open-circuit voltage is
twice the maximum power-point voltage. This value of 18 volts demonstrates
good agreement with the measured open-circuit voltage of 17 volts.
According to simplified theory the internal resistance of the generator is given
by (7)
w
(16)
R =
,DL
From known dimensions of the power channel and a measured internal resistance
of 10 ohms, the conductivity of the gas is found to be 2.5 mhos/meter. The short-
circuit current is given by equation (lb). Using this equation and a value of 2160
meters/sec for the gas velocity (this velocity is given as part of the NOTS Pro-
pellant Evaluation Program) the gas conductivity is computed to be 1.8 mhos/
meter. Using the calculation procedure of Appendix B, the gas conductivity is
found to be 27.8 mhos/m.
For the ideal generator the maximum power produced by the generator may be
given by (7)
348
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
1
4% SEED
Mg
IS
\ A
— 12
POWER
- y, "0
O
>
A
> ?
4
o
- 6
f
VOLTASE
- /
J
— 4
~
\
-
? ^
J
\?
k i
i
i
1
1
1
2 0.1 6 8 1 1.2 1.4 1.6 1.6 2 2 2 2.4
CURRENT, AMPS
FIGURE 19. Performance characteristics of RMHD generator.
^r ik
M
fkm
*&
Pi
FIGURE 20. RMHD voltage noise (gain, 0.5 volts/cm; sweep, 0.0002 sec/cm).
krzycki, laesen, and bykne: MHD Power Generation 349
From Figure 19 one finds that the maximum power point is 95 per cent of the the-
oretical power available, based on the measured values of the open-circuit voltage
and the short-circuit current.
The optical galvanometer oscillograph traces of the RMHD generator potential
and current showed that these parameters had alternating components about
10 per cent of the d-c levels. Actual cyclic phenomena were almost impossible to
interpret, but oscilloscope photographs of the open-circuit voltage indicated several
frequency modes (360, 1250 cps and others). A photograph of this voltage oscilla-
tion is shown in Figure 20. This type of MHD generator behavior has been reported
by other investigators (12).
CONCLUSION
Electrical energy was generated from an MHD interaction with an electrically
conducting supersonic combustion gas. The small scale of the experiment pre-
cluded diagnostics within the MHD channel. The external experimentally deter-
mined characteristics of the generator agreed well with idealized MHD
channel theory. The electrical conductivity of the supersonic gas within the channel
showed some variance with the values predicted by programmed thermal ionization
and gas conductivity equations.
It was found that the 2160-meters/sec gas stream created an environment of
severe heat transfer and drag on the structural elements of the power channel.
Segmented electrodes were not successful in this environment; however, further
design would probably have resulted in a suitable configuration. Knurling of the
continuous water-cooled copper electrode surfaces to break up the boundary layer
resulted in increased power output from the generator. Inspection of the electrode
surfaces and the insulating wall material after hot firings revealed that the bound-
ary layer may have been §-inch thick; the reduction of electrode area would be
about one-half. Cold flow visualization studies and inspection of the insulating
Avail material after hot firings indicated that contoured expansion nozzles are
necessary for supersonic MHD generator channels to prevent shocks and material
erosion.
ACKNOWLEDGMENT
The authors are indebted to James B. Lee for assistance in designing, operating,
and maintaining the electrical instrumentation.
NOMENCLATURE
AAA Conversion factor (5)
B Magnetic field strength, webers/m 2
b Impact parameter, cm
D Width of electrode, meters
e Electron charge, 4.803 x 10 ~ 10 esu
g Multiplicity of energy states, dimensionless
h Debye length, cm
/ Current, amperes
k Boltzmann constant, 1 .3804 x 10 ~ 23 joule/°K
k x Constant, - 1 .1616^ x 10*
fc 2 Constant, -14.946
k 3 Constant, 1.013 (AAA) x 10 5 /&
350 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
L Length of electrode, meters
M Mach number, dimensionless
m e Mass of electron, 9.1085 x 10 ~ 31 kg
n Particle density, particles/volume
P Pressure, units as indicated
Q Collision cross section with electrons, m 2
R Internal resistance of MHD generator, ohms
T Temperature, degrees Kelvin
u Velocity, meters/sec
V Voltage, volts
v Electron thermal velocity
W Distance between electrodes, meter
X Molar concentration, gram-moles/100 grams
x Degree of ionization, dimensionless
tj Parameter in equation (3)
A Mean-free-path, meters
II Maximum power density, watts/m 3
P Power, watts
a Electrical conductivity, mhos/meter
t Electron collision period, seconds
<j> Ionization potential, volts
v) Electron gyromagnetic frequency, radians/sec
Subscripts
e Electron
( Ion
} jth species
Neutral atom
oc Open circuit
s Seed
sc Short circuit
± Magnetic field dependency
Appendix A
SIMPLIFIED EXPRESSION FOR wt IN PARTIALLY-IONIZED GASES
The degree to which the transport coefficients of a partially ionized gas are
modified by a magnetic field is a function of the product on. where w is the gyro-
magnetic frequenc}^ of the electron and t is the mean time between collisions of
electrons with atomic and molecular particles. For seeded combustion gases
assumptions may be made which lead to a simplified expression for ojt.
The gyromagnetic frequency of an electron is
w = eBjm e
where e is the electronic charge. m c is the mass of an electron and B is the magnetic
field.
To calculate the collision period the assumption is made that the combustion
gas is seeded with small amounts of materials which are easily ionized and that the
fluid is a perfect gas in thermodynamic equilibrium and exhibits a small degree
of ionization. The electron collision period is
r = X!v
krzycki, labskh, and BYKNE: MHD Power Generation 351
where A is the mean-free-path for electrons and v is the electron thermal speed
which is given from kinetic theory considerations as
v = (8kTlnm e ) 112
The mean-free-path for electrons is
A = \\nQ
where n is the gas particle density and Q is the gas particle collision cross section.
The gas particle density is
n = PjkT
Combining the above relations one obtains the expression
<-"- = (e/Q)(77?:/8TO e ) 1/2 ( J B/P)(!r) 1 ' 2
Substituting the values of the electron charge and mass and assuming a value for
the collision cross section of 3 x 10" 19 square meters (6) one obtains
cot = 1.3xl0 3 (J3/P)(T) 12
Appendix B
CALCULATION OF ELECTRICAL CONDUCTIVITY
To illustrate the procedure used in calculating the degree of ionization, the free
electron density, and the electrical conductivity in a rocket engine exhaust, a
sample calculation will be made. The rocket engine burns gaseous oxygen and
methyl alcohol at an oxidizer-fuel ratio of 1.45 with a combustion chamber
pressure of 177 psia. The propellant is seeded with cesium carbonate to the amount
of 1 per cent by weight of total mass flow. The values of the thermodynamic
parameters at the nozzle exit for an isentropic expansion to 14.7 psia with shifting
equilibrium, as given by the NOTS Propellant Evaluation Program (5), are
T = 2585°K
P s = 1.563 x 10 " 3 atmospheres
AAA = 0.2562
X s = 6.1 x 10" 3 gram -moles/100 grams
The ionization potential for cesium is 3.87 volts, so that equation (3) becomes
(1.1616 xl0 4 )(3.87) ? ,
V = ~ 2585 + 2.5 In (2585) - In (1. 563 x 10 " 3 )- 14.946
r, = -6.238
The degree of ionization of the seed material is now given by equation (4) as
x = ( e 6-238 + 1) -l/2 = 0.0442
The monatomic cesium gas is ionized to the degree of 4.42 per cent. The value
of k 3 is found to be 1.881 x 10 27 , so that the electron density in the rocket exhaust
gases is found from equation (7) to be
_ (0.0442)(1.881xl0 2,7 )(6 .1 x lO" 3 )
U ° 2585^
n e = 1.96 x 10 20 electrons/m 3
12*
352 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
The electron-electron cross section is found from equation (11)
Q e = 5.85xl0- 16 m 2
and the electron-ion cross-section is found from equation (13)
Q { = 1.78xl0- 16 m 2
From equation (9) the electrical conductivity is found to be
a = 24 mhos/meter
Appendix C
CALCULATION OF MHD GENERATOR PERFORMANCE
The NOTS Propellant Evaluation and Electrical Conductivity Programs were
used to obtain the MHD channel-entrance parameter values. For a typical MHD
generator firing these values were:
Temperature 2550°K (calculated)
Pressure 17.33 psia (measured)
Seed rate 8 per cent (measured)
Magnetic field 5700 gauss (measured)
Gas velocity 2160 meters/sec (calculated)
Gas conductivity 35.4 mhos/m (calculated)
W 1.35 inches
D 0.50 inches (measured)
L 4.20 inches
Since continuous electrodes were used in this typical experiment the value of wr
must be considered. From equation (15) one finds
_ (1.3xl0 3 )(0.57)(2550) 1/2
wr ~ (17.33/14.7)(1.013xl0 5 )
wt = 0.312
where the channel-entrance pressure has been converted to newtons/m 2 . The
effective electrical conductivity of the exhaust gases is given by equation (14) as
35 4
= 32.2 mhos/meter
1 1 + (0.312) 2
The open circuit potential, V oc , is computed from equation (la) as
V oc = uBW = (2160)(0.57)(0.0343) = 42.3 volts
The short circuit current is given by equation (lb) as
I sc = a± uBDL = (32.3)(2160)(0.57)(0.0127)(0.1067)
I sc = 53.8 amperes
The maximum power density is given by equation (lc) as
n = a ± w 2 B 2 /4 = (32.2)(2160) 2 (0.57) 2 /4
If = 12.2 megawatts/m 3
From this value, the maximum generated power of the RMHD generator is
P = II x (volume of channel) = (12.2 x 10 e )(0.0343)(0.0127)(0.1067)
P = 565 watts
krzycki, larsen, and byrnb: M H D Power Generation 353
REFERENCES
1. Huth, J. H., "A Brief Study of Rocket- Powered Magnetohydrodynamic
Generators and Energy- Storage Devices", ARPA Order No. 91-59, The Rand
Corporation (May, 1960).
2. Sutton, G. W., "Design Considerations of a Steady D.C. Magnetohydro-
dynamic Electrical Power Generator", General Electric Report No. R59 SD
432 (September, 1959).
3. Zemansky, M. K., Heat and Thermodynamics (New York: McGraw-Hill, 1957),
439.
4. Francis, G., Ionization Phenomena in Gases (London: Butterworth, 1960), 46.
5. Browne, H. N, et al., "The Theoretical Computation of Equilibrium Composi-
tions, Thermodynamic Properties and Performance Characteristics of
Propellant Systems", NAVWEPS Report 7043, NOTS TP 2434, China Lake,
California (June 8, 1960).
6. Goldberg, P. A., "Electrical Properties of High-Altitude Ionized Shock
Waves", in Plasma Physics, ed. J. E. Drummond (New York: McGraw-Hill,
1961), 245.
7. Engineering Magnetohydrodynamics. Massachusetts Institute of Technology,
Summer Session Notes (June, 1961).
8. Basu, S., "Ionization in Seeded Detonation Waves", Phys. Fluids, 3, 456
(1960).
9. Brown, S. C, Basic Data of Plasma Physics (New York: Technology Press of
MIT and John Wiley and Sons, Inc., 1959).
10. Pai, S. I., Magnetohydrodynamics and Plasma Dynamics (New Jersev: Springer-
Verlag/Prentice-Hall, 1962), 164.
11. Larsen, H. M., and Turner, C. H., "Microwave Measurements of Electron
Density in Seeded Rocket Exhaust Gases", NAVWEPS Report 8059, NOTS
TP 3062, China Lake, California (September 21, 1962).
12. Blackman, V. H., et al., "MHD Power Generation Studies in Rectangular
Channels", in Proceedings of the 2nd Symposium on the Engineering Aspects
of Magnetohydrodynamics (New York: Columbia University Press, 1962), 180.
18. A. I. Carswell, M. P. Bachynski,
and G. G. Cloutier:
Microwave Measurements of
Electromagnetic Properties of
Plasma Flow-fields
12? Measurements of the transmission, reflection, and radiation of
microwave energy by a flowing plasma can, in principle, lead to an
understanding of the electromagnetic properties of the plasma. This
paper deals with (I) the limitations in setting up theoretical models
which will allow the interpretation of the measurements, and (2) the
difficulties and techniques in setting up experiments which lend them-
selves to theoretical interpretation.
The importance of such effects as near- arid far-field diffraction,
refraction, multiple-reflection, and stray scattering are illustrated by
a series of measurements conducted on a typical experimental arrange-
ment. A high time-resolution microwave technique for obtaining
simultaneous information on the phase and amplitude of the probing
microwave signal has been developed and its use for the measurement
of rapidly varying plasmas illustrated. Considerations on the possi-
bilities and the limitations of improving spatial resolution are also
outlined.
Ijoboratory investigations of the reflection of microwaves from
supersonic plasma flow streams are described. Back-scattering measure-
ments at frequencies of 9.4 Gc and 24 Gc on laminar and turbulent
supersonic plasma streams and the effects of turbulence in the flow and
polarization of the incident microwave fields on the scattering properties
of the plasma have been studied.
INTRODUCTION
Because of the present interest in the reentry environment, a need exists to
examine the properties of gas-dynamic flow-fields in which there is a significant
degree of ionization. Among the many possible methods available for studying
these plasma systems (1), microwave "probing" techniques offer many apparent
advantages.
The use of microwaves for plasma diagnostic purposes has, in recent years,
been the subject of detailed investigation by many workers (2); considerable
ed. note: Dr. Carswell, Dr. Bachynski, and Dr. Cloutier are at the Research Labora-
tories, RCA Victor Company, Ltd., Montreal, Quebec, Canada.
355
356
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
progress has been made. The purpose of the present paper is to discuss the appli-
cation of the various microwave techniques to the study of plasma properties in
the presence of a (supersonic) flow-field. Since the detailed properties of such plasma
systems are. in general, extremely complex because of the large number of phenom-
ena taking place simultaneously, it is desirable to examine the "conventional"
microwave diagnostic methods in the light of these additional effects.
In this paper the material will be somewhat restricted in that we shall orient
the discussion towards the types of plasmas encountered in the laboratory facilities
used for the generation of high-velocity plasma flow-fields, i.e., the plasma tunnel,
the shock tube, and the ballistic range (3). This area encompasses a large portion
of recent work on plasma flow effects and should serve to illustrate the essential
factors involved in the microwave study of any "moving" plasma. An attempt has
been made to examine the more practical aspects of the work with the main
emphasis being on an examination of the problems involved in making meaningful
measurements and in understanding their limitations. Experiments in our labora-
tories have indicated the importance of these problems, and results from these
investigations will be used as illustrations.
Before discussing in detail the factors relating to the microwave measurements
it is worth examining briefly the general situation which faces research workers
at present in this field. We have attempted to summarize these in the simple
block diagram of Figure 1. As shown in the diagram, the determination of the
properties of any real plasma system depends on two factors, namely the avail-
(A) THEORY
REAL SYSTEM
(COMPLEX, LIMITED
DATA)
PHYSICAL
MODEL
MATHEMATICAL
RESULTS &
MODEL
PREDICTIONS
(B) EXPERIMENT
C(
INTE
CO
)MPARI
RPRET
RRELA
SON
ATION
TION
REAL SYSTEM
(INACCESSIBLE OR
UNCONTROLLABLE)
SCALED OR
SIMULATED
SYSTEM
MEASURING
DEVICE
RESULTS
,
i
THEORETICAL
RESPONSE OF THE
MEASURING DEVICE
FIGURE 1. Block diagram showing the various considerations involved in studying
plasma flow-fields.
cabswell, bachynski, and cloutier: EM Properties 357
ability of a theory which can adequately describe the physical situation, and an
experimental capability to make measurements of the quantities described by the
theory. It is essential to remember that the theory and experiment are inter-
dependent and complementary. Because of the complexity of "flowing" plasma
systems it is often difficult to make a direct and meaningful comparison between
theory and experiment.
Usually the theoretician is restricted in his analysis not only by the complexity
of the problem but also by a lack of good quantitative experimental data which
he can use as a guide. In order to handle any problem analytically it is necessary
to select a suitable physical model to describe the particular plasma system of
interest. In most instances this step involves assumptions and simplifications that
may limit the amount of quantitative information about the real system which
can be deduced from the model. Usually it is necessary to make a compromise
between a model which is accurate (and hence very complicated both physically
and mathematically) and one which is less exact but is mathematically tractable.
Thus it is essential for the experimentalist, who is endeavouring to compare his
results with the theory, to be aware of the limitations of the particular theoretical
analysis with which he is dealing.
From the experimental point of view an entirely different set of difficulties
arises. First, in many laboratory studies, one is trying to simulate conditions
which exist elsewhere in some "full-scale" situation (e.g., the simulation of a
reentry environment). In this case the main interest is in obtaining more informa-
tion about the "full-scale" system from the laboratory measurements on the simu-
lated system. This means that for any useful information to be derived, the simula-
tion must at some stage allow a comparison of the laboratory "numbers" with the
full-scale system. In the simulation of supersonic plasma flow-fields this step is by
no means trivial.
First of all, any attempt at "simulation" tacitly assumes that a detailed know-
ledge of the full-scale system exists and, in general, this is not true (4). Secondly,
it is not difficult to show that because of the complexity of the full-scale system
(in the reentry case) it is impossible to simulate in the laboratory all of the full-
scale plasma parameters exactly in a single device or experiment (5, 6, 7).
Hence in a laboratory simulation, the experimentalist is forced to be satisfied
with something less than an exact "scaling" of the real system.
Once the laboratory system has been established to optimize the scaling re-
quirements, the major experimental problem lies in making meaningful measure-
ments of the very complicated plasma flow-field structure. Although there is a
rather large body of experimental work on plasma diagnostics, the art of applying
these methods to obtain quantitative measurements in the various supersonic
plasma flow facilities of interest is still only at a very early stage of development.
Because of this inability to relate the "measurables" in an experiment to the
"plasma physics", the experimentalist is at present in the position of having to
design and calibrate each diagnostic tool for each specific measurement. Under these
conditions it is not surprising that discrepancies often arise between some of the
measurements.
In the remainder of this paper we shall discuss the microwave techniques for
plasma diagnostics within the general framework indicated in Figure 1.
THEORY OF MICROWAVE INTERACTION WITH PLASMA
From the point of view of employing microwave techniques for plasma diag-
nostics, the ultimate aim of the "theoretical" analysis is to provide meaningful
358 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
expressions for the various plasma parameters of interest (e.g., the electron density,
electron temperature, collision frequency, etc.) in terms of the microwave measur-
ables (e.g., amplitude, phase, frequency, polarization, etc.). To do this properly
requires a general discussion of the interactions of electromagnetic waves with
plasma. An analysis of this type can be achieved in a rigorous manner only through
a study of the statistical mechanics of irreversible processes in systems containing
mixtures of electrically charged and uncharged particles (8, 9). As yet this rigorous
approach is incapable of supplying quantitative predictions which can be readily
compared with experimental measurements.
In spite of this limitation, however, great progress has been made by employing
less accurate descriptions of the interaction. One of the most useful descriptions
of the plasma is given in terms of its effective dielectric coefficient (10). By con-
sidering the kinetics of the "particles" in the plasma under the influence of the
field of an electromagnetic wave, it is possible to obtain expressions for the effective
dielectric coefficient in terms of the plasma parameters. In general, the effec-
tive dielectric coefficient of a plasma is a complex quantity of the form (11)
K = K r -iK i (1)
where K r and K t are the real and imaginary parts of the complex dielectric
coefficient K.
