Title: Electron gas behavior in the base and mixing regions of a weakly ionized plasma flow at an abrupt increase in cross section
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Title: Electron gas behavior in the base and mixing regions of a weakly ionized plasma flow at an abrupt increase in cross section
Physical Description: xii, 98 leaves : ill. ; 28 cm.
Language: English
Creator: Greene, Charles William, 1939-
Publication Date: 1968
Copyright Date: 1968
 Subjects
Subject: Controlled fusion   ( lcsh )
Plasma (Ionized gases)   ( lcsh )
Mechanical Engineering thesis Ph. D
Dissertations, Academic -- Mechanical Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
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Thesis: Thesis - University of Florida.
Bibliography: Bibliography: leaves 93-97.
Additional Physical Form: Also available on World Wide Web
General Note: Manuscript copy.
General Note: Vita.
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Bibliographic ID: UF00097797
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: alephbibnum - 000565891
oclc - 13591221
notis - ACZ2314

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ELECTRON GAS BEHAVIOR IN THE BASE
AND MIXING REGIONS OF A WEAKLY
IONIZED PLASMA FLOW AT AN ABRUPT
INCREASE IN CROSS SECTION









By
CHARLES WILLIAM GREENE


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
L" PARTIAL FULFILLMENT OF TIE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY










UNIVERSITY OF FLORIDA
1968


























With deep appreciation of her patience,
sacrifice, and constant encouragement,
this dissertation is dedicated
to my wife, Rebecca.











ACKNOWLEDGEMENTS


The author wishes to express his sincere appreciation

to his advisor, Professor R. B. Gaither, for his suggestions,

guidance, and encouragement, not only during the preparation

of this dissertation but also throughout his entire graduate

program.

He is also indebted to Professor W. O. Smith who

designed and constructed the power supply used in this

research project and who gave freely of his time and ideas

during the past three years. Particular thanks are offered

to Professor R. K. Irey for his cooperation, suggestions,

and constant interest during the course of this investiga-

tion. Thanks are also expressed to Professors T. D. Carr
and R. G. Blake who graciously served on the author's

graduate committee as representatives of the Physics and

Mathematics Departments, respectively.

The author appreciates the assistance of Professor

E. P. Patterson and Messrs. R. T. Tomlinson, J. M. Morris,

and V. D. Lansberry of the Mechanical Engineering Depart-

ment Laboratories whose skills and suggestions greatly aided

progress during construction of the experimental apparatus.

Thanks are due to Mrs. Jacqueline Ward for her coop-

oration and suggestions during the typing of this manuscript

and to Mr. Paul Weber for his help in the conducting of the

final experiments.


iii








TABLE OF CONTENTS


ACKNOWLEDGEMENTS . . . .

LIST OF FIGURES . . . .

LIST OF SYMBOLS . . . .


Page

. . . . . iii

. . . . . vi

. . . . . viii


. . . . . . . . . . x i


ABSTRACT

CHAPTERS


1. INTRODUCTION


2. THEORETICAL CONSIDERATIONS . . . . 4

2.1 Plasmas . . . . . . . 4
2.2 Jet Flow Structure . . . . 6
2.3 Ionization and Recombination . .. 9
2.4 Equilibrium and Continuum
Considerations . . . . . 16
2.5 Plasma Properties and Equation of
State . . . . . . . 19
2.5.1 State Properties and Equation of
State . . . . . . . . 20
2.5.2 Transport Properties . . . . 21
2.6 Langmuir Probe Theory . . . . 28


. . . 33


3. THEORY OF THE EXPERIMENT . .

4. EXPERIMENTAL CONSIDERATIONS


4.1
4.2
4.3


Description of Experimental Apparatus
Preliminary Testing . . . . .
Experimental Procedure . . . .


5. DISCUSSION OF EXPERIMENTAL RESULTS AND
COMPARISON WITH THEORY . . . . .

6. CONCLUSIONS AND RECOMMENDATIONS . . .

FIGURES 1-25 . . . . . . . . . .

APPENDICES

A. SUMMARY OF PHYSICAL DATA FOR ARGON . .
B. THEORETICAL CONSIDERATIONS FOR THE
DETERMINATION OF MEAN FREE PATHS . . .
C. ESTIMATE OF UNCERTAINTIES INVOLVED IN THE
MEASUREMENT OF ELECTRON NUMBER DENSITIES


52


61-84












BIBLIOGRAPHY . . . . . .

BIOGRAPHICAL SKETCH . . . .


Page


. . . . 93

. . . . 98











LIST OF FIGURES

Figure Page

1. PLASMA GENERATOR . . . . . . ... 61

2. THE AXIALLY SYMMETRIC JET . . . . .. 62

3. SCHEMATIC OF GAS FLOW ASSEMBLY . . . .. 63

4. EXPERIMENTAL TEST FACILITY . . . . .. 64

5. PLASMA GENERATOR AND TEST SECTION . . .. 65

6. PLASMA JET . . . . . . . . . 66

7. SCHEMATIC DIAGRAM SHOWING LANGMUIR PROBE
CONSTRUCTION . . . . . . . . 67

8. LANGMUIR PROBE CIRCUIT . . . . . .. 68

9. TYPICAL LANGMUIR PROBE CHARACTERISTIC . .. 69

10. SEMI-LOG PLOT OF LANGMUIR PROBE CHARACTERISTIC 69

11. DIMENSIONLESS VELOCITY PROFILES IN THE INITIAL
REGION OF AN ARGON PLASMA JET FOR TEST I . .. 70

12. RADIAL ELECTRON TEMPERATURE DISTRIBUTION IN
ARGON PLASMA JET FOR TEST I . . . . .. 71

13. AXIAL ELECTRON TEMPERATURE DISTRIBUTION IN ARGON
PLASMA JET FOR TEST I . . . . . .. 72

14. RADIAL ELECTRON DENSITY DISTRIBUTION IN ARGON
PLASMA JET FOR TEST I . . . . . .. 73

15. AXIAL ELECTRON DENSITY DISTRIBUTION IN ARGON
PLASMA JET FOR TEST I . . . . . .. 74

16. DIMENSIONLESS VELOCITY PROFILES IN THE INITIAL
REGION OF AN ARGON PLASMA JET FOR TEST II . 75

17. RADIAL ELECTRON TEMPERATURE DISTRIBUTION IN
ARGON PLASMA JET FOR TEST II . . . . .. 76

18. AXIAL ELECTRON TEMPERATURE DISTRIBUTION IN
ARGON PLASMA JET FOR TEST II . . . . .. 77

19. RADIAL ELECTRON DENSITY DISTRIBUTION IN ARGON
PLASMA JET FOR TEST II . . . . . .. 7S

20. AXIAL ELECTRON DENSITY DISTRIBUTION IN ARGON
PLASMA JET FOR TEST II . . . . . .. 79








21. RADIAL ELECTRON TEMPERATURE DISTRIBUTION IN
ARGON PLASMA JET FOR TEST III . . . .. 80

22. AXIAL ELECTRON TEMPERATURE DISTRIBUTION IN ARGON
PLASMA JET FOR TEST III . . . . . .. 81

23. RADIAL ELECTRON DENSITY DISTRIBUTION IN ARGON
PLASMA JET FOR TEST III . . . . . .. 82

24. AXIAL ELECTRON DENSITY DISTRIBUTION IN ARGON
PLASMA JET FOR TEST III . . . . ... 83

25. VARIOUS DETERMINATIONS OF THE COLLISION CROSS
SECTION FOR ARGON AS A FUNCTION OF THE ELECTRON
ENERGY AFTER SHKAROFSKY, JOHNSTON, BACHYNSKI (5) 84


vii


Figure


Page











LIST OF SYMBOLS


A = area, argon atom, emperical constant

B = emperical constant

C = Sutherland constant, specific heat

D = coefficient of diffusion

d = differential

Es = electric field vector

e = electron, electronic charge

G = center of mass velocity

h = Planck's constant

j = current density
K = Knudsen number

k = Boltzmann's constant

L = characteristic length of system, length of
cylindrical Langmuir probe surface

Lc = potential core length

Lt = tube length

M = Mach number, molecular weight

m = mass

n = number density

P = pressure

Qc = Coulomb cross section

Qi-j = momentum cross section
Q = local gas dynamic flow velocity

qz = potential core velocity
R = resistance

Re = Reynold's number

Reff = effective nozzle radius


viii






Ro = nozzle radius
r = radial length

rc = potential core radius
T = temperature
t = time

Uo = potential core velocity
u = local gas dynamic velocity in axial direction

Vi = ionization potential

Vp = probe potential

v = velocity

v = speed

X = third body (in collisional process)

z = axial length

o< = recombination coefficient

cK<. = radiative recombination coefficient

S= boundary layer thickness

S = degree of ionization

Q = permittivity of free space

3V = viscosity

- = coefficient of thermal conductivity

A = mean free path, eigenvalue

= viscosity coefficient, mobility

) = frequency

S= density

S= mean particle flux

Subscripts and Superscripts

a ambipolar

c = potential core






e = electron

h = heavy particle

i = ion, ionization

i-j = ith particle scattered by jth particle

n = neutral particle

o = condition at nozzle exit

p = plasma, at constant pressure
r = radial coordinate direction, recombination, radiative

s = probe surface

v = at constant volume

z = axial coordinate direction

+ = positively charged

= negatively charged

* = excited
** = doubly excited









Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the Requirements for the
Degree of Doctor of Philosophy


ELECTRON GAS BEHAVIOR IN THE BASE AND MIXING
REGIONS OF A WEAKLY IONIZED PLASMA FLOW AT AN
ABRUPT INCREASE IN CROSS SECTION

By

Charles William Greene

March, 1968


Chairman: Dr. R. B. Gaither
Major Department: Mechanical Engineering


An experimental investigation is made of the electron

behavior in a weakly ionized argon plasma jet (with an

initial boundary layer) exhausting into a quiescent medium.

The low pressure (1 to 20 mm Hg) subsonic jet, studied

under conditions which are steady but not necessarily

field free, is found amenable zo both theoretical and

experimental analyses.

