ELECTRON GAS BEHAVIOR OF A WEAKLY IONIZED PLASMA JET
WITH THE EFFECT OF AN ELECTRIC FIELD APPLIED
IN THE BASE REGION
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
TO MIRIAM, KAREN AND KURT--
THIS "BOOK" IS DEDICATED TO YOU
Experimental research is very rarely the sole effort of one
individual. I am deeply indebted to many individuals who contributed
a concerted effort toward the successful completion of this dissertation.
To Dr. R. B. Gaither I extend my most sincere gratitude for his
constant encouragement throughout the duration of my graduate studies,
with special thanks for his guidance and confidence in my undertaking
and successfully completing this dissertation.
To Dr. R. K. Irey, Dr. V. P. Roan and Dr. H. D. Campbell I
express my appreciation for their guidance throughout my course work,
in addition to serving on the advisory committee. I also thank
Dr. R. T. Schneider and Dr. J. W. Flowers for serving on the advisory
For technical aid in design and construction of the experimental
apparatus I am indebted to Prof. E. P. Patterson, Mr. R. L. Tomlinson,
Mr. J. M. Morris, Mr. V. D. Lansberry, Mr. H. E. Parkhurst and
Mr. E. Logsdon. Of this group I wish to express special thanks to
both Mr. R. L. Tomlinson, who lived through many hours of redesign and
reconstruction of the experimental apparatus, and Mr. E. Logsdon for
his concerted effort in the construction of all the glass parts incor-
porated in the experimental apparatus, including the numerous trials
of various Langmuir probe configurations, in addition to his unsolic-
ited, but often humorous, commentary.
To Dr. H. R. A. Schaeper I extend my appreciation for his
professional aid in solving electrical circuit problems associated
with this research. Also, I thank him for doing all the required
photographic work for the dissertation.
To Mr. R. W. Robertson, graduate student in mechanical engi-
neering, I offer my sincere appreciation for his help in conducting
the final experiments of this investigation, especially for his willing-
ness to stay in the laboratory with me for tests that ran as much as
a nearly unbearable 14 to 20 hours' continuous duration.
To the University of Puerto Rico I am indebted for the initial
granting of a sabbatical leave and the granting of continuance of
leave of absence such that I could complete my studies. Special thanks
for all his encouragement to my colleague and friend, Prof. E. Olivieri
who was Dean of the School of Engineering during the majority of the
time that I was on leave of absence from the University of Puerto Rico.
To Mrs. Edna Larrick thanks are due for the typing of the
dissertation from rough drafts to final copy, most of which were done
under the handicap of having to use communication through the U.S.
Mail because of our 1200 mile separation during these last six unfor-
To the following industrial organizations I extend my sincere
thanks for providing financial assistance and materials:
E. I. DuPont De Nemours
The Chemstrand Company
The Ford Motor Company.
TABLE OF CONTENTS
ACKNOWLEDGMENTS . . . .
LIST OF TABLES . . . .
LIST OF FIGURES . . . .
LIST OF SYMBOLS . . . .
ABSTRACT . . . .
1 INTRODUCTION . . .
2 FUNDAMENTAL CONSIDERATIONS .
2.1 Definition of a Plasma .
2.2 Plasma as an Ideal Gas .
2.3 Ionization and Recombination
2.4 Jet Flow Structure . .
2.5 Langmuir Probe . .
3 EXPERIMENTAL CONSIDERATIONS .
3.1 Description of Apparatus .
3.2 Experimental Procedure .
4 RESULTS AND DISCUSSION . .
5 CONCLUSIONS AND RECOMMENDATIONS .
APPENDIX A GAS DYNAMICS . . .
Computer Program . .
Results of Computer Program .
APPENDIX B LANGMUIR PROBE . .
1 Theory and Operation .
2 Measurement Errors . .
BIBLIOGRAPHY . . . .
BIOGRAPHICAL SKETCH . . .
LIST OF TABLES
A-i Test Conditions ................... 127
B-1 Plasma Potential Corrected from T and Floating
Potential, Test II Argon at 160 ma Base Plate
Current . . . . . . 149
LIST OF FIGURES
1 Overall View of Plasma Laboratory . . .. 68
2 Overall View of Experimental Apparatus . ... 70
3 Gas Flow Schematic . . . . ... 71
4 Plasma Generator . . . . ... 73
5 Plasma Generator Schematic . . . ... 74
6 Argon Jet with Base Plate at Floating Potential .. 76
7 Langmuir Probe in Argon Jet with Base Plate at
Floating Potential . . . . ... .78
8 Langmuir Probe in Argon Jet with Discharge on
Base Plate . . . . ... . 80
9 Test Section . . . . ... . 82
10 Probe Position Mechanism . . . ... 84
11 Lucite and Steel Sleeve Connections to Probe Stems 86
12 Instrumentation . . . .... 88
13 Langmuir Probe and Plasma Generator Electrical Circuit 90
14 Radial Electron Temperature Distribution, Test I,
with Base Plate at Floating Potential . ... 91
15 Radial Electron Temperature Distribution, Test I,
with Base Plate at 10.3 Volts . . ... .92
16 Radial Electron Temperature Distribution, Test I,
with Base Plate at 14.2 Volts . . ... .93
17 Centerline Electron Temperature Distribution, Test I 94
18 Centerline Electron Density Distribution, Test I . 95
19 Radial Electron Density Distribution, Test I,
with Base Plate at Floating Potential . ... 96
LIST OF FIGURES (CONTINUED)
20 Radial Electron Density Distribution, Test I,
with Base Plate at 10.3 Volts . . ... 97
21 Radial Electron Density Distribution, Test I,
with Base Plate at 14.2 Volts . . ... 98
22 Radial Electron Temperature Distribution, Test II . 99
23 Centerline Electron Temperature Distribution, Test II .100
24 Centerline Electron Density Distribution, Test II . 101
25 Radial Electron Density Distribution, Test II . .. .102
26 Centerline Electron Density Distributions, Present
and Previous Investigations Compared . . .. 103
27 Centerline Electron Temperature Distribution, Test III 104
28 Centerline Electron Density Distribution, Test III ... 105
29 Equipotential Curves, Test I . . . ... .106
30 Equipotential Curves, Test II . . . .. 107
A-i Axial Symmetric Jet . . . . ... .109
A-2 Velocity Distribution, Test I . . ... .110
A-3 Stagnation Pressure Data, Test I . . ... 111
A-4 Radial Spread of Jet, Test II . . ... .112
A-5 Stagnation Thermocouple Time-Temperature Response . 113
A-6 Monitored Test Data, Test I . . . ... .114
B-1 Langmuir Probe Characteristic . . ... 144
B-2 Langmuir Probe Characteristic Photographs Directly
from Oscilloscope . . . .... .146
B-3 Langmuir Probe Sample Results, Test II . ... 147
B-4 Plasma Potential Sample Curves, Test II . . 148
LIST OF SYMBOLS
A = area
C1 = empirical constant for
C2 = constant defined by
D = coefficient of diffusion,
d = sheath thickness
E = electric field strength
e = electron charge
F = force
I = current
j = current density
k = Boltzmann constant
A = characteristic length
D = Debye length
m = mass
N = rate of change of electron
density per unit volume
N = number of particles in
a Debye sphere
n = number density
P = pressure
Qn = excess charge
q = velocity
q = velocity of jet core
R = radius, resistance
r = distance between charges,
S1 = parameter defined by
= average speed
= axial distance
a = recombination coefficient
y = mobility
e = degree of ionization
e = permittivity of free space
w = frequency
X = mean free path
p = potential
LIST OF SYMBOLS (CONTINUED)
Subscripts and Superscripts
a = ambipolar
e = electron
f = floating
i = ion
n = neutral, number density
o = initial or reference condition
p = plasma
pr = probe
s = saturation
T = thermal
+ = positively charged
Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy
ELECTRON GAS BEHAVIOR OF A WEAKLY IONIZED PLASMA JET
WITH THE EFFECT OF AN ELECTRIC FIELD APPLIED
IN THE BASE REGION
Kenneth G. Soderstrom
Chairman: Dr. R. B. Gaither
Major Department: Mechanical Engineering
An experimental investigation was made of a subsonic (0.3 to
0.4 Mach number), low pressure (1 to 10 mm Hg), electrically ionized
plasma jet having a low degree of ionization (10 ). Experimental
measurements were conducted using conventional gas dynamic probes and
a Langmuir probe. Both argon and helium plasma jets were studied.
Particular emphasis in this investigation was focused on the
determination of the effects of an applied potential, in the base
region, on the behavior of the electron gas within the jet, and outside
the jet throughout the quiescent region.
Results of radial and axial electron density and temperature
distributions are compared as a function of base plate potential.
Equipotential data mapped throughout the quiescent region are compared
as a function of base plate potential.
Results of electron density distributions are compared to
previous similar investigations and discrepancies in axial electron
density distributions are discussed in relation to the importance of
metastable effects in sustaining ionization of the jet, an effect
previously considered as negligible. Radial electron distributions
are found in good agreement with previous investigations.
While basic research in plasmas or ionized gases continues to
receive attention [1,2], there is an additional need for information
relevant to engineering design as evidenced by recent efforts in the
study of plasmas associated with applications to the Space Program in
such fields as plasma propulsion systems, reentry vehicles and rocket
The investigation described herein is concerned with a study
of low pressure (1 to 10 mm Hg abs) weakly ionized plasma jets using
argon and helium as the experimental gases. Numerous studies have been
made of the fluid dynamics of jets composed of a neutral gas [4,5,6,7,8,9].
Such studies are rendered complicated when the jet is a plasma in which
the interaction of the components of the jet on a microscopic scale
A plasma is composed of neutral particles, ions and free
electrons. The plasma may be in an equilibrium or nonequilibrium
state depending on the means by which ionization is produced and/or
maintained. Weakly ionized plasmas such as those produced by an elec-
tric field discharge are typical of a nonequilibrium plasma where the
average temperature of the electrons is in the order of 10,0000K,
while the temperatures of the neutral particles and ions are in the
order of a few hundred degrees K. In such cases, the plasma as a whole
exists in nonequilibrium states, displaying a multitude of different
kinetic and spectroscopic temperatures, none of which adequately
describes what might be considered a macroscopic or true temperature
of the total system, since all of the particles do not possess equal
capabilities for transferring energy to one another. This type of
plasma however is useful for experimental studies. When the average
macroscopic temperature of a plasma is primarily a function of the
average temperature of the neutral and ion particles in the range of
a few hundred degrees K, a system amenable for experiment is provided
and the usual difficulties encountered with containment of high tem-
perature gases can be avoided. Such a system allows measurement of the
electron particle density and temperature behavior using a Langmuir
The study of charged particle behavior in plasma jets has been
carried out by several previous investigators. Graf  used both
microwave and Langmuir probe techniques to investigate the electron
density distribution in the fully developed region of a low density
free expansion argon jet. Investigation of low density, high speed
flows using Langmuir probe techniques was done by French . Inves-
tigation of high density supersonic flows of a plasma jet have been
carried out by Igra .
The more complex problem of a subsonic low speed flow near
the nozzle exit where the flow has not yet become fully developed has
been carried out by Gaither  and Greene . Gaither investigated
the charged particle behavior in the potential core region of a low
pressure field free argon jet flow. Greene investigated the charged
particle behavior of an unshielded jet in the potential core and
boundary layer of an argon jet near the nozzle exit.
The present investigation is concerned with the study of the
charged particle behavior of an unshielded jet, close to the nozzle
exit, throughout the core, boundary layer and quiescent region outside
of the jet boundary. Particular emphasis is given to the effect on
the charged particle behavior by the application of an electric field
applied in the quiescent region at the plane of the nozzle exit.
2.1 Definition of a Plasma
One of the most powerful influences upon plasma behavior is the
electromagnetic interaction of the charged particles. Since the elec-
trostatic force fields of the charged particles decay only as the
reciprocal of the square of the distance, the electrostatic forces
are long range and can act upon a considerable number of other particles
even in relatively weak plasma where only 0.01 percent of the particles
are ionized. This interaction of substantial numbers of particles
causes them to react in a collective manner to other electromagnetic
forces. The presence of collective effects constitutes the primary
plasma criteria .
A quantitative measure of the collective effects may be
calculated from a determination of the distance to which the electric
field of an individually charged particle extends before it is effec-
tively shielded by the oppositely charged particles in the surrounding
neighborhood. This shielding distance was first computed by Debye for
an electrolyte. Assuming a large number of particles so that the
electric field can be taken as a continuous function, and a condition
of quasineutrality, ne n., the shielding distance deduced by Debye is
[ e kT 2
= 2 (2-1)
e (n +n.)
which simplifies to
D = 6.64(102) (2-2)
where AD is the Debye length in units of cm, kT is the electron
temperature in units of eV, and n is the electron density in units
Equation (2-2) is a basic criterion for defining a plasma.
If the physical dimensions of an ionized gas region are large compared
to the Debye length, then the gas within the region can be defined as
a plasma. In terms of parameters, the criterion for the existence of
a plasma is defined as A >> AD, where I is a characteristic length in
the plasma region. The experimental results of the present investiga-
tion yielded a lowest value of n = 10 cm and the highest value of
T = 13,0000K or an equivalent kT = 1.12 eV. For a conservative
estimate of AD, Equation (2-2) may be approximated as
D = 03 e (2-3)
The units of kTe are actually energy. However, in plasma
applications, the temperature is frequently referred to in units of
eV as a matter of convenience. If kTe = 1 eV, then the actual tem-
perature is 11,6050K.
Inserting the values of kT = 1.12 eV and n = 10 cm results in
a Debye length of the order 10 cm or 10 mm. Compared to a char-
acteristic length of the plasma region in this study such as the diam-
eter of the anode nozzle, 12 mm, the ratio A/AD is of the order 103
which satisfies this requirement for the existence of a plasma, A >> AD
Another plasma parameter is ND, the number of particles in
a Debye sphere, which is defined as a sphere with a radius equal to
Debye length, AD. The relation for ND is given by
N = r n (2-4)
D 3 D e
If ND > 1, one has an indication that it is equivalent to Equation
(2-2), the collective effects are dominant and the primary plasma
criterion is satisfied. For a conservative estimate of ND for the
11 -3 -3
present investigation, a substitution of n = 10 cm and D = 10
cm as calculated from Equation (2-3) results in an order of 102 or
greater for the value of ND. Thus, the plasma in the present investi-
gation satisfies the requirement of ND > 1.
An additional plasma parameter is the limiting plasma frequency
for propagation of electromagnetic radiation, p, which is given by
U = / e (2-5)
which simplifies to
u = 5.62(104) 4a (2-6)
where w is the limiting plasma frequency in units of Hz and n is
the electron density in units of cm With reference to a given
electromagnetic radiation at a frequency w, if w < w there is no
propagation of electromagnetic waves through the plasma, since the
electrons and ions readjust themselves, thus forming a shield.
If w > w then the plasma cannot act fast enough, which results in
the propagation of the electromagnetic waves through the plasma.
From Equation (2-6), note that wu ~ ne This is a reduction of the
limiting frequency with a corresponding reduction in the value of n .
In the absence of large field forces or other distorting agents
a plasma always relaxes to a condition of electrical neutrality. This
provides a quasineutrality relation, n ; n., a relationship that was
utilized in the derivation of Equation (2-1). The existence of neutral-
ity in a plasma can be established by considering a sample of plasma
contained in a sphere of 1 cm radius. The electric field is given by
Q r (n -n )e
n_ eE i (2-7)
4re r 4re r
which simplifies to
E = 6(10 )(n -n.) (2-8)
where E is the electric field in units of volts/cm and (n -n.) is
the excess charge density in units of cm Consider an electron
density of 10 cm and assuming that n exceeds n. by only 1 percent,
from Equation (2-8), the resulting electric field would be 6000 volts/cm.
Such a potential could only be maintained under special conditions.
It could not be maintained in a plasma where particles are free to
move to relax the field. Therefore, a plasma tends to maintain a con-
dition of electrical neutrality.
In summary, the requirements for the existence of a plasma are:
(a) D >> L; the Debye length is small compared to a char-
acteristic length of the plasma, resulting in the impor-
tance of collective effects.
(b) N >> 1; there are many electrons in the Debye sphere,
assuring a continuity of charge.
(c) n. n ; the plasma maintains a quasineutrality condition.
2.2 Plasma as an Ideal Gas
The basic hypotheses  necessary to consider a gas as ideal
(a) The particles by which the pressure is exerted are so
small that they may be treated as points in comparison
with the scale of length provided by the intermolecular
(b) The forces between the particles are negligible except
With relation to the first requirement, consider argon with an
atom radius a 2(10 ) meters. A calculation of the volume occupied by
the atoms results in less than 0.1 percent of the total volume in which
it is contained at a temperature of 3000K and a pressure of 1 atmosphere.
The static pressure of the present investigation is less than 10 mm Hg.
At this reduced pressure the volume occupied by the atoms is of the
order of 0.001 percent of the volume occupied by the contained gas.
At this condition the ratio of the intermolecular spacing to the
diameter of the atom is approximately 50 to 1 or greater, thereby
satisfying requirement (a) of the ideal gas hypothesis for the present
The second requirement, negligible forces between particles
except at collisions, requires inertial forces > coulombic forces.
The equivalence of this inequality is KE > PE. Using kinetic theory
and this inequality, the following relation for n as a function of T
may be obtained 
n < 7.3T3(108) (2-9)
where n and T are the charged particle densities (ne n.) and temper-
e e i
atures, respectively. For a conservative estimate in relation to the
present investigation, the highest value for n is taken as 10 cm
and the lowest value for T is taken as 3000K. Substitution of these
figures into Equation (2-9) yields an order of magnitude for the
inequality, 102 << 2(1015 ), thereby satisfying the condition of
inertial forces > coulombic forces.
Having satisfied both of the aforementioned requirements for
ideal gas considerations, each species of the plasma may be treated
as in ideal gas, described by the following equations.
P = n kT (2-10a)
n n n
P = n kT (2-10b)
e e e
P. = n. kT. (2-10c)
1 1 1
where P n Pe' and Pi are the partial pressures for each species corre-
sponding to the neutrals, electrons, and ions, respectively. Because
the neutral and ion temperatures are very near thermal equilibrium with
each other, provided pressures are maintained above the micron range
, Dalton's law of partial pressures for mixtures of gases may be
used to combine Equations (2-10a) and (2-10c) to yield
P. + P = (n. + n )kT (2-11)
i n 1 n n
Combining Equations (2-11) and (2-10b) yields an expression for the
total pressure of the mixture as
P = (n. + n )kT + n kT (2-12)
i n n e e
From quasineutrality of the plasma, n. n and from
conservation of particles, n. + n = n where n is the density of
1 n o o
the neutral particles before ionization, these substitutions into
Equation (2-12) yield the expression for the total pressure as
P = n k(T + eT ) (2-13)
o n e
where e is defined as the degree of ionization, e = n./n and lies
within the range 0 5 e 0 1.0 for single ionization. Considering the
neutral particle density, n before ionization, of the order 10 cm
at a temperature of 3000K and a pressure of 10 mm Hg, and the corre-
sponding ion density, n., in the present investigation of the order
12 -3 -5
10 cm the value of e is of the order 10 Using the highest
value of Te, corresponding to the present investigation, of the order
10 4K, the term cT of Equation (2-13) is of the order 10-1 and becomes
negligible in comparison with T since Tn 3000K. This reduces
Equation (2-13) to
P = n kT .(2-14)
However, with conservation of charge, n. + n = n and n n.,
1 n o o 1
Equation (2-14) reduces to that of Equation (2-10a). Therefore, the
total pressure of the weakly ionized plasma is determined by the neutral
particle properties only, in this investigation, corresponding to
4 12 -3
T > 3000K, T < 10 K, and n < 102 cm The electron gas may then
n e n
be treated separately, knowing that its behavior will not affect the
macroscopic properties of the ionized gas except in recombination and
variation in transport properties which are discussed later. In con-
clusion, the overall or macroscopic state of the plasma is described
in terms of state properties of the neutral particles.
2.3 Ionization and Recombination
Ionization of the neutral particles of a gas may be accomplished
by several mechanisms, some of which are passing the gas through an
electric field, heating the gas, and electromagnetic radiation of the
gas with the appropriate wavelength. The method of ionization used in
the present investigation was that of passing the gas through a direct
current electric field discharge in the plasma generator. A simple
calculation serves to illustrate that ionization of a gas in a dis-
charge area is not a matter of pulling electrons from ions by means of
an applied electric field. Using hydrogen, the simplest atom, as an
example, the force of attraction between the electron and ion is given
by Coulomb's Law  as
where e is the charge of an electron or ion, e is the permittivity of
free space, and r is the distance between the charges. The electric
field required to separate the electron and ion is given by
E = (2-16)
This field turns out to be of the order 10 volts/cm. Very much
smaller fields such as used in the present investigation, of the order
10 volts/cm or less, are adequate to produce ionization. Other pro-
cesses than direct electric field ionization are evidently more impor-
tant. These processes are inelastic collision processes between the
electrons, ions, and neutral atoms. In most gas systems, including the
one chosen for this investigation, the most prevalent ionization process
is the electron-atom collision . The electron acquires a kinetic
energy in being accelerated by the applied electric field of a discharge
zone. When the kinetic energy becomes as great or greater than the ion-
ization potential for the neutral gas , it realizes a probability
for ionizing a neutral particle in an inelastic collision.
In argon, the first ionization potential is 15.8 eV. Integra-
tion of the Maxwellian energy distribution from 15.8 eV to o shows that
less than 2 percent of the electrons possess energies sufficient to
cause ionization  in the system studied in this investigation
(1 to 10 mm Hg pressure) and where the average electron energies are
in the order of 2 eV or less. The ions, very close to thermal equilib-
rium with the neutral particles at temperatures below 6000K, or approx-
imately 0.04 eV, do not have enough energy to contribute significantly
to the ionization process so their collision effects may be neglected.
The inelastic electron-atom collision is therefore the dominant process
whereby ionization is effected.
The preceding discussion applies only to the case of ionization
by single collisions. A neutral atom may be ionized by successive
collisions with electrons. This is referred to as cumulative ioniza-
tion, where a neutral atom is energized to an electronic level above
the ground state to some excited state by the first collision and higher
by successive collisions. However, the average lifetime of an excited
state is of the order 10 seconds  which prohibits a large buildup
of atoms in excited states. There are, however, certain excited states
that have considerably longer lifetimes, in the order of milliseconds.
Argon has two such metastable states at 11.55 eV and 11.72 eV, and
helium has two metastable states at 19.82 eV and 20.61 eV . The
metastable states can have important consequences for ionization of
mixtures of gases. When the ionization energy of one component of the
mixture is less than the energy of the metastable state in another
component, atoms of the latter component may be ionized by absorption
of the excitation energy during collision with the metastable atoms
. According to studies of Brewer and McGregor  on low density,
arc heated argon flows, there are large concentrations of metastable
atoms present in all such plasma flows. The importance of the metasta-
ble states in the present investigation is not their ability to cause
ionization of mixture gases with lower ionization requirements but
because they can cause continued ionization after the plasma has passed
through the generator into the test section. According to Gaither ,
the metastable effects were not present, or at least not dominant in
the field free jet region. According to Greene's investigation ,
the same conclusion was observed in the unshielded jet. Both reasoned
that the monatonic decline in electron density could be adequately
described as due to diffusion and not retarded by metastable ionization.
Both of these investigations employed only argon as the test gas.
Experimental evidence of the metastable effects on ionization in helium
by Biondi  in afterflow experiments, report that at fairly low
pressures (1 to 2 mm Hg in helium at about room temperature), the
electron density of a plasma which had been built up during a discharge
for several milliseconds, began to increase after the discharge was cut
off, rose to a maximum in about 1 millisecond and then declined, even-
tually reaching a steady state. In relation to the present investiga-
tion, this effect would indicate that further ionization by metastable
effects could occur in the jet after passing through the generator into
the test section. The velocity of the helium jet was of the order
500 m/sec in the present investigation. Considering a time interval
of 1 millisecond, persistence of the metastable ionization effect as
far as 50 cm past the anode nozzle in the axial direction is clearly
possible. Since the upper limit of data in this investigation is only
30 mm, the evidence is very strong that the metastable effect of ion-
ization persists beyond the distance of 30 mm. However, the buildup
of the charged particle densities far into jet by the metastable effect
is reduced by the effect of radial diffusion of the charged particles
from the jet. The effect of this reduction is somewhat complicated
when the electric field is applied to the base plate which not only
serves to further accelerate the electrons into the test region but
also adds to the diffusion rate of the charged particles. This diffu-
sion effect will be discussed in further detail in Section 2.4.
In addition to diffusion, another possible mechanism that
would deplete the electron and ion density in the jet is the mechanism
of recombination. In afterglow experiments with argon, this mechanism
is found to be of minor importance  in comparison to diffusion in
effecting the depletion of the charged particle density. Both Gaither
 and Greene  considered recombination as insignificant within
the jet region where data were obtained. Since the present investi-
gation involves helium, the importance of recombination can be calcu-
lated by a similar method employed by Gaither for the argon experiment.
The rate of recombination is given by
e 1 2
d- n n. m n (2-17)
dt dt e 1 e
where a is defined as the recombination coefficient and quasineutrality,
n n., is used as previously discussed in Section 2.1. Gaither
developed the following relation
n = -e3/2 n2 (2-18)
dt o e
based on the fact that a is a function of electron temperature [23,24]
and not a function of pressure. In fact, at several electron temper-
atures , he found the relation
from which Equation (2-18) was obtained. The reference state,
indicated by T is the temperature at which the values of a were
measured. Applying this relation to the present investigation, a rea-
sonable estimate of the charged particle depletion caused by recombi-
nation can be found. Integration of Equation (2-18) yields the
n e) (2-19)
eo T 3/2
1 + n ao --) t
eo o T
Replacing time, t, in Equation (2-18) by Z/qz, where Z is the
longitudinal distance along the centerline of the jet in units of cm,
measured from the nozzle exit, and q is the velocity of the jet core,
Equation (2-19) reduces to
e = 1 (2-20)
+ n (e
eo o T q
For a conservative estimate of n /n corresponding to the present
investigation, Z is taken as 3 cm, the maximum value of Z for which
data were obtained in helium. The corresponding core velocity is
5 X 104 cm/sec and the average electron temperature is 30000K for the
condition of the base plate at floating potential. A value of
a = 10 cm /sec at 3000K was found as the most conservative value
reported by previous investigators . Substitution of these values
into Equation (2-20) results in a value of n /n = 0.997. This rep-
resents a reduction in electron density along the centerline of the
jet, attributed to recombination, in the order of less than 0.5 percent
which justifies neglecting recombination as a mechanism for the deple-
tion of the charged particle density.
2.4 Jet Flow Structure
The flow field of an axial symmetric jet may be divided into
four distinct regions as shown in Figure A-i of Appendix A. These
(a) Potential core region
(b) Mixing region
(c) Developed region
(d) Quiescent region.
The potential core region is composed completely of gas issuing
from the nozzle. Owing to an absence of disturbing mechanisms in this
region, including minimal viscous effects, the dynamic and static prop-
erty changes are adequately described by one-dimensional models. It is
cone shaped owing to the action of boundary layer growth and mixing
that occurs as the jet proceeds in the axial direction. The apex of
this cone is the point beyond which the boundary layer fills the flow
field of the jet mainstream. Previous investigations of plasma jets
have provided analyses supported by experimental results of charged
particle behavior in:
(a) the potential core region within 3 to 4 nozzle diameters
measured axially from the nozzle exit plane in shielded,
field free jet, using argon ;
(b) the potential core and mixing regions of an unshielded
jet within 3 to 4 nozzle diameters measured in the axial
direction from the exit plane .
Still lacking are experimental results of the plasma potential
throughout the potential core, mixing and quiescent regions of the
unshielded jet. In addition, previous investigations have not con-
sidered the effects upon charged particles when the flow field is acted
upon by an electric field in the base region located in the plane of
the nozzle exit. The present investigation is an attempt to obtain
this information experimentally.
Charged particle behavior within a jet flow field is primarily
influenced by two mechanisms:
(a) gas dynamic movement of the jet in the axial direction
caused by an imposed pressure differential between the
upstream (plasma generator) and the region downstream of
the test section;
(b) radial diffusion of the charged particles into the quies-
cent region as a result of charged particle temperature
and density gradients between the jet mainstream and the
surrounding quiescent region.
Theoretical analyses of the charged particle gas behavior in the
potential core region were performed by both Gaither  and Greene .
Gaither derived an expression for the electron density distribution by
considering the species conservation equation for the flow. This equa-
tion is given as
V-n q V-D Vn V-DT VT = N (2-21)
e a e a e
where the first term, V-neq, represents the net increase in electrons
within the control volume caused by the gas dynamic forces. The second
and third terms, V*D Vn and V.D VT respectively, represent the net
a e a e
diffusion of the electrons from the control volume. The term N, on the
right-hand side of Equation (2-21), represents the net rate of increase of
electrons within the control volume caused by ionization or recombina-
Equation (2-21) contains two diffusion terms to account for
separate diffusion mechanisms acting in response to the presence of
charged particle density and temperature gradients. The diffusion
coefficients D and D are ambipolar diffusion coefficients and are
associated with certain plasma conditions such as those found in
a glow discharge where the electrons with a higher temperature and
therefore a higher mobility than the heavier ions could be expected to
diffuse from the discharge more rapidly than the ions. In reality,
diffusion does not occur in this manner since the result of this action
would be the creation of gross space charge fields . Rather, quasi-
neutrality, ni ; ne, as discussed in Section 2.1, is preserved in the
plasma by local electrostatic forces that cause a deceleration of the
electrons and acceleration of the ions. The result is a coupled dif-
fusion process with both species diffusing with the same velocity.
This type of diffusion process is called ambipolar.
Equation (2-21) may be simplified to the form
q zn 82n an
z e e 1 e
n 7 = --e + r (2-22)
if the following criteria are met:
(a) Both ionization and recombination are negligible in the
jet, resulting in N=0.
(b) q is considered a constant equal to qz, the potential
(c) T is considered constant in the radial direction, observed
from experimental results, thus aT /or = 0.
(d) Axial variation of n is negligible compared to radial
variation of n observed from experimental results,
thus an /3r >> n /6Z.
(e) D is only a function of electron temperature, thus, from
criterion (c), Dn becomes a function of Z only. Therefore,
the term q /D of Equation (2-22) to be defined as 1/f(Z)
where f(Z) is a function of the axial coordinate Z.
Using a separation of variables procedure, Gaither found a solu-
tion of Equation (2-22) in the form
n = exp [- 2 zf(Z) dzj Jo 2r (2-23)
o o o
where n is a dimensionless electron density and f(Z) is found from the
energy equation. When simplified by the same criterion as that used
for the species equation, the energy equation is a second-order,
nonlinear differential equation, which, when coupled with Equation (2-23),
may be solved by an analog computer.
Greene  used a similar approach with the same criteria set
forth by Gaither except he imposed the limitation that Dn was approx-
imately constant. The advantage of this limitation simplified the
mathematics since f(Z) now became a constant. In the domain 0 5 Z < o,
0 S r < m, with boundary conditions n(Z,0) = finite, n(Z,w) = 0, and
n(0,r) known from the experimentally determined initial distribution,
his solution for Equation (2-22) is
Ch CZ + 1 2Z + 1 CC2Z+-24)
where the constant C1 is chosen so that Equation (2-24) best fits the
initial electron density profile data at the nozzle exit where Z = 0.
When the value of Z= 0 is substituted in Equation (2-24), the result-
ing radial electron density profile becomes
IZ = exp [-C1i)2 ] o 2. 4(-)] (2-25)
This solution is somewhat similar to the solution of the electron
density profile of the positive column of a steady flow discharge
which is given by
n = Jo [2.4(-)] (2-26)
except for the factor (exp -C1(r/Ro )2 which is introduced into
Equation (2-26) to satisfy the boundary condition at n(O,r).
The electron density distribution along the centerline of the
jet may be obtained by setting r= 0 in Equation (2-24). This results
exp [-1.442+1 1.44
nIO = exp (2-27)
C 1C2Z +1 C1C2Z +1
where C2 is a constant given by
since Dn is considered a constant. Equation (2-27) therefore predicts
a form of exponential decay of electron density along the centerline of
the jet. The rate of decay is a function of C2 which in turn is pro-
portional to D the density ambipolar diffusion coefficient and
inversely proportional to q the magnitude of the jet core velocity.
An expression for D was developed by Gaither  based on the
Einstein relation D. = y. kT./e. His resulting expression for D is
Dn = S 1 + (2-29)
a [ + J
where S1 is defined by
46k o n
SI -e Y+ P (2-30)
in which k/e has units of volts/oK, y is the ion mobility and has units
of cm /volt-sec, T has units of oK, and P has units of mm Hg.
A value of 1.4 cm /volt was used for the mobility of argon, y refer-
enced to 3000K, based on data of several investigations [24,25,26].
With reference to the present investigation, Equation (2-29)
may be reduced to the approximate expression
D M S -- (2-31)
a 1 T
since T /T is of the order 10 or greater. In an order of magnitude
estimate of Dn, using values of T = 104 K and T = 5000K from the
a e n
present investigation for argon, the value of Dn is found to be of the
order 10 cm /sec. Since helium has a value for ion mobility approx-
imately five times that for argon , the diffusion coefficient will
be approximately 5 X 10 cm /sec for helium.
Application of the equations describing the electron density
distributions are further discussed in Chapter 4 with considerations
to the experimental results and assumptions underlying the derivations
of the equations.
2.5 Langmuir Probe
One of the earliest, most useful, and widely used methods of
plasma diagnostics is that developed by Langmuir and Mott-Smith in
1924 , commonly referred to in the literature as the Langmuir probe.
The fundamental requirements or assumptions in classical probe
theory are as follows :
(a) The ion sheath thickness must be small compared to the
charged particle mean free paths in the system, d. << .
(b) The probe diameter must be small compared to the charged
particle mean free paths in the system, D X.
(c) The ion sheath thickness must be much less than the probe
diameter, d. < D
The reason for assumption (a) is to insure, at least ideally,
that no charged particle collisions occur in the sheath. This allows
Supplementary information concerning the theory, operation and
measurement errors of the Langmuir probe is given in Appendix B.
that collected particles are in free fall to the probe under the action
of the electric field. Assumptions (b) and (c), in addition to (a),
are to assure that the probe does not disturb the plasma. For conven-
ience these assumptions may be combined and stated as d. < D << ,
where d. is the ion sheath thickness, D is the diameter of the probe
and X is the mean free path for the charged particle collisions.
An estimate of the ion sheath thickness, d., may be obtained
from an expression given by Schwartz  as
d. = 3 (2-32)
8 7 e
which is based on the Child-Langmuir law for space charge limited ion
current density where jis may be expressed as
ji n i (2-33)
When Equation (2-33) is combined with Equation (2-32) and simplified,
the resulting expression for the ion sheath thickness becomes
265 I9 3/4
d = -(2.34)
where d. is the ion sheath thickness in units of mm, 9 is the poten-
tial of the probe with respect to the plasma potential in units of
tial of the probe with respect to the plasma potential in units of
volts, n. is the ion density of the undisturbed plasma in units of
cm and kT is the electron gas temperature in units of eV.
A conservative estimate of d. for the present investigation
based on values of n. = 10 cm T = 50000K, and C = 10 volts,
results in a value for d. in the order of 10 mm. Comparison of d.
with D yields the result 102 mm << 0.65 mm which satisfies the
inequality di < Dp, the aforementioned assumption (c) of classical
French  investigated the case of small mean free paths
relative to the probe diameter, A < Dpr, and the consequence of this
with respect to plasma disturbance by the probe, since charged particle
collisions would occur throughout the ion sheath under this condition.
He concluded that there was appreciable plasma disturbance by the probe
when X < Dpr. As indicated by Schwartz , if the mean free paths
are too small compared to the probe diameter, some modifications to clas-
sical probe equations are needed.
Charged particle collision mean free paths in the present inves-
tigation were computed for the electron-neutral, electron-ion, and
electron-electron collisions based on formulations of French  and
Graf . Conservative estimates yielded the results of e = 1 mm,
e = 120 mm, and \ = 40 mm. The value of the electron-neutral mean
free path at 1 mm is the smallest of the three mean free paths calculated
and therefore is the worst case in satisfying the condition of D < X.
Since French concluded that there was no appreciable plasma disturb-
ance from the probe when D > X, the present investigation, at worst,
should have no greater plasma disturbance from the probe than that
obtained by French.
The last of the three assumptions of classical probe theory,
assumption (c) in which d << D is satisfied in the present investi-
gation, since, as a conservative estimate, d. is of the order 10 mm
and D is of the order 1 mm.
The assumptions of classical probe theory do not include the
effects of mass movement of the plasma as is the case of the present
investigation. The effect of mass motion may be investigated with the
use of two cylindrical probes, one transverse and the other parallel to
the flow. If the mass motion has negligible effect on the probe char-
acteristic, then both probes should produce the same probe character-
istic. French  investigated this for an argon plasma and found
that the retarding field region and the electron collection region of
the probe characteristic were unaffected when T./T << 1, a criterion
that is definitely met in the present investigation with T./T < 0.1
as the most conservative estimate. He did report, however, that the
effect of mass motion on the ion collection region of the probe char-
acteristic was uncertain. However, it is of interest to note that his
experiments were conducted at a Mach number of approximately 1.5,
whereas the present investigation is conducted in the range of Mach
numbers from 0.3 to 0.4. Furthermore, the pre ent investigation does
not inquire into the ion collection region of the probe characteristic
for measurements, since only ion densities of 10 cm and less were
present--too low to provide ion currents large enough for direct
measurement. Therefore, the uncertainty of the ion collection region
of the probe characteristic should have no dire consequences to the
Langmuir probe measurements of the present investigation.
3.1 Description of Apparatus
The overall view of the plasma laboratory is shown in Figure 1.
Additional detailed views of the experiment and auxiliary equipment are
shown in Figures 2 through 13. The following text will outline, first,
the general operation of the equipment, followed by detailed descrip-
tions of individual sections and components that comprise the entire
General. The experiment was conducted in steady flow. The gas
from the high-pressure tank flowed through a pressure regulation system
into a settling chamber. From the settling chamber the gas flowed into
the mixing chamber and then into the plasma generator where it was
ionized by an electric field. The ionized gas then expanded, as a jet,
through a converging nozzle into the low-pressure test section and
left the test section through the vacuum system, exhausting to the
Probes to measure pressure, temperature, and the Langmuir
probe characteristic of the jet and surroundings, were located within
the test section. All three probes were movable in both the radial
and longitudinal direction within the test section.
Gas Supply. The gases used in this experiment were argon and
helium. The majority of the experiments were performed using argon.
The principal reason for choosing argon was that results could be com-
pared to previous similar investigations [13,14]. Helium was used
in one test but presented some experimental difficulties that were
not encountered with argon. Details of this are explained later.
The high-pressure gas tank had an initial pressure of approx-
imately 2500 psig. The pressure regulation system consisted of a
single-stage pressure regulator, followed by a Fairchild-Hiller Con-
trol Regulator. This combination was, in effect, a two-stage regu-
lator. The gas then passed through a valve-flowmeter combination which
both controlled and indicated the flow rate. During exploratory exper-
imentation it was found that the single-stage regulator, by itself, was
not capable of maintaining a constant static pressure within the test
chamber for a greater time period than 3 or 4 hours. The addition of
the Fairchild-Hiller regulator into the pressure regulation system
resulted in reasonable control of the static pressure over extended
periods of time as shown in Figure A-6 of Appendix A. The low-pressure
gas, upon leaving the valve-flowmeter combination, was passed through
a settling tank. The flow was then split through a Y-connection before
entering the mixing chamber. A valve installed in each leg of the con-
nector provided a balance control for the flow rate to each inlet to
the mixing chamber of the plasma generator. This permitted the con-
trol necessary to effect radial symmetry of the jet.
AIRCO, the gas supplier for the laboratory, specifies the
purity of the argon as 99.996 percent and the helium as 99.99 percent.
Plasma Generator. Once inside the mixing chamber, the gas from
each inlet was directed through a series of baffles to insure uniform
flow before passing into the discharge region. The discharge region
was bounded by a Pyrex glass tube 16 cm in length and 7.5 cm outside
diameter, with flanged ends. This tube was in contact with flat neo-
prene gaskets set into the anode plate at the top and set into the mix-
ing chamber at the bottom which provided the discharge region with
a vacuum seal. An inner Pyrex glass tube, 17 cm in length and 4.5 cm
outside diameter, served as a guide to contain the ionized gas.
In addition, it provided a visual check of the flow through the dis-
charge region. No effort was made to seal the inner tube, since it
was completely contained within the vacuum seal.
The cathode, a 1/2-inch o.d. stainless steel, thin-walled tube
with a parabolic tip, was mounted through a three-part lucite sleeve.
Water cooling was used inside the cathode. A complete description of
the cooling system is in a subsequent paragraph. The upper part of the
sleeve was attached with screws to the bottom of the mixing chamber.
O-rings fitted to the sleeve served as vacuum seals, and, in addition,
provided a vertical alignment support for the cathode. The longitud-
inal position of the cathode, relative to the anode, could be varied
by loosening the lower two parts of the lucite sleeve, thereby reliev-
ing the compression on the 0-rings against the cathode, and allowed for
a manual vertical movement of the cathode to any desired position.
Preliminary experimentation to determine the optimum anode to
cathode spacing indicated that the spacing should be as large as
possible to sustain both plasma stability and radial symmetry. The
maximum spacing, however, was restricted by the maximum voltage avail-
able from the power supply to "start" the plasma. The most suitable
cathode to anode distance that would suffice over a range of flow con-
ditions, within the aforementioned restrictions, resulted in a spacing
of 95 cm.
The anode support plate was a 5-inch diameter, 1/3-inch thick
brass plate with a 1-inch tapped hole in the center. Several anode
nozzles, each wit a different inside diameter, were used in the test-
ing. Each was factured to fit the threaded hole in the anode plate.
A 12-mm inside dic:ieter nozzle was finally chosen for all of the exper-
imentation. This was the maximum allowable size for this configuration
which thereby provided the largest flow area for surveying the jet with
probes. The inside surface of the nozzle was hand polished with crocus
cloth which resulted in minimizing fluctuating discharges of the plasma
on the nozzle surface. These fluctuating discharges, observed during
exploratory experimentation, were found to cause instability in the
plasma. Periodic removal and repolishing the nozzle remedied this
Test Section. The test section was bounded by a Pyrex glass tube,
40 cm in length, 9.5 cm outside diameter, flanged and vacuum sealed at
each end by neoprene gaskets to the anode plate at the bottom, exhaust
housing at the top. The vacuum itself plus the weight of the apparatus
provided the force required to hold the ends on the tube. Four static pres-
sure taps were located along the side of the test section at distances of
4.5, 9.8, 14.9, and 20.0 cm from the bottom of the test section. The
lower tap at 4.5 cm was used as a passage for the electrical connection
to the base plate. The tap at 9.8 cm was used to install an air bleed
valve. The upper two taps were blocked off with a loop of Tygon tubing.
Either of the unused taps could have been used to measure the static
pressure in the test section but it was found more convenient to use
the pressure probe for this purpose.
The exhaust housing was connected to the laboratory exhaust
manifold by 3-ply, 1-3/16 inch o.d., 3/4 inch i.d., flexible vacuum
hose through a ball vacuum valve. The manifold was connected to a
Consolidated Vacuum mechanical pump with a 225 m3/hr pumping capacity
which was capable of pumping the test section down to, and maintaining,
an equilibrium pressure of approximately 0.4 mm Hg before the test gas
was introduced into the system. A surge valve was also installed in
the vacuum housing which was used for back pressure control.
The base plate, a 1/16-inch copper plate, was mounted on top
of, but insulated from, the anode plate by a 1/16-inch lucite disk.
An inner lip on the lucite disk also insulated the base plate from the
anode nozzle. An electrical connection was made to the base plate by
a No. 20 insulated copper wire, fastened by a nut to small (No. 6-32)
screw located near the outside edge and brazed to the plate. The wire
passed through the lower pressure tap of the test section and was
vacuum sealed on the outside with an arrangement of glass tubing,
Tygon tubing, and vacuum grease to allow movement of the wire through
the pressure tap while still maintaining a vacuum seal.
Cooling System. The cathode was designed for internal water
cooling. A 1/4-inch copper tube was inserted inside the cathode, there-
by forming an annulus between the copper tube and the inside wall of the
cathode. Deionized water was pumped from a 5-gallon stainless steel
storage tank, through Tygon tubing into the cathode, upward through the
copper tube, returning downward through the annulus, and into an exit
header. Tygon tubing connected the header to the storage tank, thereby
completing the cooling loop. The thermal energy gain of the cooling
water was removed by evaporative cooling as a result of blowing com-
pressed air through the water by way of a 1/2-inch diameter stainless
steel tube contained in the storage tank. Small holes, 1/32-inch diam-
eter, spaced 1/2 inch apart, were drilled into the tube to allow the
passage of the air into the water.
For the argon experiments, it was not necessary to cool the
anode. The use of helium, however, with a higher value of thermal
conductivity than argon, required cooling of the anode. This was
accomplished by blowing compressed air radially around the anode plate
through Tygon tubing.
Probes. Three probes used in surveying the test section were
constructed with a 1-3/8-inch offset to allow for radial movement across
the test section through the centerline of the jet. The probe stems
were made of 3-mm capillary glass tubing. Glass, as the material,
provided the required electrical insulation. The choice of capillary
tubing, with a greater wall thickness than standard tubing, increased
the mechanical strength of the stem.
The stagnation temperature probe was constructed with 0.005-
inch diameter copper-constantan thermocouple wire with the junction
surrounded by a thin-walled brass cylindrical radiation shield, open
at both ends, to minimize flow disturbance. The exit point of the
thermocouple wire at the top of the glass stem was sealed with epoxy.
The sensing element of the pressure probe was a 20-degree
chambered brass tube with an inside diameter of 0.067 inch. This probe
was used to measure the stagnation pressure, when placed within the
jet, and the static pressure, when the stem was rotated to any posi-
tion outside the jet boundary. The top of the glass stem was con-
nected to a pressure gage with Tygon tubing.
The Langmuir probe, although apparently simple in construction
compared to the pressure and temperature probes, was the most delicate
to manufacture. Several trials with various design configurations
were attempted. Both cylindrical and flat probes were tried during
exploratory investigation with the flat probes yielding the best results
with regard to reproduction of recorded data. An added advantage of
the flat probes over the cylindrical probes was the increased accuracy
in measurement of its axial position, since the flat probe was a small
flat circular plane, perpendicular to the longitudinal axis, whereas
the cylindrical probe had its longitudinal axis parallel to the longi-
tudinal axis of the jet, thereby exposing the collecting surface over
a greater axial distance. The probe configuration that was chosen for
the experimentation consisted of a 0.025-inch diameter tungsten wire
with a metal to glass seal at the tip to 3320 Canary Uranium glass.
The probe was connected to the stem by inner and outer No. 725 stan-
dard ground glass taper joints. The tungsten wire was silver soldered
to the inner conductor of a coaxial cable. The tapered joints were
then sealed together with epoxy. Exploratory investigation indicated
the capability of the epoxy to maintain a vacuum seal when exposed to
the plasma. The coaxial cable passed up through the glass stem and
out to a BNO connector which in turn was connected by coaxial cable to
the input of the Langmuir probe circuit.
The probe tip was made as small as possible to minimize
disturbance to the flow. Within practical limitations of the facil-
ities available, the minimum wire diameter and minimum glass seal
thickness were used. It was also found that the condition of the
exposed surface of the probe was an important factor in reproducing
the Langmuir curve to obtain enough data points in the positive probe
voltage region. If the probe surface was not highly polished the
Langmuir probe characteristic would go to discharge early in the nega-
tive space charge region, thereby reducing the amount of data points
available to determine the probe saturation current.
Positioning Mechanism for the probes was located on top, but
electrically insulated from all other parts of the experimental appara-
tus. The maximum positioning range of the probes was 110 mm in the
axial direction and across the entire test section in the radial direc-
tion. This range was more than sufficient to survey both the jet and
surroundings where data could be obtained within the limitations of the
The glass stems from the three probes were each mounted through
a three-part lucite sleeve, similar to that used by the cathode. Each
was threaded into a hollow brass nut, which in turn was threaded into
the exhaust housing. The vacuum seal was made by using an O-ring seal
between the nut and the upper surface of the exhaust housing. In addi-
tion to maintaining the vacuum seal, the nut-sleeve combination also
served as a vertical guide for the glass stems within the test section.
Stainless steel sleeves, 12 inches in length and 1/2 inch in outside
diameter, were slipped over the glass stems and attached to the stems
by set screws at each end of the sleeve. The sleeves were then con-
nected to a parallel threaded rod drive mechanism which in turn was
connected through gearing to control drive shafts. Each drive shaft
was rotated by hand to provide axial movement, either up or down, of
the probes. A millimeter scale held perpendicular to the top of the
lucite sleeve was used to measure the longitudinal displacement of
each probe. The stainless steel sleeves also had a keyway cut in the
longitudinal direction into the outside surface of the sleeve. The
sleeve was keyed through a spur gear and connected through appropriate
linkage to an output shaft, the rotation of which moved the probes in
the radial direction. Micrometer shafts were attached to the output
shafts and the readings calibrated to the radial location of the
probe, relative to the centerline of anode nozzle.
Vertical alignment of the probes with the centerline of the
anode nozzle was accomplished by replacing the nozzle with an alignment
jig. The jig was composed of a lucite cylinder, threaded to fit the
anode plate, with a movable length of drill rod mounted as a slide
fit through the longitudinal center of the lucite cylinder. The probes
were centered and aligned longitudinally at any distance from the
nozzle exit plane up to 60 mm above the exit plane along the axial
centerline of the nozzle. Maximum radial deviation from the center-
line was found to be less than 0.25 mm at an axial distance of 60 mm
above the exit plane.
Instrumentation. The data recorded during a full test were
obtained from the pressure, temperature and Langmuir probe surveys
within the test section. In addition, other data, as shown in
Figure A-6 of Appendix A, were obtained, corresponding to the auxil-
iary equipment associated with the experiment.
The Tygon tubing from the pressure probe was attached to a
Wallace and Tiernan absolute pressure gage with a range of 0.1 to 20 mm
Hg. The smallest division marks were spaced at intervals of 0.1 mm Hg.
Readings between the marks were interpolated visually to 0.01 mm Hg.
The pressure of the mixing chamber was measured, using a Tygon tubing
connection between the chamber and a second Wallace-Tiernan absolute
pressure gage, similar to the aforementioned but with a range of 0 to
50 mm Hg. The smallest division marks were spaced at intervals of
0.5 mm Hg. Data from this latter gage were used for monitoring
The output of the thermocouple from the stagnation temperature
probe was read on a Thermo Electric Potentiometer Pyrometer with read-
ings taken directly in degrees Fahrenheit. The smallest division marks
were spaced at intervals of 10F. The thermocouple was calibrated in
boiling water with the output to the Thermo Electric Pyrometer and
found to be within 10F at that point.
The Langmuir probe circuit, as shown in Figure 13, was designed
to produce the Langmuir probe characteristic by a continuous alternat-
ing sweep, or a d.c. point by point manual sweep. For the case of the
continuous sweep, an oscillating signal from the signal generator, capa-
ble of producing up to 30 volts positive or negative amplitude, was
impressed on both the probe and the horizontal input to the scope.
The probe current was obtained by measurement of the voltage drop
across resistor R1 to ground, which became the vertical input to the
scope. The range of R1 could be varied from 0 to 5 kn and its value
measured on the bridge by switching the resistor out of the circuit to
across the bridge. Polaroid photographs were recorded of the result-
ing Langmuir probe characteristic (see Figure B-2 of Appendix B) dis-
played on the screen. A d.c. amplifier was used in the horizontal
circuit in place of a time base, since the sweep signal was impressed
from the signal generator.
If the signal generator was switched out of the circuit, the
Langmuir probe characteristic could be obtained by manually sweeping
the floating d.c. power supply from negative to positive, using a DPDT
switch to change the polarity. The readout of the probe characteristic
could either be obtained by a photographic time shot of the point as
it moved across the screen or could be read directly on a digital
voltmeter, point by point, by switching between horizontal and vertical
voltage input at each point. After trying both methods in exploratory
investigation, the continuous sweep method was decided upon. This
method had the advantage of reducing the time required to take the
data, provided a more consistent data reduction method, and provided
a permanent record of the data recorded in the photos.
The floating potential of the probe was obtained by connecting
the probe directly to the digital voltmeter with everything else dis-
connected so that the probe could not draw current through any ground
Both the vertical and horizontal scales of the oscilloscope
were calibrated with the internal calibrator and also checked with the
digital voltmeter. This was done for all scales of the horizontal and
vertical amplifiers. All were found to be within the stated 3 percent
accuracy of the oscilloscope.
The power supply for the circuit was supplied by a 0-1500 volt,
0-3 amp DC Rapid Electric Silicon Rectifier. A 0-2000 0 high voltage
ballast resistor unit was connected in series with the rectifier. The
ballast resistor was actually a combination of 12 variable resistors.
The current through the plasma generator was obtained from an ammeter
that was mounted on the rectifier. A voltmeter was installed between
anode and cathode. The positive output of the rectifier was connected
to the anode and grounded. The negative output was connected to the
A voltage power supply was installed between the anode and
the base plate, the positive output connected to the base plate with
the anode at ground. Both a voltmeter and ammeter were installed to
measure the base plate voltage with respect to the grounded anode and
the base plate current, respectively.
3.2 Experimental Procedure
Preparation for Test. Before any complete test was performed,
several preparatory steps were taken, usually one day in advance of
The plasma generator section was removed and the anode nozzle
replaced by the alignment jig. The test section was then evacuated,
thereby holding the probe stems in a fixed position relative to the
vertical glass wall of the test section. Each probe was aligned with
the centerline of the jig and the corresponding reading of the microm-
eter shaft noted. This reading became the probe radial index. The
alignment jig was then replaced by the nozzle and the plasma generator
reinstalled in the experiment. Each probe was then vertically adjusted
so that the tip of each probe coincided with the exit plane of the
anode nozzle. The reading of the vertical mm scale was noted for each
probe in this position and referred to as the probe vertical index.
To prevent any slippage of the probes from their reference
index positions, all set screws in the probe positioning mechanism
The tip of the thermocouple probe refers to the alignment of
the thermocouple junction with the exit plane, not the actual tip of
the probe which was, in reality, the end of the shield.
were checked with a set screw wrench to assure that they were tight.
Reference marks were placed on the stainless steel sleeves and glass
stems to provide a visual check on any radial or vertical slippage
between the stem and sleeve. An additional check on radial slippage
was provided by the Langmuir probe characteristic display on the
oscilloscope since the maximum probe current for any radial sweep would
always coincide with the longitudinal centerline of the jet.
Before any test was started, a new bottle of gas was installed.
This provided the capacity for approximately 24 hours of continuous
steady flow operation which was sufficient time for the completion of
the tests and within the limit of human stamina requirements to com-
plete the test while remaining in a relatively sane mental state.
After the installation of the new gas bottle, all inlet valves
were closed and the system was pumped down by the vacuum system for
approximately 10 to 12 hours. During this time period, the oscillo-
scope, signal generator, and digital voltmeter were in operation, but
disconnected from the circuit. This allowed sufficient time for the
instrumentation to stabilize prior to the start of the test.
Pretest Procedure. A small flow of gas was introduced into the
plasma generator, the cooling water flow started, and the voltage of the
rectifier increased to the starting breakdown voltage of the gas. In the
case of argon, for the particular configuration used, the starting volt-
age was approximately 900 volts. To prevent a large current surge, the
ballast resistor was adjusted to its maximum resistance value of 2000 Q.
The plasma voltage reduced to 400 volts after initial breakdown.
The plasma current was then increased to the desired value by reduc-
ing the value of the ballast resistor. The desired flow condition
was obtained by further opening the flow meter valve. The combination
of gas flow rate, gas pressure, plasma voltage, cathode to anode sepa-
ration, and plasma current adjustments were not independent. Certain
combinations of these controls would result in nonstability of the
plasma. This restricted the combinations of gas flow rate and plasma
current that would satisfactorily maintain stability of the plasma.
The best procedure found was, first, an initial setting of the plasma
current followed by adjustment of the gas flow until a stable condi-
tion was achieved. However, achieving a stable condition did not
guarantee the continuation of that condition over the long period of
time required to obtain the data for a full test. This point is
further discussed later in Chapter 4, concerning each individual test.
The experiment continued running for about 3 or 4 hours, dur-
ing which time the stagnation temperature and pressure at the anode
nozzle exit were monitored until their values remained essentially
constant over a time period of about 1 hour. A voltage was then
applied to the base plate and then increased until a discharge appeared
at the inside edge of the base plate. The air bleed valve of the test
section was then cracked open to allow a small amount of air to bleed
into the test section. This small amount of air bleed would cause
an increase in static pressure of less than 0.3 mm Hg, an equivalent
of less than 5 percent increase over the steady state static pressure.
The control of the small amount of air bled in through this valve would
result in controlling the suppression of the discharge. By simultan-
eous adjustments of the base plate voltage and the air bleed rate,
a controlled symmetric ring of small discharges could be sustained
around the inside edge of the base plate. This condition is shown
in Figure 9. The correct adjustment was very critical, thus it was
difficult to obtain. Too much voltage caused a short circuit between
one of the discharge points and the jet, resulting in a large base
plate current and loss of radial symmetry. This condition could
be corrected by an increase in the air bleed. However, too much air
bleed resulted in the jet becoming turbulent, thus unstable. Adjust-
ments were made to yield a maximum plate voltage while maintaining
both a stable jet and symmetrical discharge around the inside diameter
of the base plate. Once this condition had been established, the base
plate voltage could be reduced to any desired value. In fact, the base
plate power supply could be shut off completely for any time period
and then turned on again, the base plate voltage adjusted to match any
previous condition of current, voltage and Langmuir probe character-
Test Procedure. Langmuir probe data were first taken along the
jet's axial centerline, starting at 2 mm from the anode nozzle exit
Since radial sweep measurements were made not only within the
jet, but also in the quiescent region, the vertical index position for
each probe was set at 2 mm above the anode nozzle exit plane. This
assured clearance for a complete radial sweep and allowed a safety
factor for override in vertical adjustments.
plane. Proceeding upward, data were taken at intervals of 4 mm.
At each position data were taken, first, with the base plate floating
and then with a voltage or series of voltages applied to the base
plate. After the data were obtained along the centerline, the probe
was lowered to its vertical index position of 2 mm from the anode
exit plane, on centerline, and the Langmuir probe characteristic dis-
played on the oscilloscope (see Figure B-2 of Appendix B) was checked
as to its identity against the photo previously taken at the same posi-
tion at the start of the centerline test.
Data from radial sweeps of the Langmuir probe were obtained
at radial intervals corresponding to convenient units of the micrometer
radial shafts. These intervals were the equivalent of approximately
1 mm. At each longitudinal level chosen to obtain the radial data,
readings were first taken for a complete sweep with the base plate
floating, followed by a repeat procedure for each individual base
For both centerline and radial data of the Langmuir probe,
readings were taken as far away from the anode nozzle exit plane
and the axial centerline, respectively, as possible within the sensi-
tivity limitations of the probe.
The floating potential data were obtained in a similar manner
to the radial sweep Langmuir probe data. However, since the probe
current was zero for this measurement, the sensitivity of the probe
was not restricted by probe current. Therefore, floating potential
data could be obtained outside the boundary of the jet when making
a radial sweep. The floating potential was read out and recorded
directly from the digital voltmeter. Between each reading a 30-volt
potential was applied to the probe to remove any possible contamination
that might have accumulated during the previous measurement. The float-
ing potential measurements were taken at approximately 1 mm radial
increments, sweeping first with the base plate floating, followed by
a repeat procedure for each individual base plate voltage. The probe
was then moved to a new vertical position and the procedure of the
radial sweeps repeated.
Stagnation pressure measurements were obtained by radial point
by point sweeping of the pressure probe across the jet, starting from
the quiescent region, passing through the jet across the centerline
and out the other side into the quiescent region. Figure A-3 of
Appendix A shows the data obtained from a typical pressure probe sweep.
These data were plotted directly on the graph as they were taken during
the test. This gave an immediate indication of any variation of the
jet from radial symmetry. These sweeps were taken at several longi-
The stagnation temperature readings were taken immediately
after the pressure data were taken at each longitudinal level. Only
the centerline data were taken with this probe. As the probe was moved
radially away from the centerline of the jet, part of the cylindrical
shield became exposed to the region outside the jet boundary. When
measuring the temperature, the probe was placed in the centerline posi-
tion and allowed to remain within the jet for a period of about 15 min-
utes, during which time, the temperature was monitored until it was
found to approach thermal equilibrium. Figure A-5 of Appendix A
demonstrates a typical time-temperature response of the thermocouple
During the period of a full test, other data were taken that
concerned the operation of auxiliary equipment associated with the
experiment. Some of these data were the mixing chamber pressure, gas
bottle pressure, cooling water temperature, and room temperature (see
Figure A-6 of Appendix A). In addition, the plasma generator current
and voltage were also monitored to assure their continuous steady
The entire test procedure from initial "starting" of the
plasma to the final shut-down of all equipment would consume between
14 and 20 hours, depending on the number of variations in base plate
voltage that were used. This was reflected in the time required to
obtain the Langmuir probe photos and floating potential measurements.
Since the stagnation pressure and temperature measurements were not
affected by the base plate potential, the total time required to take
these measurements was essentially constant for any test.
RESULTS AND DISCUSSION
Following is a presentation and discussion of the results of
three tests. For convenience they are designated as Test I, Test II,
and Test III. Each test on its own merit contributes information to
the desired objectives set forth in the investigation. The controlled
conditions for each test are shown in Table A-i of Appendix A. A dis-
cussion of the results for each test follows.
Both Tests I and II were performed using argon as the test gas.
The primary objective of Test I was to determine the variation of elec-
tron temperature, electron density, and floating potential measurements
throughout the jet and surroundings as a function of base plate voltage.
The initial intent was to obtain data corresponding to three different
values of base plate voltage:
(1) Weak field without any visible discharge on the plate.
(2) A strong field with the maximum base plate current pos-
sible without a short circuit from the base plate to
(3) A condition between (1) and (2) above.
The results of condition (1) showed that there was no change
in the Langmuir probe characteristic from the condition of the base
plate floating for any plate voltage below the minimum value of voltage
required to sustain a visible discharge on the plate. Throughout this
range of voltage, the base plate current was very low, 2 ma or lower,
and the base plate voltage was lower than 10 volts. One might have
expected a distortion of the electron density distribution of the jet
(effect upon the electron diffusion), at least near the nozzle exit,
corresponding to the higher base plate voltages. However, for the par-
ticular configuration herein tested, the resulting electron temperature
and density points in the jet did not vary with changes in base plate
voltages if the value of the voltage was below that required for break-
down to discharge on the base plate.
Having found that result from comparison of Langmuir probe
characteristics for condition (1) of Test I, the experiment was contin-
ued under the restricted conditions of discharge on the plate which
satisfied the aforementioned conditions (2) and (3) of Test I. Under
conditions (2) and (3) (threshold of secondary glow discharge appear-
ing on the base plate), the current was found to be greater in sensitiv-
ity than the base plate voltage by at least an order of magnitude. Thus,
the base plate current was used as a control condition instead of the
base plate voltage. Data were taken with the base plate current set
at 100 ma, 50 ma, and 0 ma throughout Test I. The respective voltages
were recorded as dependent variables. The setting for 0 ma corresponded
to the condition of the base plate floating.
The resulting Langmuir Probe Data for Test I are shown in
Figures 14 through 21.
The most dramatic result from the effect of the applied base
plate potential was the increased electron temperature in the region
near the nozzle exit where the effect of the base plate had its greatest
influence in accelerating the electrons, thus increasing the electron
temperature. The resulting average electron temperatures at a dis-
tance of 2 mm from the nozzle exit were 12,6000K, 11,6000K, and9,7000Kfor
corresponding base plate currents of 100 ma, 50 ma, and 0 ma, respec-
tively. As would be expected, the electron temperatures decayed with
increasing distance from the nozzle exit. At 30 mm from the exit, the
average electron temperatures decreased to 80000K, 72000K, and 63000K,
An additional effect of the applied base plate potential was
the reduction of the electron density along the jet centerline in the
region near the nozzle exit. This phenomenon is explained by the fact
that the applied base plate potential increased the radial diffusion,
thereby reducing the electron density at the centerline of the jet.
This effect could be observed easily in the Langmuir probe character-
istic directly on the oscilloscope as the base plate current was changed.
This is illustrated in Figure B-2 of Appendix B in a typical display of
the reduction of the electron saturation current to the probe, Ipr'
with an increasing base plate current. The governing equation used
to calculate the electron density corresponding to the Langmuir probe
characteristic is given by the proportional relation
Since I decreased and T increased with a corresponding increase in
base plate current, the reduction of n with the applied base plate
potential would be expected.
The effect of varying the applied base plate potential with
respect to reduction of the centerline electron density can be seen
in Figure 18. Near the nozzle exit there is an approximate 10 percent
reduction of n with the base plate current at 100 ma compared to the
case of the base plate floating (0 ma). The influence of the base
plate potential decreases with distance as shown by the convergence
of the data.
Near the nozzle exit, the decay of n along the centerline did
not follow the theoretical predicted monotonic decay as predicted by
Equation (2-27) of Section 2.4. In fact, the value of n remains
fairly constant in the region close to the I: zzle exit, up to about
16 mm, before a monotonic decrease in n occurs. The same trend
appeared for all values of base plate current used in Test I. This
point will have additional discussion after the discussion of Test II.
Radial distributions of the electron density for conditions
(2) and (3) of Test I are shown in Figures 19 through 21. Best fit
curves were drawn through the data. The accuracy of the data fit to
the theoretical predictions will be further discussed after the dis-
cussion of Test II.
From the results of the electron temperature and density data
from Test I, two important results were evident and worth further
(1) At any particular value of Z, there was no substantial
difference in the electron density radial distribution
with variations of the base plate current except on the
centerline of the jet, within 10 to 15 mm from the
(2) Corresponding to (1) above, the reduction of the center-
line electron density was about 20 percent as a result of
the 100 ma base plate condition compared to the 0 ma base
plate condition. Also the centerline electron density
did not decrease until the distance from the nozzle exit
was greater than about 15 mm.
The objectives of Test II were concerned primarily with obtain-
ing electron temperature and density measurements such that additional
information would clarify aforementioned results (1) and (2) of Test I.
The maximum base plate current was increased from 100 ma to 160 ma to
check the effect on the radial distribution. A separate centerline test
was run using data point intervals of 4 mm. Also a new Langmuir probe
was manufactured to the same specifications as that used in Test I.
The results of Test II are shown in Figures 22 through 25.
Only two base plate variations were used for this test, 160 ma and 0 ma.
Test I centerline data were obtained at data point intervals
of 7 mm, taken at distances of 2, 9, 16, 23, 30, and 40 mm from the
exit. The data taken at 9 mm were rejected because of a miscalibration
of one of the oscilloscope scales. The rejected data were attributed
to a human error but more important, it was found in error by human
foresight, since a special test procedure had been designed to check
the photographs for precisely this type of accident.
After Test I another test in which helium was used, resulted
in a thermal stress crack of the glass in the glass to metal seal at
the probe tip. Although changing the probe was not particularly desir-
able, it had at least the advantage of providing a comparison with two
different probes manufactured to the same specifications.
Knowing from Test I that the results corresponding to the condition of
100 ma base plate current were not particularly significant with respect
to reducing the electron density at the centerline, it was decided, for
Test II, to use only one base plate condition, 160 ma, and compare the
results of this condition to that of the base plate floating (0 ma).
The results of the centerline electron density for Test II are
shown in Figure 24. These results support the data from Test I with
regard to the region of constant n near the nozzle exit along the
centerline. Furthermore, it indicates that the maximum value of n may
occur slightly downstream of the nozzle exit instead of at the nozzle
exit. Figure 25 shows the results of the radial distribution of the
electron density. Equation (2-25) was fit through the data at Z=2 mm
with the proper choice of the constant C1, in this case equal to 5.0.
Since the Langmuir probe is more sensitive at the centerline of the
jet, corresponding to higher values of ne, the centerline data points
are more reliable than data points near the edge of the jet. Therefore
the data points near the centerline were used to determine the value of
the constant C1. For a basis of comparison, Figure 26 is a plot of
the centerline electron density distributions taken from the results
of previous investigators, Gaither  and Greene , in addition
to the results of the present investigation. Since the order of magni-
tude varies from one investigation to the other, the data were plotted
on semilog coordinates so that all the data could be plotted on the
same graph for the convenience of comparison.
Compared to the present investigation, Gaither's resulting data
for n are two orders of magnitude less than the results of n in the
present investigation. However, Gaither's experiment employed the use
of wire mesh across the nozzle exit for the purpose of shielding the
jet. He reports exploratory experimental results, with the shield
10 12 -3
removed, yielding electron densities between 10 and 10 cm-
This falls within the same range of values for n found in the present
Greene's resulting centerline distributions of n for the
unshielded jet were three orders of magnitude below the present inves-
tigation. Since Greene's approach to solving the theoretical equation
of the n distribution relied upon normalizing the equation to the
experimental value of n at Z=0, and r= 0, the order of magnitude of
ne would not affect the shape of his resulting theoretical curves for
radial and longitudinal distribution.
Before continuing further discussion of the comparison of the
data and theoretical curves of Figure 26, it is of importance to discuss
the results of the data for Test III. Although this test was conducted
using helium as the gas instead of argon, the results are quite inter-
esting and are plotted in Figures 27 and 28. Helium as the test gas
was very difficult to stabilize, compared to argon. The plasma would
periodically discharge to the anode. This effect would cause the
Langmuir probe characteristic to oscillate. This same condition
occurred with the argon plasma but could be restabilized to a steady
state condition merely by changing the plasma current or the plasma
flow rate. Some limited success in stabilizing the helium plasma was
accomplished by using a very low flow rate. However, at this condition,
the electron density of the jet at nozzle exit was so low that the
Langmuir probe was not sensitive enough to obtain any data. Increas-
ing either the plasma current or flow rate to effect an increase of
the electron density up to the sensitivity range of the Langmuir probe
usually resulted in the plasma breaking into an oscillating, unstable
On rare occasions when the helium plasma could be stabilized,
it would not remain in that state for more than 5 to 10 minutes before
breaking into the unstable condition. There was only one occasion
that was an exception to the short-lived stable condition. On that
occasion the data for Test III were obtained. This did allow enough
time, however, to obtain at least the centerline electron density data
with conditions of the base plate at 0 ma and 25 ma. The results of
the centerline density distribution are shown in Figure 28. The
results of this test indicate electron density increases with distance
to maximum values at Z = 12 mm and Z = 20 mm for the 0 ma and 25 ma
base plate currents, respectively. The centerline electron temper-
ature distributions are shown in Figure 27.
Although the resulting information in Test III is limited to
a centerline test only, it does support the premise that the electron
density does not start an immediate decay at the nozzle exit as
Equation (2-27) predicts. Knowing the experimental results of the
centerline n for the three tests, re-examine the theoretical predicted
Recall Equation (2-27) from Section 2.4
1 a z o 2n
of this equation will result in a monotonic decreasing value of n r=O
with a corresponding increase in Z.
Knowing that D is not really a constant but given by
Equation (2-29) of Section 2.4
Dn = S 1[ +
the value of the ambipolar diffusion coefficient, D ,n will then decrease
with a corresponding decrease in Te, since Tn is approximately constant.
From the data of all tests conducted in this investigation, T decreased
with a corresponding increase in Z. Therefore, the value of C2 would
really decrease as Z increases, being affected of course by the decay
of the electron temperature. The experimental results of the centerline
electron temperature distribution shows a very rapid decay of T within
the first 15 mm after leaving the nozzle exit, at least for all the
tests of this investigation in which a potential was applied to the
base plate. Accounting for this phenomenon and correcting D for
each datum point, a corrected prediction for the rate of electron
density decay near the nozzle exit would be retarded compared to that
predicted by Equation (2-27). This corrected prediction for the
centerline electron density would be closer to the actual experimental
results of this investigation. It is of interest to note that Gaither's
experimental results shown in Figure 26 also indicate a retarded decay
near the nozzle exit as noted by the location of the first few data
points near the nozzle exit. It seems therefore that a probable cause
for discrepancy in theory and experiment lies in the correct evaluation
of the ambipolar diffusion coefficient D A more precise mathemat-
ical description of the diffusion coefficient would result in complicat-
ing the mathematics to such an extent that a closed form solution of
Equation (2-22) would no longer exist if D was not considered to be
a constant. An additional complication that would cause discrepancy in
theory and experiment is the mechanism of sustained ionization in the
jet as discussed in Section 2.3. In Test III using helium, the results
of the centerline electron density, as shown in Figure 28, demonstrate
the possibility of sustained ionization in the jet near the base region.
Note that the maximum point of electron density occurs at approxi-
mately 20 cm and 12 cm for the conditions of a +10 volt base plate
potential and floating base plate, respectively.
Presuming that some ionization does persist in the base region
close to the nozzle exit when the electron gas is at its highest energy
level, the increase of the electron density caused by sustained ioniza-
tion would be counteracted by the mechanism of a high diffusion rate
in this region where the electron temperature is at its highest value.
Various combinations of diffusion and ionization rates could produce
the resulting centerline electron density to remain constant or possibly
increase with Z instead of a nr-notonic decay from the nozzle exit.
The results of the helium centerline electron density distribution are
more dramatic than the results of Tests I and II using argon in demon-
stration of this possibility.
Considering the mechanism of diffusion for argon and helium,
the mobility of the helium plasma is approximately five times greater
than for argon , which would yield a greater radial diffusion rate
for the helium than for that of the argon. Prediction of the electron
centerline density as a result of the diffusion mechanism alone would
result in a faster decay of the helium centerline density compared to
that for argon. Presuming the importance of the metastable states
of helium to supply the mechanism for the sustained ionization of the
jet, coupled with a high diffusion rate near the base plate, the
centerline electron density distribution could increase as a function
of axial distance if the diffusion mechanism dominated over the sustained
ionization rate near the exit, and then gradually lost its influence
over the sustained ionization mechanism as the jet proceeded further
into the test section. By the appropriate combination of these mechan-
isms, ionization and diffusion, one could expect the results of the
centerline electron distribution as shown in Figure 28. The maximum
point of the electron density occurs at approximately 20 cm and 12 cm
for the conditions of a +10 volt base plate potential and floating base
plate, respectively. Because of the increased energy of the plasma
with the applied base plate potential, the probability of sustained
ionization is greater than the condition of the base plate floating
and could account for shifting of the maximum point of the electron
density distribution to a position further downstream.
The results of the centerline electron temperature distribu-
tions for Tests I, II and III are shown in Figures 17, 23, and 27,
respectively, and the radial electron temperature distributions for
Tests I and II are shown in Figures 14 through 17. Best fit curves
through the centerline electron temperature data indicate a monotonic
decay as a function of Z, the longitudinal distance along the center-
line, for all three tests. Results of the radial electron temperature
distributions indicate that T remains constant for fixed values of Z;
the straight lines through the data are the arithmetic averages of the
electron temperature with Z as a parameter. This assumes that T is
constant in the radial direction for any fixed value of Z for which
data were obtained. This assumption conforms to the results found by
previous similar investigations [13,14]. The maximum deviation of any
datum point from the average did not exceed 15000K or 15 percent for
average temperatures above 10,0000K and did not exceed 10000K for
average temperatures below 10,000K.
Since radial electron temperature measurements from the Langmuir
probe characteristic were restricted, as a result of probe sensitivity,
to the region within the jet, it was not possible to obtain electron
temperature data in the quiescent region. A previous investigation of
Greene , however, in which data were obtained outside the jet,
yieldsexperimental results that indicate the continuation of constant
radial electron temperatures as far out as 4 mm beyond the edge of a
6 mm radius nozzle under similar test conditions with argon used as the
test gas. In fact, there does not appear to be any trend toward increas-
ing or decreasing radial electron temperatures, even in cases where
data were reported by Greene at a distance of 10 mm from the centerline.
Thus constant T in the radial direction within the jet and out into
the quiescent region surrounding the jet is assumed and used in the
determination of the plasma equipotential curves throughout the
quiescent region. The consequence of the assumption relative to the
results obtained in this investigation is discussed in the following.
Equation Q3-18) of Appendix B yields the resulting expression
for the potential difference between the floating potential and the
where the term [kT /2e] kn [2m./nm ] is the correction factor to convert
e 1 e
the floating potential to the plasma potential, presuming that T is
known for each data point. The previously discussed assumption of
constant T for the radial temperature distribution outside the jet,
within the quiescent region, was used here. The results of the calcu-
lations for Test II are shown in Table B-1 of Appendix B. Best fit
smooth curves were drawn through the data plots of voltage as a func-
tion of Z with r as a parameter. This was done for 19 radial positions
in each condition of the base plate in each test. Samples of two of
The same procedure was performed for Test I. However, the dis-
cussion here is concerned with Test II, since the base plate current was
the highest in this test and the centerline electron density and temper-
ature distributions were determined from more than twice as many data
Since curves were drawn for every value of where data were
taken, this amounts to 19 curves for each value of base plate voltage,
resulting in a total of 57 curves for Test I and 38 curves for Test II.
the curves are in Figure B-4. Values for equipotential lines were then
selected for a field plot. Before doing so, however, the equipoten-
tial values were adjusted to a common datum where the case of the base
plate floating was taken as 0 volts. This was done to provide data that
could be easily compared rather than attempt to plot raw data from differ-
ent tests. The resulting normalized equipotential curves for Test I
and Test II are shown in Figures 29 and 30, respectively. The values
shown on these equipotential curves will be referred to as the corrected
Recall the results of constant radial electron temperature distri-
butions for any particular value of Z (see Figure 22 of Test II), and
the assumption of continued constant temperature beyond the edge of the
jet into the quiescent region. With an applied base plate potential
the entire base plate is at an equipotential value. Therefore it would
be expected that close to the base plate the equipotential curves of
the corrected plasma potential would be parallel to the base plate.
This indeed is demonstrated here (see Figures 29 and 30) with refer-
ence to the equipotential curves close to the base plate. As a check
on this result, a similar equipotential plot was made from the original
floating potential data without using the correction for T Although
the curves were somewhat similar in shape, the equipotential curves
close to the base plate were not parallel, but, in fact, sloped upward
at an approximate angle of 45 degrees relative to the plane of the
base plate. In the quiescent region, had the electron temperature been
a function of r, the equipotential curves near the base plate of
Figures 29 and 30 would not be parallel to the base plate under the
condition of an applied base plate potential. This observation provides
additional justification for the aforementioned assumption that the
radial electron temperature remains constant well out into the quiescent
region. Thus, this investigation revealed that the effect of the con-
stant radial electron temperature was demonstrated over a distance of
about 12 mm beyond the inside nozzle edge which is the equivalent length
of one nozzle diameter. Therefore the information from the equipoten-
tial curves of corrected plasma potential adds additional insight into
the behavior of the charged particles once they have diffused out of
Attempts to obtain equipotential curves of the corrected plasma
potential inside the jet resulted in meaningless and sometimes contra-
dictory data. Because the jet was comprised of a plasma with higher
electron densities at or near that of glow discharges, it would not be
expected to sustain fields greater than about 1 volt/cm . The
resulting data in this region were scattered to such an extent that it
was not possible to define the locus of equipotential curves. Previous
investigations  reported the same difficulty within the unshielded
jet. Because of the reduced measuring sensitivity and the weak field
in this region, any disturbance of the plasma by the probe would be
A computer program was used for the calculation of the velocity
distributions. The results are shown in Appendix A. The calculation
of the velocity at each point was obtained by using pressure and tem-
perature data in one-dimensional gas dynamic flow equations .
The apex of core was found to be somewhere between 40 and 60 mm above
the nozzle exit for both Tests I and II. Previous investigations 
indicate the core length of 4 to 5 nozzle diameters based on formula-
tions of Schlichting . That range would correspond to 48 to 60 mm
in the present investigation. The approximate length of the core could
be determined from the original stagnation pressure data curves. Corre-
lation of these data to the resulting calculated velocities indicated
that the ratio of V/V was 0.95 or above in the core region. Also,
from the original data of stagnation pressure, an estimate of the spread
of the jet was obtained. For both Tests I and II this spread was
between 3 and 4 degrees. The determination of this is shown in
Figure A-4 of Appendix A.
For Tests I and II an initial boundary layer thickness of approx-
imately 2 mm was observed. This value is within reasonable range of
that reported in , 2.3 mm, using the same size nozzle and within the
same range of the Reynolds number, 500 to 1000, thereby corresponding
to laminar flow (< 2300 for tube flow).
CONCLUSIONS AND RECOMMENDATIONS
This investigation has provided some additional information of
charged particle behavior in weakly ionized plasma jets. From the
results of the data and calculations obtained from this investigation,
the following conclusions were derived:
1. A condition of base plate potential below that required
to sustain a discharge on the base plate (approximately + 10 volts)
has no effect on the electron density or temperature distributions
throughout the jet.
2. For both argon and helium, under the condition of a sus-
tained discharge on the base plate (+ 10 to + 20 volts), near the
nozzle exit, the resulting electron temperatures are observed to be
as much as three times those found with the condition of a floating
3. The aforementioned base plate condition, with a sustained
discharge, results in decreasing the electron density along the center-
line near the nozzle exit, as much as 50 percent for argon and 75 per-
cent for helium.
4. Metastable atoms of the plasma appear to be an important
factor in sustaining ionization in the jet, as far as two nozzle diam-
eters past the nozzle exit, when using helium. Some evidence of the
sustained ionization seems likely in the argon but supporting experi-
mental evidence of this is not as strong in the case for argon as that
5. The need for including the effect of sustained ionization
and variable ambipolar diffusion coefficients are important in develop-
ing valid analytical predictions of the electron densities along the
6. Potential data, obtained from floating potential measure-
ments by the Langmuir probe, indicate an alteration in both geometrical
shape and values of equipotential curves is obtained in the quiescent
region of the jet, when the condition of a sustained discharge is main-
tained on the base plate, compared to the condition of a floating
From the results of this investigation, the following areas of
research for future investigations are suggested:
1. A helium plasma jet should be further investigated, espe-
cially in regard to designing an appropriate plasma generator and test
section that would allow maintaining the helium plasma in a stable
condition. If this could be accomplished, additional investigations
of sustained ionization and its relation to centerline electron density
could be undertaken.
2. Higher electron densities (> 10 cm ) should be investi-
gated, especially in the argon plasma, since evidence from the present
investigation indicates sustained ionization in argon may be important
in the prediction of electron density distributions at a higher range
of electron density than used in the present study.
3. A larger cross-sectional area nozzle should be used so
that the Langmuir probe will cause less disturbance to the jet flow
field. With a larger cross-sectional area a double probe could also
be used effectively. Comparison of data from both single and double
probes could be studied to investigate the effect of the probe on
4. Improved techniques of data reduction should be developed
such as incorporation of a differentiating circuit and a log amplifier
to read out the Langmuir characteristic directly in a more convenient
5. A redesign of the base plate structure, allowing it to be
movable in the axial direction, would better allow investigation of
electron temperatures and densities as a function of both base plate
potential and position.
6. From the experimental results in the present and similar
previous investigations, a theoretical study of possible analytical
relationships of ambipolar diffusion coefficients and measured jet
parameters should be investigated.
Figure 1. Overall View of Plasma Laboratory
Figure 2. Overall View of Experimental Apparatus
/ AND FLOW CONTROL
To Vacuum Pump
Gas Flow Schematic
Figure 4. Plasma Generator
n2l l -- -r ,
Figure 5. Plasma Generator Schematic
Figure 6. Argon Jet with Base Plate at Floating Potential
Figure 7. Langmuir Probe in Argon Jet with Base Plate at Floating Potential
Figure 8. Langmuir Probe in Argon Jet with Discharge on Base Plate
Figure 9. Test Section
Figure 10. Probe Position Mechanism
Figure 11. Lucite and Steel Sleeve Connections to Probe Stems
Figure 12. Instrumentation