Hence, using this approach, the problem of electromagnetic wave propagation
in a plasma reduces to one of wave propagation in a medium of complex dielectric
coefficient (12). For a plane wave with harmonic time variation (e iM( ) propagating
in the ^-direction in such a medium, the electric field variation may be written as
E = E e tot e-'' 1 (2)
where y is the propagation constant given by
y = ikK 112 (3)
and Jc = 2tt/\, A = free space wavelength.
In general, y may be written in the form
y = a + ifi (4)
where
,UK?+K?) ll2 -KJ 112
(5)
_ } UK? + Kf)U* + K T y?
(6)
with a and /} being termed the attenuation and phase constant, respectively.
The attenuation of the wave (in decibels) in traveling a distance d in the medium
is given by
A = 20 log 10 ^ (7a)
or
A = 8.68^2^) (7b)
The phase shift (over a path length d) arising from the presence of the plasma is
given by
AO = led -fid (8a)
A<D = 2tt C - 1 -t I radians (8b)
cabswell, bachynski, amd cloutiek: EM Properties 359
If the values of a and /8 from equations (5) and (6) are inserted in equations (7)
and (8) the resulting expressions for the attenuation and phase shift are given by
(9)
AO = 6^{l-[W±^±?r] ls ). (10)
As they stand, these equations are purely a formal result of the solutions of
Maxwell's equations for a plane wave in a medium with a complex dielectric
coefficient, giving expressions for the measurable quantities A and A<1> in terms
of the dielectric coefficient. For plasma diagnostics by microwaves it is necessary
to have explicit expressions for K T and K x in terms of the plasma parameters and
in the derivation of these it is necessary to introduce a specific model of the plasma.
UNBOUNDED PLASMAS
One of the models widely used in diagnostic applications considers the motion
of an "average" electron in an unbounded homogeneous plasma. This results
in an effective dielectric coefficient of the plasma which is given by (10)
where wl = ne 2 jme is the "plasma frequency", n = electron density, e — electron
charge, m = electron mass, and ineffective electron collision frequency.
By inserting the values of K r and K { from equation (11) into equations (9) and
(10), a direct relationship is obtained between the measurable quantities, A and
AO, and the plasma parameters, n and v.
From the form of equation (11) it is evident that for v=0 microwaves will only
propagate in the plasma for <o>a> p . This so-called "cut-off" of propagation occurs
for K = and this fact is often used to determine the electron density in the plasma
at "cut-off" from the relationship
o = at p or f x 9000VM (12)
where / is in units of (sec)" 1 and n is in units of electrons/cm 3 . If the collision
frequency differs from zero, however, the concept of a "cut-off" is not really valid
since for any nonzero collision frequency propagation can occur even when w p > w.
Also, for v x0 it is evident from equation (10) that
AO
-jM'-sn
and this expression is often utilized in the study of plasmas by microwave inter-
ferometry techniques (13). For co p ?a> equation (13) reduces to
. , Trd ne 2 ....
A<t> = 5 (14)
A me w
showing that in this approximation the phase shift caused by the plasma is
proportional to the electron density.
At present, the simple theory outlined above is often used for microwave
studies of plasma systems. To examine the complex plasmas in gas-dynamic
flow systems, however, this analysis is not sufficiently realistic for most cases of
practical interest.
360 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
It is not possible in the space available to describe the limitations in detail but
it is hoped that a brief summary of them will serve to emphasize the fact that the
errors introduced by the application of an over-simplified theoretical model are
not negligible.
It should be mentioned, at first, that one of the basic parameters used in the
definition of the plasma, i.e., the effective collision frequency, v, is in fact, not a
simple entity, but a lumped parameter describing the interaction of the electrons
with each of the species (ions, electrons, neutrals) in the plasma. Since the definition
of this parameter can vary depending on the interactions which are included in
the theory, restrictions which are not readily apparent may be placed on the final
results. The definition of "a collision frequency" in complex systems requires care,
especially if the plasma is undergoing "chemical-kinetic" reaction and if the
conditions are far removed from the idealized "equilibrium" situation.
In addition, the theory outlined above is based on the assumption of an un-
bounded, homogeneous plasma. In practice, any plasma used for laboratory
studies is neither unbounded nor homogeneous, so it is necessary to re-examine,
from the practical point of view, the various relations derived.
For an unbounded plasma the foregoing theory can be modified to incorporate
inhomogeneities by allowing the various plasma parameters to depend on the
spatial coordinates. Strictly speaking, in this situation, one should also consider
the effects of diffusion currents which necessarily exist in the plasma, but these
effects are usually small and are generally neglected in comparison with the electron
"conduction" current.
The basic wave equations for the non-homogeneous plasma are of the form
(10, 14)
V 2 E + k 2 KE = - V (e ■ ?\ (15a)
V 2 H + FM=-^x(VxH) (15b)
where the plasma permeability is assumed equal to the free space permeability
H (which is, in most cases, a legitimate assumption). The behavior of an electro-
magnetic wave in a nonhomogeneous plasma is obtained from a solution of equations
(15a) and (15b). In order to proceed with such calculations it is necessary to assume
specific spatial variations of the plasma dielectric coefficient (15, 16, 17) and often
for practical problems this variation is not known or is too complicated to allow
anything but machine calculations of the problem.
In the presence of an external magnetic field a plasma becomes an anisotropic
medium and as a result, the effective dielectric coefficient is no longer a scalar
quantity but must be expressed as a tensor. In this case the formal mathematical
analysis involves the propagation of electromagnetic waves in a medium possessing
a tensor dielectric coefficient (18, 19). The specific form of the dielectric coefficient
tensor depends on the plasma variables (particle densities and collision frequencies,
etc.) as well as the magnetic field strength and orientation with respect to the
electromagnetic wave field. If the plasma is nonhomogeneous as well as aniso-
tropic, the elements of the tensor are functions of position and again any detailed
analysis involves specific spatial variations of these quantities. In general, the
wave equations are very difficult to solve, with solutions being available only
for specific cases, and no further discussion will be fiven here (18. 1ft. 20^
carswell, bachykski, and CLOiJTiEE : EM Properties 361
FINITE PLASMAS
The discussion thus far has been concerned only with the propagation of electro-
magnetic waves inside a plasma. Any effects of boundaries on the problem have
been ignored so all of the preceding treatment is only applicable to unbounded
plasmas. In order to make any meaningful comparison with experiment it is
necessary to take into account the effects of boundaries on the wave propagation.
Using again the "dielectric" concept of the plasma, this is usually achieved by
matching the fields on both sides of a boundary in the conventional manner of
electromagnetic theory (21). This approach involves the inclusion of a reflected
wave at any interface, and for multiple boundaries the reflections become
increasingly important.
In a recent report (22) Bachynski et al. have considered in detail some of the
problems encountered when making microwave diagnostics of finite plasmas. It is
shown that the presence of boundaries can cause very significant changes in the
attenuation and phase measurements on a plasma and can lead to errors ranging
up to factors of ten or larger in the plasma parameters deduced on the basis of the
"unbounded" theory.
For example, it is shown that for a uniform plasma slab bounded by dielectric
plates (a configuration closely approximating many experimental arrangements)
the signal transmitted through the system can be greater with the plasma than
that with no plasma in the container. This apparent negative attenuation simply
shows that the container (the parallel dielectric plates) reflects more signal when
the electron density is zero than in the presence of the plasma. The reason for this
is that the varying refractive index of the plasma can "match" the two dielectric
plates causing less reflected signal. It is interesting to note that recent measure-
ments in a plasma flow facility have produced this same effect (23).
A second important effect encountered when dealing with finite plasmas is that
of refraction. Since the refractive index of the plasma (^=K 1/2 ) is in general dif-
ferent from its bounding medium (e.g. , free space, or a dielectric container), refraction
will occur at each interface, if the angle of incidence differs from zero. The net
result of the refraction is that the nature of the incident beam of energy is altered.
The plasma can be considered to act as a lens of refractive index less than unity.
Hence in any measurement of microwaves transmitted through a plasma the
energy density in the transmitted beam is changed not only by the amount of
energy absorbed in the plasma but also by the amount of focusing or defocusing
which has taken place.
Using the concepts of geometrical optics (i.e., plasma dimensions large compared
to wavelength, losses in the plasma small, etc.) it is possible to make estimates of
the refractive effects for plasmas of simple geometric shape. These calculations
require specific assumptions concerning the plasma geometry, the spatial variation
of the electron density, and the nature of the incident microwave beam (i.e.,
whether it is parallel, convergent, or divergent) and for details the reader is
referred to the literature on this subject (22, 24). As would be expected, the calcu-
lations show that under certain conditions the refractive effects can be very large
and in general it is preferable in most experimental arrangements to try to remove
the effect of refraction by maintaining the microwave beam normal to the inter-
faces of interest.
For plasmas which are only of the order of a few wavelengths in size (as is usually
the situation in the laboratory) it is also necessary to consider diffraction effects.
Again, the geometry of the plasma and the nature of the incident wavefront
must be specified to allow solution of these problems. In some cases it is possible
362 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
to employ the Kirchhoff scalar diffraction theory (25) to provide useful results (26).
For simple geometric shapes (e.g. cylinders and spheres) the problem can be
treated as a scattering problem (27, 28) wherein the electromagnetic field is consid-
ered to be composed of an incident (plane) wave and an outgoing scattered
wave possessing either cylindrical or spherical symmetry. By knowing the spatial
dependence of the dielectric coefficient of the plasma scatterer, it is then possible
to apply the usual boundary conditions and obtain a solution (16). Again, all but
the simplest problems require computer analysis to obtain numerical results (29).
"FLOWING" PLASMAS
In the foregoing analysis of the interaction of microwaves with plasma, there has
been no specific consideration of systems possessing a "bulk" flow velocity. The
only motions accounted for have been the thermal motions of the particles and the
motions induced by the applied electromagnetic fields. That this analysis is valid
even for the hypersonic velocities generated in modern gas-dynamic test facilities
can be seen by examining the magnitudes of the various parameters involved.
First of all, if we consider the U x B force arising from the interactions of the
electrons (possessing the mean flow velocity U) with the magnetic component
of the microwave field it is seen that this force is of the order of Ujc smaller than
the microwave electric field force acting on the electrons (12) (where c is the velo-
city of light). Hence for the nonrelativistic fluid velocities of interest, this magnetic
interaction is negligible.
Secondly, if U?c the electromagnetic wave sees an essentially stationary gas.
The correction for the relative motion of the fluid and the microwave field is again
of significance only for relativistic fluid velocities, and can be neglected for the
systems of gas-dynamic interest.
In addition, it is apparent that since the microwaves are predominantly affected
by the electron component of the plasma, any direct effects of fluid flow would
not be expected to appear when V<V, the average thermal velocity of the elec-
trons in the plasma. Since the electron thermal velocity is of the order of 10 7
cm/sec, most of the velocities of current experimental interest are not sufficiently
large to impose any significant velocity contribution to the existing motions of the
electrons in the plasma.
Hence, insofar as the electromagnetic theory of microwave propagation in
plasmas is concerned, the presence of nonrelativistic flow velocities in the system
introduces basically no new concepts. There are, however, serious "secondary"
complications introduced by the fluid flow. These arise from the presence in a
supersonic flow-field of the space- and time-dependent nonhomogeneities in the
plasma properties. The existence of shock fronts, boundary layers, turbulence,
and chemical-kinetic reactions in the flow-field make any realistic computation
of the effective dielectric coefficient of the plasma virtually impossible, and hence
it is very difficult to provide realistic expressions for the measurable quantities.
It is for this reason that the flow effects do introduce significant complications
in the application of microwave diagnostic techniques to supersonic flow facilities.
MICROWAVE TECHNIQUES FOR PLASMA DIAGNOSTICS
Experimentally, the application of microwave techniques for plasma diagnostics
involves essentially a measurement of the effective dielectric properties of the plasma
by microwave methods. Hence, in principle, one could employ any of the conven-
tional microwave methods described in the literature (e.g. [30]) for measuring
such properties.
CAESWell, bachynski, and clotjtiee : EM Properties 363
For plasmas, however, certain limitations arise which often greatly reduce the
number of techniques which can be applied. As already indicated, any microwave
probing of plasmas must employ a frequency of the order of the electron plasma
frequency of the system of interest. This consideration thus establishes the range
of wavelengths which can be usefully employed in any experiment and usually
places a strong limitation on the spatial resolution of the measurement. In addition,
if the diagnostic technique is to be of general value it should be capable of exam-
ining plasmas of rather arbitrary geometry and composition over a wide range of
experimental conditions.
Broadly speaking, the possible microwave diagnostic methods for plasmas may
be divided into three separate classifications. The first involves the propagation
of microwaves in bounded structures, such as resonant cavities or waveguides,
which contain plasmas. The second is usually termed the free-space propagation
method in which a microwave "beam" is directed through the plasma of interest.
Finally, there are the techniques involving the insertion of microwave probes or
antennas into a plasma to measure the effects of the plasma environment on the
"impedance" of the antenna. The classification into these three types of measure-
ment is, of course, somewhat arbitrary since the distinction between them is not
rigorously denned and is dependent in many cases on the size and geometry of the
system and on the approach of the investigator.
When these methods are considered for diagnostics of the aerodynamic systems
of current interest, it is apparent that the free-space propagation method shows
the greatest possibilities. Although the cavity and waveguide techniques have been
widely used in laboratory studies of plasmas and have been developed to a high
degree of refinement and reliability (31-34), they are of limited usefulness in flow
systems where the plasma geometry can generally not be tailored to fit inside the
microwave enclosure. The method has been used with some success in both shock
tube and ballistic studies of plasma flow-fields (35). In shock tube studies it is
possible to use the shock tube itself as a portion of the waveguide and in this way
propagate signals through the shock front. In this application, however, the
usable microwave frequency range is limited by the dimensions of the shock tube.
Measurements in ballistic ranges have been reported (35) in which the projectiles
have been fired through cavities and waveguides but in view of the experimental
and analytical difficulties, this approach appears to be of limited usefulness.
However, a recent application of "resonant structure" techniques involving
Fabry-Perot-type interferometry in a ballistic range (36) may have promise for
future studies.
An example of the results which can be obtained using waveguide techniques
for studies of continuous supersonic plasma flow streams is shown in Figure 2
(37). These results were obtained by passing a small plasma jet (enclosed in a glass
tube) through a hole in a section of X-band waveguide as shown and measuring
the attenuation and phase shift of the transmitted signal. As the sample results
show, quite consistent and reproducible results can be obtained, but to derive
the plasma parameters from these requires some rather "over-simplifying" assump-
tions about the plasma properties.
The microwave or radio frequency probing techniques using antennas immersed
directly in plasma systems have been studied by several workers recently (38-41).
Since very small radiating surfaces can be used, the method offers the possibility
of improving the spatial resolution of the microwave measurements. In general,
however, the measurements of the plasma properties by this method are only
semi-quantitative, and much more work is required before this method can be
fully utilized. For applications to the study of flowing plasmas, this method
364
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
DISTANCE FROM NOZZLE (cm)
FIGURE 2. Sample results showing the phase shift and attenuation of a 9.2 Gc signal
passing through a supersonic argon plasma jet as shown in the inset. The results for two
separate measurements show the reproducibility obtained.
suffers from the usual disadvantage associated with the probing of supersonic
flow streams. The disturbances introduced into the flow are difficult to assess and
the interpretation of the measurements is thus complicated.
The free-space propagation method is particularly attractive for plasma diag-
nostics in conventional flow facilities. It can be readily adapted to suit existing
plasma geometries and the plasma stream can be observed with no perturbations
other than those caused by the microwave signal itself which are negligible for the
low microwave power levels used. In the remainder of this paper the free-space
propagation techniques will be discussed in more detail.
FREE-SPACE PROPAGATION MEASUREMENTS OF PLASMA
FLOW-FIELD PROPERTIES
Because of its greater versatility of application, the free-space propagation
used in conjunction with a wide range uf gas-dynamic facilities
caeswell, bachysski, and cloutier : EM Properties
365
(35, 37, 42-54). Although a variety of experimental arrangements is possible,
they may all be summarized under the four basic arrangements shown in Figure
3, i.e., the measurements involve a study of: (a) transmission, (b) reflection, (c)
scattering, or (d) radiation by the plasma flow-field. By using the appropriate
theoretical model and experimental system, each of these microwave methods
can be used to deduce information about the plasma. The direction of microwave
(a) TRANSMISSION
(b) REFLECTION
TRANSMITTER
RECEIVER
TRANSMITTER-
RECEIVER
(c) SCATTERING
TRANSMITTER
(d) RADIATION
RECEIVER
FIGURE 3. Schematic diagram showing the four basic experimental arrangements for
microwave diagnostics of plasma by the free-space propagation method.
propagation can be at any angle to the direction of plasma flow, but in most cases
only the parallel and transverse orientations are employed since for these arrange-
ments the interpretation of the results is generally somewhat simpler. In all cases
the measured parameters are the amplitude and phase (with respect to an arbitrary
reference point) of the microwave signal. In some instances, particularly when
external magnetic fields are involved, the polarization of the microwave field can
also be used to study certain properties of the plasma (55), but these cases will not
be discussed here.
In any of the experimental arrangements of Figure 3 it is desirable to be able to
probe the plasma with good spatial and temporal resolution. Unfortunately, the
spatial resolution of the microwave method is rather poor in comparison with
other methods (e.g., optical or probe studies) since even with focusing techniques,
the resolution is limited to distances of the order of the wavelength employed
(56, 57), which generally varies from a few millimeters to a few centimeters. Since
the usable wavelength is dictated by the electron density in the plasma, as men-
tioned previously, it is not, in general, possible to improve the spatial resolution
by arbitrarily reducing the wavelength. In addition, the propagation method
always involves a "line of sight" integration of the plasma properties, and the
parameters deduced from the microwave measurements represent only an average
over the plasma volume within the microwave beam. For flow systems in which
366
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
large spatial variations exist this is a great disadvantage and for these systems
it is essential that supplementary measuring techniques with better spatial
resolution be employed (53, 58).
Until recently the time resolution of microwave plasma measurements was
rather poor. This was caused by the fact that although microwave signal ampli-
tudes could be measured very rapidly, the measurements of the phase were
rather slow. The phase measurement involves a comparison of the unknown wave
with some fixed phase reference, and the usual microwave bridge techniques (30)
involve slow "balancing" operations. However, several new systems (59, 60, 61)
have been developed specifically for plasma studies so that now the phase measure-
ments can be made in times of the order of 10" 7 sec which is sufficiently rapid for
most requirements.
A system of particular usefulness is the "multiple-probe" device recently
described by Osborne (60). In this system the "unknown" microwave signal is
combined with a reference signal to produce a standing wave in a waveguide section.
This standing wave is then sampled by four detectors (probes) at one-eighth guide
wavelength intervals and the instantaneous phase and amplitude of the unknown
wave are displayed on an oscilloscope simultaneously as the orientation and length,
respectively, of a vector in a polar plot. One of the arrangements for utilizing this
device is shown in Figure 4. Using trace brightening, only the tip of the vector can
be made visible and hence the value of the amplitude and phase of the "unknown"
microwave signal can be displayed as a single point on the oscilloscope screen.
TRACE
BRIGHTENING GEN.
t
MODULATION
GENERATOR
I
KLYSTRON
POWER
-CATH00E->
53-^
AMPLIFIER
= | ATTENUATOR | = | PROBE SECTION | =^j r ;.''- '.'■'■':'■ ?y D^
PLASMA '
^ FREQ. METER[=| PHASE SHIFTEr|=JATTENI)ATOR|=
FIGURE 4. Block diagram of the multiple-probe system used for transmission measure-
ments.
