• TABLE OF CONTENTS
HIDE
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 List of Symbols
 Abstract
 Introduction
 Fundamental considerations
 Experimental considerations
 Results and discussion
 Conclusions and recommendation...
 Gas Dynamics
 Langmuir probe
 Bibliography
 Biographical sketch
 Copyright






Group Title: Electron gas behavior of a weakly ionized plasma jet with the effect of an electric field applied in the base region,
Title: Electron gas behavior of a weakly ionized plasma jet with the effect of an electric field applied in the base region
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00085806/00001
 Material Information
Title: Electron gas behavior of a weakly ionized plasma jet with the effect of an electric field applied in the base region
Physical Description: xii, 154 leaves. : illus. ; 28 cm.
Language: English
Creator: Soderstrom, Kenneth Gunnar, 1936-
Publication Date: 1972
 Subjects
Subject: Plasma rockets   ( lcsh )
Plasma (Ionized gases)   ( lcsh )
Electric discharges through gases   ( lcsh )
Mechanical Engineering thesis Ph. D
Dissertations, Academic -- Mechanical Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 150-152.
Statement of Responsibility: by Kenneth G. Soderstrom.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00085806
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 000582678
oclc - 14161768
notis - ADB1056

Table of Contents
    Title Page
        i
    Dedication
        ii
    Acknowledgement
        Page iii
        Page iv
    Table of Contents
        Page v
    List of Tables
        Page vi
    List of Figures
        Page vii
    List of Symbols
        Page viii
        Page ix
        Page x
    Abstract
        Page xi
        Page xii
    Introduction
        Page 1
        Page 2
        Page 3
    Fundamental considerations
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
    Experimental considerations
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
    Results and discussion
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
    Conclusions and recommendations
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
    Gas Dynamics
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
        Page 124
        Page 125
        Page 126
        Page 127
    Langmuir probe
        Page 128
        Page 129
        Page 130
        Page 131
        Page 132
        Page 133
        Page 134
        Page 135
        Page 136
        Page 137
        Page 138
        Page 139
        Page 140
        Page 141
        Page 142
        Page 143
        Page 144
        Page 145
        Page 146
        Page 147
        Page 148
        Page 149
    Bibliography
        Page 150
        Page 151
        Page 152
    Biographical sketch
        Page 153
        Page 154
        Page 155
        Page 156
    Copyright
        Copyright
Full Text

















ELECTRON GAS BEHAVIOR OF A WEAKLY IONIZED PLASMA JET
WITH THE EFFECT OF AN ELECTRIC FIELD APPLIED
IN THE BASE REGION












By


KENNETH G.


SODERSTROM


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
1972




































TO MIRIAM, KAREN AND KURT--

THIS "BOOK" IS DEDICATED TO YOU
















ACKNOWLEDGMENTS


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

committee.

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-

gettable months.

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


Page


ACKNOWLEDGMENTS . . . .

LIST OF TABLES . . . .

LIST OF FIGURES . . . .

LIST OF SYMBOLS . . . .

ABSTRACT . . . .

CHAPTER

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 . . .


1

4

4
8
11
17
24

29

29
41

48

64

108

115
116

128

129
136

150

















LIST OF TABLES


Table Page

A-i Test Conditions ................... 127


B-1 Plasma Potential Corrected from T and Floating
e
Potential, Test II Argon at 160 ma Base Plate

Current . . . . . . 149

















LIST OF FIGURES

Figure Page

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)


Figure Page

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


viii
















LIST OF SYMBOLS


A = area

C1 = empirical constant for
Equation (2-24)

C2 = constant defined by
Equation (2-28)

D = coefficient of diffusion,
diameter

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,
radial distance

S1 = parameter defined by
Equation (2-30)


= Temperature

= time

= average speed

= axial distance


a = recombination coefficient

y = mobility

e = degree of ionization

e = permittivity of free space
o

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

By

Kenneth G. Soderstrom

August, 1972


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
-5
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.















CHAPTER 1


INTRODUCTION




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

exhaust [3].

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

is significant.

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

probe.

The study of charged particle behavior in plasma jets has been

carried out by several previous investigators. Graf [10] 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 [11]. Inves-

tigation of high density supersonic flows of a plasma jet have been

carried out by Igra [12].

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 [13] and Greene [14]. 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.
















CHAPTER 2


FUNDAMENTAL CONSIDERATIONS




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 [15].

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 1












[ e kT 2
= 2 (2-1)
e (n +n.)
e I


which simplifies to


/ IkT
D = 6.64(102) (2-2)
e


where AD is the Debye length in units of cm, kT is the electron
ij e

temperature in units of eV, and n is the electron density in units
-3
of cm

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-

11 -3
tion yielded a lowest value of n = 10 cm and the highest value of
e

T = 13,0000K or an equivalent kT = 1.12 eV. For a conservative
e e

estimate of AD, Equation (2-2) may be approximated as


/ kT
D = 03 e (2-3)
D n
e




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.