The flow field of the plasma jet is artificially broken

down into three separate regions: the potential core

region, the jet mixing region, and the developed flow

region. Results obtained in the core and developed flow

regions are in agreement with those obtained by other

investigators. Particular attention is given to the

electron gas behavior in the base and jet mixing regions

due to both normal and superimposed potentials in the base

region. A mathematical model, based on a known initial

election density profile, is developed for predicting elec-

tron number densities within the jet flow.






Detailed velocity, electron temperature, and electron

number density profiles, obtained using conventional gas

dynamic probing techniques, including the Langmuir probe,

are presented.


xii











1. INTRODUCTION


In recent years the particular result of an electrical

discharge, the creation of a plasma, has received consider-

able attention (1) (2) (3).1 Notable among the engineering

applications spurring on these recent studies are plasma

propulsion systems, rocket exhaust and re-entry simulators,
magnetohydrodynamic generators, energy conversion devices,

arc welders, etc.

While basic research in plasmas has been and continues

to be attractive to a large number of investigators (4) (5)

(6), research with a clear objective of obtaining information
in flow systems particularly significant to engineering

design remains somewhat limited. This is particularly true
in situations where the fluid dynamics of a problem are not

fully understood.

A flow situation of this type, which is of considerable
interest in gas dynamics, and consequently in plasma dynamics,
is found in pressure induced flow systems where an ionized

gas proceeds past an abrupt increase in cross section into
a zone where -for some distance the flow is not fully

developed. This includes flows in such common configurations
as free jets, ejector systems, and flows past orifices. In
all of these, the behavior of a neutral fluid in the base

and mixing regions is both difficult to predict and of
considerable engineering significance. If the fluid is a

plasma, the situation is further complicated.



1Underlined numbers in parentheses in the text of this
dissertation refer to references listed in the bi, biography.
Numbers in parentheses refer to equations.












.i'- *.J,-i











.~- C Z





y~~G~L .~






C3' \ 2


Z~o

C



































s CJ
va C, a n


. _...


As -iL


Y_.-- c


\ri;






In the more complex problem of a plasma flow near a

nozzle exit, the current information available is even

more restricted than it is in the pure gas dynamic problem.

Research in this area has been limited to a great extent

by the lack of suitable diagnostic methods and the prohibi-

tively high temperatures involved. Nevertheless, several

noteworthy contributions have been made in this area. Using

Langmuir probe techniques, Gaither (15) investigated the

electron gas behavior in the potential core region of a low

pressure, field-free argon jet flow. Graf (16) 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. Other signifi-

cant studies have been made by Warder (17), Sherman (18),

and Cobine (19). These studies will be considered in more

detail later in this dissertation.

In the following chapter some of the more fundamental

aspects of plasma behavior, especially those of importance

in the configuration under study here, are presented.

These basic considerations form a background for Chapter 3

which deals with the theory of the experiment. Chapters 4

and 5 are concerned with the experimental procedure, results,

and comparison of these results with theory. In Chapter 6

the conclusions drawn from this experiment are presented,

and recommendations for future investigations are set

forth.














































LrLk
It is






S%


2&~.O~. LA ~~c u"






.~ ~ * uJLV -A

(1cC~C 1C~2-


i-


.;-


C-\ C1Gt- \





)jj *




C. -2




5
where ni is the ion number density and nn is the neutral

particle number density. This relation, as expressed here,

is restricted in utility to the case of single ionization

and for neutral plasmas having ni _- ne, where ne is the

electron number density. Since it is possible to have

plasmas of low degrees of ionization as well as plasmas

which are completely ionized, E may vary from zero to one.

It is important to note that 6 is a relative term and does

not depend upon absolute values of the numerical density

terms. Therefore, it is possible to have plasmas of
different densities, exhibiting completely different

properties, with the same degree of ionization. However,
there are many similarities which exist between low and

high density systems, and the investigations of low density
systems where prohibitively high temperatures can be
avoided often lead to generalized results which can be
applied to high density systems (21).

Plasmas may be produced through energization by elec-
tromagnetic, mechanical, nuclear, or thermal means.

Depending upon the method by which the ionization is

produced and/or maintained, the gas may be in either an

equilibrium or non-equilibrium state. In the equilibrium
state, the temperature of the gaseous constituents are

approximately equal and extremely high.

Non-equilibrium plasmas are usually produced by methods
other than thermal and at low pressures and densities where

the gaseous constituents can be maintained at different

temperatures. In low density, electrically energized
plasmas, the electron temperature is usually of the order

of thousands of degrees, while the ion and neutral particle
temperatures are kept at values of a few hundred degrees.
The non-equilibrium character of the plasma is determined
primarily by the strength and configuration of the1 external






field producing the ionization, as well as by the energy
transfer mechanisms between the constituents.

In a DC excited, low pressure gas system, such as the

one under consideration, the plasma is in a non-equilibrium

state. Only the charged particles receive energy directly

from the electric field. The electrons, because of their

low mass and consequent high mobility, receive sufficient

energy to impart to them high velocities and consequently

high temperatures. The ions, on the other hand, because

of their relatively large mass are not as greatly affected

by the applied field, at least in a direct sense.

One very convenient method of experimentally studying

the non-equilibrium plasma as it tends toward a state of

thermal equilibrium is to use an electrode configuration

which permits the plasma to flow to a region remote to that

of the applied external field. As the plasma is caused to

leave the discharge region, the collisional processes in

the plasma tend to cause it to approach a state of thermo-

dynamic equilibrium. As pointed out by Goldstein (21), in

the absence of applied fields the interaction processes that

lead to this equilibrium state are the case of all the
phenomena, whether observable or not, that take place in

the plasma.




2.2 Jet Flow Structure

The electrode configuration chosen for this investigation

is shown schematically in Figure 1. It consists simply of a

stick cathode and an annular anode. This particular configura-

tion has the inherent advantage of forcing all the gas to

flow through the established electric field before proceeding

into the test section. A glow discharge is created in the
plasma generator, and the positive column of this discharge






-j Toicec t.: .



UlOIIS.



:-,ay bo a..tiLi*-'c--'aIi-y ~co.~

t'-e inoto:,tial 2C01: co_

fvclcod roe-.jicn.
na zz- l nc. o 'L1 i, i L U





ni-cclid a. cL i n -Lco '

tile C~aplc.u anaIy6is is id



contains a p o --, nLi aIc co> 0) o ~ D
L - ,l_'10 OL -6 -

0~ n a .1 n u iD C'n \V11a- c 6Z





0a nJO o 6 u, i, d n




cox 111 c~~ 6 a' n --:",; aC;2 Os s. '0



tnce fh --%, is C o )D- '






!",'IIL C; 2L Ol-S C










C;






where Ro is the nozzle radius. Clearly, this equation is

suitable only when the initial boundary layer at the nozzle

exit is negligibly small, and the jet flow leaves the

nozzle at a uniform velocity Uo. Otherwise, R is replaced

by an effective nozzle radius Reff, over which the axial

velocity is found to be uniform.

The axial length of the core region at low subsonic

velocities for an axially symmetric plasma flow was

experimentally verified by Gaither (15) to be between 4 and

5 nozzle diameters. One of the objectives of Gaither's

investigation was to determine the core length and its

effect upon the mixing of the plasma components with the

surrounding gases with attention being given to the effect

of core length upon plasma properties.

In the core region of an ionized gas flow, a very

significant effect which occurs is that there is a much

greater lateral diffusion by charged particles than by the
neutral particles. This is primarily due to action by the

electron gas component which possesses an extremely high

mobility (due to light mass and high temperature). The

ion gas component follows in accordance with the ambipolar

effect to be discussed later. Recombination does not

become a significant factor until the electron temperature

nears that of the ions and neutral particles (23) (24).

At the point where the emerging jet flow and the

quiescent fluid meet, a free jet boundary is formed. The

zone between the free jet boundary and the potential core

is called the mixing region. This is a zone of complicated
mass and energy transfer, and,at a sufficiently high Reynolds

number, it becomes turbulent in character. The effects of

this mixing region on the behavior of the charged particle
components in an ionized flow had not been determined prior






to this investigation. The lack of such information
initiated the particular study described herein.

The base region, as shown in Figure 2, is that region

immediately outside the mixing region and near the nozzle

exit.




2.3 Ionization and Recombination

Although the region of most interest in this investi-

gation is the plasma stream after it leaves the discharge

region, it is necessary, in view of future discussions, to

consider briefly the ionization processes occurring in the

plasma generator. The consequent recombination processes

will also be discussed.

The energy necessary for ionization may be imparted to
an atom as it passes through a discharge by an electron

collision, a positive ion collision, a collision with a
high energy neutral atom, the absorption of a quantum of

radiant energy, or by some combination of these. However,
at gas temperatures equivalent to less than one electron

volt, the most important mechanism for increasing the

charged particle population in a gas subjected to an applied

electric field is ionization by electron impact. A neutral

particle will be ionized by an approaching electron if the

combined energies of the two particles, relative to the

motion of the center of mass, exceed the ionization poten-
tial of the gas Vi, i.e.,



L reI I+ .Lpn/' (3)


where me, mrn, v., and vn arc the electron and neut'rnI

particle masses and velocities, respectively (25) (26). G

is the center of mass velocity defined by










^ 777eVe +nrT 7f7'V W
M e Mt VAI

Elimination of G between equation (3) and (4) yields the
following criterion for ionization in a single collision:

2
77e M I (5)
2 (7e + ) (5)

Since mn>> me and (v -' e, this criterion reduces
to the simple relation



T Ve'r > V (6)


Thus, the electron must acquire a kinetic energy in its
acceleration by the applied electric field which is at least
as great as the ionization potential for the neutral gas.
The first ionization potential for argon Vil, i.e.,
the energy required to remove the first electron from an
argon atom, is 15.8 ev, while the second ionization poten-
tial Vi2 is 27.6 ev (27) (28). Each succeeding ionization
potential is correspondingly higher. The probability of
ionization higher than first order in systems at electron
temperatures such as the one under consideration is very
low. Integration of the Maxwellian energy distribution from
15.8 ev to oo shows that less than 0.2% of the electrons
possess energies sufficient to cause ionization for an
argon plasma maintained at 3 mm Hg and exhibiting an
electron temperature of approximately 5,000 K. Under the
same conditions only 0.005% of the electrons possess
energies greater than 27.6 ev. Thus, it is clearly seen






^ nah ^ 0 n ll o^l'-v -0 .. ..-,- ".I-- ,- .
- o -,5 i l


in this invest .aion.






p a s s -nhou a in a
alec-rots do no- bpro.,cA -.iz. -.. . _

01ec'onas are also relatively o J ......'. ,

pass -hrough an atone's sp : 'e o2 i.n-

n. e ec-cron ( ) Th s- .axi: .." .

w',itl'.n an C-, .:C a Cc. o o.-.

i- must bS poin-ed ou i ......

tion greatly exceeds tosc aL 2.

In argon ave:-.go occc'on kineji. -'. _
11,000 X) give rise to c o lls 'll..

ol. 4/cm. A .;2axi:.i:. is no l 3U .

approx :.12ately 1.35 x 10" X, \v. .- ....

o-/c,. (20).
o z- b-, s
o :- ;L 1, 0 r -C

The pr co .i cis .. .. .

- onization by si.'jl-; e .- ..G ....

elec -on havi

ionization r 0 '.- .l ... ..

level abov ..



5..U ...






selection rules of quantum mechanics. Argon has two such
metastable states at 11.5 and 11.7 ev, respectively (18).
Metastable states occur principally in noble gases and have
mean lifetimes of the order of milliseconds. With such

comparatively long mean lifetimes, atoms in metastable
states may undergo several collisions before radiating

spontaneously. Thus, they may lose their excitation energy

through collisions without radiating. Such collisions are

usually referred to as collisions of the second kind.

According to recent studies by Brewer and McGregor (29)

on low density, arc-heated argon flows, there are large

concentrations of metastable atoms present in all such
plasma flows. However, experimental information in this
area is lacking, and no analytical techniques are currently
available that permit accurate determination of the number
densities of metastable atoms in such flow systems. The
most promising technique appears to be through the use of
optical absorption measurements.
In the flow region downstream of the nozzle only weak
field forces are present. This is due to the particular
electrode configuration being used and the fact that a
plasma is incapable of supporting a large potential gradient
(usually less than 1 volt/cm). Thus, further ionization is
essentially negligible. Experimental verification of this
will be presented later.

Allowing that further ionizing effects are not present
in this region, the rate of change of ion and electron

number densities is simply the rate of recombination given

by


dn-e dn (7)
drc dc






where the quasineutrality condition ne c ni is imposed.

4o is the coefficient of recombination. It is a function

of electron temperature, as well as electron density, gas
pressure, and type of gas involved (30).
Experimental values of c< are difficult to obtain

directly in jet flow systems because the electrons are lost

from the jet by both diffusion and recombination. Conse-

quently, most measurements of o( for electron-ion recombina-

tion are made using microwave techniques and probes in the

afterglow of non-flow decaying plasmas (28). The reader

is referred to the works of Biondi (31) and Bates and

Dalgarno (32) for recent developments in experimental

techniques and values for recombination coefficients in

neon and argon. Biondi (31) observed a decaying argon

discharge (P in the range of 1 to 25 mm Hg; Te = 300 K;

ne of the order of 108 to 109/cm3) and found the electron-
ion recombination coefficient to be approximately 10-6 cm3/

sec.

There are several known mechanisms for electron-ion

recombination. The more important ones are enumerated as

follows: (a) radiative recombination, (b) dielectronic

recombination, (c) dissociative recombination, and (d) three
body recombination. In the following paragraphs these
mechanisms are considered separately, with comments as to
their applicability to this investigation.
In radiative recombination, a free electron and a

positive ion undergo a collision in which radiative emis-

sions of energy occur as given by the following reaction
equation


A + eh- A 7. (S)






h is Planck's constant and ) is the frequency associated
with the emitted photon. This reaction has a very small
cross section and is normally of no significance, except
in plasmas of very low densities (18) (28). According to
Papoular (33), the total effective cross section Cr for
such recombination decreases as 1/ve2. He gives a table
of 6, values for several low electron energies, where the
radiative recombination coefficient od is given by


S= e' (9)


Considering a typical set of conditions for the discharge
under investigation where an average value of Te is 5,000 K,
ve is determined to be 1.2 x 106 m/sec. 65 is approximately
1.5 x 10-19 cm3/sec (33). This gives a value of 1.8 x 10-19
cm3/sec for o< which is negligibly small compared to the
recombination coefficient of 10-6 cm3/sec given by Biondi (31)
for a similar argon discharge. Thus, it is highly improbable

that this type of recombination could be present to any
significant degree in the plasma flow system under study.
Dielectronic recombination is represented by the
reaction equation


A + e --- A (10)


In this type of recombination reaction, an electron and a
positive ion undergo a collision in which the two are
bound, with part of the excess energy being absorbed by a
second electron in the neutral atom. This produces a doubly
excited neutral atom A** which is unstable. Under circum-
stances where-reionization does not occur, the excited atom
then proceeds to complete the recombination process, either
by undergoing a radiative transition to a lower energy level





or by transferring the excess energy to other particles
during the collision processes. Dielectronic recombination
coefficients are believed to be generally smaller than
corresponding values for radiative recombination (18) (28).
+
Traces of rare gas molecules, e.g., A2, in argon
discharges have been verified by mass-spectrographic studies

by Tuxen (34). The possible presence of such molecules in

argon plasma flows as well as static discharges leads to
consideration of the mechanism of dissociation recombination.

This mechanism can be described for argon by the reaction

equation


Az + e- Az -v A (11)


The electron initially collides with the molecular positive
ion A2, transforming it into an excited state. A radiation-
less transition then occurs in which the molecular bond is
broken, and the atoms of the excited molecule recede one
from the other. Further de-excitation may then take place

(18) (28). Although possibly present, dissociation recom-
bination has not been reported to be of much importance in
rare gas discharges (18).

Three body recombination can be represented by the
reaction equation


A + e +X A +.X (12)


If an electron encounters a positive ion in the vicinity of
a third body X, it may impart sufficient energy to the
third body to slow it down to where it will readily recon-

binc. The third body may be another particle or a containing
wall. The possibility also exists that turbulence in the
mixing region of a jot flow could provide a psuedo third body.






In gas discharges near and below 10 mm Hgit has been

found that the dominant mechanism for removing the charged

particles from the plasma is ambipolar diffusion (to be
discussed later) (35). Neutralization of these particles

usually takes place at the container walls by three body

recombination. Further comments regarding possible recom-

bination mechanisms in the plasma flow of this study are

presented in Chapter 5.




2.4 Equilibrium and Continuum Considerations

The plasma model adopted in this investigation is that

of a set of charged gases (electron and positive ion) and

a neutral gas mutually penetrating into each other. Par-

ticles of each gas interact with the other particle types

and with each other. The transfers of momentum and energy

during these interactions are the basic microscopic events

governing the plasma's macroscopic properties and leading

to the transport phenomena of diffusion, mobility, viscosity,

and thermal and electrical conduction.

During collisions appreciable kinetic energy exchanges

are made only between particles of relatively equal mass.

Thus, in a plasma the mean energy of the electrons and the
mean energy of the heavy particles are only weakly coupled.

Under circumstances where the velocities of all of the

particles in a plasma are allowed time to randomize, the

heavy particles quickly achieve an equilibrium distribution

with temperature Tn (or Ti, assuming Ti -' Tn) after only

a few collisions with each other. The electrons also achieve

an equilibrium distribution with temperature Te after a few

electron-electron collisions. Thus, .for some period of

time two temperatures exist. In the absence of any selective

accelerating field they will approach a final equilibrium






temperature. The number of collisions required for Te and

Tn to relax to an equilibrium temperature is approximately

equal to the neutral particle to electron mass ratio, i.e.,

approximately mn/me collisions (2).

Complete thermodynamic equilibrium exists in a plasma

system only if all of the components of the system are in

thermal, chemical, electrical, and mechanical equilibrium

with each other as well as within their own species. It

is recognized that this is not the case in the jet flow field

under consideration since finite property gradients exist

in all flow systems. However, since the flow is subsonic

and the particle densities are high enough to support

continuum analyses, these gradients are very small. The

deviation from local equilibrium is then small (15) (18).

The effect of the large difference between the electron and

neutral particle temperatures will be shown later to have

negligible effect on the macroscopic character of the flow.
Thus, the picture of the plasma being studied is that of a

mixture of gases with each component having an equilibrium

(or at least quasi-equilibrium) distribution, characterized

by a temperature T. The densities are such that close energy

coupling between the neutral and ion species exists, but

the coupling between the electrons and heavy particles is

weak.

The assumption of radiation equilibrium is implicit

in the assumption of local thermodynamic equilibrium.

Radiation originates in the system as a result of recombina-

tion of charged particles and de-excitation of excited atoms.

However, the energy contribution due to radiation in systems

at extremely low degrees of ionization is negligibly small

(18)

As a basis for future discussion, it is important to
examine the component gases of a plasma flow to sec whether






they behave as continuous media or exhibit characteristics
having to do with molecular structure. The Knudsen number
K is a measure of the importance of these molecular effects
and is defined by


K = -- (13)


where A is the mean free path of the component gas and
L is some characteristic length of the system. A Knudsen
number of 0.01 is usually taken as the value above which
molecular effects should not be ignored (36), i.e.,


< o0.01 (14)
L

is taken as justification for using a continuum analysis
to describe a flow situation.
For a continuum boundary layer theory to be applicable
in the jet mixing region for both charged and neutral gases,
it is necessary that the appropriate mean free path be
small compared to the mixing region thickness < or


< o0.01. (15)


For this particular investigation the values of both
A and vary with position. Thus, values of K must be
examined near the center of the jet flow and near the outer
edge of the jet mixing region.

According to simple kinetic theory (no field or body
forces being considered) in the scattering of the ith-type
particle by the jth-type particle, the mean free path is
given by


.1. ci ? (16)
i3 j





where the first subscript refers to the particle being
scattered, and the second subscript refers to the
scatterer (27). Qi-j is the cross section for momentum
transfer, and nj is the number density of the jth-type
particle. The V does not appear in the denominator of
equation (16) for electron-heavy particle interactions
because of the large mass differences. A method for
determining the necessary mean free paths has been out-

lined by Graf (16) and is given in Appendix B.
Another method for justifying a continuum flow
hypothesis has been presented by Gaither (15). Following
a procedure outlined by Shapiro (37) and Jeans (38), he
showed that if the boundary layer thickness S was the
smallest characteristic dimension of the system, i.e.,
L = the criterion for continuum flow was given by the
inequality

Ie7 > i00. (17)


Both the Reynold's number Re and the Mach number M are to be
determined at the point of interest in the flow field.




2.5 Plasma Properties and Equation of State
The properties used to describe an ionized gas system
can be conveniently classified into two categories:
1. State properties which describe the system locally.
2. Transport properties which describe the behavior
of the system as regards diffusion, thermal and
electrical conduction, and viscosity.






2.5.1 State Properties and Equation of State
The use of argon as a test gas at low pressures (1 to
10 mm Hg) and at temperatures higher than room temperatures

(approximately 300 K) permits the assumption of ideal gas
behavior (27). However, justification must be given to
permit treatment of the charged particle components as
ideal gases because of the interparticle forces involved.
Requiring that the inertial forces be much greater than
the Coulombic forces, Gaither (15) showed that the charged
particle components may also be treated as ideal gases if
the following criterion is satisfied:

3 8
-<<) 3 Tx I0 ( 8)



T and n are the temperature (in degrees Kelvin) and number
density, respectively, of the component under consideration.
As may be seen, this inequality is easily satisfied for

experimental conditions where the number densities are less

than 1012/cm3 and the corresponding temperatures are at
least a few hundred degrees.
Allowing that each of the component gases can be
treated as an ideal gas, the corresponding equations of state
are given by


?p 3-j~ (19)


where j denotes the jth component, and k is Boltzmann's
constant. Pj is the partial pressure of the component, and
Tj denotes the translational kinetic temperature.
Assuming the ideal gas relation and Dalton's law of
partial pressures to hold for the type of gas system under
consideration, the total pressure of 'the system may be
expressed as








?p^J Tj(20)



or


p= ~knTN + TIT + nT &Te). (21)


For a weakly ionized gas at low pressure, where nn>> ni,
Tn- C Ti, ne ni, and Te < 105 K, the last two terms in
parentheses on the right hand side of equation (21) are
negligibly small compared to the first term. Thus, the
equation of state under such conditions is given by


p=-, -k TN- (22)


It is important to note at this point that although
the gas flow is slightly ionized, this ionization is not
sufficient to appreciably affect the macroscopic character
of the flow. Thus, the flow may be adequately described
in terms of the state properties of the neutral component.
Other state properties may be determined by applying
the appropriate relations for mixtures of ideal gases.
These properties can also be approached with the knowledge
that the charged particle components have very little
effect on their behavior if the degree of ionization is
very small.




2.5.2 Transport Properties
The transport properties of a gaseous medium are those
properties that determine the behavior of the gas as regards
diffusion, mobility, thermal and electrical conduction, and
viscosity. Transport properties arise from the fact that






the component particles of all fluid media are in motion
and constantly interacting with each other. Unlike state
properties, the transport properties are related to the
momentum transport cross sections between the particles.
These cross sections, in turn, are usually complicated
functions of temperature and the interaction mechanisms.
The current difficulties involved in the determina-
tion of transport properties are given by Sherman (18) as
(a) lack of a suitable theory, (b) lack of appropriate
physical section data, and (c) absence of techniques for
carrying out the complex calculations.
Two approaches are commonly taken in determining
transport properties: (a) the exact or formal method, and
(b) the approximate method. The so-called "exact" method
starts with the Boltzmann equation, and the mathematical
difficulties involved are enormous. Thus, only under
certain assumptions and for special cases can any useful
solution be obtained (18). For the purposes of this
investigation only approximate methods will be considered.
Chapman and Cowling (39) invoked the approximate but
simple concept of the mean free path A in establishing
the transport coefficients of a single component monatomic
gas. They expressed the coefficients of diffusion, viscos-
city, and thermal conductivity as follows:


D= 3 (23)




5Tr 777 V, (24)
/ 1 32



^ 777,1 i lRv (25)





where
7= (26)



and = (27)




In these equations v is the mean particle speed, n is the
number density, m is the particle mass, k is Boltzmann's
constant, T is the temperature, and Q is the momentum
cross section.
Fay (2) suggested that the above equations could be
extended to the case of a partially ionized gas by
assuming that the transport of mass, momentum, and energy
within the plasma could be expressed as the summation of
the transports due to each particle species. He suggested
the following summation formulae:



3D3 3T (28)








((30)
T (29)




128 (30)



where .- j (31)

J


Qi-j is the momentum transport cross section for collisions
of ith-type particles with jth-type particles.





Because of their extremely small mass, the electrons
make essentially no contribution to the viscosity of the
plasma as a whole. Thus, equation (29) may be expressed as


/ rr (, + j ), (32)




-1
where + N "=[ O 7"V,0/A 77 i-,)l (33)



and =[ 1i Q )] (34)



For plasmas where the electron temperature is
considerably greater than the heavy particle temperature,
Fay (2) has further suggested that the thermal conductivities
of the heavier and lighter particles be considered sepa-
rately. His final results are as follows:


=-5 Cpz /r (35)





and {e 128 kflS('-eQ e Qc (36)



where the subscript h refers to the heavy ion and neutral
particle components, and the subscript e refers to the
lighter electron component. Cpn denotes the specific heat
of the neutral (or ion) particles. Qc is the Coulomb cross
section for charged particles and is given in dimensional
form as









Q, L.S(O ) 12- (37)


Simplified relations for determining the appropriate momentum
transfer cross sections from cross section information
commonly available are given by Graf (16).
A more practical set of formulae, as far as ease of
numerical calculations is concerned, is given by Powers
(40). He gives the viscosity and thermal conductivity
relations in dimensional form for pure argon as follows:



A,= O.816o(10)7 -39., (Jo- ) 1. 073(/o-) (3s)




and { = 0.18&67/ (39)


For determining electron and argon ion viscosities
and thermal conductivities, the following equations were
given:


0 = .434 (Z10 Zo ) 24 O(10 Te 79Z- (40)



.k-= 0.58 1e- ,( ) 1'r 7, "1 (41)



r =1.17(W61'024 0/7j] (42)








2* = 0 ..2Q( ^ za4t)7 (43)




As the gas of a free jet flow leaves the discharge
region, particle density and temperature gradients are
established within the jet. Because of these gradients

particle diffusion proceeds from regions of higher toward

regions of lower concentration and temperature. The
electrons, because of their comparatively low mass and

consequent high mobility, tend to diffuse faster than the
ions or neutral particles. The ions, on the other hand,
tend to remain behind, thus creating a space charge
region and an electric field. A coupled diffusion process,
known as ambipolar diffusion, results in which the electron
diffusion is decelerated and ion diffusion is accelerated.
Both particle types eventually diffuse with the same
velocity.
The particle density level above which space charge
effects produced by the interaction between electrons and
positive ions becomes important rather than independent
electron and ion diffusion is given by the criterion (41)



7e > (44)


Eo is the permittivity of free space, e is the electronic
charge, and y is a length which is characteristic of the
diffusion region. For the case of free jet mixing, an

appropriate value of y is the boundary layer thickness
across which diffusion takes place.

The equations governing the diffusion of electrons
and ions in the neutral parent gas of a weakly ionized flow
are given by (33) and (35) as









V4 ^V7Z +1A4E, (45)



and a = 7f j = Ve +r/e 1, (46)



where P= nv is the mean particle flux, Es is the electric
field created by the space charge effects, D is the self-
diffusion coefficient, and fr is the mobility of a charged
particle as defined by


/ V--* (47)
/*6 Es

The subscripts e and i refer, of course, to the electrons
and ions, respectively.
Equations (45) and (46) may then be rewritten as


S- (48)




and V = - Vi +e Cs. (49)



If the charge density in the plasma is sufficiently
high for ambipolar diffusion to occur, a quasi-neutrality
condition ne ni then exists. Thus, the net current is
zero, and nivi r_ neve. Thus,



V= D + (Deu,)
SVe - (50)
/tL +14C






The coefficient



= e (51)
1-4 + /e



is known as the ambipolar diffusion coefficient.




2.6 Langmuir Probe Theory

One of the earliest and most useful methods employing
probe measurements for plasma diagnostics was that

employed by Langmuir and Mott-Smith in 1924 (42). The
Langmuir single probe concept has been found useful in
obtaining local measurements of electron temperature,
electron number density, and wall and space potentials.
Although the "classical" Langmuir probe theory is restricted
to stationary and particular types of time-varying discharges,
it is probably the plasma research tool which has provided
the bulk of experimental knowledge to date. Many investi-

gators have used this single probe technique and found the
quantities measured to compare quite favorably with those
obtained by other means (16) (43) (44) (45). Slight
modifications for using the probe techniques in circum-
stances which are outside the limits of the restrictions

of classical theory, e.g., in a strong magnetic field, have

also been developed (46) (47) (48).
The basic theory of Langmuir probes has been outlined
in many writings on the subject. Extensive treatments of

this theory are presented in references (48) (49) (50) (51).
Therefore, only a brief summary of the Langmuir probe and
its operation as pertinent to this investigation will be
included herein.





In the Langmuir single probe method a metallic probe
is immersed in a plasma. The probe is insulated except for
a small area which is exposed to the plasma. An electric
circuit designed so that the probe potential may be varied
with respect to a reference electrode, permits the measure-
ment of probe current as a function of its potential.
Depending upon the voltage impressed, the probe will either
emit or collect current. An analytical interpretation of
the current drawn by the probe as a function of the voltage
applied to it.provides information about the local conditions
in the plasma. The current-voltage curve is usually
referred to as the probe characteristic.

The basic assumptions of classical probe theory are
outlined by Schwartz (48) as follows:
1. The sheath thickness is small compared to any of
the mean free paths in the system under considera-
tion. This permits the region of effective charge
collection to be considered collisionless.
2. The probe diameter is small compared to the mean
free paths in the system.
3. The sheath thickness must be less than the probe
diameter.
4. A Maxwellian distribution of electrons exists at
the sheath edge.
If the electron motion in the plasma is purely random,
as would be the case under the last assumption above, the
electron concentration at the probe surface nes is given by
the kinetic relation



Yes= 7 ep (52)






where nep is the electron concentration outside the plasma
sheath. As pointed out by Gaither (15), when small uniform
field forces are present, this equation differs only by an
additive constant.
The random electron current density to the probe je
s
may then be expressed as



e=e eXtp.- (53)



where the random plasma current density je is given by the
kinetic relation



17ep e Vep
e 4e- V (54)
4



By adding the ion current density to the probe jis to
the electron current density, the total random current
density to the probe can be obtained. However, in the
region of the probe characteristic which is of interest
(the retarding field region) the ion current drawn by the
probe is negligible compared to the electron current. Thus

ji, will be neglected in further discussion.
Taking the natural logarithm of each side of equation
(53), one obtains



(55)




Noting that In(je ) is a constant and differentiating both
sides of this equation with respect to Vp yields










C_ e *(56)
dVP, fTa


Thus, if a graphical plot is made of ln(jes) versus Vp for
the retarding field region, the resulting curve should be
a straight line with slope equal to -e/kTe. If the curve
is indeed a straight line, the original assumption of a
Maxwellian distribution is verified according to theory.
If the curve is not a straight line, the distribution is
either non-Maxwellian or other factors have affected the
resulting curve, e.g., an unclean probe (49) (50) (51).
The electron temperature can then be obtained from
the equation



Te=i.ii0) V (57)



where Te is in degrees K and Vp in volts.
From kinetic theory the average electron speed in a
plasma is given by


1/2
=- (53)
Ve 0e (5S)
P Tr Me



The electron current density in the plasma jep may also be
expressed in terms of the electron current in the plasma

lep and the probe surface area A as



p =P A (59)





By combining equations (57), (58), and (59), the following
relation is obtained for calculating the electron number
density:



.0 (io (60)



where A is in cm2, ie is in milliamps, and ne is in
electrons/cm3. The value of ie to be used in this
p
equation is that corresponding to the plasma potential,
i.e., at the break in the curve of ln(ie ) versus V (19).
Certain criticisms have been levied at the use of
probes to measure plasma properties. Chief among these is
that the insertion of the probe into the plasma alters the
properties to be measured. Other criticisms pertain to the
reflection and secondary emission of electrons by the probe
and to possible thermal electron emission. Extensive
discussions of these possible sources of error are given
in references (48) (49) (50) (51).











3. THEORY OF THE EXPERIMENT


This study is a part of a large scale effort to obtain

a complete solution and understanding of the problem of
charged particle behavior in low pressure plasma flows. The

complete problem involves simultaneous consideration of the

macroscopic character of the flow as well as individual
component behavior. Fortunately, in flow systems such as

the one under consideration for cases of weak ionization,
the macroscopic properties are affected very little by the
fact that the gas is slightly ionized. Thus, these proper-
ties may be examined with the knowledge that the macroscopic

behavior of the jet flow differs very little from that of
an unheated gas flow.

Earlier studies of the process of free expansion of a
gas from a nozzle or orifice have been made by several
investigators using both macroscopic and microscopic view-

points. Pai (10) (11) studied the laminar mixing of neutral

gas flows and was able to obtain complete analytical solu-
tions for the macroscopic velocity and temperature profiles.

Gaither (15) and Graf (16) investigated free expansion

argon plasma jets and were able to determine the charged

particle behavior in the inviscid core and developed
regions, respectively. Thus, the analytical description
of fl,..w processes in the region near the nozzle is essen-

tially complete except for knowledge of charged particle
behavior in the jet mixing and base regions. It is this

author's intent to complete this picture.






In this study considerable effort was expended in the

control and elimination of complexities that might be found

in flow systems outside the laboratory. However, the

complex character of the flow was still such that certain

simplifications had to be made to obtain meaningful infor-

mation. The objective of the work was accomplished using

a relatively simple theoretical model having the following

restrictions:

1. Only three species need to be considered: (a) argon

atoms in the ground state, (b) singly ionized argon

ions in the ground state, and (c) electrons.

2. Each component, as well as the mixture, obeys the

perfect gas equation of state.

3. Local thermodynamic equilibrium is maintained

throughout the jet flow.

4. Radiation effects are negligible.

5. The flow is axisymmetric.
6. The flow is steady.

7. The flow is laminar.

8. Compressibility effects are negligible.

9. The pressure is constant throughout the region of

interest.
10. Specific heats are constant.

11. The boundary layer approximation is valid for the

mixing zone.

12. The average properties of individual components

are appropriately described by classical mechanics

(see Appendix B).

13. Charged particle diffusion takes place as ambipolar

diffusion.

14. There are no externally applied fields (including

gravity), except that of the base region which is

considered separately.





The validity for establishing these restrictions has either
been brought out or will be discussed later in connection
with the experimental results.
In keeping with the aforementioned boundary layer
approximation as it applied to a circular jet mixing region,
the equations of continuity, momentum, and energy for the
axially symmetric laminar mixing of an incompressible fluid
may be written:


a u.. i 3
+_ i v O (61)




z 3r rU r ar/ (62)



L + 4vT- Kr T+ + (63)



u and v are the velocity components in the z and r directions,
respectively. ). is the viscosity, and 1< is the thermal
conductivity.
With no pressure gradients in the flow, a Prandtl
number equal to unity, and constant specific heats, Pai (11)
shows that


T= A u. ut/2Cp. (64)


T is the temperature at a given point in the jet, and u is
the corresponding axial velocity. A and B are constants to
be determined by the boundary conditions.
For the case where the velocity and temperature in the
jet differ only slightly from the surrounding quiescent






medium, Pai (11) uses small perturbation techniques and
the boundary conditions at the nozzle exit, namely

at z = 0: u = uc = constant for 0 6 r = Ro

u = Uo for r > Ro


to obtain the velocity distribution relation



__R, e (Ar) o) (65)
U,



The subscript 0 refers to some reference state, and ?\ is
the eigenvalue determined by the boundary conditions. R
is the nozzle exit radius. Jo and Jl are the bessel func-
tions of zeroth and first order of the first kind, respec-
tively. Thus, the velocity distribution may be plotted
for various values of c(2z, where g2 is defined by



2.U (66)



By introducing the stream function into the equation of
motion, Pai (11) takes a more rigorous approach to obtain
an exact velocity distribution solution for the laminar
case. His final equation can be integrated numerically
using a step-wise finite difference method to give the
velocity distribution. The results of this method and that
of the small perturbation method are shown in graphical
form for various values of o<2x in reference (11).
Of fundamental concern in this investigation are the
spatial variations of electron number density and electron
temperature in the jet mixing and base regions of such a
jet flow field. An extensive investigation of these






parameters in the inviscid core region of a low pressure
argon plasma jet has been made by Gaither (15). He found
the electron temperature in this region to be constant in
the radial direction. In the axial direction the electron
temperature dropped off in an exponential manner. The
electron number density in the radial direction correlated
quite well with his theoretical prediction of behavior as a

Bessel function of zero order. It also dropped off expo-
nentially in the axial direction.
Graf (16) investigated a low density, free-expansion
argon plasma jet and examined the electron density profiles
in the developed region downstream of the core region. The
electron density was found to have a Gaussian radial distri-
bution, while falling off approximately exponentially along
the jet axis. No information regarding the electron
temperature profiles in the jet was given. Neither Graf
nor Gaither relied upon Pai's theoretical model development.
Radial electron temperature profiles in the positive
columns of low pressure discharge tubes have also been found
to be essentially constant (33) (35). The question then
arises as to whether or not such a characteristic is also
maintained throughout the base and boundary layer regions
in a jet flow field. In particular, it is of interest to
know if the electron temperature also remains constant
radially throughout the region in which the gas mixes with
the surrounding medium. Perhaps the mixing action of this
region affects the electron behavior in such a manner as to
cause the electron temperature to relax toward the tempera-
ture of the parent gas.
Cobine (19) has shown that for a given gas the following
relation holds for the positive column:


e i. 10 CPr, (67)
(67)


































2=j c~ic -.




I flcfl C. L







' ',








.I ? <. -L C .. '


a c










-. L 1\.







S-f1xic 1. "ch i..v ... .. S ..

s,) '1 na ci




of intees is co.
Ohen -Ll "S - C -- :. .








t lhen b- e _--^- -


~-oY c Q.


- .1'r


I


, ,,


c,


--i

--
j .,


'.'..(- ^





















.1, ~.-.


of 001:-on 7-


I1

L



? io ..c: TOuL 2


0-
-II o\:








t Il.o:



t-4~,i.~


025~~-


2.


. I.- -






The initial eloecc r~ .unL c. .. i.
plasma jet has been sho,:., to Lc a~. ,' r. c', .

both thoorozical-y .,d o::;ozi; cn--ll/ y *..- -. ,.

of zero order a:ni, firs' ki.d (15) ( L.':v, l -

vious theore-jiccl a. alys.s have.o b.;n .. c, -o ........

that ne approachd zero a~ r 0 C-r v-lu, o- .

assumption is not en-c.ire corrc-;, sice -- c.asLL ';

for radial sp:'ad of the oloc1c i-c. .,.J' i,,.-_ ,oiil.

as the jet procueds f2o:;. t-.o .ozz3l. Tohe a3ppZrcc 2.,c

herein eliminates chat assu.p-.ion.











4. EXPERIMENTAL CONSIDERATIONS


4.1 Description of Experimental Apparatus

The experiments were carried out in the Graduate Research

Laboratory of the Mechanical Engineering Department at the

University of Florida. The general features of the experi-

mental apparatus and related instrumentation are shown

schematically in Figure 3. The test gas was supplied from

a high-pressure bottle through a flow regulator and control

valve to a settling chamber before entering the plasma

generator proper, where it was ionized. Argon was chosen
as the working gas since it was free from any tendency to

form negative ions upon being ionized and its physical

properties were well known. The ionized gas, or plasma,

then expanded through a converging nozzle into the test

section. A continuously operating mechanical vacuum pump

then removed the gas from the test section. Figures 4 and 5

show the facility and test apparatus used for the experiment.

The following is a description of the apparatus wherein

each of the components is explained separately.


Plasma Generator

The plasma generator, shown in Figure 5 and schematically
in Figure 1, consisted of five basic components: the settling

chamber consisting of several baffling chambers, the chamber

nozzle, the discharge zone housing, the cathode rod, and the
anode plate assembly. The gas initially entered the base of

the generator through two 1/4 inch inlets and then proceeded

to flow through the baffling chambers, which served to direct






the flow unif orn:-l y c

This lzion>" ) cI,)

the g-3as flow, U:1-.ifo1.. 7,-C--- .~

S1/i h OD

as the cathode. Q:. o t c)1' tL.o.

to a s zo o h a j o c c e jm wr.

cath-ode a 1/8 inch, CD v~~ a~s

c athode -o o aiO c m. h

that it was .acu:: -,i:
T'


oj o a



1/ oils t0iC ,--. '-C, I a















1:1 SS G '
"os'1' \ was o ~.s ;

~h2Ck ~ O~. Th eY.


:,ic tQ


C






the anode and/or the exhaust lead housing to see its effect

upon the electron diffusion process. Thus, it was necessary

to isolate this region from the anode plate assembly. This

isolation was obtained by placing a 1/16 inch thick lucite

disk between a 1/16 inch thick copper disk and the anode

assembly.


Test Section and Vacuum System

The test section was a vertically mounted 100 mm ID

Pyrex glass tube, 75 cm long, supported by and sealed to

the anode assembly and the exhaust lead housing. Static

pressure taps were located along the side of the test

section at distances of 3.7 cm, 7.8 cm, 11.7 cm, and 19.7

cm from the base region.

A Consolidated Vacuum mechanical vacuum pump, with a
225 m3/hr pumping capacity, maintained a pressure of 40-60

microns Hg in the test section when the test gas flow was

shut off. A nominal mass flow rate of 0.2 gm/sec raised the

pressure to 3-4 mm Hg. A surge control valve located in

the exhaust line to the vacuum pump and a valve in the

exhaust lead housing, permitting test gas to be introduced

downstream of the plasma jet, allowed the back pressure in

the test section to be adjusted quite accurately.


Electrical System

Two power supplies of the type needed to create the

discharge were available for the experiments: a 0-3 ampere,

0-1500 volt DC Rapid Electric Silicon Rectifier and a 0-1

ampere, 0-2000 volt DC High Voltage Generator Unit. Both

power supplies were used in the preliminary testing and

neither showed any particular advantage over the other. The

latter was chosen for use with the plasma generator in the
final experiments. To assist in current and voltage control






of the electrical discharge, a 0-2040 ohm High Voltage
Ballast Resistor Unit was connected in series to the cathode

side of the power supply. The anode plate assembly was

grounded. Probe circuitry is discussed later in this section.


Cooling System

Initial system design provided for internal cooling of

both the anode and cathode assemblies,using laboratory

supplied compressed air. Electrical insulation and flexi-

bility were obtained by using 1/4 inch high pressure rubber

hoses, fitted with 1/4 inch rubber hose fittings. Early

experiments indicated that it was unnecessary to cool the

anode plate assembly due to the low degree of ionization in

the plasma jet. A rather large volume of air was required,

however, to properly cool the cathode.


Probe Positioning Mechanism

Design of the exhaust lead housing provided for the

insertion of three probes into the flow stream. These

probes were positioned by the probe positioning mechanism.

This device was located on top of, but electrically insulated
from, the exhaust lead housing.

All positioning of the probes was accomplished manually.

Gear ratios were such that the probes could be positioned
axially to the nearest 0.30 mm and radially to the nearest

0.06 mm.


Probes and Instrumentation

The plasma jet flow field, shown in Figure 6, was

surveyed using three types of probes: an impact pressure

probe, a thermocouple probe, and a Langmuir probe. All throe

probe stems were constructed of 5/16 inch OD Mulltitc

ceramic tubing which provided the necessary electrical






insulation. A 1 3/8 inch brass offset was attached to

each probe stem, permitting the probe to be moved radially

through the plasma jet as the stem was turned. Wilson-type

seals were used in the exhaust lead housing to insure proper

vacuum sealing of the probes.

Impact pressures were measured with an open-ended
brass tube (attached to the brass offset) which pointed

into the flow stream. The tube had an inside diameter of

0.067 inches and was cut to a 20 degree chamfer. The other

end of the probe was connected with Tygon vacuum hose to a

0.1-20 mm Hg Wallace & Tiernan Absolute Pressure Indicator.

Corresponding static pressures were obtained by recording
the pressure when the impact pressure probe was completely

outside the jet flow.

Stagnation temperatures were measured using a shielded
thermocouple constructed of 0.010 inch diameter chromel and

alumel wires. A thermo Electric Potentiometer Pyrometer

was used to obtain the temperature readings directly in

degrees Farenheit.

Both cylindrical and flat Langmuir probes were used for
the investigation. The plane probes were constructed of

0.020 and 0.030 inch diameter tungsten wire, while the

cylindrical probes were constructed of 0.005 inch diameter
wire with the exposed surface being approximately 0.065 inches

in length. The Pyrex glass insulation on the probe was made
as small as possible so as not to disturb the flow stream.
Since it was difficult to clean the collecting surface near
the insulation, an attempt was made to keep the glass from
touching the probe metal in the vicinity of the collecting
surface. Figure 7 shows a sketch of the Langmuir probe
construction.

The voltage-current characteristics for the Langmuir
probe were obtained using the circuit shown in Figure S. A






110 volt, 60 cps Variac was used to establish the desired
potential at point A. A one-to-one isolation transformer
was used purely for isolation purposes. By suitable adjust-
ment of the Variac, resistor R1, and the probe bias, the
probe potential HB could be swept over any desired amplitude
about a suitable bias. The probe potential was input to the
horizontal deflection plates of a Tektronix Type 502 Dual-
Beam Oscilloscope.

The probe current was measured across resistor R1.
Both resistors R1 and R2 were made variable so as to give
flexibility in measuring the electron current at positions
throughout the plasma jet, although R1 had to be accurately
measured using a resistance box for each probe reading.
Since the signal VC VB was proportional to the current
drawn across R1, the voltages VC and VB were input to a
differential amplifier on the vertical deflection plates of
the oscilloscope.
The maximum current across R1 was approximately 10
milliamps near the centerline of the jet. Near the edge of
the jet the current was considerably less. Thus, resistor
R2 was necessary to account for the finite input impedance
(1 Meg ohm) of the oscilloscope. The proper setting for R2
was obtained by disconnecting the probe from the probe
circuit at the BNC connector on the circuit box and observing
the oscilloscope trace. It was desired to have a horizontal
line as the trace under such conditions, and this was
usually the case. However, for large values of R1 and high
vertical displacement sensitivities the trace was sometimes
inclined. The resistor R2 was then adjusted so as to make
the trace become horizontal and thus form a consistent base
line from which to measure the vertical deflections.
A typical Langmuir probe characteristic is shown in
Figure 9. The corresponding current-voltage curve is plotted
in Figure 10.






4.2 Preliminary Testing

A rather extensive preliminary investigation was made
to determine which plasma generator configuration would
yield plasma flows suitable for studying jet mixing and
diffusion processes. This required the production of a
stable jet large enough in size to permit insertion of
conventional probes and yet sufficiently ionized that the
plasma properties could be determined.

Initial generator designs allowed for air cooling of
both cathode and anode assemblies. Functional tests showed

that it was not necessary to cool the anode assembly. Thus,
this assembly was reduced in relative physical size to that

shown in Figure 1. Using air to cool the cathode presented

two rather complicated problems: (a) a large amount of drift

in the electron temperature and electron density in the
plasma jet, and (b) the appearance of dark blue spots on
the cathode from time to time, causing the Langmuir probe
characteristics to become very erratic. The first problem
was attributed to the fact that the air compressor used
was positioned too close to the test apparatus. This
permitted all pressure variations in the air storage tank
to be sensed by the cathode. The blue spots which occasion-

ally appeared on the cathode were attributed to a slight
condensation of the water vapor in the cooling air,
resulting in an uneven cooling of the cathode. A filter
trap was installed in the air line, essentially eliminating

these two problems. An isolated water supply, employing a
recirculating pump, was also built and found to be rather
effective in eliminating these cooling problems. However,
it appeared that either a larger cathode or a higher
pumping pressure would also be needed.to permit water cooling.

It was desired to have the plasma generator operate
over as wide a flow and pressure range as possible. Early






generator designs showed very turbulent flow conditions
inside the discharge housing near the anode plate assembly.

The installation of a small Pyrex glass tube inside the

discharge housing and concentric to the cathode, as shown

in Figure 1, served to better guide the flow and eliminate

this turbulence.

Throughout the preliminary investigation numerous

Langmuir probe surveys of the plasma jet flow field were

made. Results from the cylindrical probes compared favor-

ably with the plane probe results; however, the break in

the electron saturation part of the probe characteristics

was more defined for the cylindrical probes. For this

reason and due to the fact that the cylindrical probes
appeared to disturb the flow less than the plane probes,

they were chosen for use in the final testing.

Converging nozzles of 1/4, 15/32, and 9/16 inch diam-
eters were used to determine which size was best suited for
the experiment. The 1/4 inch nozzle did not permit easy
access for probing the flow field and was eliminated for

that reason. However, it did yield nozzle exit electron
temperatures on the order of 8,000 to 12,000 K which were
comparable to those obtained by Gaither (15) under quite

similar conditions. Both the 15/32 and 9/16 inch diameter
nozzles provided more room for probe measurements. The

15/32 inch diameter nozzle was chosen since under the same

flow conditions it would yield considerably higher electron

temperatures.

Total pressure surveys for each of the above nozzles

indicated the presence of a rather thick boundary layer

build-up at the nozzle exit. Slight changes in nozzle

contours had negligible effect on the presence of the

boundary layers. These boundary layers will be discussed

in more detail in conjunction with the final test results.






4.3 Experimental Procedure

Upon completion of the preliminary testing, a series

of test runs was made to determine the effects of pressure,

power input, electrode separation, and mass flow rate on

the electron temperature and electron number density

distributions in the jet. Each of these runs was given a

corresponding test number, e.g., test I, test II, etc. A

complete run consisted of the gathering of Langmuir probe,

pressure, and temperature data from the entire flow field

up through the initial developed flow region.

Each run, usually lasting from six to eight hours, was

begun by allowing the plasma jet to stabilize for about one
hour. After the stabilization period all pertinent pre-run

information was recorded, followed by the recording of the

Langmuir probe data. These probe characteristics were

recorded by taking oscilloscope photographs of the traces

corresponding to the various probe positions. Experimenta-
tion showed that several traces could be recorded on the

same photograph by superimposing them. Langmuir probe

readings were taken at radial intervals of approximately

0.3 mm and at axial intervals of approximately 10 mm. Near

the edge of the jet the radial readings were sometimes taken

at approximately 0.15 mm intervals in an attempt to better

define the profile information in the mixing region.

Upon completion of gathering the Langmuir probe data,

impact pressure readings were taken, followed by thermo-

couple probe readings. Both pressure and temperature

readings were taken at radial intervals of approximately

0.6 mm and axial intervals of approximately 10 mm. The
run was ended by the recording of all pertinent post-run

information.
The recording of the necessary Langmuir probe data

usually took from two to three hours. Slow variations in




51
electron density were noted during this time by making

periodic checks near the jet centerline or by monitoring

a given point for a period of time. These variations were

usually no more than about 10% of the original reading at

the point under consideration. No attempt was made to make

any adjustments for these variations.











5. DISCUSSION OF EXPERIMENTAL RESULTS AND
COMPARISON WITH THEORY


Following the preliminary testing previously outlined,

several test runs were made in direct accordance with the

specific objectives of the investigation. The results of

three of the tests are reported herein. The controlled

conditions under which the tests were conducted are as

follows:

Test I


Argon Inlet Temperature

Discharge Voltage

Discharge Current

Jet Static Pressure
Mass Flow Rate

Potential Core Velocity

Electrode Separation Distance

Base Plate Potential

Base Plate Current

Test II

Argon Inlet Temperature

Discharge Voltage

Discharge Current

Jet Static Pressure

Mass Flow Rate

Potential Core Velocity

Electrode Separation Distance

Base Plate Potential

Base Plate Current


300 K

370 volts

600 ma

5.29 mm Hg
0.227 gm/sec

220 m/sec

55.6 mm

(floating)

0.0 ma


29S K

424 volts

870 ma

3.2S mm Hg

0.222 gm/sec

304 m/sec

55.6 mm

(floating)
0.0 ma






Test III

The test conditions for this run were the same as those

for Test II, with the following exceptions:

Base Plate Potential +71 volts

Base Plate Current 145 ma

The particular experimental objectives of the first

two tests were as follows: (a) to obtain gas dynamic infor-

mation in order to define flow characteristics and identify

different flow regions, (b) to obtain electron temperature

and electron number density profiles throughout the entire

flow field near the nozzle and as far away radially from

the jet centerline as instrumentation would permit, and

(c) to examine the effects of certain variables, e.g.,

pressure and power input, on these profiles. The primary

purpose of Test III was to determine the extent to which

an applied potential in the base region would alter the

electron diffusion characteristics of the jet and thereby

establish what changes in electron temperature and electron

number density profiles could be effected by this means.

The basic test conditions for this latter run were inten-

tionally kept the same as those for Test II for purposes

of exact comparison. Experimental results for these tests

are presented graphically in Figures 11 through 24.

Test I was run at an exit flow Mach number (at jet

centerline) of 0.62, while for Test II the Mach number was

0.91. Examination of the corresponding velocity profiles
in Figures 11 and 16 reveal the presence of initial boundary

layers at the nozzle exit. The presence of such thick

boundary layers served two very useful purposes: (a) they

gave the jet mixing region an initial thickness, thus

making it wider and more accessible to probe studios, and

(b) they permitted electron density and electron temperature






profiles to be determined within this initial region at
the nozzle exit.
Reasonable justification for the existence of these

relatively thick boundary layers was made by a very
simple theoretical analysis. The Reynolds number Re,
based on nozzle diameter and exit flow conditions at the
centerline, was determined to be 980 and 1038 for Tes-s I

and II, respectively. These low values of Re (compared
to the critical Re value of approximately 2300 for pipe
flow) indicated that the jet flow was laminar. The nozzle
was then temporarily treated as a circular flow channel.
Kays (36) gives the length to diameter ratio necessary
for a laminar flow velocity profile to fully develop at the
entrance of a circular pipe to be


length _Re
diameter 20 (78)


Thus, for the case under consideration these ratios had
approximate values of 50, which was many times larger
than the nozzle length (measured along the curvature of
the nozzle) to diameter ratio of 2.4. These calculations
were interpreted to mean that the flow over the curved

surface of the nozzle was probably not fully developed by
the time it reached the exit. Therefore, the boundary
layer, as determined experimentally, should exist.
Schlichting (55) gives the boundary layer thickness
of a tube with infinite radius of curvature to be


= SLt (79)


referred to the tube length Lt. The length of the nozzle
was 2.86 cm. Based on this model S equals 2.95 mm and






2.S7 mm for Tests I a. -

experimental value s o- r-., e L.5 ...... .....

respectively. Alough, alc c .. .L

differed so:mewa: they v2 a o o .

Thus, the cxperima.. Londar -.

reasonable. It ''as cXku..wva. ,

of Re was di-icul- to obtain sin.-l vc.l vuc2/, w..6z'w:

etc., were changing alone ..z.. L. .'Zi z

more sophistica-od theoretical a.:uly nc ....

since the initial condition col, > :..s...

Theoretical modelsls ior v-_ocy o. .o z.

exits, such as those of Pai \- ( -11

usually based on theo ass'.jion .

layer is present at the ozz;,- .

problem in trying to co-: l.t .: ... ... . ... .

files with their thcol';._c.. .... o c

situation the nondien. '. .- ."...

with the theoreoicl ... c.-l ,,as .od

length to account the .nita

magnitude of --.in corr:cion ,: 3.... ..

mm for Test I1. h. r invostil:;c "

similar conizia

an appr j l n .






\ ith ....


,'Up ...l ,,, ,

GsSCnt.

o only co


xphicn 7.






Upon examination of the experimental data two conclu-

sions become immediately clear. First, recombination is

essentially negligible within the jet and must therefore

occur primarily at the walls. Secondly, a mechanism must

be present within the flow which accounts for the fact

that the electrons along a given radial direction possess

a constant average energy, i.e., a uniform temperature.

This mechanism can best be understood in terms of the

transport processes occurring within the plasma jet.

As has been pointed out previously, the electrons

receive most of the field energy because of their

relatively small mass and consequent high mobility. This

energy is transported to regions remote to the discharge

zone by both diffusion and conduction. In the diffusion

process electrons move from one location to another while

transporting finite amounts of energy to the new location.

During the diffusion process the electrons undergo colli-
sions with other particles and with other electrons. These

collisions give rise to energy transport by conduction.

The electron-neutral particle collision frequency is

very high compared to the electron-electron collision

frequency. However, the change in kinetic energy during an

electron-neutral particle collision is extremely small since

a more effective energy transformation occurs between

particles of equal mass. Thus, the energy transferred in

electron-electron collisions becomes important, and it is

this mechanism that accounts for the uniform radial electron

temperatures. The importance of this mechanism was also

recognized by Gaither (15) in his investigation of the

potential core region.

In Chapter 3 an equation was derived for evaluating
the electron number density as a function of r and z. In
order to make use of this equation the initial electron






number density profile .(r) :ajat bc .~. ,..... .Z,

of this investi"at ion it w.s obsrv. (see j a C;

19) that f(r) wa,,s adcqua.oljy dscril in '... of-

zeroth order Bessol func-ion o m 'irs- 1.:. 1.

best curve fit of the iii cial ex cri:.:.. ala. o'iL-c ta
2 :, 2
factor e-Cr / as irodced sucs C




0 '* -- -


C 0 .





Note that C1 is an -li ..'i- ..

initial electron ::umbir c> .3i ...

value of 141.8 in ths i.--.

for the electron ..:..2 ..




-9













5 I n* "C OL *
^-j












...unit .'o-' x c ... Of r

,hc c..c t b L;..C : i.<


.OOCc C CL-r w i^- j-. i Cn -liy ..


-nd c / ,ur> i ..- .. ... .:

cOsi.c .x ccn

i.ot bue .. c o.:i C ,u .






investigators using this theory. Further discussion of

these and other assumptions are given in Appendix C.

In Test III a potential of +71 volts was applied to

the base plate in the base region. This particular voltage

level was chosen because field distortion effects could be
introduced at this level while holding secondary ioniza-
tion effects to a minimum. The experimental results are

shown graphically in Figures 21 through 24, An approximate

increase of 30% over Test II was observed in the electron

temperature at the nozzle exit, while the corresponding

electron number density was decreased by approximately 50%.

The superimposed field had the expected effect of acceler-

ating the electrons, resulting in a higher initial electron

temperature. Also, the rate of electron diffusion was

increased such that a lower electron number density was

observed along the jet centerline. Comparison of Figures

19 and 23 shows an increase in the electron number density

in the base region, particularly near the base plate, when

a potential is applied to this region.

It was concluded from this test (and others not pre-

sented herein) that the electron diffusion process in a

plasma jet flow can be accelerated or retarded by applying

a potential in the base region. The extent of the effect

depends on the potential applied. Large gradients are
observed in the plasma potential under such conditions,
making it necessary to properly bias the Langmuir probes.
Otherwise, the probes will be damaged.












6. COXCLUS C, .. ... ., O ._ .



As previously SiLC, J..is .

step toward es J.lishi>g co:.. o a > .... '-

standing of the pobic.. o ch ~ . _c be ,

low pressure pl-asL je, t lo','s. ..nt.

presented herein h.ve bc.-. -.,- .s ..

agreement with t h

results of other -.'. ..

following co.cl .







c .

2. \4 -n- n L o .....



t 1:, "














...-- .. .c O ... .
L- ..u c .2 u e






This writer has found the plasma jet to be an extremely
valuable research tool and recommends the following areas

of research for future investigations:

1. The extension of this investigation to the

supersonic regime.

2. The extension of this study to flows having an

initial turbulent mixing region.

3. The devising of a series of experiments, similar

in nature to the one considered herein, with the

objective of determining the effects of pressure

over a wide range (low micron range to atmospheric)
on electron gas behavior.

4. The development of techniques, particularly

electronic, which would permit rapid analysis of

Langmuir probe characteristics.
5. Further examination of the effects of applied

fields on transport properties.







PRESSURE
TAP











PRESSURE
TAP











BAFFLING
CHAMBERS -






TEST GAS
INLET


TEST SECTION


ANODE PLATE
ASSEMBLY


DISCHARGE ZONE
HOUSING


CATHODE


TEST GAS
----INLET


COOLANT OUT


COOLANT IN


FIGURE 1. PLASMA GENERATOR








































(n
C).









C?


zC

0,


o

0

0



SO
bf-l


0
O




















0

4-)

o 0
0 0
O O


,-4
O0





o
O p


OP


cn)
u) en


o &
0
cP


0

0 'r
Me, r













F1; 'r *-"


@000;-


(~- 14.~~L


I ifr
A *


IP
ro




















wip





I r


FIGURE 5. PLASMA GEITERATOR AND TEST SECTION






































'cI'~?


FIGURE 6. PLASMA JET
































































r4
M4 E-4
Q Z
00
ul ll






























































P4u


r4o


























Probe Potential (1.0 volts/division)


FIGURE 9.


10.0


5.0
4.0
3.0


TYPICAL LANGMUIR PROBE
CHARACTERISTIC


2.0-


1l. 0


0.5
0.4
0.3

0.2


o.1 1 I 1 I
-2 -1 0 1 2 3
Probe Potentia'l-- volts


FIGURE 10. SEMI-LOG PLOT OF LANGMUIR
PROBE CHARACTERISTIC


Two




70







0o















0 0
o O o o







o -O O O
coo






- oo0 0 o -
0 o In H E4
O r -i o w0


*r4 f <
o 0 o0 C) 4 0

0O lo v 0e-



0O a Nx 0<
0 O 2
r l *-l




0 z C/o
i C.) ?ri rn z0


m) ( 4-) 0


o, Z Z,
E- -- 4X 0 0
6/ rO-iA ro u / -O C Mo,
(p H 2
/ 4- X -1 Q















0 co c, 0
0 0 a 0
r-l 0 0

n/ 'X.TOT;A oto T~:T~o~d /X^TOTA Too





























































R.dial Distance


from Ccntcrline,


FIGURE 12. RADIAL ELECTRON TEMPERATURE DISTRIBUTION
IN ARGON PLASMA JET FOR TEST I


r mm































0




0




0




0




0


c+OT > Mo --1 "o.xnjt.iodmoj uo.T4oo3Ta3


z


0





0








.-1



0
E-





0 )
Q=
3-
Cj
cr n
& ^


N





o o

N
C








C)
U
Z!







o o









I-i




73




6




0 0.0 mm

6 6.4 mm
5 -
co \ 012.7 mm

0 0 19.1 mm

A
g \ Solid lines
S 4 represent
theoretical
0 0\ distributions




3 -


0
S0 \










o o
0 1 2 4 5

E3)






0 1 24 5 7 S





Radial Distance from Centerline, r mm


FIGURE 14. RADIAL ELECTRON DENSITY DISTRIBUTION
IN ARGON PLASMA JET FOR TEST I
































































M) cq


+01 x muo3/suo.IOaTo -o0u ".&TSua(I .Joqu:nN 1.uoJ4lo3O


















S ES S S
S ES S S


0


0
------------------D------0--


0 0 < 3 0


o o.~
0 0









/ o0




0 0

9 X rj
O CO

0C C)
0












f I
0 cO a ^
r( o 0 0


-1


I I I


o q/L ',ITnOTOA O.T03 UTLT1UO.Od/,AI'TOOT,3A T101


i I i iy
i







Ilh


'// ')


10 o

L il



C)


C)
0






u




r7l


"-i
CM r-


r(
rl

3
C3
H
Fr(


1 '












0


S000 0 o0 00 z = 0.0 mm
5 0 0
0O
0
O
O




4
AA z = 6.4 mm




z = 12.7 mm

< ^ ^ O 0 O0


n00 ,00


z = 19.1 mm
00l 0o
o nO O


O00 O 0
00


I I I I I I I I I


0 1 2 3


4 5 6


Radial Distance from Conterline,

FIGURE 17. RADIAL ELECTRON TEMPERATURE


7 8 9 10

r -mm


F DTSTTRTTiTTTfl'


IN ARGON PLASMA JET FOR TEST II


10 0 1 0
0 0 0














0
C-




0
z
Oo



O
0 c
C> -












0
E
























00
o o










0 o o







in < O

<<


0
O co C
or CI


















S-0 0

0 I o
o 0
0








X CCi



-r tf
Fr


+OTI 0o L "o.inu.toduioL uo..oo3- r




















0 0.0




0 12.7

0 19.1


Solid lines
represent
theoretical
distributions


0 1 2 3 4 5


Radial Distance from Centerline, r/vmm





FIGURE 19. RADIAL ELECTRON DENSITY DISTRIBUTION
IN ARGON PLASMA JET FOR TEST II


00





E


O


1-4

4-)

O
C.)












0
rC



C)











-4



0(




79


















z










o










0



<0




0c
Hs =-


CN H-l


+OT >0': ,II/SuO.T).OOT1O -u


'X4TSLuOa joqrnS UO.XVDOI




O8






7



0
z = 0.0 mm
---0 O 0
o O O O
0 0 0



O

x 5



z = 6.4 mm
o L
z =12.7 nim
o







S0 0
O O 3Oz = 25.4 mm


r-4
S2













0 1 2 3 4 5 6 7 8 9 1

Radial Distance from Centcrline, r -mm


FIGURE 21. RADIAL ELECTRON TEMPERATURE DISTRIBUTION
IN ARGON PLASMA JET FOR TEST III





81









o






'i-
0

0

I-















Sz
O
o H










0
E-i



O E







O N o




0 4
00 i-i
-) 0H






-0
0 0
O O







0




0
0 0
O K~
0 -<
Z WS
^ '-




0~V P K
r 0 ^U
R M <
0 I -
0 h &.








0 O

c;
*r- CMllh r


xM .o I x0 'o.nl.pTocIuio,L


c-OT


UO.T OT -I







































































Radial Distance


FIGURE 23.


from Centerline,


r ,- mm


RADIAL ELECTRON DENSITY DISTRIBUTION
IN ARGON PLASMA JET FOR TEST III


2.0


1.5













1.0


x

U~

0
-4








C.,





C.,






































































to O tL O
r -4 O O


g--O r uto/s.Io.'l0ooTo --Du ',ATsuIo .ToquimnN u o.I'oT[



































































0 CO 0


zg 9+OT1 Z- '"uOT4OS SSO.T3 uos110TS 03























APPENDICES










A SL:..:ARY O -L.. -, -


.

Zolecular voight


2:ass of ato:..


Radius of aito...


-jJ I-


'J, ', -~ '


Symbol





1311


SI



R



Cp




Cv



k



C






Vi,


Vio


Specific a-
COnst-ant r, ..,o








heats








b irst 0..
co .ol..- ...








SCO .: ., i uj
poten c


1C-.vcni 2022


Gas constanz










B. TH-IEORETIC._ CrL,, _.. c . T
DETERM:NAT:On 1 ML C- .... P, 3



In the plasi.a low yc, ... .. ....,. .. c..

type of particle ccllidjj t...- s of

particles as well : ,; ,i't: its o0 .. .- ;-, ... ......

interactions have -a bo~:"In on proe b v-l.3-:u .ri-..- :.

continuum consiCerations, it i o i ..o. co 1:-.-: .1

mean free paths involved. A nr.:0t:.o^ io ae '.... .:c

mean free paths has been outlined by G'f* ( 3) ..

given in the followvin paragraphs.

For neutral-neutral particIe il:: ction ....

free path is given by Sears (57) a




\ ^. -



where is the visc ... 2 is .the ..., -. ... .

the pressure. Fr.- iv -

tion of this equo-n ..L., on .l; ...- .. _

potential model o--o .. c.cul.. .

AssuLi-.g" -.. : .. .... C.. .. .. ..- o.

encounters to ,. ...- ..-s- .,...

the c:.us sc'Lio/. Q ar, K.on v.





.oe co.Ll ^. c. i .
trans-ur \'vi.. a .,,. t .. .

2It rust .. .. .
,incc clhr.;c c c\.
cro s C..oc ,T .. ..
olatio.. o . .
0o nI .. .
as tii..




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