Apart from the obvious advantage of providing both phase and amplitude
information, this device provides phase measurements accurate to within a few
degrees and unambiguous even for phase variations greater than 360°. It has also
been operated with sampling times of the order of 10 " 7 sec.
TRANSMISSION MEASUREMENTS
The transmission technique is probably the most widely used at present for
plasma flow diagnostics. Experimentally the method is attractive because the
necessary microwave apparatus can be kept quite simple, and it can be readily
appended to existing flow systems. By transmitting the microwave beam across
carswell. BACHYXSKi, and CLOfTiEE: EM Properties
367
the test section of a "plasma tunnel" or a shock tube, or through the plasma
generated by a hypersonic projectile in a ballistic range, it is very simple to measure
the phase and amplitude of the transmitted signal. Basically, this method can be
applied whenever the condition a>>aj r is satisfied in the portion of the plasma
examined, although detailed calculations are required to accurately define the
useful range (42). In general, the theory for unbounded, homogeneous plasma
outlined in an earlier section is utilized to obtain values for the electron density
and the collision frequency employing formulas such as those given by equations
(7) through (14). Some of the theoretical difficulties encountered in applying such
equations to real systems have already been outlined and the required corrections
indicated. Experimentally, additional problems are encountered in trying to satisfy
the necessary criteria in the apparatus. One of the most important of these is the
nature of the incident wave front. Ideally this should be plane, but in fact, unless
considerable care is exercised, this condition is very poorly satisfied and large
errors can result (22. 26. 53). By using lenses, far-field radiation from a simple
horn antenna, or other techniques, it is generally possible to minimize this error
(22). Very often, however, there is a great temptation to ignore this effect and
simply place a pair of microwave horns on opposite sides of the apparatus when the
separation is often only of the order of a few wavelengths. It is not surprising that
in such cases inconsistent measurements are often found.
The problems of refraction and diffraction have already been mentioned and
in any transmission measurements the error introduced by these effects must
be taken into account. This often involves the 'calibration" of the apparatus by
FIGURE 5. Sample results showing the difference in a multiple-probe display between
a stationary plasma and a turbulent flowing plasma: (a I a stationary argon plasma
excited at 60 c sec with a sampling rate of 10 4 sec for a period of approximately 3 msec;
(b) a turbulent (Mach 2) argon plasma with a sampling rate of 5 x 10 6, sec for a period of
^0.5 sec.
368 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
using samples of known geometry and dielectric properties in place of the plasma
(23, 51, 53).
In transmission measurements it is also necessary to consider the effects of
multiple reflections in the apparatus since these can introduce spurious signals
at the receiving antenna. Apart from the obvious reflections from the walls of the
vacuum system, it has been found that in some cases reflections arising from the
receiving antenna itself can cause significant alterations in the measurements (22).
Apart from these considerations which mainly concern the apparatus limitations,
one is confronted with the inherent complexities of the plasmas which are generated
in the flow systems. In addition to the presence of spatial irregularities, the plasma
often displays the randomly fluctuating properties characteristic of turbulent flow.
In Figure 5 an illustration is given of the complications introduced into microwave
measurements by such plasma turbulence (37).
The two photographs show the multiple probe display (see Figure 4) of a 9.2 Gc
microwave signal transmitted through time-varying plasmas. In Figure 5a the
signal is transmitted through a non-flowing argon plasma excited by a 60 c/sec
source and in Figure 5b the signal is transmitted through a supersonic argon
plasma stream. In both cases a time exposure was used so that the time develop-
ment of the plasma could be photographed. In the first case only the variation
during a quarter cycle of the excitation voltage is shown for a 10 4 /sec sampling
rate and in the second, a time exposure of about one-half second is used with a
sampling rate of 5 x 10 6 /sec. Since each spot on the screen gives the amplitude and
phase of the transmitted microwave signal at a particular instant of time, such a
time-integrated display shows the degree of variation (fluctuation) and the frequency
of occurrence of the plasma parameters. This is shown by the spread and number
density of the spots respectively in any region of the display. This comparison of
Figures 5a and 5b shows clearly the problems involved in making meaningful
measurements of complex plasma flow systems.
REFLECTION MEASUREMENTS
Many of the comments made concerning the instrumentation for transmission
measurements apply equally well in the case of reflection studies. One major differ-
ence, of course, exists in the fact that reflection measurements are, in general,
limited by the condition that co < u> r must be satisfied to provide reflected signals
of reasonable magnitude. Thus for a given plasma one is again limited in the
range of wavelengths which can be utilized.
Whereas transmission measurements can be used to measure the properties
of a plasma in a given volume, reflection measurements tend to examine "surface"
effects since they are only able to penetrate the plasma until the electron density
is such that <i> v = (xi (again assuming v?a>). Any changes in electron density within
the plasma beyond this region are not detectable in the reflected microwave
signal. This difficulty can, in principle, be alleviated to some extent by using several
frequencies (13) so that the "reflection" can be made to occur at different regions
in the plasma, but this procedure is usually limited by the cost and bulk of the
apparatus required.
Stray reflections from the apparatus are a serious problem in reflection measure-
ments since they can often be of greater magnitude than the useful signal and it is
difficult to separate the "useful" from the "stray". Matching techniques which
involve the introduction of additional reflections to "tune out" the unwanted
stray signals must be employed with considerable caution. Often the stray signal
reaching the detector when there is plasma in the apparatus is quite different
CAK SWELL, BACHVSSKI, AND fLOTTIEK: EM Properties
369
(a) NO PLASMA U p -o)
<--,
R
TRANSMITTER-
RECEIVER
(b) WITH PLASMA U p >
?)
\ ^7
TRANSMITTER-
RECEIVER
FIGURE 6. Schematic diagram to illustrate the change in "matching" conditions in a
microwave reflection system as the plasma density changes. T represents transmitted
signals. R reflected signals.
LAMINAR
< PLASMA
§ FLOW
& TURBULENT
g PLASMA
< FLOW
CO
TIME
FIGURE 7. Comparison between the signal amplitudes of microwaves reflected from a
laminar and a turbulent plasma flow-field. Time scale: 1 msec div.
370
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
1.0
lo-
ss
o
10-2
10
10
-4
24 Gc
x- 9.4 Gc
_i i i i i 1 1
i I i i i 1 1
i i I i ■ ■
10 '
10'
10 3 10 4
f (CYCLES/SEC)
FIGURE 8. Frequency content of the fluctuating microwave signal (X and K band)
reflected from a turbulent plasma stream. The results have been normalized to unity at
25 c/sec.
from that obtained with no plasma in the apparatus. Hence the matching of
the system in the absence of a plasma (as is usually done experimentally) does
not assure a matching when the plasma is present.
This fact can be readily illustrated by the simple example shown in Figure 6
in which a plasma is shown to be enclosed between two (dielectric) bounding walls.
In the absence of plasma in the apparatus the stray signal reaching the receiver
has contributions arising from both walls of the plasma container. If a plasma is
introduced, however, the stray signal from the back wall is reduced to zero as w p
cars-well, bachynski, axd clo r ti eh : EM Properties
371
increases above w. In this case the stray signal from the container now comes only
from the first dielectric wall and the necessary matching condition is quite different.
This case is very often encountered in many simple reflection measurements.
As with transmission measurements, time-dependent variations of the plasma
properties can cause difficulties in the interpretation of the measurements. Figure
7 shows a sample photograph of the amplitude of a 9.4 Gc signal reflected from a
supersonic plasma flow-field for both laminar and turbulent flow conditions as a
function of time (53). In the laminar case the return is quite steady, whereas in the
turbulent case the signal exhibits random fluctuations in amplitude. An analysis
of the frequency content of this signal can be made with the aid of a wave analyzer
and the results for two microwave frequencies (9.4 Gc and 24 Gc) reflected from
the same plasma jet are shown in Figure 8 (53). It is seen that the spectrum has
a frequency content similar to that measured for velocity fluctuations in turbulent
flows (62). The full significance of these measurements is not as yet clear but the
results serve to indicate some of the problems encountered in flowing plasmas as
veil as the applications of microwave techniques to the study of turbulence in
plasma flow systems.
BACKSCATTER SIGNAL
>
>
n
cr
70
FIGURE 9. Sample resonance patterns for 9.4 Gc microwave scattered from a 5 mm
diameter plasma column (mercury discharge tube).
Another quite different microwave reflection method involves the use of Doppler
techniques to measure the velocities of moving plasma surfaces (57, 63). Using
these techniques accurate measurements can be made of the motion of the effective
"reflecting surface" in the plasma and this method has been used by various workers
in both shock tube and ballistic range studies. It is also possible to employ pulsed
"radar" techniques to define the plasma geometry to some extent by the time delay
and shape of pulses reflected from plasma systems. Some laboratory measurements
of this type have been reported (47, 48). but because of the small distances
encountered in laboratory studies, these measurements require rather specialized
equipment involving nanosecond pulse gear.
372
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
3
SO
e
UkiiiiiiiiiiMiiim
-nwmmMMW
^jVavyava^wfrtt^^
CC LU
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I— <c
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43
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55
cakswell, bachynski, and clotttier: EM Properties
373
SCATTERING MEASUREMENTS
As already mentioned, the concepts of "transmission" and "reflection" of
microwaves by plasma become less clear if the plasma geometry differs appreciably
from the simple quasi-slab approximations indicated in Figures 3a and 3b. In
such cases it is often simpler to apply the analysis of conventional scattering
theory (16), and the transmitted and reflected components of the wave field are
then merely the "forward" and "backward" components in the scattered field.
Because of the theoretical and experimental problems involved in measurements
of such plasmas by microwaves, only a limited amount of laboratory investigation
has been attempted — even for the simpler case of stationary plasmas in gas dis-
charge tubes. Much of this work in recent years has been concerned with the scatter-
ing of microwaves by cylindrical plasma geometries with the emphasis being placed
on the examination of the still unexplained resonance phenomena which occur for
certain conditions of the incident wave fields and plasma properties (64-68).
Figure 9 is a sample photograph (53) of the "resonances" obtained in the micro-
wave signal backscattered from a cylindrical plasma as the discharge current
(electron density) varies.
Scattering techniques can be extended to allow examination of the properties
of flowing plasmas although they are somewhat limited in scope. In a recent
investigation our laboratory has undertaken to examine some of the character-
istics of microwave scattering from supersonic plasma jets (53).
FIGURE. 11a. Theoretical aspect-angle dependence of the microwave signal back-
scattered from a metal cylinder of length L.
0°
ASPECT ANGLE
FIGURE lib. Measured aspect-angle dependence of the microwave signal (9.4 Gc)
back-scattered from an 0.5-inch diameter metal rod mounted in the tunnel (Figure 10)
in place of the plasma.
UJ
Q
Q
111
a:
UJ
<
u
00
U
<
co
Mr
%/
\J
'?/%
V
V
'i /\
-20°
i
+20°
ASPECT ANGLE
FIGURE lie. Measured aspect-angle dependence of the microwave signal (9.4 Gc) back-
scattered from a Mach 2 plasma jet in the tunnel.
caeswell. bachynski. and c loftier: EM Properties 375
(I
Q
LU
+-0-*
Position in Column of Plasma
FIGURE 12a. Sample probe sweeps in the plasma jet showing the variation of the
electron density in the flow-field at various distances from the nozzle.
13 +
376
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
E
u
LU
_l
N
N
O
z
O
OH
u_
Ill
u
z
<
Q
FIGURE 12b. A contour-type display of the electron density in the flow-field showing
the effective reflecting surfaces (if = surfaces) of the plasma for both X and K band
microwaves (i.e., 9.4 and 24 Gc). The nozzle exit diameter, 2r is also indicated.
The apparatus (69) shown in Figure 10 was specifically constructed for this work
and hence the techniques are not generally applicable to conventional flow facili-
ties. Using the rotatable nozzle in this continuous flow device it is possible to
examine the scattering of microwaves from the (cylindrical) plasma stream at
various angles of incidence.
In Figure 11 results are shown for back-scattering (reflection) measurements
using this system. In Figure 11a the theoretical results (28) of the variation of the
amplitude of the back-scattered signal from a metal rod as a function of aspect
angle are shown, and in Figure lib and Figure lie sample scattering results are
shown for both a metal rod and a plasma jet. The electron density in the jet as
derived from probe measurements is shown in Figure 12a. From such measurements
considerable information concerning the plasma may be obtained. The plasma
used in obtaining Figure 1 1 had verv little axial variation of the electron density
( ahswell. bai'HYNSKI. .ixn cloutier: EM Properties 377
in the portion of the jet probed by the signal (X-band curve in Figure 12b) hence
the shape of the amplitude-versus-angle plot is very similar to that of the uniform
metal cylinder.
The effects of axial gradients in the electron density can be seen in Figure 13
in which the amplitude-versus-angle plot is no longer symmetric about the
"broadside" position. Measurements show that this curve is similar in form to that
obtained by scattering from a tapered metal cylinder. Using this method it is thus
possible to obtain some information as to the spatial variations of the pla.sma within
Q
3
u
<
CD
#.??■?.*
f \f it/* ***4
_20° 0° +20°
ASPECT ANGLE
FIGURE 13. Aspect-angle dependence of the back-scattering from a turbulent plasma
jet. The asymmetry of the curve is due to the large axial gradient of electron density
in the stream and the '"noisy" fluctuations of the signal are due to stream turbulence.
the microwave beam, but in all of this work it has been found essential to supple-
ment the microwave measurements with probe diagnostics of the plasma (53, 58)
In addition, by using incident microwave signals polarized in a direction per-
pendicular to the axis of the plasma jet it has been possible to observe (53) in
the streams the resonance effect mentioned above. Since these resonances are
intimately related to the ratio of <o/a; r it is possible that future findings may permit
their use as a diagnostic technique (70).
RADIATION MEASUREMENTS
In principle, microwave radiation measurements are ideal for plasma studies
since they introduce no perturbation of the plasma. The radiation, by the electrons
in a plasma, of electromagnetic energy over a wide frequency range is a well-
known fact and has led to the application of microwave radiometry for the measure-
ment of electron temperature in plasmas (1, 2).
378 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
If the radiation received from the plasma is in a frequency range which is higher
than the plasma frequency, the plasma is then essentially transparent to the
radiation. Under these conditions the intensity of the radiation emitted can be
expressed in terms of the emissivity of the plasma as computed from the basic
radiation processes such as brems-ttrahlung, recombination, and Cherenkov radia-
tion. When the observed radiation is in the range of frequencies which corresponds
to the plasma frequency, the absorptivity of the plasma to the microwaves is
appreciable and one can use (assuming thermodynamic equilibrium) the generalized
form of Kirchhoff 's law (71) of thermal radiation for relating the intensity of emitted
radiation to the electron temperatures. If the emitted radiation is at a frequency
lower than the plasma frequency, then the reflectivity of the plasma to the electro-
magnetic radiation must be taken into account. In this case, the absorptivity of
the plasma as appearing in Kirchhoff 's law is reduced by the reflectivity of the
plasma at that frequency.
When measuring radiation from plasmas which are not confined in a waveguide,
particular care must be given to account for the directivity of the receiving
antenna and the solid angle subtended by the plasma. This problem has been
considered by Bachynski et al. (72). In all cases it is found that the power level of
the microwave radiation emitted by plasmas is very low and consequently micro-
wave receivers of very low noise level must be used. Microwave radiometers with
the required sensitivity can be easily designed (73) for examining stationary plas-
mas (74, 75) but difficulties arise when one desires to observe rapidly time-varying
and nonrepetitive plasmas (46, 76). In order to meet this requirement one needs
to use a wide-band, low-noise receiver and at microwave frequencies this requires
rather elaborate and expensive systems. As yet a very limited number of measure-
ments have been reported on flowing plasmas and the results are rather unsatis-
factory. There is no doubt that the measurement of the microwave radiation emitted
by a plasma can be of great value in determining the temperature of the electrons
in the plasma. It is felt that a concentrated effort should be made (74) to develop
a reliable technique for measuring microwave radiation from nonrepetitive,
time-varying plasmas and to correlate such measurements with the transmission,
reflection, and scattering measurements.
CONCLUSION
Microwave techniques have proven to be of considerable value in the study of
"simple" plasma systems. A high degree of accuracy is possible in the determina-
tion of the microwave parameters (phase, amplitude, frequency, etc.) with time
resolutions of up to 10 ~ 7 sec and space resolution of the order of a radio frequency
wavelength.
A major difficulty exists, however, in relating the measurable microwave
parameters to the detailed properties of the plasma. This is particularly true in
gas-dynamic flow studies since such plasma systems are inherently quite complex.
The studies undertaken to date do not permit one to deduce the plasma para-
meters from microwave measurements with a precision approaching that of the
microwave data.
A greater emphasis should, therefore, be placed on theoretical analyses which
will take into account the significant influence of the practical experimental micro-
wave techniques and upon the design of experiments which can approach more
closely the requirements of the idealized theory. It is in this way that meaningful
advances will be made.
carswell, bachynski, and cloutier: EM Properties 379
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45. Brundin, C. L., Talbot, L., and Sherman, F. S., "Flow Studies in an Arc-
Heated Low-Density Supersonic Wind-Tunnel", University of California Inst,
of Eng. Res. Rep. HE-150-181 (April 1960).
46. Talbot, L., Katz, J. E., and Brundin, C. L., "Comparison Between Langmuir
Probe and Microwave Electron Density Measurements in an Arc-Heated
Low-Density Wind Tunnel", Phys. Fluids, 6, 559 (1963) and University of
California Inst, of Eng. Rep. HE-150-186 (Jan. 1961).
47. Rothman, H. S., "Electromagnetic Scattering From an Extended Laminar
Plasma Column", Stanford Res. Inst. Tech. Rep. No. 10 (February, 1963).
48. Rothman, H. S., Guthart, H. and Morita, T., "Electromagnetic Scattering from
Extended Targets", Stanford Res. Inst. Tech. Rep. No. 6 (September, 1962).
49. Schultz, D. L., "Micro 1 ave Studies of the Properties of Ionized Air in a
Shock Tube", Proc. IV Conf. on Ionization Phenomena in Gases (Amsterdam:
North-Holland, 1960), 1118.
50. Oshima, L., "Microwave Measurements of Plasma Flow in a Supersonic Wind
Tunnel", University of S. California Eng. Center Rep. 83-208 (AFOSR 1556)
(September, 1961).
51. Pass, H. R., "K-Band Microwave Interferometer Description and Initial
Experiments in Pilot Model of USC Low-Density Wind Tunnel", USCEC
Rep. 56-217, AFOSR TN 60-1087 (1960).
52. Lin, S. C, "A Survev of Shock Tube Research Related to the Aerophysics
Problem of Hypersonic Flight", AVCP Rep. AMP63 (AFCRL 700) (1961).
53. Carswell, A. I., "Microwave Scattering from Supersonic Plasma Flow-Fields"
RCA Victor Res. Rep. No. 7-801-24 (January, 1963).
54. Huber, P. W., "Experimental Techniques for Exploring the Interaction of
Microwave Energy with Ionized Flowfields" in Electromagnetic Effects of Re-
entry (New York: Pergamon Press, 1961), 172.
55. (a) Goldstein, L., "Non-reciprocal Electromagnetic Wave Propagation in
Ionized Gaseous Media", IRE Trans. MTT, 6, 19 (1958).
(b) Bachynski, M. P., and Osborne, F. J. F., "Microwave Techniques for
Measurement of Transient Plasma Properties", in Gas Discharges and the
Electricity Supply Industry (London: Butterworths, 1962).
56. Brown, J., Microwave Lenses (London: Methuens, 1953).
57. Primich, R. I., "Microwave Techniques for Hypersonic Ballistic Ranges", in
Electromagnetic Effects of Re-entry (New York: Pergamon Press, 1961).
58. Carswell, A. I., "Probe Studies of Supersonic Plasma Flow-Fields" (to be
published).
59. Wharton, C. B? Howard, J. C, and Heinz, 0., "Plasma Diagnostics Develop-
ments in the UCRL Pyrstron Program" Second U.N. International Conf. on
Peaceful Uses of Atomic Energy, 32, 388 (1958).
382 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
60. Osborne, F. J. F., "A Multiple-Probe Microwave System for Plasma Studies",
Can. J. Phys., 40, 1620 (1962).
61 . Lisitans, G., "Mikrowellen-Polar- Interferometer fur Plasmadichte-Messungen"
in Proc. Vth International Symposium of Ionization Phenomena in Gases
(Amsterdam: North-Holland, 1962), 405.
62. Franzen, B., and Fuchs, W., "Use of the Corona Discharge for Measurements
of Turbulence", in Proc. IVth International Symposium of Ionization Pheno-
mena in Gases (Amsterdam: North-Holland, 1960), 549.
63. (a) Maiden, J., and St. Pierre, C, "Some Measurements of the Physical
Properties of the Plasma Sheath Around Hypersonic Projectiles", in Electro-
magnetic Effects of Re-entry (New York: Pergamon Press, 1961), 196.
(b) Hey, J. S., "A Radio Method of Determining the Velocity of a Shock-
Wave", Nature, 179, 1184 (June, 1957).
(c) Cook, M. A., Doran, R. L., and Morris, G. L., "Measurement of Detonation
Velocity by Doppler Effect at Three Centimetre Wavelength", J. Appl. Phys.,
26, 426 (1955).
64. Dattner, A., "The Plasma Resonator", Ericson Technics No. 2, 310 (1957),
Stockholm.
65. Herlofson, N., "Plasma Resonances in Ionospheric Irregularities", Arkiv fur
Fysik, 3, 247 (1951).
66. Herschberger, W. D., "Absorption and Reflection Spectrum of a Plasma",
J. Appl. Phys., 31, 417 (1960).
67. Messiaen, A. M., and Vandenplas, P. E., "Comparison of Experiments with the
Theoretical Scattering Behavior of a Cold Plasma Cylinder", Phys. Letters,
2, 193 (1962).
68. Battocletti, J. H., "The Dipolar Resonance of the Cylindrical Low -Pressure
Arc Discharge", IEEE Trans. MTT-11, 193 (May, 1963).
69. Carswell, A. I., "Radio Frequency Excited Plasma Tunnel for Laboratory
Studies of Supersonic Plasma Flow-Fields", Rev. Sc. Instr., 34, 1015 (1963).
70. Crawford, F. W., Kino, G. S., Self, S. A., and Spalter, J., "Some Measure-
ments of Steady and Fluctuating Plasma Number Densities by a Microwave
Method", Stanford Univ. M. L. Report No. 961 (October, 1962).
71. (a) Rytov, S. M., Theory of Electrical Fluctuations and Thermal Radiation
(Moscow: Acad. Sci. Press, 1953).
(b) Levin, M. L., "The Electrodynamic Theory of Thermal Radiation",
Dokl. Akad. Nauk., 102, 53 (1955); See also JET P, 4, 225 (1957).
72. Bachynski, M. P., French, I. P., and Cloutier, G. G., "Antenna Noise Tem-
perature in Plasma Environment", Proc. IRE, 49, 1846 (1961).
73. Dicke, R. H., "The Measurement of Thermal Radiation at Microwave Fre-
quencies", Rev. Sci. Instr., 17, 268 (1946).
74. Fields, H., Bekefi, G., and Brown, S. C, "Microwave Emission From Non-
Maxwellian Plasmas", Phys. Rev., 129, 506 (1963).
75. George, N., "Radiation Patterns of the Noise Emission from a Gaseous
Discharge", Proc. IVth International Symposium of Ionization Phenomena in
Gases (Amsterdam: North-Holland, 1960), 743.
76. Keren, D., "Detection of Microwave Radiation from the Re-entry Plasma",
IEEE, Millimeter and Submillimeter Conference, January, 1963.
19. Allen E. Fuhs: Flight
Instrumentation for Reentry
Plasma Sheath
12? A number of instruments for probing the plasma sheath during
reentry are described. The instruments respond to the induced mag-
netic field formed by the interaction of the ionized gas flowing through
an applied magnetic field. Flight models to measure the product of
electrical conductivity and velocity, au, and the au profile are discussed.
In addition, analysis and description of laboratory transducers for
determining velocity, au fluctuations, and average electron collision
frequency are presented.
INTRODUCTION
Surrounding vehicles traveling at high speeds within the earth's atmosphere is a
plasma sheath arising from the heating of air in the shock-wave, in the boundary
layer, or in separated shear layers. The plasma sheath, which completely encases
the vehicle and feeds the wake that extends downstream a distance of many body
diameters, interferes with radio communication to and from the vehicle. These
facts have been well known to the professional missileman and space scientist
for many years; since the Mercury flights, the facts are equally familiar to the
layman.
In addition to communication blackout, the plasma sheath causes other prob-
lems. Less dense plasmas, while not causing blackout, have adverse effects on
electromagnetic wave propagation, including refraction of the waves, introduction
of noise, distortion of antenna patterns, and mismatch of antennas. The radar
cross section of a reentry vehicle may be enhanced by one, two, or three orders of
magnitude depending on the radar frequency and the reentry vehicle. Refraction
of the electromagnetic waves may make angular information from on-board radar
of questionable value.
However, the plasma sheath is not entirely detrimental. Magnetoaerodynamic
attitude control attempts to exploit this flow of conducting gases by developing
forces on the vehicle. The advent of practical superconducting coils has caused
renewed interest in this aspect of attitude control. The plasma sheath also makes
possible magnetohydrodynamic (MHD) power generation. If one considers the
enormous amount of kinetic and potential energy dissipated during reentry, it is
apparent that only a small fraction of this energy need be extracted to have
megawatts of power.
ed. note: Dr. Fuhs is with the Plasma Research Laboratory, Aerospace Corporation,
El Segundo, California. This work was sponsored under Air Force Contract
No. AF 04(695)-169.
13* 383
384
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
This paper reports on flight instrumentation being developed to gain information
about the reentry plasma sheath. Discussion of the plasma sheath is continued in
the next section. Topics to be discussed are the plasma sheath, flight instrumentation
and laboratory meters developed to obtain information about the ionized air.
THE PLASMA SHEATH (1-7)
In order to circumvent or to find solutions for the problems (e.g., telemetry
blackout and enhanced radar cross section) and exploit the opportunities (e.g.,
magnetoaerodynamic attitude control or MHD power generation during reentry),
detailed knowledge of the ionized air forming the plasma sheath is essential.
Information can be obtained from calculations, but in order to proceed with the
calculations, idealizations and simplifications are often necessary. Experiments in
hypersonic facilities yield useful information; however, it is difficult to duplicate
all the similarity parameters. In-flight measurements can be used to provide
valuable guides for additional theoretical and experimental work and as criteria
to indicate where the calculations are sound and where important physical pheno-
mena have been omitted.
In order to design instruments to measure a certain property of the plasma
sheath it is necessary to know approximately the range of values that will be
encountered during reentry. It is necessary to know the correct gain for the
amplifiers. Although the information presented in this section was initially
obtained to answer the obvious questions of amplifier gain and instrument design,
it is of sufficient general interest to warrant inclusion here.
PARAMETERS INFLUENCING THE PLASMA SHEATH
The trajectory, or more specifically the altitude and Mach number of the vehicle
has a pronounced influence on the plasma sheath. Table I, which is intended to
demonstrate that increased velocity compounds the difficulties with electro-
magnetic wave propagation, lists typical values of the electron density, N e , for
equilibrium air behind a normal shock.
TABLE I. ELECTRON DENSITIES FOB DIFFERENT TRAJECTORIES
Trajectory
Typical velocity
(ft /sec)
Electron density, cm 3
200,000 ft alt
300,000 ft alt
Suborbital IRBM
Suborbital ICBM
Orbital
Superorbital (parabolic)
15,100
23,200
25,600
36,700
7x 10 i2
8xl0i 3
2x10"
3 x 10 16
6x101°
8x10"
3xl0i 2
5x10"
Body shape also influences the plasma sheath. Simple axisymmetric bodies
are usually categorized as blunt- or sharp-nosed, depending on whether or not the
bow shock wave is attached; however, for the purposes of plasma sheath analysis,
these bodies are differentiated by the manner in which their sheath properties are
determined. Thus, a blunt-nosed body is one whose sheath properties are determined
by air that has passed through a normal or nearly normal shock wave. A sharp-
nosed body is one whose sheath properties are determined by the viscous dis-
sipation in the boundary layer, which on a sharp-nosed vehicle is supplied with
air that has passed through a weak oblique shock.
fuhs : Reentry Plasma Sheath
385
There is also an intermediate category of vehicle that may be described as
slightly blunted. The boundary layer on the forward part of a slightly-blunted
vehicle is fed by high-entropy gases from the nose. At some point along the vehicle,
the high-entropy flow is absorbed by the boundary layer; downstream from that
point the boundary layer feeds on air that has been processed by an oblique
shock.
The spatial distribution of temperature and electron density normal to the sur-
face obviously depends on body bluntness. There are, of course, more complex
body shapes, especially for manned reentry vehicles, aerospace planes, and other
lifting bodies.
Another factor determining the properties of the plasma sheath is the ablation
material. Vaporization and injection of the ablation material has a fluid mechanical
effect on the boundary layer. Impurities in the ablator may seed the boundary
layer and increase N e . Ablation products influence the chemistry of the high-
temperature air by altering compositions and electron densities. An additional
degree of complexity is thus added to the plasma sheath.
PARAMETERS CHARACTERIZING THE PLASMA SHEATH
When a macroscopic approach is used to analyze wave propagation, (8) the
plasma is characterized by its electrical permittivity, e, and an electrical conduc-
tivity, a. Attenuation and phase shift can be calculated if these are known.
In terms of microscopic plasma variables, e and a are functions of the plasma
frequency, ot p (or N e ), and the electron collision frequency, v. In the presence of
magnetic fields the ratio of electron- cyclotron frequency to collision frequency
may be of importance.
Spatial distribution of e and a, which is defined both as the profiles normal and
tangential to the vehicle surface, is required information for the analysis of wave
propagation (9, 10). The model of a plasma filling a semi-infinite half space is
inadequate for obtaining realistic predictions about the plasma sheath.
Table II contains information concerning the plasma sheath surrounding a
sharp cone. The quantity w c jvB determines the strength of magnetic field required
to make a> c jv equal to unity. This is the strength of the magnetic field required
to make the plasma behave as an anisotropic medium. For example, in the flank
TABLE II. DATA FOR PLASMA SHEATH ON SHARP CONE
Altitude
(ft)
a> c [vB
(per gauss)
(rad/sec)
V
(collision/sec)
a
(mho/m)
u
(m/see)
era
(mho/sec)
8
(em)
A'.
(cm" 3 )
Stagnation Region
250
200
150
100
50
8.8xl0- 3
1.25xl0- 3
2.3x10-*
3.2 xlO" 5
5.5 xlO- 6
1.77 x 10"
5.22x10"
1.51 x 10 12
4.97 x 10 12
4.46 X 10 12
2 xlO 9
1.41 xlO 10
7.6 xlO 10
5.6x10"
3.2 xlO 12
140
170
270
390
55
—
—
—
10 13
9 x 10 13
7x 10 1 *
8xl0 15
8xl0 15
Flank Region
250
200
150
100
50
0.28
0.0354
6.4 xlO" 3
8.4x10"*
1.3x10"*
3xl0 9
10 10
3xl0 10
7xl0 10
4.3 xlO 10
6.3 xlO 7
5xl0 8
2.75 xlO 9
2.1 x 10 l °
1.3x10"
1.4
1.8
2.4
2.3
0.12
3500
3600
3600
3500
2800
4900
6500
8600
8100
340
5
1.5
0.6
0.2
0.08
3xl0 9
3xl0 10
3x10"
1.6 xlO 12
6 x 10"
386
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
region at 150,000 feet a magnetic field of 157 gauss gives co c jv= 1. The d-c electrical
conductivity, equal to atf,e jv, has been calculated. The plasma sheath thickness,
o, has been taken as being equal to the boundary-layer thickness. In Table II,
8 is for a station 3 feet from the nose. The data are for a semivertex angle of 10
degrees, a wall temperature of 2000°K, and an ICBM trajectory with a velocity
of 23,500 ft/sec at an altitude of 150,000 feet. The data were calculated using the
information from Dix (4).
The instruments described in the following section measure au. Hence era has
been calculated using as an estimate u = u cc j'2. One advantage of an instrument
that responds to au is the relatively small change in this quantity with altitude.
In the altitude range 250,000 to 100,000 feet, au varies by less than a factor of 2,
whereas N e changes by a factor of 500. Instruments responding to N e must have
a wide dynamic range. The reason the a does not change appreciably is that
increases in N e are compensated for by increases in v.
In contrast to sharp-nosed vehicles, values of au as high as 5 x 10 5 mho/sec may
be observed in the flank region of blunt-nosed vehicles. This is 100 times larger
than for a sharp-nosed vehicle. As a consequence, measurements of the plasma
sheath on a sharp-nosed vehicle are significantly more difficult.
?- X
PRIMARY COILS-
z- AXIS IS NORMAL TO AND OUT OF
THE PLANE OF THE PAPER
FIGURE 1. Transducer coil arrangement. An emf is induced in the sensing coil by the
time rate of change of normal component of ?>.
fuhs: Reentry Plasma Sheath 387
FLIGHT INSTRUMENTATION DEVELOPED AT THE PLASMA
RESEARCH LABORATORY
The several instruments described here for measuring plasma sheath properties
are in various stages of development at the Plasma Research Laboratory. The
first instruments described— three average au meters and a era profile instrument
— have been flown or are soon to fly. The MHD flow angle indicator, the velocity
meter, and the turbulence indicator have been tested in the laboratory. An
instrument for the measurement of electron collision frequency has been theoretically
analyzed but has not yet been tested in the laboratory. These instruments may be
used to measure not only the reentry plasma sheath but also other high-speed,
ionized-gas flows, including rocket exhausts, MHD generators, and arc plasma
jets.
RELATION OF SIGNAL TO FLOW PROPERTIES
In previous publications (1, 11) the signal, which is the voltage induced in the
sensing coil, was analyzed in detail. The analysis will be briefly reviewed here.
Consider a coil arrangement consisting of a sensing coil located between two
primary coils as shown in Figure 1. The primary coils are driven at audio frequen-
cies and provide a magnetic field B that penetrates into the plasma flowing at
velocity u. Currents, J, are induced as a result of the motion of the conductor
through the magnetic field. The induced magnetic field B t , which fluctuates
at the frequency of B, links with the sensing coil that has a voltage e. The currents
Tare equal to a(E + u x B). The electrical conductivity a is the d-c value and for
ionized gases equals copCo/v. It can be shown (2, 12) that for the two-dimensional
case E is zero,, and for oblong primary coils (long dimension in the z-direction) E
is negligible. The voltage in the sensing coil is
4tt 8t] v r 3 aj A
(1)
The second integral represents the primary field that links the sensing coil; it is
an unwanted voltage and is termed the null signal. By careful balance of the
primary field this signal can either be eliminated or made negligibly small. Manipu-
lation of the vectors as indicated in the first integral leads to
_ NAfj. w
j* f Wywy**?i*> S'^ixdydz (2)
4ff
which can be rewritten as
e = I ouK dy (3)
Jy
where
K{y) = NA W> f f *B y fry,z) dxdz w
The function K(y) is known as the influence function and can be readily measured
in the laboratory (11). The influence function equals the signal that would result
388
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
from a unit layer of conducting material with unit conductivity moving at unit
velocity and located at distance y.
AVERAGE au TRANSDUCERS
A transducer with a single influence function and hence one signal yields a
measurement of the average value of au as given by
° U JKdy
An average au transducer was flown successfully aboard a reentry vehicle.
(5)
Flight on RVX-2A
An instrument (12) using a transducer geometry similar to that shown in
Figure 1 was flown on board the RVX-2A, a sphere-cone reentry vehicle. This
reentry vehicle (R/V) followed a typical ICBM trajectory. Figure 2 shows the
location of the transducer on the R/V and the geometrical relation of the flow
field to the applied magnetic field. Figure 3 shows the results of the measurement.
SHOCK WAVE
OUTER SURFACE
OF BOUNDARY
LAYER
SHOCK
WAVE
SURFACE OF
REENTRY VEHICLE
FIGURE 2. Flow field and location of transducer on reentry vehicle. The coils of the
conductivity meter are located well aft on the reentry vehicle. The flow of conducting
gas u interacts with the magnetic field B to provide a current density i.
The upper curve in Figure 3 is a plot of the angle of attack of the R/V as a
function of time. Also indicated are the periods of fade and blackout of the tele-
metry. The lower solid curve shows au as a function of time; au was obtained
fuhs: Reentry Plasma Sheath
389
from the flight measurements of e, laboratory measurements of j K dy, and
equation (5). The electrical conductivity behind a normal shock was calculated
for the RVX-2A trajectory. Results of the calculations for a, based on the method
outlined by Meyer (13), are shown on the right-hand side of the lower graph by the
dashed curve, with values for mho/m.
uj o
m
O
?x
If
br FADE -
1
h-
- BLACKOUT —
-hJ
r
1
I
1
■■
1
1
r
T
J_+
I
L
f - !
1
1
r — i
1 i i
1 ' :
1
1
i
1
/
*"*
^
L
6^U
o
1
1
1
240
1
1
>
I
V
1
1
Z
A
A.
,. j
X
'
ft
,,f
I
\
1 -
160
I
f\\
u
i
1,
^
/v
\
la
v
1
*?
4*
i
^?
*=-
A
r?-
1
V
p
r
\
I "
80
' i
}
i
i
K
o
X
TIME ■-
FIGURE 3. Observed value of au and the angle of attack of the reentry vehicle.
The meter signal follows the oscillation of the angle of attack, i.e., a local
minimum of the signal corresponds to zero angle of attack. At time A (Figure 3)
the angle of attack is zero, and au is at a minimum. At time B the angle of attack
is at its peak value, and au has increased to a local maximum. This fact suggested
the flow angle indicator, described in another section.
Axisymmetric Transducer Geometry (14-16)
Aerodynamic stability requires the center of gravity of the vehicle to be in
front of the center of pressure. Conical reentry vehicles frequently require dense
ballast placed far forward to achieve this condition. The ballast replaces a part
of the payload. A transducer has been developed that serves two functions: it
provides measurement of an average value of au, and its weight serves as ballast.
Figure 4 shows the coil arrangement, which has been tested in an arc jet. Analysis
shows that most of the signal is due to the induced currents in a narrow region
of the plasma flow concentric with the sensing coil. Two reasons account for this.
First, the magnetic coupling between the sensing coil and the current rings in the
gas falls off sharply as the separation between the two increases. Second, the applied
magnetic field, which drives the currents, falls off rapidly with distance from the
sensing coil. For the geometry shown in Figure 4, 95 per cent of the signal is due
to the currents within a region in the gas twice the width of the sensing coil.
390
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
I.
,
—
- 1
■ ' Be
■
o 1
■ ■- J
,,
H ' H lx
,
B3 \
/ v fl
/ > w 1
B I 1
■ . Bco
"" < < \
/ 2 w H
CO
■ B
*
—J ?? rr> \
/ E ■
_J
■ ■?-
— f
/ Q -
o
ON ABL A
2 < en \
O _l — ' \
o
"
OF SI
HE P
IN TH
>-
<I
2
-rt
~ ?" 3= \
a:
■ ■Ll
m i— i
a.
■ 11x1
*
en O r
nv I?
cii- 5 1 ■
A f XT
/
i \ f N
,?..,, ?w , ' i , ^^|j*H
.
ff '?
1 ?*-'? P
■?■■■■ ?■■ io
■ col
■ col
P
\1
^41
c
a
a
?a
C4
o
Mi
3
-O
X
B
0)
bt
IS
5
p
(See the inset diagram in Figure 4.) This means that the plasma flow is sampled
in the vicinity of the sensing coil, and interpretation of the signal is more meaning-
ful since only a localized region contributes to the signal.
Transducer Using Permanent Magnets (17)
When the instrumentation program (2) was first initiated at the Plasma Research
Laboratory it was necessarj- to decide whether to use a d-c or an a-c applied mag-
netic field. The first instruments developed used a-c. However, it is obvious that the
induced field, B t , exists with a d-c primary field. In order to measure au with a
thick metallic skin between the conducting flow and the transducer, a d-c meter is
essential. If an a-c method is attempted, eddy currents in the skin attenuate both
the applied magnetic field and the induced magnetic field.
fuhs: Reentry Plasma Sheath
391
The earth's magnetic field is approximately 500 milligauss. For one application
aboard a reentry vehicle the calculated B { varied between 1 and 10 milligauss.
Hence cancellation of the earth's magnetic field is necessary. One method of cancel-
lation is to use two magnetic detectors whose outputs are sensed differentially
such that the signal due to earth's magnetic field cancels, whereas the signal due
to plasma flow adds. Figure 5 schematically depicts one arrangement. Figure 6 is a
photograph of the flight instrumentation package.
EARTH'S MAGNETIC
FIELD
EARTH'S MAGNETIC
FIELD
APPLIED MAGNETIC
FIELD
INDUCED
CURRENT J
MAGNETIC DETECTOR
PERMANENT
MAGNET
FIGURE 5. Cancellation of earth's magnetic field and addition of induced magnetic
field due to plasma flow.
CONDUCTIVITY/VELOCITY PROFILE METER (1, 11)
If transducers with different magnetic field geometries are used, the flow of
ionized gas can be sampled differently. Each geometry provides a different signal
given by
?shock wave
au-Ki dy
J ablation surface
(6)
where the subscript i identifies the different signals. The K { are measured in the
laboratory; the e t are measured in flight. Distinctly different K t can be obtained
by changing the primary magnetic field geometry and by altering the geometrical
relation between the induced magnetic field and the sensing coils.
From this information the au profile can be calculated. One procedure is to
divide the integration interval into discrete intervals Ay,, which may be of unequal
length. Having chosen the Ay ; , the corresponding {au), values can be determined
392
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
a.
3
T3
ir.
S
a
=
a
S
o
a
3
c o
u ?>
S a
3 O
- '-s
?- C
*- &
H s
m
ss
O x
M O
as shown in Figure 7. For the case illustrated in Figure 7, a five-signal transducer
is required. A three-signal transducer is shown in Figure 8. Other geometries,
including a nine-signal transducer, have been considered and are discussed by
others (1, 11).
The transducer illustrated in Figure 8 is designed to sample the plasma flow in
different ways by having different scale primary fields. A plasma layer of Ay
thickness appears to the small primary coil to be AyjR=l inch thickness and to
be centered at y/R = 2. The same plasma layer appears to the large primary coil
to be AyjR = ^ inch thickness and to be centered at y/R — %. The plasma layer is
measured by use of different portions of the influence function.
Using knowledge of e ls e 2 , and e 3 , and the influence functions, K x , K. 2 , and K 3 ,
from the system shown in Figure 8, the profile of a spinning graphite disk was
SHOCK
WAVE
SURFACE OF
ABLATION
MATERIAL
<r u
7 77777777777777777 ~
FIGURE 7. Illustration of the results of a calculation of a au profile.
LARGE PRIMARY COIL
/ MIDDLE PRIMARY COIL
SMALL PRIMARY COIL
>lasma
BAND PASS
FILTERS
FIGURE 8. Coil geometry providing three different scale primary fields.
394
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
calculated. A comparison of the actual and measured profiles is shown in Figure 9.
Three different experiments are plotted, with the disk located at 0.5, 1.0, and 2.0
inches from the transducer. The influence function for the smallest primary coil
has been plotted in the bottom graph. The error in predicting the disk thickness,
when the disk was 2 inches from the transducer, is due to the fact that the meter
is not sensitive beyond about 3 inches.
<ru
ACTUAL PROFILE
MEASURED PROFILE
<ru
y.lN.
-y.iN.
I 3 5
FIGURE 9. Comparison of actual and measured profiles.
-y.lN.
A MHD profile meter (18) was built for flight aboard reentry vehicles. Figure 10
is a photograph of the instrument, which provides four continuous samples of the
flow.
fuhs: Reentry Plasma Sheath
395
EU
CD
>-.
CC -J
o ~
"S
3 |-
?*
°>
< w
5
?
3
FLOW ANGLE INDICATOR (19)
The instruments described in this and the following two sections have been
tested in the laboratory but have not been developed as flight instrumentation.
Using the MHD flow angle indicator is analogous to using two total head tubes
displaced at a small angle to measure flow angles. When the pressure in each tube
is equal, the bisector of the tube angle is parallel to the flow. The MHD flow angle
indicator is shown in Figure 11. The transducer is not rotated to give equal signals.
but the ratio of signal strength is used to calculate the flow angle. The equation
relating signal ratio B to flow angle is
= arc tan
\l + R tan a)
(7)
396
PHYSICO-CHEMICAL DIAGNOSTICS 01' PLASMAS
FIGURE 11. Crossed sensing coil geometry.
The symbols are defined in Figure 1 1 . The angle a measures the location of the
sensing coils in relation to the reference axis. When the plasma flow, which is
above and parallel to the plane of the paper, deviates by an angle 6 from the
reference axis, sensing coil 2 has a larger signal than sensing coil 1. Equation (7)
gives 9 as a function of the signal ratio R and a. The transducer can yield the local
flow angle 8 without knowledge of a or u of the ionized gas. However, if e 1 and e 2
are measured separately and the transducer is calibrated, simultaneous measure-
ments of au and 6 are obtained.
Two different configurations have been built and tested: one is shown in Figure
11; the other is described in (19). The accuracy of the flow angle measurement is
ftths : Reentry Plasma Sheath
391
1 degree + 5 per cent for —45 degrees < < 45 degrees. (For an angle of 40 degrees,
the error may be +3 degrees.) For bounded 6, the a can be adjusted to give
optimum performance.
AVERAGE ELECTRON COLLISION FREQUENCY (20)
A scalar electrical conductivity has been assumed in the previous sections. If a
sufficiently large magnetic field is applied, the a becomes a tensor. Table I gives the
value of B required for a ratio of electron cyclotron frequency co c to collision
frequency v equal to unity. Equation (1) has been expanded, considering a to
be a tensor. For the coordinate system and coil arrangement shown in Figure 1,
the result is
NA/xp 8
4^~ dt
^[(^+7')(-^) + ('?)
(8)
+
(^-t)^)-^*?)^)]"
where <o z , ut y , and w z are the components of <o c , and a' equals a>pe jv. Fortunately,
most of the terms drop out in the integration as a result of symmetry. In final
form the equation for the signal voltage is
e =
NAfjLp 8
4tt dt
(9)
Note that when (o? c /i<) 2 ? 1 , equation (9) reduces to equation (2).
PRIMARY COIL
GENERATOR GIVING THE
CURRENT B e i ?" t
GENERATOR GIVING THE CURRENT
FOR B DC OR ZERO CURRENT
SENSING COIL
'DC
r2B
mAw?w "iJWWW*
-B FOR w c /v
EQUAL TO UNITY
TIME
p-TIME
SIGNAL _|
FIGURE 12. The excitation of the primary field and the anticipated signal.
398
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
An average value of the ratio cojv can be measured by using an applied magnetic
field as illustrated in Figure 12. When an appropriately strong d-c field is applied,
the denominator of the integrand in equation (9) exceeds unity, decreasing the
signal. When the primary coil is excited only with weak a-c, the denominator is
nearly unity and a signal e is measured. An average value of the frequency ratio
is given by
(-) =(— r <??
\ w c/ average \^0 W
where a>' c = eB dc jm.
VELOCITY MEASUREMENT
An experiment was performed using the coil arrangement shown in Figure 13
and an arc plasma jet. The primary coils were excited d-c and had alternating
en
_i
o
o
u.
o
h-
■CO
ft
■_J
Ho
2
H°
<S
Bll.
Hk ^^
o:
■o
H
Ht-
^P .? i^|
CO
■uj
a.
3
■co
H<
■ rr
■ lu
■ h-
■uj
■ ? CO
■<r
■ ^ rr
^K ^^H
i^afcs^. j
■h-
■co
■ lu lu
1*^
■ 2
.;,#' !■ BSHl
P
■°°i
L o| F*?
■o
loo
o ,
HRLllH ^KalH^^I
■^
< UJ
->
^TrJt
■^
gco
F ■*'*" i-
\ %
co
y- <t
3 5.
VA
%
w?
Q
1
f
Ho
IOLES
VER
w
"TJ
1°
■ x o
^1 o
Ho
Bh
■ z
■ ^ 2
■ co
■oo
■ m _i
^B u.
■ UJ
■ U. m
Jco
3
-a
s
J2
-a
c
a
a
si
P
fuhs : Reentry Plasma, Sheath
399
poles. Emitter followers were used to isolate the sensing coils from the distributed
capacitance in the external leads. A flat frequency response from 10 to 100 kc
was thus obtained.
Typical traces of the voltage induced in the sensing coils as a result of the plasma
jet flowing through the steady applied magnetic field are shown in Figure 14.
Voltages appearing at the upstream and downstream sensing coils are closely
correlated. The cross correlation function
F(t)
I e^e^t + ^dt
(jeUty^je'dtj
1/2
(11)
was calculated as a function of t for several oscillograms similar to Figure 14.
Maximum values of F ranged from 0.85 to 0.92.
<
ti
o
>
o
<_>
o
Ul
100 200 300 400 500* 600 700 800 900 1000
TIME,/! SEC
FIGURE 14. Typical signals from velocity transducer.
For the case shown in Figure 14 the peak value of F occurred at t = 22 [Asec. The
distance between the upstream and downstream coil sets was 7.9 cm giving a
velocity of 3600 m/sec.
TURBULENCE INDICATOR
The preceding experiment is an example of serendipity. The aim was to measure
velocity, and an average velocity measurement was obtained; however, it was
discovered that additional information about the flow is contained in the noisy signal
traces. The amplitude and spectrum of the signals illustrated in Figure 14 are
related to au fluctuations in the plasma stream.
Although the data obtained await thorough analysis, preliminary observations
can be made. The time dependent terms in equation (1) are a and u, and not B.
The close correlation between the upstream and downstream signals indicates that
400 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
the au fluctuations are convected, with only small changes due to the nonstationary
terms. The spectrum is dictated by the response of the transducer to the different
scale au fluctuations. Experiments using wire loops that are moved through the
applied magnetic field indicate that only loops in the range 0.5L to 2.0L cause
significant signals (L being the length of one complete coil set in the streamwise
direction).
The signals were obtained in an arc jet facility. It is not known whether similar
fluctuations occur in the plasma sheath surrounding a reentry vehicle. One appli-
cation of the turbulence indicator would be to detect on a reentry vehicle the
transition from laminar to turbulent flow. Since the skin depth at 10 to 100 kc
in most metals is very small, the turbulence transducer should be separated from
the flow by dielectrics only.
SUMMARY
Several instruments have been developed which depend for their operation on
the interaction of a high speed flow of ionized gas with an applied magnetic field.
These meters are admirably suited for reentry experiments because the transducer
can be located behind a protective wall and does not require probes that have to
be inserted into the plasma.
The average au meters in two geometrical arrangements have been developed
for flight. One au profile meter has been assembled (Figure 10) as a flight instru-
ment; another model is under development. Instruments to measure local flow
angle (Figure 11), average flow velocity, and fluctuations (Figure 13) have been
tested in the laboratory. An average electron frequency meter (Figure 12) has been
explored theoretically.
ACKNOWLEDGMENT
The first in the series of the electrical conductivity/velocity instruments was
conceived by R. X. Meyer. His help and encouragement with the development
of the other transducers is appreciated.
Frequent discussions with R. Betchov concerning various aspects of the instru-
ments were extremely helpful. In addition, he suggested the velocity measure-
ment experiment and helped with the development of the d-c version of the
average au transducer.
L. S. G. Kovasznay, consultant to Plasma Research Laboratory, provided new
insight into the au profile meter. He also reviewed the work done on the tensor
conductivity (average v measurement) and made helpful suggestions.
0. L. Gibb assembled, calibrated, and assisted with the design of the trans-
ducers. In addition, he is co-inventor of the MHD flow angle indicator. A. Y. Lu
translated rough sketches into polished engineering designs. His assistance has
been invaluable.
REFERENCES
Fuhs, A. E., "A Technique for Obtaining the Velocity-Electrical Conductivity
Profile", TDR-594(1215-01)TN-2, Aerospace Corporation, El Segundo,
California (30 June, 1961); see also Proceedings of the Second Symposium on the
Plasma Sheath (Baltimore: Spartan Press, 1964).
Fuhs, A. E., "Development of a Device for Measuring Electrical Conductivity
of Ionized Air During Reentry", STL/TR-60-0000-09256, Space Technology
Labs., Los Angeles (September 20, 1960).
fuhs: Reentry Plasma Sheath 401
3. Rotman, W., and Meltz, G., eds., "Electromagnetic Effects of Reentry,
Selected papers from Symposium on the Plasma Sheath: Its Effects on Com-
munication and Detection", in Planetary and Space Science, 6 (June, 1961).
4. Dix, D. M., "Typical Values of Plasma Parameters Around a Conical Reentry
Vehicle", TDR-169(3230-22)TN-1, Aerospace Corporation, El Segundo,
California (November 7, 1962).
5. "Reentry Physics and Project Press Programs, Semiannual Technical Sum-
mary Reports to ARPA", Lincoln Lab., M.I.T. (June 30 and December 31,
1960; June 30 and December 31, 1961; June 30, 1962).
6. Huber, P. W., and Nelson, C. H., "Plasmas Frequency and Radio Attenu-
ation", paper 61, NASA University Conference on the Science and Technology
of Space Exploration (Chicago, 1962), 2, 347-60 (NASA SP-11).
7. Pippert, G. F., and Edelberg, S., "The Electrical Properties of the Air Around
a Reentering Body", IAS paper 61-40, AIAA(IAS), New York (1961).
8. Plugge, R. J., Chen, S., and Long, R. K., "Some Calculations of the Phase
Shift and Attenuation Rates of the Hypersonic Plasma Sheath", Report
1021-3, Ohio State Univ. Research Foundation, Columbus (January 31, 1961).
9. Albini, F. A., and Jahn, R. G., "Reflection and Transmission of Electro-
magnetic Waves at Electron Density Gradients",/. Appl. Phys., 32 (1), 75-82
(1961).
10. Daiber, J. W., and Glick, H. S., "Plasma Studies in a Shock Tube", AF-1441-
A— 4, Cornell Aeronautical Lab., Inc., Buffalo (July, 1961).
11. Fuhs, A. E., "Additional Comments on a Technique for Obtaining the Elec-
trical Conductivity-Velocity Profile", TDR-930(2230-03)TN-5, Aerospace
Corporation, El Segundo, California (March 22, 1962); see also Proceedings of
the Second Symposium on the Plasma Sheath (Baltimore: Spartan Press, 1964).
12. Betchov, R., Fuhs, A. E., Meyer, R. X. and Schaffer, A. B., "Measurement of
Electrical Conductivity of Ionized Air During Reentry", TDR-930(2230-
03)TR-1, Aerospace Corporation, El Segundo, California (January 16, 1962);
see also Aerospace Eng., 21 (11), 54-55, 68-78 (1962).
13. Meyer, R. X., "The Electrical Conductivity of Air Up to 24000°K", GM-TR-
0127-00420, Space Technology Labs., Inc.' Los Angeles (June 26, 1958).
14. Fuhs, A. E., and Gibb, 0. L., "A Velocity-Electrical Conductivity Transducer
for Axisymmetric Reentry Vehicles", Technical Documentary Report,
Aerospace Corporation, El Segundo, California (to be published).
15. Sheriff, J. A., The Theory of Electromagnetic Flow Measurement (New York:
Cambridge University Press, 1962).
16. Lehde, H., and Lang, H. T., U.S. Patent 2,435,043 (1948).
17. Fuhs, A. E., Betchov, R., Gibb, O. L., and Abshear, J. R., "An Electrical
Conductivity- Velocity Instrument Using DC Applied Magnetic Field",
Technical Documentary Report, Aerospace Corporation, El Segundo, Cali-
fornia (to be published).
18. Fuhs, A. E., and Gibb, O. L., "Magnetohydrodynamic Electrical Conductivity-
Velocity Profile Instrument", Technical Documentary Report, Aerospace
Corporation, El Segundo, California (to be published).
19. Fuhs, A. E., and Gibb, O. L., "A Magnetohydrodynamic Flow Angle Indi-
cator", TDR-169(3153)TN-^, Aerospace Corporation, El Segundo, California
(November, 1962); also, presented at Fourth Symposium on Engineering
Aspects of Magnetohydrodynamics (April 10-11, 1963).
20. Fuhs, A. E., "Signal from the Electrical Conductivity/Velocity Meter for
Tensor Conductivity", TDR-69(2119)TN-5, Aerospace Corporation, El
Segundo, California (May 22, 1962).
20. Boris Ragent:
X-Ray Densitometer for Use in
Plasma Streams
I2? An instrument has been constructed for the measurement of the
mass density of a gas in a localized volume element. The density
measurement is independent of the thermodynamic or hydrodynamic
state of the gas and independent of the presence of equilibrium or
transient flow conditions. The instrument is especially designed for
application to density measurements in high-temperature gas streams.
The principle of operation involves the measurement of the scattering
of a beam of moderately hard X-rays to establish the number of scatter-
ing centers present in a scattering volume. This volume is defined by
the geometrical intersection of a well-defined pencil of X-rays and
collimated viewing paths of detectors. The X-ray energy utilized is
high enough so that the scattering is primarily incoherent from electrons,
both bound and free, so that the number of X-rays scattered into a
detector per unit time is proportional only to the total electron density
in the gas and not the chemical state of the gas. The gas mass density
may be related to the total electron density since the number of electrons
per gram is approximately constant for all common gases except
hydrogen.
Sample calibration data taken in helium and air are shown and
typical applications are discussed.
INTRODUCTION
The utility of devices for producing high-enthalpy gas streams is often contingent
upon the ability of the investigator to measure the internal properties of the gas or
the interaction of these gas streams with matter. The measurement of the internal
properties of the gas stream, which are necessary to define the state, may be
distinguished by whether or not the measurement process itself depends upon the
distribution of energy states within the gas or its motion. For example, measure-
ments of temperature require that certain assumptions about energy partition in
the gas be verified. On the other hand, it is desirable that independent measure-
ments of such quantities as ambient pressure, velocity, or mass density should not
require such considerations. It is further desirable that instruments to measure
any of these latter quantities be designed to make localized measurements in the
ed. note: Dr. Ragent is with the Vidya Division, Itek Corporation, Palo Alto,
California.
403
404
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
gas stream since the quantity to be measured may vary strongly from point to
point in the gas. The accuracy of a measurement made in a specified time must, of
course, be consonant with the desired application.
This paper describes a technique for the measurement of the mass density of a
gas in a localized volume element. The measurement is essentially independent of
the state of the gas and only requires electrical neutrality in the volume element
under consideration. The device described is especially designed for application to
density measurements in high-temperature gas streams such as those generated in
arc-heated wind tunnels, although the apparatus is equally well suited to measure-
ments in lower-temperature gases.
PRINCIPLES OF THE METHOD
GENERAL
The scattering of X-rays in low-atomic-number gases, such as air and air
constituents in the energy range from about 1 mev down to about 10 kev, is
dominated by the Compton process, in which X-rays are scattered from electrons,
both bound and free. The theoretical description of this process is given by the
treatment of Klein and Nishina and predictions of the theory have been well
verified experimentally. At energies below about 10 kev, the relative contribution
to the total scattering due to coherent (Rayleigh) scattering becomes important.
The total mass density for a neutral gas can be related to the total electron
density, including free and bound electrons if the elemental composition of the gas
is known. Even if this composition is unknown, it is possible to relate the mass
density to electron density to a high order of accuracy for the light gases unless
hydrogen is present, in which case proper corrections must be applied. Thus, by
selecting an energy region between 10 kev and 1 mev, the total scattering becomes
TO ELECTRONIC
COUNTER
.w.r t "- , .- J ;J!& , :\'-
FIGURE 1. Schematic drawing of X-ray densitometer.
RAGENT: X-Ray Densitometer
405
dependent only upon the total electron density or gaseous mass density rather than
upon both the mass density and the chemical state of the gas or its state of motion.
The X-ray energy range is easily established at the lower end by biasing detectors
and associated discriminating circuitry to register only X-rays of energy greater
than 10 kev, and at the upper end by the maximum energy available from the
X-ray generator. The shape and size of a volume element under investigation is
determined by the intersection of a geometrically well-defined beam of X-rays
and similarly well-defined collimated scattering paths to detectors.
A sketch of the scattering geometry is shown in Figure 1. The counting rate in
the detectors, /, is given by
1 =***!&?> a)
where n = density of scatterers, the total number of bound and free electrons
per cm 3 (~3.8xl0 +le at P l Po =\Q-* for air)
= differential cross section for scattering into solid angle dQ. at angle 6
with the original beam direction ( j (dajdQ)dQ~2Ax 10" 27 for a
typical geometry)
= incident flux (~2 x 10 12 photons/cm 2 -sec for an X-ray tube operating
at 100 ma at 100 kev)
?= detection efficiency, including window losses, geometric effects in the
detector, etc. (~J)
Using the values cited 7~46 counts per second at pjp ~ 10 " 4 for air.
da
da
CORRELATION OF MASS DENSITY WITH ELECTRON DENSITY
As a typical example, the number of electrons per gram for various air-impurity
mixtures as a function of impurity mass fraction x is shown in Table I and the
fractional difference in the number of electrons per gram from pure air for the same
air-impurity mixtures is given in Table II. It is evident that the number of electrons
per gram in air mixtures remains constant to a very good approximation even for
large admixtures of impurities. An exception to this statement occurs in the case of
a mixture of hydrogen with other gases, since the number of electrons per gram of
hydrogen is roughly twice as large as for all other low-atomic-number gases.
TABLE I. ELECTRONS PER GRAM, Q, FOR VARIOUS AIR-IMPURITY
MIXTURES AS A FUNCTION OF MASS FRACTION OF IMPURITY
(xlO- 23 ).
Fractional
mass of
impurity
Impurity element
Copper
Carbon
Wolfram
(tungsten)
lO" 5
io-?
10~ 3
lO" 2
10" 1
3.00882
3.00882
3.00879
3.00856
3.00622
2.98280
3.00882
3.00882
3.00882
3.00882
3.00883
3.00894
3.00882
3.00881
3.00876
3.00823
3.00297
2.95036
406
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
TABLE II. FRACTIONAL DIFFERENCE IN NUMBER OF ELECTRONS PER CRAM
FOR AIR AND VARIOUS AIR-IMPURITY MIXTURES.
Fractional
mass of
impurity
X
Copper
Valr - Vco
Valr
Carbon
Valr — Vc
Valr
Wolfram
(tungsten)
Valr - Vw
Valr
10" 5
io-*
10" 3
10" 2
10- 1
9.97 x 10- 6
8.64 x 10" 5
8.64 x 10" 4
8.65 x 10" 3
-3.32x 10- 6
-3.99 x 10" 5
3.32x10-°
1.99 x 10" 5
1.96 x 10" 4
1.94 x 10" 3
1.94x 10" 2
THE DIFFERENCE IN X-RAY SCATTERING FOR HOT AIR AS
COMPARED WITH COLD AIR
The utility of the densitometer depends upon the relative constancy of the
response of the instrument when used with either hot gas or cold gas at the same
mass density. Scattering differences that exist between hot gas and cold gas are
due to the different component species present at different temperatures. For
example, for air at p=10" 5 p the diatomic molecule 2 begins to dissociate into
two atoms of at approximately 1500°K; at 4000°K, 2 no longer exists (1)
having been entirely converted to 0. The scatter from a molecule of 2 differs in
detail from the scatter from an atom of 0, since, due to interference among the
electrons, the coherent scattering for photon energies of to 40 kev is a function
of the electronic structure of the particle and the scattering angle. At higher
energies, the effect of the electronic binding and structure of the scattering
particle becomes negligible.
The scatter intensity at angle d per atom from a monatomic specie is (2)
,._?.[?+?(, _2?)]
(2)
where
[■
R = |]+_?L(l_cos0)l
mc\ J
The ratio of the scattered intensity per bound electron to the Thomson scattering
for a free electron is (2)
s = 4 = ^ + *(i-^f)
zl e z
The scattered intensity at angle 6 per diatomic molecule is
/*
where
= -?[?(> +^M'-?)]
(3)
(4)
and
x = 4tt -22 sin -
A Z
interim clear distance 2
eagent: X-Ray Densitometer
407
We also have that the ratio of scattering of a bound electron in a molecule to the
scattering from a free electron is
*=^?( 1+ ^M'-?)
(5)
The values of F and 2/ 2 are given for a number of species in the literature (3).
Equations (2) and (3) are in excellent agreement with experimental data (2),
but there is some difference between calculations made with equations (4) and (5)
and the experimental data of Wollan (4). The values used here are the experimental
values.
In order to compare the scatter from cold and from hot air, the ratio
was computed. This gives the ratio of the scatter at 273°K with that at T°K. In
order to compute S alr the 8 for each particular component was obtained and the
results weighted according to the specie population proportion at the temperature
in question; the results were then summed. The air component population propor-
tion at various temperatures was obtained from the tables of Moeckel and
Weston (1) and the values of * mn were taken from Compton and Allison (2).
In a wind tunnel air may be assumed to be heated in one chamber at a pressure
of, say, 10 atmospheres and then expanded through a nozzle into another chamber
at a pressure of approximately 100 microns. If the initial temperature is 8000°K,
the air-stream temperature would be approximately 2400°K if the expansion is
isentropic; if immediate freezing of the flow is assumed, the equilibrium composition
corresponding to the temperature of 8000°K is maintained. Molecular dissociation
is greatest for the frozen 8000°K case and, hence, the difference in X-ray scattering
for the hot air as compared with the cold air will be larger for this case.
TABLE III. RESULTS OP CALCULATIONS OF DIFFERENCE IN
SCATTERING FOR FROZEN AIR FLOW AS COMPARED WITH AIR AT
273°K (0 = 5O D ).
Photon
"273^
<->273*K
<- > 273K
energy
(kev)
"8000°K
<%)
"Sl0.OOO°K
(%)
(%)
10
91.6 + 5
89.7 + 5
164 + 5
20
96.5 + 5
96.5 + 5
107 + 5
25
95.7 + 5
92.3 + 5
100 + 5
30
95.4 + 5
92.8 + 5
96 + 5
35.3
98.5 + 5
97.3 + 5
97 + 5
45
~ 100 + 5
~100 + 5
~ 100 + 5
The computational results are shown in Table III. In order to obtain the overall
effect of the scattering difference, the results must be combined with the incident
X-ray spectrum for the densitometer equipment. Operation of the X-ray tube at a
peak energy of 100 kv was assumed. For this calculation the normalized spectrum
of relative intensity per kv interval was assumed to be similar to that for 200 kv
peak given in Hine et al. (5), on page 541.
14 +
408
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
The scattering per electron is then given by
A comparison of N T ° to iV 273 - then gives the measure of the difference in scattering
at T° as compared with 273°K. For the typical cases investigated for air at 8000°
and 10,000°K the differences from air at 273°K amounted to less than 2%.
DESCRIPTION OF APPARATUS
Figure 1 is a schematic drawing of the apparatus and Figures 2a and 2b show
the apparatus in place for a low-density wind-tunnel experiment.
FIGURE 2a. Densitometer installed in low-density wind tunnel: south view.
X-RAY SOURCE AND COLLIMATOR
The X-ray source is a copper-backed, tungsten- insert, rotating-anode, high-
voltage X-ray tube which is oil-cooled and is mounted in a specially-modified
aluminum housing. The X-rays are emitted from a spot about 1.5 mm by 1.5 mm,
and pass through a thin glass window, oil jacket, and plastic exit window. The
total inherent nitration of the exit path is approximately 0.5 mm of equivalent
aluminum absorber.
ragent: X-Ray Densitometer
409
FIGURE 2b. Densitometer installed in low-densitv wind tunnel: north view.
A typical calculated energy spectrum for the X-ray photons emerging from the
X-ray tube through 0.5 mm of inherent aluminum filtration at 100 kev peak
voltage is given in Figure 3 and was calculated using the results of Kulenkampff as
reported by Condon and Odishaw (6).
After passing out of the exit part of the X-ray tube housing, the X-rays pass
through a collimator hole 0.062 inch in diameter by \% inch long in a block of lead.
The external edges of this hole are shielded by a projecting block of lead so as to
410
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
prevent radiation scattered from these exit "lips" from reaching the detector
collimating hole regions. The shape of the beam produced by this collimator is
shown in Figure 8.
The alignment of the hole in the collimator with the focal spot of the X-ray
tube is accomplished by using the alignment adjustments which allow motion of
this collimator in the two transverse directions. The collimator is roughly located
by taking "pin-hole" X-ray film exposures using a thin lead sheet with a small
hole. Final adjustment of this collimator is accomplished by taking film exposures
at different settings of the collimator screws. When the maximum intensity on the
film has been obtained, the adjustments are locked in place. The final orientation
of the X-ray beam with respect to the detector centerline is accomplished by moving
the entire X-ray tube housing using the adjustment screws provided on the
housing mounting brackets.
100
30 40 60 80
X-RAY ENERGY, KEV
FIGURE 3. Typical thick-target X-ray spectrum for full-wave rectification at 100 KVP
and 0.5 mm aluminum filtration.
rag ext: X-Ray Densitometer
4J1
FIGURE 4. Collimator plate.
412 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
The entire housing is installed in a lead shielding box designed to contain all
radiation scattered from the X-ray tube. All electrical connections to the X-ray
tube are made through airtight flexible metal tubing connected to the atmosphere
so that the X-ray tube operates at a pressure of 1 atmosphere.
DETECTOR UNIT
The detector unit consists of a collimating plate, scintillation detection units,
monitor unit and X-ray catcher, amplifier chassis, and an airtight container.
The collimator unit consists of a forged brass plate If -inches thick containing
846 holes averaging about 0.100 inch in diameter drilled in five concentric rings at
an average angle of 50° to the collimator plate axis. These holes are drilled so that
their axes intersect at a point on the plate axis 3 inches above the face of the plate.
The average axial dimension of the volume intercepted by the intersection of rays
drawn from the extreme edge of these holes and a narrow axial beam of X-rays is
thus about 2 centimeters. Photographs of the collimator plate are shown in
Figure 4.
The main detector unit contains eight photomultiplier scintillating crystal units
installed inside the periphery of the detector unit housing so as to detect scattered
X-rays which pass through the collimating holes. For the photomultiplier crystal
units we used the Harshaw Integral Line Model No. 8-S-2. Electrical, magnetic,
and radiation shielding have been provided by utilizing (in addition to the shielding
furnished by Harshaw) three layers of magnetic shielding, -fg inch of lead, and
encasement of the entire assembly in a soft iron tube. The assembly is well grounded
to the case. Electrical leads are brought out through the back end of the photo-
multiplier housings and are connected to the preamplifier chassis immediately
below the detectors.
The major portion of the beam from the X-ray tube experiences no attenuation
due to interaction with the gas in the wind tunnel in traversing the distance from
the X-ray tube to the detector unit. The beam passes through a hole in the colli-
mator plate into a hole in a lead block and is dissipated at the bottom of the lead
block. A tube inserted into this lead block serves as an air-sealing mechanism.
Some of the X-rays striking the bottom of this tube are scattered into the back-
ward direction and impinge on the walls of the tube. A side hole in the lead block
allows some of these scattered X-rays to be scattered again through the sealing-
tube walls into the monitoring photomultiplier crystal detector. This unit is
identical with the main counter assemblies. The output of the monitor tube is thus
proportional to the X-ray beam and serves to act as a monitor for the beam. For
very high air sample densities the response of the monitor detector will be caused,
in part, by air scattering in the sealing tube. This contribution is negligible in most
of the density ranges of interest. Figure 5 shows several views of the detector unit
during assembly.
RECORDING AND CONTROL APPARATUS
Standard electronic power supplies, amplifiers, and counters are used to provide
necessary power and to register the outputs of both the detector measuring the
scattered events and the detector monitoring the intensity of the X-ray beam.
The outputs of these counters as well as an electronic timer are registered on a
digital recorder, which also registers the position of the apparatus in a traversing
mechanism.
The lower energy detected by the detectors is established by a precision dis-
criminator located in the non-overloading amplifiers and the peak energy of the
ragent: X-Ruij Densitotneter
4K5
FIGURE 5. Photographs of detector unit in various stages of assembly.
414
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
X-RAY
TUBE
X-RAY I,
OUTPUT
MONITOR
6292 NA I
PRE -AMR
JOHN FLUKE H.V
POWER SUPPLY
X-RAY
TRANS.
A-
X-RAY
CONTROL
UNIT
v-
X-RAY PREP ON
LAMBDA PS.
200V AT 65ma\<
6.3 V AT 3A |3
X-RAY DET.
8-6292'S
NA I
MIXER PRE-AMP
PREP CIRCUIT READY
TURN X-RAY H.V ON-QFF
AMP DISC.
BAIRD MOD.
215
TIMER HP
522B-95A
X-RAY H.V. ON
- START
RESET
STOP
START
2.
HAMNER
MOD. 270
SCALER
PRINT
INFO.
PRINT
INFO.
AMP DISC.
BAIRD MOD.
215
RESET
STOP
START.
CONTROL
CHASSIS
PRINT
COMMAND
v n
END PRINT
(DISPLAY
HOLD)
1
HAMNER
MOD. 270
SCALER
START REPOSITION
REPOS. FINISHED
PRINTER JUNCTION BOX ' PRINT INF0 '
PRINT
COMMAND INFO.
PRINT
DISPLAY
HOLD
m
■*~
POSITION
TIMER
|ll|IO|9|8|7|6|5l4|3|2|ll
HAMNER SCALER
VEEDER ROOT
ELEC. READOUT
REGISTER
POSITIONING
MOTOR AND
CONTROL UNIT]
HP MODEL 560 A
DIGITAL RECORDER
FIGURE 6. Block diagram.
X-ray source is controlled by the use of a well-established X-ray control unit and
power supply. Figure 6 shows a block diagram of the apparatus and Figure 7 is a
photograph of some of the electronic components.
TEST PROCEDURE AND CALIBRATION
SIZE OF SCATTERING VOLUME
The size of the scattering volume is determined by the intersection of the
collimated paths to the detector and the pencil of X-rays emitted by the X-ray
tube. From geometrical considerations the cross section of this volume was
estimated to be as shown in Figure 8.
r agent: X-Ray Densitometer
4K
FIGURE 7. Counting rack.
The size of the scattering volume was measured by inserting a thin plate of glass
in the beam and measuring the X-rays scattered from the plate into the detector
as a function of the plate position. Figure 9 shows a typical response curve when the
scattering plate was positioned in a plane perpendicular to the X-ray beam. The
half-width of the response is about 2 centimeters. A direct exposure to the X-ray
beam at 3 inches above the collimator plate shows that the beam is approximately
a square in cross section with sides equal to about 0.3 inch in length.
I i* +
X-RAY BEAM
0.30 |—
DETECTORS I [ DETECTORS
' . + _4_0.30
FIGURE 8. Sketch showing scattering volume dimension.
5 6 7 8 9 10
HEIGHT ABOVE DETECTOR COLLIMATOR, CENTIMETER
FIGURE 9. Response of detector to thin glass plate in plane perpendicular to X-ray
beam versus height of plate.
ragent: X- Ray Densitometer 417
CALIBRATION
The calibration of the densitometer is accomplished by measuring the amounts
of scattered X-radiation relative to the incident X-ray intensity for a series of
known gaseous densities. The readings in the scattered radiation counters and
monitor counters must be corrected for counts due to background radiation or
random spurious noise events.
For the lowest densities a correction must be made for the small contribution to
the readings of the detectors caused by radiation scattered into the detectors by the
apparatus itself even at />=0. Great care has been taken to minimize this latter
quantity; however, this "leakage" radiation, in conjunction with statistical
accuracy considerations, determines the lowest densities which can be measured.
Using this correction, densities below 10~ s p may be measured.
The density measurements at high densities are limited by multiple scattering
of X-rays in the test gas and by an increased contribution to the monitor detector
readings due to scattering from the gas in the vicinity of the volume viewed by the
monitor detector. Corrections for the latter effect may be made so that the multiple
scattering in the gas and apparatus becomes the effective limitation on density.
The upper density limitation for the present apparatus is estimated to occur at
densities greater than 10p .
The apparatus was installed and calibrated in a low-density wind tunnel
evacuated by a pumping system utilizing a 5-stage stream ejector. Blank-off
pressure levels of about 10 microns were available. It was found that the com-
position of the gas in the test volume contained appreciable proportions of water
vapor due to backstreaming from the ejector system. It was therefore necessary
that mass spectroscopic analyses of samples of gas taken from the region of the
test volume be obtained in order to calculate the gas density from temperature and
pressure measurements.
The calibrating test gases used were subsonic streams of air and helium, at
approximately room temperature. Subsonic flow through a nozzle was established
and the temperature and static pressure of the gas at the test volume were
measured. Simultaneously, samples of the test gas were obtained for mass spectro-
scopic analysis. These data established the density of the gas at the test volume.
Measurements of the scattered intensity detector reading and monitor reading at
this density were then made.
If the readings in the scattered radiation detector, background readings in this
detector, monitor readings, and monitor background readings are denoted as
/, Bj, M , and B M , respectively, it is evident that in the absence of secondary
effects the density measured is proportional to the quantity (I — Bj)j(M — B M ).
B M is generally negligible compared with M . Taking into account the amount of
radiation scattered into the main detector by the apparatus itself, A, which is
directly proportional to the beam intensity such that A\M is a constant (important
at low density), and the effect of the gas itself in contributing counts to the monitor
detector (important at high density) the expression for density becomes
-.^^<'-*-44-:)
where M x = M + k 2 p is the monitor reading including its contribution due to air
scattering.
The quantity k x is readily measured in the medium density ranges extending
from 10 ~ 3 p to 10 _1 p , A is determined by measuring the value of I as p goes to
418
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
SI
l±J
_1
CD
<
or
%
tr
UJ
h-
o
\-
-z.
UJ
Q
AY DUE TO
INCREASED
SCATTERING
NTO MONITOR
FOUND BY CALIBRATION
DENSITY RATIO, P/ P Q
FIGURE 10. Schematic representation of typical calibration curve.
10
CD
I
#— i
y io"' h
00
<
a:
or
t! IO" 2
C/3
Q I0" 3
10-6
HELIUM, COLD
AIR USING MOST RECENT
DATA, COLD
AIR WITH PREVIOUS DATA
REDUCED TO SINGLE POINT
AT ONE DENSITY, COLD
J I i
10-5 10-4 10-3
DENSITY RATIO, P/P
10-2
10-
FIGURE 11. Calibration curve.
eagent: X-Bay Densitometer
419
zero, and k 2 may be determined from measurements made in the higher density
regions.
The accuracy of any measurement is limited by statistical considerations
imposed by the limited number of random scattering events which occur during
any measuring period and the random nature of the background. The maximum
integrated X-ray beam flux is limited by heating considerations of the X-ray tube
anode, and the period for a measurement is usually fixed by the experimental
conditions so that at a given density level the maximum statistical accuracy
which may be achieved in a given measurement is fixed. If the background rate
without the X-ray beam on has been well established it is easily shown that the
fractional standard deviation in a measurement is given to a good degree of
approximation by
^
Po
/1/2
(8)
Figures 10, 11, and 12 summarize these considerations. Figure 10 is a schematic
representation of the typical calibration curve showing the deviation from linearity
at low density due to the internal scattering and at high densities due to enhanced
monitor readings. Figure 11 is an actual calibration curve showing that the useful
range of the instrument extends from high densities down to densities well below
10 ~* pjp . The points on this diagram indicate actual data points and the shaded
band indicates the standard deviations in a measurement at the indicated density
for a 10-second sampling time for the actual apparatus. Figure 12 shows the
percent standard deviation in the density ratio p/p as a function of density ratio
for two sampling times for the apparatus as finally constructed.
DENSITY RATIO, P/P Q * I0 5
FIGURE 12. Percent standard deviation as a function of density ratio.
420 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
PRELIMINARY APPLICATIONS USING THE APPARATUS
The first application of this apparatus in discovering the extent of backstreaming
from the steam ejector pumps has already been mentioned. The utility of the
device in calibrating other static and dynamic density measuring techniques has
also been established.
Measurements of the density and density profiles of an arc-heated gas after
expansion in a hypersonic nozzle are in progress, aimed at comparing the state of the
gas with predictions based upon various criteria for freezing of the flow. Another
application of this apparatus involves its use in conjunction with an impact probe
to measure the localized velocity of a hypersonic gas stream. The results of these
experiments will be reported in the future.
NOMENCLATURE
A Contribution to reading in scattered radiation detector due to radiation
scattered into detector at p =
B, Background reading in scattered radiation detector
B M Background reading in monitor detector
c Light velocity
da
dii Differential cross section for scattering into solid angle d?l at angle 6
with the original X-ray beam, cm 2 /steradian
da c
d{] Differential cross section defined above for Compton scattering
F Atomic scattering factor
h Planck's constant
/ Counting rate in scattered radiation detector
I e Thomson scattering per electron
I e Intensity of radiation scattered at angle 6
ki Calibration constant
k 2 Constant of proportionality relating additional contribution to
monitor detector to air density p
m Electron mass
M j Reading in monitor detector
M Reading in monitor detector corrected for air scattering effect
n Density of scatterers, total number of bound and free electrons per cm 3
N T Net scattering per electron in gas at temperature T°
Q Electrons per gram
R Defined in equation (2)
8 Ratio of scattered intensity per bound electron to the Thomson
scattering from a free electron at a given X-ray energy
s mn Internuclear distance between mth and wth atoms in a molecule
T Temperature
x Impurity mass fraction
Zj Number of electrons per neutral j particle
d Scattering angle
A Wave length
| Detection efficiency
p Density, gms/cm 3
Po Air density at 70°F and 1 atmos, 7.52 x 10 " 2 lb/ft 3 , 1.205 x 10 ~ 3 gm/cm 3
<J> Incident X-ray flux, photons/cm 2 -sec
2/ 2 Incoherent scattering function
ragent : X-Ray Densitometer 421
ACKNOWLEDGMENTS
The author wishes to acknowledge the contributions of Messrs. C. E. Noble and
J. Crumal of Vidya who actively participated in the design and construction of the
densitometer. Thanks are also due to the entire Heat Transfer Branch, Ames
Research Center, NASA, and especially to Professor George Leppert and Mr.
Charles Landrum who calibrated the instrument.
This work was supported by the National Aeronautics and Space Administration
under Contract NAS2-261.
REFERENCES
1. Moeckel, W. E., and Weston, K. C, "Composition and Thermodynamic
Properties of Air in Chemical Equilibrium", NACA TN 4265 (1957).
2. Compton, A. H., and Allison, S. K., X-Rays in Theory and Experiment
(New York: Van Nostrand, 1957).
3. James, R. W., and Brindley, G. W., "Some Numerical Calculations of Atomic
Scattering Factors", Phil. Mag., Series 7, 12, 81 (1931).
4. Wollan, E. 0., "Scattering of X-rays from Gases", Phys. Rev., 37, 862 (1931);
Proc. Nat. Acad., 17, 475 (1931).
5. Hines, G. J., and Brownell, G. L., Radiation Dosimetry (New York: Academic
Press, 1956).
6. Condon, E. U., and Odishaw, H., Handbook of Physics (New York: McGraw-
Hill, 1958), 7-119.
21. T. Herbert Dimmock and
William R. Kineyko:
Ionization Profiles in Low-
Pressure Exhausts
I? The ionization profile along the axis of a seeded, Mach 3, high-
altitude rocket exhaust has been mapped by microwave and probe
techniques. The ionization density in the jet was as high as 10 13
electrons /cm 3 and was found to vary half an order of magnitude
between expansion and shock regions.
The relaxation in the jet was evaluated from the measured data.
Since the ionization was found to follow the gas density profile, it was
concluded that the relaxation time was at least as long as the transit
time between the shock waves, and that the residence time in the shock
zone was sufficient to sustain this ionization. Cases in which the
residence time is less than the thermalizing time are also illustrated.
The thermodynamic properties in the jet were measured by pressure
and temperature probes and by line reversal spectroscopy. Unfor-
tunately, it was necessary for the probe dimensions to be comparable
to the jet dimensions, thus reducing the excursions in pressure and
temperature along the profile and resulting in average values only.
The microwave method was found to be suitable for analysis of low
pressure seeded jets as long as the collision frequency is of the order of
10 9 sec' 1 and the electron density lies between 5x 10 11 and 2x 10 13
electrons! cm 3 . Such a plasma would then have a d-c conductivity of
the order of 100 mhosjm.
INTRODUCTION
At the high combustion temperatures required for efficient rocket propulsion
some of the combustion species are ionized even when conventional rocket fuels are
used. If easily-ionized additives are introduced along with the propellants, simple
calculations show that one might expect 10 14 ions/cm 3 or a mole fraction of 10 " 5
ions/neutral particle. One would thus predict that a suitable electric, magnetic, or
Lorentz force field could be used to accelerate the charged particles which would
ed. note: Mr. Dimmock and Mr. Kineyko are with the Thiokol Chemical Corporation,
Reaction Motors Division, Denville, New Jersey. This work was supported
by the Air Force Office of Scientific Research under Contract No AF
49(638)-305.
423
H**
424
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
exchange momentum with the neutral particles to produce a measurable alteration
of the rocket thrust vector. This research program was therefore undertaken to
determine whether such ionization could be produced, and to determine the
interaction of the ionized plasma with external electric, magnetic, and electro-
magnetic fields. Specifically, the objective was to study ionization relaxation pro-
cesses in seeded, high-temperature, supersonic exhausts, to consider the effects of
ambient pressure and chemical composition on this relaxation, and to investigate
some of the parameters which control the electromagnetic interaction process in
the high-altitude exhaust.
The significance of the ionized species in rocket exhausts cannot be emphasized
too strongly. It is well known that the ionized jet and plume in the wake of a
rocket booster or sustainer attenuate and deflect electromagnetic control signals
making the problem of sustained ground guidance difficult, if not impossible.
Although much has been done to suppress ionization in the wake of high-per-
formance rockets by the use of electron-scavenging additives, this approach
invariably occurs at the expense of the high performance which dictated the a
priori selection of propellants. The aim of this program is to investigate some of the
Vortex Injector flange
FIGURE 1. Rocket test engine.
sources of ionization, and the time scale for relaxation in a seeded, high-altitude,
low-Mach-number exhaust. Some of the thermodynamic and transport properties
in the jet have been determined; information on rate processes was inferred from
these properties. In addition, a variety of plasma measurement techniques were
employed, and the range, accuracy, and limitations of each method for jet
diagnostics was found and will be indicated.
APPARATUS
The test engine sketched in Figure 1 consisted of a water-cooled cylindrical
chamber 3.5 inches long with 1.25-inches I.D. The chamber was fitted with an
uncooled copper nozzle having a j^-inch throat diameter and a 3.08 exit/throat
/
i
"'feF-
1
/
/
\
■7
?5
■2
.0
M
\
^^C
FIGURE 2. Shock structure in the rocket jet and on the conductivity probes.
426 PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
area ratio. | The injector which completed the chamber closure consisted of a
copper block with two J-inch gas ports and a surface-gap spark plug igniter. Two
types of injectors were used: premixed and vortex. In the premixed injection,
stoichiometric mixtures of ethylene (C 2 H 4 ) and oxygen (0 2 ) were introduced into
the chamber by the impinging jet injector attached to the chamber. In the vortex
injection, oxygen was fed through both ports of the impinging injector, and
ethylene was introduced through another tangential injector block located between
the impinging injector and the chamber. The entire engine assembly was mounted
on a platform which could be raised or lowered by a motor-driven worm gear.
This was done in order to explore the axial properties of the jet without having to
move the probing equipment.
The rocket engine was fired into a 20-cubic-foot tank fitted with a pumping
system having a capacity of 600 ft 3 /minute at 1-20 torr. Figure 2 is a sketch of the
typical shock structure which occurs in the jet under running conditions. The
propellant flow rate was 40 standard liters/minute (SLM) and the tank (ambient)
pressure was 5 torr.
The rocket engine was seeded with aqueous solutions of alkali metal salts which
were metered into the chamber through a hypodermic needle in the injector plate.
Alkali seeding could be controlled by changing either injection flow rate or salinity.
For most of the tests, a cesium injection of 1% of propellant mass injection was
maintained while using a 1 -molar cesium nitrate solution.
The propellant flow rates, which were 28 and 40 SLM, and the throat diameter
were chosen to provide a subatmospheric chamber pressure (125 and 180 torr,
respectively) and thus a low Mach number, high-temperature jet. The area ratio
between the exit and the throat was selected for optimum expansion to an ambient
pressure of 10 torr. A conical nozzle was used with an 18 degree half-angle.
Since it was desired to conduct a heat balance on the engine, the chamber
coolant flow rate and temperature rise were monitored. The chamber temperature
could readily be found from a measurement of the heat loss per mole of propellants,
the total propellant injection, and the chamber pressure.
The density and temperature profile of the jet were measured in order to compare
the ionization which was to be measured with the equilibrium value. The density
was determined from either (1) measured values of free-stream pressure and
temperature, or (2) isentropic calculations based on measurements of stagnation
pressure and temperature and free-stream pressure.
Two methods of temperature measurement were used; shielded thermocouples
and spectroscopic sodium -line reversal. The plasma probes used for pressure and
temperature measurement are sketched in Figure 3. Referring to Figure 3a, it can
be seen that the tungsten/iridium thermocouple junction was located in a semi-
stagnant gas zone and was double-shielded by boron nitride tubes. Successful use
of this probe was limited, mainly by erosion, to pressures below 10 torr and to mass
flow rates of 28 SLM or lower. To supplement this restricted range of temperature
measurements, the jet was seeded with sodium and the temperature was measured
by line reversal using a 15,000-lines/inch, 1.5 meter grating spectrograph. This
method was only useful at 10 torr and above, and at flow rates of 40 SLM or
greater. J
Figures 3b and 3c show the boron nitride probes which were used for total and
t The L* for this engine (chamber volume/throat area) was 56 inches.
J This was mainly due to the weak line intensity which necessitated the use of a larger
entrance slit so that the reversal line could not be accurately detected. At 5 torr there was
enough luminosity in the first two shock diamonds to measure the temperature with a 50-degree
uncertainty, however.
dimmock and kineyko: Ionization Profiles
427
JW i
?
FIGURE 3a. Stagnation thermocouple.
FIGURE 3b. Total pressure probe.
Ut-
ITTIZ^
i i
I i
1 i
i i
I i
i '
i i
i i
i i
FIGURE 3c. Static pressure probe.
FIGURE 3d. Conductivity probe.
static pressure measurements. Although these probes were made as small as possible,
their dimensions were still comparable with the spacing between shocks in the jet
(as determined from lines of maximum luminosity). For measurements in regions
of rapid pressure change (shock diamond), it was decided, therefore, that the reading
most nearly represented the pressure at the port-holes rather than at the nose, and
this convention was used throughout."]'
The ionization in the jet was measured by probes and microwave absorption
methods. Figure 3d shows the probe used for conductivity measurements. This
probe, which is supported by an insulated mount and is water-cooled, has a
conducting surface \ inch long and 0.020 inch in diameter. Two of these probes were
inserted into the name so that their axes were parallel and separated by \ inch.
The plane of the probes was made normal to the direction of gas flow. The probes
were used in a series circuit which included a variable potential source (monitored
by a precision voltmeter) and an X- Y recorder. The X- Y recorder, which measured
the voltage drop across a precision resistor in the series circuit, had a maximum
sensitivity equivalent to 1 microampere per inch on the F-axis. Axial profile
measurements were made by changing the position of the test engine as described
above and applying a known d-c voltage to the probes. An a-c sweep voltage was
applied to the X-axis of the recorder whose frequency was adjusted until the
horizontal travel of the pen matched the traverse of the probes down the jet axis.
In this way a fully resolved profile of probe current versus axial position was
obtained for any desired d-c probe voltage.
The microwave measurements were made using the two standard circuit
arrangements shown in Figure 4. The Raytheon QK 290 reflex klystron was
modulated by a square wave. The transmitted, received, and reflected signals
t The magnitude of this error was indicated by a separate experiment in which the probe
diameter was halved but the LjD was maintained at 10. It was found that the effect of a larger
probe was to moderate the variation in the pressure profile.
428
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
were monitored on a multi-channel recorder. The transition from wave guide to
the horn/lens system was through a transition piece at the entrance to the horn.
The radiant, circularly polarized energy from the horns was focused into a f -inch-
diameter (for 90% of the transmitted energy) beam at the flame. This was done by
using teflon lenses (//1 = 8.75 inches, //1.5) whose dielectric constant was fixed
over a wide frequency range.
DISCUSSION OF IONIZATION MEASUREMENT METHODS
Conventional Langmuir probe theory as applied to static gases is unsuitable for
supersonic flow applications. The principle problem which arises in employing a
ATTENUATOR
IORN & LEJ4S
ATTENUATOR
<
T
POWER
SUPPLY
WAVE
METER
PLASMA'
T
o
OSCILLOSCOPE
ATTENUATION CIRCUIT
ATTENUATOR
KLYSTROh
PHASE
i H?TER_
ATTENUATOR
i
T
HORN L IE*NS
c
PLA!
o Q>
WAVE
METER
Z\ CRYSTAL
POWER
SUPPLY
o
OSCILLOSCOPE
+*-
CRYSTAL
INTERFEROMETER CIRCUIT
FIGURE 4. Block diagram of microwave circuits
dimmock and kineyko : Ionization Profiles 429
Langmuir probe in a plasma jet is that if a conventional electrode is used, the
space charge sheath formed around the probe is so distorted by the flow as to make
interpretation of the measurements impossible. In a laboratory experiment on
unseeded exhausts at Reaction Motors Division, however, Dr. Fleischer demon-
strated experimentally that in an unseeded supersonic stream the voltage- current
relationship between two probes follows Ohm's law rather than the Langmuir-
Childs theory, exhibiting a linear volt-ampere relationship instead of the usual
sigmoid curve characteristic of space-charge limited currents. The slope of this
volt-ampere curve, i.e., the probe resistance, was found to be linear and to increase
with increasing probe separation.! If an infinite parallel cylinder approximation is
used, the relationship between probe resistance and jet conductivity is a geometric
one given by the equation
cosh- 1 C/d) log(2c/rf) m
a = RL ~ RL U)
where c, d, and L are electrode separation, diameter, and length, respectively, and
i?= Y\l is the probe resistance. Further tests in seeded jets revealed, however, that
the method was only valid for regions with homogeneous plasma between the
probes, and that in highly seeded jets, a deposit forms on the probe which inhibits
current flow in the plasma circuit. For this reason the ionization densities reported
herein were obtained from microwave measurements exclusively.
A complete analysis of microwave measurements of plasma properties is given
by Warder et al. (1, 2), and Kannelaud (3). It will be briefly summarized here using
the notation of Warder.
The propagation through a plasma by a plane wave of incident amplitude E is
E = E [l - exp ( - yx + jwt)] (2)
where j= V — 1, u> is the microwave angular frequency, x is the plasma thickness
and y is the complex propagation constant given by
y = ct+jj8 (3)
In equation (3), a is the attenuation constant and j8 is the phase constant. By
combining with Maxwell's equations the Lorentz macroscopic equation for charged
particle motion in an oscillating electric field, one can relate a and /3 to u>, and to the
properties of the plasma of thickness x as follows:
ft, r o.> 2 Ml (4)
2 L(l-?g/? a ) 1 ' a WJ
js = /yi-oSM 1 " (5)
A/3 = *(/??- |S) < 6 )
where v c is the electron-atom collision frequency, w p is the plasma frequency
(a> a = rec 2 /e m), s , and |3 are the permittivity and phase constant (/3 = a>/c) of free
space, respectively, and n, c, and m are the concentration, charge, and mass of the
electrons, respectively.
Finally, the electrical conductivity of the plasma may be written
\EJ m v 2 + co 2
t Such linearity, of course, occurs only in a uniform plasma. The uniformity of the plasma
was first demonstrated by stepwise measurement across the plasma made with a fixed probe
separation.
430
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
and the d-c conductivity derived from equation (7) is:
a dc = ne 2 jv c m
(8)
In the highly-seeded, low-pressure jet, however, the plasma frequency is often
very close to the microwave angular frequency. Under these conditions a/ we > 1
and the reflections at the interface likewise reduce the received signal. Warder has
shown that the reflection can be calculated from the phase and attenuation:
<* 2 + |SWo+l) 2
(9)
IX 10'
5X10
2XI0 12
1X10
5X10
2X10
1X10
5X10'
0^-4 .6 .7 S .9 35 J98 1.0
FIGURE 5. Microwave transmission through plasmas.
dimmock and kineyko: Ionization Profiles
431
Then, from elementary optical considerations, the transmitted fraction, A, of the
received signal is
A=l-r-T ( 10)
where T = e~ ax is the attenuation through the flame. Figure 5 is a plot of the
transmitted fraction, A, versus the electron concentration for a KA-band frequency
of 31.8 Kmc in reduced pressure plasmas.
TABLE I. OPTIMUM PROFEIXANT PEBFOBMANCE — SEEDED
A. Ingredients
Name
Symbol
Feed temp.
Density
Mol. wt.
Ethylene
Oxygen
Cesium Nitrate
Water
C 2 H 4
o 2
CsN0 3
H 2
298.15°K
298.15°K
298.15°K
298.15°K
0.001 gm/cc
0.001 gm/cc
3.685 gm/cc
1.00 gm/cc
28.05
32.00
194.92
18.016
Composition Weights
7% Seeding
14% Seeding
C 2 H 4
o 2
CsN0 3
H a O
22.614
77.386
1.206
6.194
22.614
77.386
2.282
11.718
B. Thermal Data
7% Seeding
14% Seeding
Gamma bar
1.069
1.074
C. Rocket Parameters
7% Seeding
14% Seeding
Shifting
Frozen
Shifting
Frozen
A/ A*
C*
I sp (ideal)
I sp (space)
7.628 6.13
4729.5 4402.8
234.08 209.23
261.09 232.67
7.55 5.806
4678.8 4632.7
231.09 218.22
257.58 238.44
Exhaust Conditions:
Pressure, psia
Temp., °K
Mol. wt.
0.10 0.10
2083.7 1492.7
28.508 26.33
0.10 0.10
2002.5 1341.8
28.294 26.304
Chamber Conditions:
Pressure, psia
Temp., °K
Mol. wt.
3.87
2646.8
26.33
3.87
2583.7
26.304
432
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
D. Products of Combustion
7% Seeding
Chamber
0.11307
14% Seeding
Shifting
0.03714
Frozen
0.11307
Chamber
Shifting
0.06122
Frozen
0.14023
CO
0.14023
co 2
0.25501
0.36671
0.25501
0.25892
0.36299
0.25893
Cs
0.00152
0.00164
0.00152
0.00270
0.00291
0.00270
H
0.01733
0.00465
0.01733
0.01267
0.00227
0.01268
OH
0.04908
0.01549
0.04908
0.04174
0.01009
0.04174
H 2
0.03500
0.01692
0.03500
0.03196
0.01218
0.03196
NO
0.00046
0.00013
0.00046
0.00056
0.00012
0.00056
o 2
0.07393
0.03725
0.07393
0.06367
0.02633
0.06367
N 2
0.00053
0.00076
0.00053
0.00107
0.00139
0.00107
O
0.01560
0.00394
0.01560
0.01073
0.00137
0.01073
H 2
0.41132
0.49219
0.41132
0.46290
0.54321
0.46290
RESULTS
Table I lists propellant performance data which were obtained theoretically for
the stoichiometric CH 4 /0 2 propellants seeded (7° and 14%) with CsN0 3 solutions.
The propellant flow rate was 40 SLM.f For the 7% seeding case, these values were
used to determine the equilibrium ionization in the chamber, which was 9.9 x 10 13
electrons/cm 3 .
The exit plane conditions for frozen and shifting chemical equilibrium in the
nozzle are also given. Depending upon pressure and velocity conditions in the
nozzle, the chemical process may be in frozen equilibrium to the exit plane, shifting
equilibrium to the exit plane, or shifting part way and frozen the remainder of the
way. If the reaction is in frozen equilibrium, the heat loss by expansion in the
nozzle will depress the gas temperature to a low value T x at the exit plane. If
chemical equilibrium prevails, the continuing exothermic reaction in the nozzle will
result in an exit temperature T 2 . If the reaction freezes part way down the nozzle,
an intermediate exit temperature T 3 will result. The ionization density may also
be considered in the same way. If it follows the density changes in the nozzle, the
kinetic process may be considered to be frozen; if it is described by the Saha
equation, it may be considered to be in shifting equilibrium. The frozen and
shifting data of Table I were used to obtain equilibrium ionization densities at the
exit plane, namely 4.1 x 10 9 and 2.2 x 10 12 electrons/cm 3 respectively. The values
of ionization in the chamber (n ch ) and at the exit plane for frozen (n fc ) and shifting
(w sc ) chemical equilibrium in the nozzle are shown in Figure 6.
In order to properly analyze the relaxation of ionization in the jet, it is necessary
to measure the changes in ionization apart from the gross density changes. For
this purpose a density profile down the jet axis is required. Such a profile was
calculated from the theoretical exit-plane conditions and the measured pressure
and temperature profile of the jet. Figure 7 shows the pressure and temperature
profiles in the 40 SLM jet. The temperature was determined by sodium line reversal;
the pressure was measured with a mercury manometer using the probes shown in
Figure 3b and 3c. The location and approximate shape of the shock diamonds are
also shown for reference. The stagnation pressure, p 0y , is the pressure behind the
normal shock on the probe. When the tip of the probe passes through a pressure
discontinuity in the jet stream (e.g., the leading edge of a shock diamond), the
f The measured heat loss was included for these calculations.
dimmock and kineyko: Ionization Profiles
433
9 _
10
o <r>
Distance from Exit Plane, in.
~ ' ir~ 3 4 5^
3 4
FIGURE 6. Electron concentration in the jet.
shock on the probe ceases to be a normal shock due to interaction with the jet shock.
For this reason the p 0y curve shows the unexpected rising inflection at the shock
diamonds. Likewise, in measuring stream pressures, if the jet shock lies between
the probe tip and the probe port, the indicated stream pressure will be affected by
the interaction of the two shock fronts. Thus the indicated pressure is incorrect
for the region immediately upstream of the leading edge of the shock diamonds.
It is of interest to calculate the electron-atom collision frequency in the plasma
from the measured temperature, pressure, and composition of the plasma. The
collision frequency in a weakly ionized plasma may be defined as
v c = c ^ n iQt =cm^ x t Qi
(11)
where c= VHkTjnm is the random thermal speed of the electrons and n t x t and Q t
are the number density mole fraction and collision cross-section of the tth specie.
434
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
TABLE II. FACTORS AFFECTING
ELECTRON COLLISIONS IN THE JET
Element
QxlO 15
(cm 2 )
Mole fraction x t
XtQ, x 10 15
(cm 2 )
Shifting
Frozen
Average
Cs
3.6
0.0029
0.0027
0.003
0.0108
H 2
3.6
0.543
0.4629
0.503
1.8100
o 2
0.31
0.026
0.0637
0.045
0.0140
CO
0.81
0.037
0.113
0.075
0.0607
co 2
1.2
0.363
0.259
0.311
0.3910
OH
—
0.010
0.042
0.026
—
H 2
0.85
0.012
0.032
0.022
0.0187
Other
0.8
—
—
0.015
0.0120
I
1.000
2.3172
Table II shows the pertinent species in the combustion exhaust and their collision
cross sections (4). Thus equation (11) may be written
v c = 7.24 xlO^p/T 112 sec" 1 (12
where pressure and temperature are in psia and °K, respectively. This expression
was plotted for our pressure and temperature profiles (Figure 7) and is shown in
Figure 8.
T
t
P P
dej.K. torr
1600 80 20-
1600 ?0 16
1400 40 12
1200 20 8
1000 4
800
o Reversal Temperature
a Stream Pressure
o Stagnation Pressure
I 2 3 4 5 6
FIGURE 7. Pressure and temperature profiles in the jet.
dim mock and k i n b y k o : Ionization Profiles
435
FIGURE 8. Collision frequency profile in the jet.
10
Mo e Fraction of Cesium in Exhaust
-I 1 1 1 — 'I I I '
H 1 1 — I — i ! ■ I
-t 1 1 1 I !
10
10
,-5
10
-4
10
-3
FIGURE 9. Influence of seeding on jet ionization.
436
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
Before attempting to measure the jet ionization profile, the linearity of the
detection equipment was established. Cesium nitrate solutions with molarities from
0.01 to 1.0 were prepared and injected into the 40-SLM 5-torr jet. Attenuation and
phase shift measurements were then made using the circuit shown in Figure 4.
The resulting electron concentration in the first shock diamond is plotted in
Figure 9. The concentration obtained from the microwave measurements, n A , was
obtained from Figure 5. The linearity of the n A curve implies that the microwave
measurements are at least self- consistent over the range of additive concentrations
which were used. Furthermore, the slope of one-half agrees with the value obtained
by Padley and Sugden for large additive concentrations (5). Static tests indicated
that reflections from the nozzle plate of the engine could be detected as long as the
beam axis was less than 2 inches from the metal plate. For this reason a traverse
down the axis was limited to that portion of the jet in excess of 2 inches downstream
from the exit plane. To obtain a correct reading in the first expansion, therefore, a
stationary measurement was first made so that the effect of reflection could be
eliminated by subtraction.
The ionization in the 7% seeded jet was measured by microwave attenuation at
the center of the first two shock diamonds and the first two expansion regions.
The curve labeled n A in Figure 6 is a typical ionization profile through these
measured points. (The shape of this curve was made similar to the conductivity
probe curves as discussed below.)
If the cesium concentration in the jet remains at 0.15 mole % (i.e., if frozen
chemical equilibrium is assumed), the equilibrium ionization at each point in the
jet can also be computed when the jet pressure and temperature are known. This
was done by using the temperature pressure profiles of Figure 7 and is shown in
Figure 6 by the curve labeled n eq . Finally, if the exit-plane ionization density,
n sc , is multiplied by the normalized density in the jet,f p/p , a completely frozen
ionization profile in the jet will be obtained, and this is indicated by the curve
labeled n f .
From Figure 2 it can be seen that the thickness of the shock diamonds for the
first two shocks was 1.25 and 1.0 centimeters, respectively. Since this value is less
than the beam width of the microwave probe, the measured electron density of the
diamonds is less than the true axial density. The relative size of the shock diamonds,
expansion regions, and the microwave beam are given in Table III along with the
attenuation data shown in Figure 6. The indicated electron densities are calculated
by assuming a homogeneous core with thickness given by the average value in
Table III.
TABLE III. JET MICROWAVE MEASUREMENTS
Location
Distance
to exit
(inches)
Trans,
frac.
Jet diameter
n a
(x 10 12 )
a
(fim)- 1
Uniform core
(cm)
Total
(cm)
Avg.
(cm)
First expansion
First shock
Second expansion
Second shock
1.00
2.25
3.50
4.75
0.724
0.276
0.704
0.363
3.00
1.25
3.00
1.00
3.00
2.25
3.00
2.00
3.00
1.75
3.00
1.50
7.4
11.3
7.6
11.2
105.00
159.00
107.00
158.00
The d-c conductivity as shown in equation (8) was determined from the micro-
wave attenuation measurements in the jet; it is also given in Table III. The
t Assuming shifting chemical equilibrium in the nozzle, p? is the density at the exit plane.
dimmock and kine yko : Ionization Profiles
437
averaged value ct lies between 100 and 160 mhos/m, and was evaluated from the
average thickness using 2 x 10 9 coll/sec for v c .
In searching for a mechanism which would explain why n A always exceeded n eq
in Figure 6, it was decided to make measurements of the characteristics of the
spectral emission from the jet. If equilibrium conditions prevail in the jet, the
spectrum of the jet should be similar to the spectrum of the mantle of a propane/air
atmospheric flame; absence of such equilibrium could easily explain the anomalous
high ionization.
Two types of injection were used in these tests: premixed and vortex. In both
cases the C 2 H 4 was bubbled through liquid iron pentacarbonyl, Fe(CO) 5 , to insure
the presence of iron in the exhaust. Table IV lists the tests and the results. Spectra
were made to determine the effect of jet mixing, stoichiometry, and injector type.
TABLE IV. SPECTRAL LINES IN SEEDED EXHAUSTS AT 10 TORE (FUEL, C 2 H 4 /0 2 ; FLOW
RATE, 28 SLM; ADDITIVE, Fe (CO) 5 )
No.
Type
Mixture
Exposure
Shroud
Color
Lines
Inten-
sity
Stoich
Rich
Iron
Air
None
1
Premixed
X
10 min
X
light blue
OH band
—
2
Premixed
X
X
10 min
X
orange and
green
3922.51
3895.66
3856.37
3820.43
3760.05
3749.49
55
35
85
500
6
400
3
Premixed
X
10 min
X
invisible
4
Premixed
X
X
10 min
X
light green
3840.44
3760.05
3743.56
3581.20
80
6
60
600
5
Premixed
X
10 min
X
light violet
none
6
Premixed
X
X
10 min
X
white
plume
with
orange
exit cone
3824.44
3749.49
3733.32
3649.51
3631.46
3621.46
3605.46
3581.2
3570.1
3100.67
3055.26
2999.51
2813.3
2788.1
2733.6
80
400
70
16
200
24
24
600
400
26
6
36
42
70
70
7
Vortex
X
X
20 sec
X
see Fig. 10
For the jet mixing tests, a laminar air flow shrouded the jet and the pumping
capacity was increased to maintain the ambient pressure at 5 torr. Figure 10a
shows a spectrum which was obtained with the vortex injector and the air shroud ,
using a Hilger spectrograph (50 micron slit) and Type 1-0 film. Figure 10b shows a
60-second exposure of the propane/air flame mantle made for comparison.") - The
t This was a flame burning on an open burner.
438
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
2491
30ZI
3^0-
mm — m ^h
I 'I I
Is.;: ■ ....*■
g?" ___-! ? ,i- ■ !#
E
?
e
6
1
fa
O
a
55
C
3
-
40*6
a.
Ed
OS
P
< OQ
jet spectrum shows strong iron lines down to 2200 A indicating a very high excita-
tion temperature. In the propane flame, although the flame temperature is approxi-
mately equal to the jet temperature, the iron lines in the far ultraviolet are missing
and the intensity distribution is dissimilar. The 4050 A group of iron lines is a
dimmock and kineyko : Ionization Profiles 439
good indication of non-equilibrium conditions. Iron appears strong in the jet
spectrum but weak in the propane spectrum. Thus there seems to be strong
indication that non-equilibrium conditions prevail in this case.
DISCUSSION
By comparing the n? n A , and n eq curves in Figure 6, the evidence indicates that:
(1) the ionization, which is in kinetic equilibrium in the chamber, maintains
this equilibrium only part way down the supersonic nozzle;
(2) when the collision frequency is sufficiently reduced in the nozzle, the
ionization relaxation becomes kinetically frozen, i.e., it varies with gas
density only; and
(3) the ionization which occurs in the jet exhibits variations in intensity which
follow the density profile in the jet and not the Saha equilibrium profile, and
thus the jet ionization may be considered kinetically frozen.
Frozen kinetic equilibrium is not hard to visualize if the transit time between the
shock diamonds is much smaller than the relaxation time. To find the transit time,
the jet velocity is required. The jet velocity was determined to be 1.75 km/sec by
measuring the Mach angle and using the equation
M = v/a = (sinfl)- 1 (13)
where a = Vy g RT is the speed of sound and 6 is the Mach angle. Thus the transit
time is seen to be
Ax
t = — ~ 25 usee
v ^
If this time is assumed to be the minimum electron half-life, then the maximum
relaxation rate is just
dn n ? t electrons
— =- = 7.4x 10 16 =
at t cm d sec
It is known from shock tube experiments (6) that the ionization process is not
instantaneous for gases passing through a shock front but requires approximately
20 ixsec to thermalize. If the residence time of the jet gases in the leading half of the
shock diamond exceeds this time, ample time for the gas to come to ionization
equilibrium should be available. Then one would expect that the exit plane electron
concentration would be suddenly raised by the first shock to a value proportional
to the shock strength. It would then decrease at an exponential rate governed by the
relaxation process and the cycle would be repeated at each successive shock. When,
however, the residence time in the shock is less than the thermalizing time, the gas
does not reach the ionization level which theoretically exists behind the shock.
Furthermore, if the time interval between the shock diamonds is small, the
reduction in ionization will also be small so that the average value of ionization
may even increase down the jet axis. Figure 11 shows this effect demonstrated by
probe curves made in the 28-SLM unseeded jet. The underexpanded 2-torr jet had
an axial velocity of approximately 900 m/sec and a residence time in the first shock
of approximately 30 fisec. The 10-torr jet had axial velocity of 1700 m/sec and
residence time of approximately 13 fzsec. The rise in the average intensity level
down the axis of the 10-torr jet is apparent.
440
PHYSICO-CHEMICAL DIAGNOSTICS OF PLASMAS
2 torr - 63u a/in.
Current sensitivity; '
10 torr- 12.6^, a/in.
Probe Potential: 16 volts
12 3 4 5 6
FIGURE 11. Typical conductivity probe curves in unseeded jets.
CONCLUSIONS
A study of the electrical and thermodynamic properties of a seeded, Mach-3
rocket exhaust at an equivalent altitude of 20-25 miles has been undertaken.
This operating range was decided upon since the jet can be uniformly seeded, and
the temperature and ionization can be measured by radiation methods.
The variations in the ionization density and dielectric properties of the jet were
mapped, and the relaxation and attenuation properties of the seeded, high-
altitude rocket exhaust were investigated. It was found that the profile of ionization
down the jet depends upon the conditions at the exit plane and upon two other
major factors: (1) the gas residence time in the shock diamond; and (2) the gas
transit time between shocks.
Moreover, the data allows two possible relaxation mechanisms: (1) shock-induced
ionization, which decays slowly according to the jet time-scale; and (2) frozen
ionization, which is controlled only by chamber and nozzle conditions and follows
the density profile identically.
The ionization in the jet is seen to exceed the Saha value (Figure 6) at all points
in the jet of the premixed stoichiometric rocket. This is evidence of an electron
density greater than the equilibrium value. The spectrographic analysis of the jet
showed that the energy distribution in the excited states was also modified; excited
lines were obtained which were not evident in the mantle of an atmospheric
propane/air flame. Such non-equilibrium was attributed largely to an after-
reaction of fuel-rich jets with the surrounding environment, since it was most
prominent with shrouded, vortex jets.
dimmock and kineyko : Ionization Profiles 441
It was fortuitous that our seeded jet (at 5 torr) produced a microwave opera-
ting point in the center of the narrow band lying between transparency
(rc = 5xl0 11 cm" 3 ) and opacity (w=1.2xl0 13 cm" 3 ). Thus the 1-cm, KA-band
microwave system is well suited to the study of seeded flames only at low pressures
(where the collision frequency is of the order of 10 9 sec - 1 ).
ACKNOWLEDGMENTS
The authors wish to thank Mr. V. J. Siminski for his assistance in performing the
experimental work, and Mr. W. Marsh, Dr. David Fleischer, and Mr. Ernest Hinck
for their assistance in data evaluation. The funds granted to this project by the
Air Force Office of Scientific Research are gratefully acknowledged.
REFERENCES
1. Warder, R. C, Brodwin, M., Cambel, Ah Bulent, "Microwave Measurements of
Magneto-Gas-Dynamic Plasmas", ASTIA AD-266-593 (August, 1961).
2. Warder, R., Nighan, W. L., Brodwin, M., and Cambel, Ah Bulent, "Micro-
wave Diagnostics of Arc Heated Plasmas", in Dynamics of Manned Lifting
Planetary Entry (New York: Wiley and Sons, 1963).
3. Kannelaud, J., and Whitmer, R. F., "Improved Microwave Techniques for
Measuring Plasma Parameters", ASTIA AD-225-405 (July, 1959).
4. Sutton, G. W., "The Theory of Magnetohydrodynamic Power Generators",
G. E. Space Sciences Laboratory R62 SD990. Contract AF49(638)-914
(December, 1962).
5. Padley, P. J., and Sugden, T. M., "Some Observations on the Production and
Recombination of Ions and Electrons from Metallic Additives in Hydrogen
and Hydrocarbon Flames", Proc. 8th Int. Symp. Comb. (Baltimore: Williams
and Wilkens Co., 1962), 164.
6. Wiese, W. C, Berg, H. F., and Griem, H. R., "Measurement of the Structure of
Strong Shocks in Helium-Filled T-Tubes", Phys. Fluids, 4, 2, 250 (1961).