-11 -3
Inserting the values of kT = 1.12 eV and n = 10 cm results in
e e
-3 -2
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


4 3
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


2
en
U = / e (2-5)
p me
eo


which simplifies to


u = 5.62(104) 4a (2-6)
p e











where w is the limiting plasma frequency in units of Hz and n is
p e
-3
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
e I

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


4 3
Q r (n -n )e
n_ eE i (2-7)
2 2
4re r 4re r
o o


which simplifies to

-7
E = 6(10 )(n -n.) (2-8)
e I


where E is the electric field in units of volts/cm and (n -n.) is
e 1
-3
the excess charge density in units of cm Consider an electron

12 -3
density of 10 cm and assuming that n exceeds n. by only 1 percent,
e 1
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.
i e


2.2 Plasma as an Ideal Gas

The basic hypotheses [16] necessary to consider a gas as ideal

requires that

(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

distances.

(b) The forces between the particles are negligible except

during collisions.

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

investigation.

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 [13]


n < 7.3T3(108) (2-9)
e


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
12 -3
present investigation, the highest value for n is taken as 10 cm
e

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

[13], 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
1 e

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
i o

within the range 0 5 e 0 1.0 for single ionization. Considering the

17 -3
neutral particle density, n before ionization, of the order 10 cm
Oc












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

4 -1
10 4K, the term cT of Equation (2-13) is of the order 10-1 and becomes
e

negligible in comparison with T since Tn 3000K. This reduces
n n

Equation (2-13) to


P = n kT .(2-14)
o n


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 [17] as


F (2-15)
o r



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


F
E = (2-16)
e


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 [15]. 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 [18], 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 [14] 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
-8
state is of the order 10 seconds [18] 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 [19]. 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

[19]. According to studies of Brewer and McGregor [20] 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 [13],

the metastable effects were not present, or at least not dominant in

the field free jet region. According to Greene's investigation [14],

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 [21] 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 [22] in comparison to diffusion in

effecting the depletion of the charged particle density. Both Gaither

[13] and Greene [14] 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


dn dn.
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
e 1

developed the following relation


dn To\3/2
n = -e3/2 n2 (2-18)
dt o e
r 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 [22], he found the relation


S- T-3/2
e


from which Equation (2-18) was obtained. The reference state,

o
indicated by T is the temperature at which the values of a were
e o
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

expression

n
e 1
n e) (2-19)
eo T 3/2
1 + n ao --) t
eo o T
e


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












n
e = 1 (2-20)
n o
eo T
+ n (e
eo o T q
e z


For a conservative estimate of n /n corresponding to the present
e eo

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
-8 3
a = 10 cm /sec at 3000K was found as the most conservative value
o

reported by previous investigators [22]. Substitution of these values

into Equation (2-20) results in a value of n /n = 0.997. This rep-
e eo

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

regions are:

(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 [13];

(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 [14].

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 [13] and Greene [14].

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
n T
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-

tion.

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
a a

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 [22]. 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)
D r
a


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

core velocity.

(c) T is considered constant in the radial direction, observed
e
from experimental results, thus aT /or = 0.
e













(d) Axial variation of n is negligible compared to radial

variation of n observed from experimental results,
e
thus an /3r >> n /6Z.
e e
(e) D is only a function of electron temperature, thus, from
a
criterion (c), Dn becomes a function of Z only. Therefore,
a
the term q /D of Equation (2-22) to be defined as 1/f(Z)
z a
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 [14] used a similar approach with the same criteria set

forth by Gaither except he imposed the limitation that Dn was approx-
a
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











2
r Cr



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)
o


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

in

exp [-1.442+1 1.44
nIO = exp (2-27)
C 1C2Z +1 C1C2Z +1


where C2 is a constant given by
21












4C Dn
C2 (2-28)
q R
zo


since Dn is considered a constant. Equation (2-27) therefore predicts
a

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-

n
portional to D the density ambipolar diffusion coefficient and

inversely proportional to q the magnitude of the jet core velocity.
z
An expression for D was developed by Gaither [13] based on the
a

Einstein relation D. = y. kT./e. His resulting expression for D is

given by


Dn = S 1 + (2-29)
a [ + J
n


where S1 is defined by


T3/2
1T
46k o n
SI -e Y+ P (2-30)
n


in which k/e has units of volts/oK, y is the ion mobility and has units
2
of cm /volt-sec, T has units of oK, and P has units of mm Hg.
n n
2 o
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


T
n e
D M S -- (2-31)
a 1 T
n













since T /T is of the order 10 or greater. In an order of magnitude
e n

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
a
2 2
order 10 cm /sec. Since helium has a value for ion mobility approx-

imately five times that for argon [27], the diffusion coefficient will
5 2
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 [28], commonly referred to in the literature as the Langmuir probe.

The fundamental requirements or assumptions in classical probe

theory are as follows [29]:

(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
I pr
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 << ,
1 pr
where d. is the ion sheath thickness, D is the diameter of the probe
1 pr
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 [29] as


3/4
d. = 3 (2-32)


8 7 e
0



which is based on the Child-Langmuir law for space charge limited ion

current density where jis may be expressed as



e FeW
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)
nio e


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
-3
cm and kT is the electron gas temperature in units of eV.
e

A conservative estimate of d. for the present investigation
1
-11 -3
based on values of n. = 10 cm T = 50000K, and C = 10 volts,
1o e
-2
results in a value for d. in the order of 10 mm. Comparison of d.
1 1
-2
with D yields the result 102 mm << 0.65 mm which satisfies the
pr

inequality di < Dp, the aforementioned assumption (c) of classical
i pr

probe theory.

French [11] 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 [29], 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 [11] and

Graf [10]. Conservative estimates yielded the results of e = 1 mm,
e-n

e = 120 mm, and \ = 40 mm. The value of the electron-neutral mean
e-i ee

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.
pr

Since French concluded that there was no appreciable plasma disturb-

ance from the probe when D > X, the present investigation, at worst,
pr













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-
i pr
-2
gation, since, as a conservative estimate, d. is of the order 10 mm
1

and D is of the order 1 mm.
pr

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 [11] 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
I e
that is definitely met in the present investigation with T./T < 0.1
1 e

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

12 -3
for measurements, since only ion densities of 10 cm and less were

present--too low to provide ion currents large enough for direct








28




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.















CHAPTER 3


EXPERIMENTAL CONSIDERATIONS




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

experiment.

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

outside atmosphere.

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

situation.

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

recording instrumentation.

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

purposes only.











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

loops.

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

cathode.











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 test.

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-

istic.

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

plate voltage.

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-

tudinal locations.

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

probe.

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

state operation.

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.














CHAPTER 4


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

the jet.

(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,

respectively.

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


I
pr
n {
eo T
e

Since I decreased and T increased with a corresponding increase in
pr e

base plate current, the reduction of n with the applied base plate
eo

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
e

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
e

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
e

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

investigation.

(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

nozzle exit.

(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 [13] and Greene [14], 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
e e











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

investigation.

Greene's resulting centerline distributions of n for the
e
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
e

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

condition.

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

distribution.











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
a

Equation (2-29) of Section 2.4




Dn = S 1[ +
a T



the value of the ambipolar diffusion coefficient, D ,n will then decrease
a'

with a corresponding decrease in Te, since Tn is approximately constant.

From the data of all tests conducted in this investigation, T decreased
e

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
a

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-
a

ical description of the diffusion coefficient would result in complicat-

ing the mathematics to such an extent that a closed form solution of

n
Equation (2-22) would no longer exist if D was not considered to be
a

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 [27], 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;
e

the straight lines through the data are the arithmetic averages of the

electron temperature with Z as a parameter. This assumes that T is
e

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 [14], 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
e

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

plasma potential




e



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,
e

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
points.
**
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

plasma potential.

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
e
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

the jet.

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 [13]. 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 [13] 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

magnified.

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 [30].











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 [13]

indicate the core length of 4 to 5 nozzle diameters based on formula-

tions of Schlichting [31]. 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,
c

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 [14], 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).
















CHAPTER 5


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

base plate.

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

for helium.

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

jet centerline.

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

base plate.

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.
12 -3
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

plasma disturbance.

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

semilog form.

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



























" fb
lip0



0 0
i L-r
7-7c






































Figure 2. Overall View of Experimental Apparatus








70














EXHAUST
HOUSING


TWO-STAGE REGULATOR
/ AND FLOW CONTROL


VACUUM
VALVE




To Vacuum Pump


TEST
SECTION


BALANCE
CONTROL
VALVES


SETTLING
CHAMBER


HIGH PRESSURE
GAS TANK


MIXING '
CHAMBER


Gas Flow Schematic


Figure 3.






































Figure 4. Plasma Generator









73




n2l l -- -r ,







































































Figure 5. Plasma Generator Schematic




























Figure 6. Argon Jet with Base Plate at Floating Potential










































I











































cr,

























Figure 7. Langmuir Probe in Argon Jet with Base Plate at Floating Potential

















m


























Figure 8. Langmuir Probe in Argon Jet with Discharge on Base Plate













































































0
0~c






































Figure 9. Test Section




82


I -


11 ,Jr




































Figure 10. Probe Position Mechanism








84



























































::r wWOO


























Figure 11. Lucite and Steel Sleeve Connections to Probe Stems










































s



















~7r

;t
2--r*Ps,

















oo




























Figure 12. Instrumentation



















































300










,"OD




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs