MACROSCOPIC INVESTIGATIONS OF A

MICROWAVE GENERATED PLASMA

Bv

Duane Weldon Dinkel

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

Department of Chemical Engineering

1991

Am;

‘7
l

62% / ‘

ABSTRACT

MACROSCOPIC INVESTIGATIONS OF A

MICROWAVE GENERATED PLASMA

By
Duane Weldon Dinkel

The Microwave Electrothermal Thruster (MET) has been demonstrated,
both theoretically and experimentally, to be a viable substitute for chemical
propulsion and to possess lifetime advantages over systems where electrodes
are in contact with the propellant. A specially designed resonance cavity
transfers energy from the microwave power source to the electrons in the
propellant. The electromagnetic field accelerates these electrons to sufficient
energies for ionization to occur. The plasma thermalizes the propellant, which
undergoes thermodynamic expansion and produces the desired thrust.

The goal of this work is to further the development of the MET concept
through assessing the macroscopic influences the plasma has on its

surroundings and vice versa. The general diagnostics used include

photographic, calorimetric, and spectroscopic measurements of pure gases and
binary mixtures using the TMmz mode in the resonant cavity. The data from
these investigations are consolidated in a model that describes the velocity and
temperature distributions around and downstream of the plasma. The
advantage of modeling these macroscopic properties over microscopic
phenomena is that the former can be evaluated experimentally to better assess
the modeling assumptions. This model can be used to predict nozzle

performance and improve thruster designs.

With the most sincere appreciation, I dedicate this thesis to

my wife, Kristin, who has graciously endured this experience with me.

iv

Acknowledgements

“Science is nothing but developed perception, interpreted

intent, common sense rounded out and minutely articulated."

[George Santayana: 771a Life Of Reason: “Reason in Science“ V]

In helping to develop the “perception”, the author wishes to thank Dr.
Martin C. Hawley for providing an excellent research environment.
Acknowledgement is also extended to the folks at NASA - Lewis Research -
Center, particularly Dr. John Power, for his assistance and support on the
project. Additional recognition is given to Dr. Jeff Hopwood, for his patient
replies to the many questions asked at most inopportune times, to Scott
Haraburda, for providing a solid foundation to build upon, and to Dr. Ted
Tsakumis, for his stimulating phiIOSOphies and guidance. The author is most
of all grateful to Weldon and Hazel Dinkel for their many significant
contributions to this project.

Portions of this work was supported by the National Aeronautics and

Space Administration - Lewis Research Center.

LIST OF TABLES ..................................... viii
LIST OF FIGURES ...................................... ix
CHAPTER 1 Introduction ................................. 1
1.1 Research Summary ............................ 1

1.2 Motivation for Plasma Diagnostic Research ........... 2

1.3 Research Objectives ........................... 4
CHAPTER 2 Theory .................................... 7
2.1 Introduction ................................. 7

2.2 Equilibrium in Gases .......................... 10

2.3 Mean Free Path ............................. 12

2.4 Validity of the Ideal Gas Law .................... 13

2.5 Microscopic Plasma Phenomena .................. 16

2.6 Microscopic Mass Balances ..................... 19

2.7 System Thermodynamics ....................... 23

2.7.1 Chemical Potential ....................... 26

2.7.2 Saha Equation .......................... 28

2.7.3 Degree of Ionization ...................... 32

2.8 Electromagnetic Theory ........................ 38
CHAPTER 3 Plasma Diagnostic System ...................... 41
3. 1 lntrod uction ................................ 41

3.2 Microwave Source ........................... 45

3.3 Gas Flow System ............................ 47

3.4 Plasma Containment Assembly ................... 48

3.5 Microwave Cavity ............................ 50

3.6 Spectroscopic System ......................... 54
CHAPTER 4 Plasma Dimensional and Quality Analysis ............ 61
4.1 Photographic Method of Analysis ................. 61

4.2 Plasma Overall Volume ........................ 62

4.2.1 Pressure Dependence ..................... 63

4.2.2 Gas Flow Dependence .................... 66

4.2.3 Composition Dependence .................. 68

4.2.4 Power Dependence ...................... 71

TABLE OF CONTENTS

vi

4.3 Gas-Surface Interactions ....................... 71

CHAPTER 5 Calorimetric In vestiga tions ...................... 77
5.1 Macroscopic Energy Balance .................... 77
5.2 Energy Distribution ........................... 80
5.2.1 Pressure Dependence ..................... 81
5.2.2 Gas Flow Rate Dependence ................. 81
5.2.3 Composition Dependence .................. 84
CHAPTER 6 Spectroscopic Investigations .................... 86
6.1 Introduction ................................ 86
6.2 Theory ................................... 87
6.2.1 Spectroscopic Temperature Measurements ...... 87
6.2.2 Degrees of Freedom ...................... 90
6.3 Methods of Analysis .......................... 96
6.3.1 Single Atomic Line Method ................. 96
6.3.2 Two-line Radiance Ratio Method ............. 99
6.3.3 Atomic Boltzmann Plot Method ............. 100
6.4 Species Concentrations ....................... 101
6.5 Advanced Methods of Analysis .................. 102
6.5.1 Laser-Induced Fluorescence Spectroscopy ...... 102
6.5.2 Actinometry .......................... 104
6.6 Electronic Temperatures ...................... 106
6.7 Concentrations of Species ..................... 116
6.8 Conclusions .............................. 118
CHAPTER 7 Model Formulation .......................... 123
7.1 Introduction ............................... 123
7.2 Assumptions .............................. 125
7.3 Characterizing Dominant Forces ................. 128
7.4 Model A - Penetratable Plasma with Plugflow ........ 130
7.5 Model B - Penetratable Plasma with Parabolic Velocity
_ Profile ................................... 134
7.6 Model C - lmpenetratable Plasma with No-inp Boundary
Conditions ................................ 1 37
7.7 Model D - lmpenetratable Plasma with Slip Conditions
Around the Plasma .......................... 142
7.8 Summary ................................. 145
CHAPTER 8 Summary and Conclusions ..................... 149
CHAPTER 9 Recommendations for Future Research ............ 155
REFERENCES ....................................... 159

vii

Table 3.1
Table 4.1

Table 4.2

Table 5.1
Table 6.1
Table 6.2
Table 6.3
Table 7.1
Table 7.2

Table 8.1

LIST OF TABLES

Tungsten Calibration Data for Spectral Response ...... 60
Plasma Volume Conditions ...................... 65

Inner and Overall Volumes and Color Transformations for

Helium/Nitrogen Plasma ........................ 70
Calorimetric Conditions ........................ 80
Spectroscopic Conditions ...................... 106
Observed Transitions ......................... 107
Spectroscopic Data for Helium .................. 109
Helium Plasma Dimensions with Pressure ........... 124
Reynolds Number at Varying Conditions ............ 129
EXperimental Conditions Used to Evaluate LTE ....... 152

viii

Figure 1 .1
Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7

Figure 3.8

Figure 3.9

LIST OF FIGURES

Proposed MET Concept on Board a Satellite ........... 5
Mean Free Path as a Function of Pressure

Volumes Obtained by Ideal Gas Law Compared to those
Obtained by Peng-Robinson Equation of State ........ 17

Relative Plasma Deformations Caused by Changes in

Pressure .................................. 20
Thermodynamic System for the MET ............... 22
Helium Plasma Degree of Ionization Obtained from the Saha

Equation as Functions of Pressure and Temperature . . . . 35
Helium Plasma Molar Constituents at 76 mTorr Obtained

from the Saha Equation ........................ 36
Experimental Configuration ..................... 42
Microwave Source and Peripherals ................ 46
Plasma Containment Assembly ................... 49
Top Collar Design ............................ 51
Bottom Collar Design ......................... 52
Microwave Resonant Cavity ..................... 53
Fiber Optic Cable with Terminations ............... 55
Helium Spectra Obtained With and Without the Fiber Optic

Cable .................................... 57
Spectroscopic System ......................... 58

ix

Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4

Figure 4.5

Figure 5.1
Figure 5.2
Figure 5.3

Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8

Figure 6.9

Overall Plasma Volumes for Helium, Nitrogen, and Mixture
as a Function of Pressure ........ , ............... 64

Overall Plasma Volumes for Helium, Nitrogen, and Mixture

as a Function of Gas Flow Rate .................. 67
Overall Plasma Volumes as a Function of Composition (by
volume) ................................... 69
Overall Plasma Volume for a Helium Plasma at 200 and 300
W as a Function of Gas Flow Rate ................ 72
Comparison of Wall Recombination Rate Equations for a
Helium Plasma as a Function of Gas and Wall
Temperatures ............................... 75
Plasma Energy Absorption for Helium, Nitrogen, and
Mixture as a Function of Pressure ................. 82
Plasma Energy Absorption for Helium, Nitrogen, and
Mixture as a Function of Gas Flow Rate ............. 83
Plasma Energy Absorption as a Function of Composition (by
volume) ................................... 85
Atomic Energy Levels ......................... 91
Potential Energy Curves for Diatomic Species ......... 93
Degrees of Freedom for Diatomic Species ........... 95
Energy Level Diagram for Helium ................ 108
Helium Plasma T, as a Function of Pressure ......... 111
Typical Graph Generated for Single-line Method ...... 112
Helium Plasma T, as a Function of Gas Flow Rate ..... 113
Argon Plasma T, as a Function of Gas Flow Rate ..... 115
Helium Plasma Neutral Atom Density as a Function of Gas
Flow Rate. ................................ 117

$I.r|(([i“("[[[t(([(l'l’l‘lrliilti rili‘rlllll'lill II

Figure 6.10

Figure 6.1 1

Figure 7.1
Figure 7.2
Figure 7.3

Figure 7.4

Figure 7.5
Figure 7.6
Figure 7.7
Figure 7.8

Figure 7.9

Helium Plasma Degree of Ionization as a Function of Gas

Flow Rate - number 1 ........................ 119
Helium Plasma Degree of Ionization as a Function of Gas

Flow Rate - number 2 ........................ 120
Prandtl Number of Helium with Temperature ........ 127
Plugflow through Plasma ...................... 130
Parabolic Velocity Distribution through Plasma ....... 134
Parabolic Velocity Profile Around Annulus, No-slip

Conditions at R0 and Ri ....................... 138
Theoretical Pressure Drop for Model C ............. 140
No-slip along Containment Walls, Slip along Plasma . . . . 143
Theoretical Pressure Drop for Model 0 ............ 144
Comparison of AP Obtained for Models C and D ...... 146
Final Modeled Region ......................... 147

xi

 

'(I I ( I'll ill I J] l'i III. I

CHAPTER 1

 

In tro duction

1.1 Research Summary

The plasma diagnostic research at MSU is a single dimension of a group
effort oriented towards realizing and optimizing microwave generated plasma
technology for practical and economic industrial use. Though each application
may be specifically unique, they are all based on the fundamentals of plasma
behavior. The diagnostics of these fundamentals utilize the latest
instrumentation and knowledge to evaluate the chemistry, physics,
thermodynamics, electrodynamics, and transport properties within the plasma.
Some of these methods are used to evaluate the overall system, such as the
efficient coupling of energy from the microwave source to the plasma and
energy distribution within the cavity. Other methods are used to study the
microscopic phenomena that occur within the plasma system, such as surface

reactions and collisional processes between species.

2

1.2 Motivation for Plasma Diagnostic Research

Historically, plasmas have maintained a low profile as a phenomenon
solely of academic interest, primarily researched by the physicist, who noted
the many disciplines of physics that are combined into the single study of
plasmas. In fact, low-density, high-pressure plasmas, where quantum effects
are negligible, provide almost all the elements of classical physics‘ . Since the
early sixties, however, researchers have found methods of harnessing the
abundant potential energy within plasmas and converting it to numerous
practical applications. These applications span the engineering disciplines
ranging from nuclear fusion to research and diagnostics of medicine and
agriculture to environmental tracking of pollutantsz. In addition to these
applications, plasmas can also be used for:

0 the low pressure processing of materials

0 the use of plasma thermocouples which allow greater extraction of
thermoelectric power from nuclear reactors, especially compared to
conventional metal combinations’

0 the fabrication of sophisticated circuitry in the semiconductor industry
that possesses higher speeds and densities

e plasma deposition of thin films, growth of oxide layers, and etching

e providing an efficient oxidation medium to make toxic chemical

environments benign4

O the propulsion of spacecraft

The potential for plasma propulsion as a substitute for chemical
propulsion in deep space travel and station keeping has been under evaluation
for the past decade. In fact, plasma propulsion has become a reality for the
low-thrust, high-specific impulse applications commonly found in gravity-free
environments. However, conventional methods of plasma formation and
sustainment with high-voltage electrodes possess lifetime limitations due to the
erosion of electrode tips. The Microwave Electrothermal Thruster (MET) was
developed to eliminate this limitation since it has no electrode in contact with
the working fluid. The MET concept has been demonstrated, both theoretically
and experimentally, to be a viable substitute for chemical propulsion.

The basis of plasma propulsion, in general, lies in the conversion of
electrical energy into kinetic energy to generate thrust. With the MET, this is
accomplished by interacting electromagnetic radiation with a flowing gas. The
free electrons are accelerated in the electromagnetic field to energies
sufficiently high to ionize other atoms by collisions. The resulting chain of
collisions caused by the released electrons produce the plasma, which is simply
a collection of electrons, ions, and neutral species. When the ionized species
recombine back to their atomic states they release their energy of dissociation
as heat, thus increasing the temperature of the gas as it flows out of the

system. This high energy gas is thermodynamically expanded through a nozzle

4

to produce thrust. In one version of the MET concept, illustrated in Figure 1.1,
the power would be beamed to the spacecraft from a space station or planetary
base. Another option would be an on-board microwave frequency oscillator
powered by solar or nuclear energy. The conversion from electrical to kinetic

energy occurs in the energy absorption chambers.
1.3 Research Objectives

Plasma diagnostic research has been conducted for the past decade to
better ascertain fundamental principles underlying the plasma process. The
goal of this research is to develop a physical understanding of plasma behavior
and the effects of plasma interaction on various engineering systems. The
objectives are met through analytical investigations of various macroscopic
properties governed by microwave generated plasmas over a broad range of
operating conditions. These parameters, which include various gases and their
gas mixture ratios, gas flow rates, gas pressure, discharge power,
electromagnetic resonance modes, and containment geometry are accurately
measured and controlled with the latest instrumentation. The empirical
observations are coupled with theory to provide models that will accurately
predict the effects of plasma behavior. These models will not only enhance the
current understanding of plasma processes, they will also describe the flow

fields and temperature distributions around the plasma. These distributions can

 

 

 

f/ff/f—i $3.941; j—-—- I~//////

 

 

 

| LINEROY SOURCEJ—j

'__ POWER
CONDITIONER j

 

 

 

 

 

 

     
 
 

   
   

ENERGY ' ENERGY NozzLE
-- ABSORPTION 4‘ ABSORPTION --
cNANaER , CHAMBER

 

 

I
l
I
1

(PROPEuANt stoueg

 

Figure 1.1 Proposed MET Concept on Board a Satellite

6

then be used for boundary conditions in the evaluation of nozzle performance
and design. I
Though several gases will be used throughout these experiments, helium
will be the gas of primary concern and the others (N2 and Ar) will be used to
confirm general trends. Helium was chosen due to its simple atomic structure
whereby only two electrons can be detached and consequently, atomic data are
widely available. Under the experimental conditions used in these
investigations, the helium gas can also be treated as an ideal gas which allows
numerous simplifications to be made. Another key advantage in the diagnostics
of helium lies in its potential candidacy as a propellant in the aerospace
industry. The properties of helium that make it a desirable propellant are"3
e it is a monatomic gas having no rotational or vibrational modes, as well
as no dissociation, which reduces frozen flow losses
e the high ionization potential of helium allows electronic excitation and
ionization to occur at much higher temperatures than in any other gas,
including hydrogen
0 low molecular weight (higher specific impulses, I,,)
0 density is 75% higher than the density of hydrogen which results in a
45% reduction in storage volume and a 32% reduction in surface area
0 greater launch safety due to inertness
NASA and other researchers agree that helium will compete favorably with

hydrogen systems if adequate efficiencies (> 0.7) can be demonstrated.

CHAPTER 2

 

Theory

2.1 Introduction

A gas in its normal state is considered an electrical insulator due to the
fact that it contains no free charged particles, only neutral molecules. The gas
particles collide with each other in times that are short by comparison with their
oscillation periods, and they move an "average“ distance, which is short
compared with the characteristic wavelengths of the oscillation within the
medium. This medium is namely the wavelength of sound and this "average“
distance is the mean free path; The internal energy within the gas is
transmitted by chains of collisions rather than individual particles“. If the gas
behaves ideally then the internal energy, and subsequently, the collisional
processes, are solely functions of temperature. If a hot gas is in complete
thermodynamic equilibrium, its physical state can be completely expressed by
a finite number of thermodynamic variables, temperature, pressure, and

concentration. The number of particles or "oscillators” can be easily calculated

 

lt‘ldl‘IlraI'l[[[l[[‘II l'l‘l‘llll.

from these thermodynamic variables.

If electric fields of high intensity are applied across the gas, the free
electrons are accelerated to energies sufficiently high to ionize other atoms by
collisions, producing a gas discharge. These gas discharges produce an ionized
gas containing electrons, ions and neutral particles. When the degree of
ionization is equal to unity, the gas is then said to be completely ionized. This
collection of free, charged, and neutral particles have a net charge that is small
when compared with the charge of either sign. Thus the plasma ensemble may
be considered electrically neutral and the high electron mobility makes the
plasma a good electrical and thermal conductor. Compared to an unionized
gas, the effective collision time within a plasma is long. These unusual
characteristics deviate from those of the three known states of matter, and
plasmas are consequently referred to as the '4‘“ state of matter" 7.

The three components of a plasma (electrons, ions, neutrals) are
characterized by temperature, component pressure, mass (or molar) fraction,
and three velocity components. The state of a plasma is also dependent on
electric and magnetic field strengths, which are vectors that have three
components each. At first, an attempt to thermodynamically characterize the
state of a plasma seems hopeless when visualizing the tremendous number of
atomic interaction processes which occur among the particles, and between the
particles and the photons of the radiation fields. This task is indeed tedious

when compared to the relatively simple thermodynamic relationships that are

9

used for an unionized gas. In fact, the local state of a plasma can only be
determined if the values of 6f thermodynamic equations and 6 electromagnetic

equations are solved, where f represents the degrees of freedom. Therefore,

6f+6 (201,

equations are needed to thermodynamically describe the local state of a
plasma. This expression can be simplified if the plasma is in a state of
equilibrium.

The plasma state approaches equilibrium as the number of interactions
increases. The closer the plasma is to complete equilibrium the less important
it is to know the detailed processes, since individual processes can be grouped
together (ie. In equilibrium, particle densities can be calculated from total
densities and temperatures). A quantitative description of this process in
equilibrium is depicted by Delcroix from a classical mechanics perspective’:

“If a great number of systems are enclosed in a container at

constant temperature and if, due to their interaction, they reach

a state of thermodynamic equilibrium, then each of these systems

in this equilibrium state will possess a chaotic energy of thermal

motion whose mean value is proportional to the absolute

temperature of the container and equal to N times KTl2, where N

is the number of degrees of freedom of each of the systems."

Equation 2.1 can be simplified by assuming that the interactions giving

10

rise to the excitation and ionization of particles is mainly caused by particle

impacts and not by radiative processes. Such plasmas are called collision—

dominated plasmas. Most plasmas found in the laboratory are collision-

dominated and therefore, the above simplification, along with the condition of

LTE, appear to be valid”. Details of the LTE concept are discussed below.

2.2 Equilibrium in Gases

In general, thermodynamic (or thermal) equilibrium utilizes a well-defined

temperature as the essential parameter. It is a restrictive concept requiring

that”:

Velocity distribution functions of all particles (especially electrons) are
Maxwellian.

Population densities of excited states are Boltzmannian.

Distribution of molecules and their dissociation products obey the mass
action law of Guldberg and Waage.

Distribution of atoms and ionization products (ions and electrons) obey
the Saha-Eggert equation, which is a special case of the mass action
law.

The electromagnetic radiation field has a Planckian distribution, where
the radiation temperature equals the kinetic temperature of the reacting

particles.

11

Most laboratory plasmas are opticallyothin and the plasma radiation
completely escapes from the plasma, thus invalidating the Planckian criterion
along with the concept of complete thermal equilibrium‘. Therefore, the less
restrictive concept of local thermal (or thermodynamic) equilibrium is
introduced. The basis of LTE lies in the existence of a microreversibility
between collisional processes and the assumption that collision-induced
transitions and reactions are more frequent than radiative ones. In LTE, all the
above criteria hold true for the reacting particles, especially the electrons, but
the radiation distribution is allowed to deviate from the Planck function”. The
assumption of LTE allows all particle densities to be calculated from total
densities and temperatures.

For the gas to be in "true' non-equilibrium, different degrees of freedom
of the gas must have different temperatures. Furthermore, the energy
distribution of an internal degree of freedom must be appreciably different from
a Maxwell-Boltzmann distribution and the velocity distribution must be
appreciably different from Maxwellian. These conditions may occur when
energy is rapidly added to or extracted from a gas at such a high rate that the
equilibrium is continuously perturbed or when the different degrees of freedom
weakly interact, such as for low density systems where collisions may be too
sparse to maintain equilibrium. Non-equilibrium may also be observed when
the temperature is measured within a time interval approaching the time

required to reach equilibrium.

12

The equilibrium relation is needed to justify that every atomic process
occurs as frequently as its inverse process. Consequently, the relation is
invaluable for information concerning collisional and thermodynamic processes.
As mentioned earlier, laboratory plasmas normally revolve around the principles
of LTE, which differs only slightly from ideal equilibrium. The inner and outer
energy state of individual particles in the plasma are populated as in complete
thermodynamic equilibrium, but accompanying blackbody radiation, which is
created mainly by electronic interactions, is missing or reduced“.

The number of unknowns is reduced considerably if various global
quantities are introduced that cover, macroscopically, the plasma region. In

particular, one temperature is taken for all three components. That is
T? = T1 = T, = TN (2.2)

- where TP, T,, TE, and TN represent the temperatures of the plasma, ions,
electrons, and neutrals, respectively. This simplification is the basis for local

thermal equilibrium.

2.3 Mean Free Path

As mentioned earlier, the validity of LTE requires that the intensive
variable gradients be small over the mean free path. lntuitively, it is then
reasonable to expect the mean free path, defined as the average distance

traveled by a molecule or atom between successive collisions, to be as small

13

as possible for this condition to apply. The mean free path, I, is not a directly
measurable quantity, but it can be computed by dividing the average molecular

(or atomic) velocity by the collision frequency or‘

, a (v) kT
Z find“?

(2.3)

where:

(v) . average molecular speed
Z = collision frequency
1: Boltzmann’s constant
T a- temperature
d . molecular diameter
P = pressure

It is obvious that l .is proportional to temperature and inversely
proportional to the pressure. Figure 2.1 illustrates the mean free path as a
function of pressure for various gases at 1000°K. This figure shows that the
mean free path approaches infinity as the pressure approaches zero. Therefore,
it is reasonable to expect LTE to become increasingly more valid at higher
pressures. This estimation was used to define the pressure range of 0 - 400

Torr for the laboratory experiments of this work.
2.4 Validity of the Ideal Gas Law
An assumption that is continuously made throughout these investigations

is that the gases in the system behave ideally in the plasma state. Fortunately,

this assumption can be objectively confirmed. Wisniewski et al. have

Mean Free Path. m

(Er-4)

0.1 3

0.10

0.08

0.03

0.00

 

14

Mean Free Path
Function of Pressure for Various Gases

 

Temperetwe - 1000'K

 

 

 

52?

 

 

 

Figure 2.1 Mean Free Path as a Function of Pressure

15

established the limit from which the ideal gas laws and equations are applicable

J2
_:_1/3]

n, . number of ions per cm3
s . electron charge

It a 801 tzmann’s constant
T a temperature

to the plasma state by the condition"

1.5
(( 1 (2.4)

 

     

 

21. 5(kn31

where:

Equation 2.4 is based on the low plasma densities that occur at high
temperatures and low pressures. For these conditions, the energies due to van
der Waals attractions and Coulomb forces can be neglected and the plasma
may be treated as an ideal gas.

The results of this criteria for the helium plasmas at the lower
temperatures begin at 10" and get lower as the temperature and thus, the ion
density, is increased. The number of ions per cm3 plasma (n,) was
conservatively determined, assuming 100% ionization, from the Saha equation
and ideal gas law. It therefore validates the assumption that the plasma state
is indeed represented as an ideal gas under these conditions.

The ideal gas law was also directly compared to the more accurate Peng—
Robinson equation of state to determine if significant changes occurred in the
pressure regions of interest. Data was generated for the Peng-Robinson
equations using a FORTRAN program to solve the cubic equation. The

temperature was held constant at 1000°K and the pressure was varied from

16

0.01 bar to 20,000 bar. The resulting volumes and compressibilities were
compared to that obtained using the ideal gas law. As illustrated in Figure 2.2,
the criteria of

V3331. - 1 (2.5)
is met for pressures up to 5 bar (3750 Torr). Since the experimental pressures
seldom exceed 1000 Torr, this again confirms that the ideal gas law applies to

the plasma state in these investigations.

2.5 Microscopic Plasma Phenomena

The plasma consists of a collection of electrons, ions, and neutral species
continuously interacting through elastic and inelastic collisions. The elastic
collisions are important for the transfer of kinetic energy, such as the elastic
collision between an electron and a molecule in the presence of an
electromagnetic field. The inelastic collisions, which are responsible for the
sustainment of the plasma, occur during the ionization processes whereby an
electron is made available for further interaction. It is therefore reasonable that
the reaction rate around the plasma is the collision rate of the constituent
species. In the case of laboratory systems, these collisions are mostly binary

and can be generally divided into the following interactions”:

17

Validity of Ideal Gas Law
LQL. vs. Pang-Robinson E.O.8.

 

      

 

 

 

 

1.0000
“ 0.00070 Helium en
5 . 1’ - 1000°K
: 0.00000 ~
5 b
\ 0.00020 r
41 0.00000 - E
> I
a i i
:5 0.00070 - :
~ 5
l
0.00000 ‘ ‘ ‘ * l L ‘
0 0 10 10 20
Preeeue. bar

Figure 2.2 Volumes Obtained by Ideal Gas Law Compared to those Obtained
by Pang-Robinson Equation of State

W
A + e' ~ A‘ + e' electron excitation
A' + e‘ -' A + e‘ electron de-exci tation
A + e‘ *A‘ + 2e’ electron ionization
A’ + e' - A + by radiative recombination
W
A” + B -o A + B’ electron transfer
A’ + A - 2A’ + e‘ ion ionization
W
A + A - A’ + A neutral excitation
A + A - A’ + A + 9' neutral ionization
A’ + B -o A + B' excitation transfer
RADIAHQN
A + by ~ A‘ radiativeexci tation
A‘ -° A + by radiative deexcitation
A' + hv -° A’ + e‘ radiative ionization

The radiation group is typically excluded from these investigations due
to the assumption that the plasma is collision dominated. This assumption is
validated by the fact that most of the emitted radiation is immediately lost to
the apparatus". Ion-neutral and neutral-neutral interactions can also be
disregarded since they result in either electron transfer or neutral excitation,
both of which are incorporated into the electron-neutral/ion interactions.
Therefore, only electron-neutralfion interactions will be of primary concern since
they contain the de-excitation and recombination processes that are responsible
for the thermal energy generation.

Though single atoms are used in these mechanisms, the relationships

apply equally well for gas atoms or molecules due to the thermal dissociation

19

that occurs at sufficiently high temperatures"

. At temperatures of the order
of 5000°K, it is safe to assume molecular dissociation has occurred and the
ionization processes have formed an electronic gas due to the detachment of
electrons from the atoms“.

The physical attributes of a plasma are also directly related to the local
placement of these microscopic phenomena. Concentration gradients are
generated in the plasma due to relatively slow surface reactions and fast
interior reactions. These gradients induce diffusion of species within the
plasma whose rate is primarily pressure controlled. The rate of ion-electron
recombination tends to increase dramatically at pressures greater than 400
Torr, which leads to the contraction of the plasma. At low pressures, and
hence large interionic distances, expansion of the plasma occurs and
approaches the dimensions of the containment due to wall recombination. The
relative plasma deformations are illustrated in Figure 2.3. The size of the
plasma also affects the density of species, which is proportional to the

hatchings in the figure. Variations in plasma dimension are measured through

photographic techniques, which are discussed in Chapter 4.

2.6 Microscopic Mass Balances

Knowing the exact amount of energy distributed to the plasma from the

calorimetry experiments, the microscopic system can be reduced to the plasma

20

TYPICAL PLASMA FORMATIONS

AT VARIOUS PRESSURES WITHIN QUARTZ CONTAINMENT

I I

 

 

 

 

 

 

 

 

«:3; 0A 9’?
CF w

 

200 Torr

Figure 2.3 Relative Plasma Deformations Caused by Changes in Pressure

21

medium which is open to the surroundings with respect to mass and heat
flows. The surroundings include the region of recombination. The overall
system for the MET concept is found in Figure 2.4. For illustrative purposes,
Figure 2.4 shows the direction of flow with gravity but actual experiments are
conducted with the gas flow directed against gravity.

The cold propellant entering the quartz discharge tube is coupled with
microwave energy 'focused" by the specially designed cavity into a specific
area to produce the plasma. Radiative, convective, and conductive heat is
transferred from the plasma to the immediate surroundings. The radiant energy
arises from changes of quantum levels of electrons. One mechanism by which
this occurs is by the incoherent emission of photons which causes the
blackbody radiation mentioned earlier. The net sums of these energy terms are
accounted for from the macroscopic energy balance introduced in Chapter 5.
The excited and other charged particles also flow towards the surroundings
which through collisional processes recombine downstream with increased
kinetic energy. The neutral and recombined species absorbs sufficient energy
to detach an outer-shell electron. This energy may come from the collision of
the atom with an electron or positive ion, from absorption of a quantum of
radiation energy, or from collisions of unionized atoms. Thermodynamic
expansion of this highly thermalized propellant generates the desired thrust for
the MET application.

The overall mass balance for the MET system is quite simple since it is

22

 

THERNODYNAMIO SYSTEM
AND SUR‘ROUNDINGS

 

 

 

 

 

 

 

 

 

 

 

WW: ]\ -—-II¢R0'AVIOAVITY
m,

Figure 2.4 Thermodynamic System for the MET

23

open to the surroundings, giving

Min T Moat (2“)

01'

”neutral: T ”recombined species ( 2 7,

T Mione T Melectrons T “unionized species

The solution to this equation requires experimental data to account for the
ionized species and electrons. A solution to this problem can be approximated
without experimental data using the Saha equation, which is based on
ionization potentials and describes the degree to which neutral species are
ionized. Though limited in several respects that will be identified, the Saha
equation incorporates many fundamental thermodynamic principles, such as
enthalpy, internal energy, and entropy into its derivation. Electrochemical,
electrostatic, chemical (or partial molar Gibbs free energy), and ionization
potentials of the systemls) under study are used in this equation which makes

its popularity widespread in electromagnetic environments.

2.7 System Thermodynamics

In general, a local thermodynamic state is used to define individual points
of a nonhomogeneous system, that is, a system in which at least some of the
intensive variables are functions of time and position. A postulate of LTE

states that although a thermodynamic system as a whole may not be in

24
equilibrium, arbitrarily small elements of its volume are in local thermodynamic
equilibrium and have state functions which depend on state parameters through
the same relationships as in the case of equilibrium states in classical
thermodynamics‘ 1 .
For a system in which this postulate is applicable, the specific entropy
and internal energy may be determined at every point in the same way as for

substances in equilibrium. The thermodynamic volume, temperature, and

pressure can then be defined through the following identity derivation“:

(if! = TdS - Pd! (2.8)
__ all _ all
CHI- (Eizds ('3?)de (2.9)
and therefore
611) _(&U)
T=(— P8 — (2.10)
35 r 61 a

where U and S represent the internal energy and entropy. Under these

conditions, the classical thermodynamic equations of state

f‘YlPln = o or 15“!“an = o (2011’

hold at every point, along with the Gibbs and Gibbs-Duhem relations, which are
used when considering multicomponent systems and are of particular interest
when dealing with the plasma state.

A condition that must be met before this assumption can be accurater

25

applied is that any gradient that appears among the intensive variables be small
over the molecular mean free path". This condition thus requires that all
macroscopic variations be sufficiently moderate so that the microscopic
collisions are significant. Plainly stated as it relates to plasmas, where the
collisional processes tend to dominate over the radiative processes, LTE
assumes that the velocity distributions of electrons, atoms, and ions and the
degrees of ionization may still be close to those pertaining to a system in
complete thermodynamic equilibrium'. Local thermal equilibrium then assumes
that the temperatures of the electrons, ions, and neutral species equal the
temperature of the plasma whole.

The presence of LTE enables critical plasma properties, such as electron
number density and electrical conductivity, to be evaluated solely as a function
of gas temperature. It is evident that this assumption provides significant
simplifications to plasma analysis, but can also provide erroneous conclusions
if unjustly applied to systems. Micci et al. recognized the questionable validity
of LTE in their conclusion which found that the electron densities of their model
were not properly accounted for“. Another case whereby the assumption of
LTE proved incorrect was in a study involving a low power arcjet nozzle
conducted by lube and Myers". Their results concluded that the plasma is
actually in nonequilibrium due to the relaxation times exceeding the particle
residence times.

It is clear that the plasma state must be represented thermodynamically

26

as a multicomponent system with the entropy of the system a function of the
internal energy. the volume, and the quantity of the individual components, N.

The internal energy can be equated to these variables as well. That is,
s= S(U,V,N1) and Us U(5,V,N,) (i=1,2,3,...,k) (2.12)

and the exact differential of the internal energy for an open system is of the

form similar to that giving in Equation 2.9,

6U BU 6U
dU :- — d3 — dV — dN 2.13
(as V.N1 + (av)3.N1 + 2( 6N1)3'y 1 ( ’
and
6U 6U 6U
T .. — -P = -— = — 2.14
(as v, N1 Iavi“, ”1 (M1)“, I ’

2.7.1 Chemical Potential

The partial derivative, [1,, is commonly referred to as the chemical
potential of the i"‘ component. The chemical potential is a useful relation as
evidenced by the following derivation. Equation 2.13 can be rearranged to

yield the Gibbs relation

dU = TdS - PdV + 2 pidNi (2.15)

Other Gibbs relations can be obtained similarly by utilizing the

fundamental definitions of enthalpy, H, Helmholtz free energy, A, and Gibbs

27

free energy, G, which are

H=U+PV A=U-TS G=H-TS (3-1‘)

to give

dH ‘ TdS + VdP ‘1’ EnidNi
dc .. -SdT + VdP + 201cm,

Rewriting the chemical potential to include the above partial derivatives gives

8!! 3A
8 —— 8 —- 3 —— (2e1.)
“1 (6N1)s.a (6N1)r.v (6N1 1.9
= (71 + 9‘71 - T51 “-1”
= C; (2.20)

i
From Equations 2.18 - 2.20 it can be seen that the chemical potential is
therefore equal to the partial molar Gibbs free energy".

Continuing the assumption that the gas behaves ideally, the molar

fraction, xi is

X! . (it) . fi (2.21)
P v2- V1
and hence

which can be more precisely defined as

28

1' T
dT P
u. = u,,<r,.z=,) +19,de - Tlcm'm'? + RTln-Fi— (2.23)

This finalized expression for the partial molar Gibbs free energy, where ”or
denotes the chemical potential of component i in the reference state at
temperature To and pressure Po, provides the basis for following derivation of

the Saha Equation".
2.7.2 Saha Equation

Typically, the ionization of a gas atom A occurs by the following

mechanism:

A *3 A‘ + e' (2.24)

where A decomposes into positive ions, A“, and negative electrons, e'. At
equilibrium, the summation of chemical potentials for these three components

multiplied by their corresponding stoichiometric coefficient is zero
23"le = 0 or In - up - II. = 0 (2.20)

where the subscripts A, A”, and 0 denote the unionized atoms, positive ions,
and electrons, respectively. A similar expression can also be derived using the
electrochemical potentials, which is a more extensive property that utilizes the

chemical potentials as well as the electrostatic potentials and electron charge.

29

In accordance with Equation 2.19 and the ideal gas assumption whereby

Dalton's law

k
z: P1 . P (2.20)
-1

holds true, the chemical potential can be expressed as

"1 3 Hi "' Tgi (2.27)

or, more specifically

”1 a FIT " CpiTlnT + RTlnPI + H01 " CPITO

+ (CpilnTo - Rlnpo ' SOI)T (202.,

where Ho, and So, are molar enthalpy and entropy of component i in the
reference state. If the reference state is taken at T0 = 0°K Equation 2.28 can

be simplified to

p, = FIT - cpiTlnT + RTlnPJl + Ho, - SociT (2.29)

where:
5001 g 01 ‘ pilnToo "’ RlnP,

is the reference constant introduced for the entropy at a new reference
temperature given by Too-
Equation 2.29, combined with Equation 2.25 yields the general

expression

30

(z: V1Cp1)T - (z: V1C91)TlnT + RTll{—Pi-;-€-'-] (2.30,
T zleoi " (213‘515001)T ‘ 0

This is an important expression in that it is composed of the vital
thermodynamic properties necessary to adequately quantify the plasma state.

The sub-expression
zvicpi " put) * cp(el ’ cpuu (2.31)

compensates for any change in the heat capacity that may occur during the
ionization reaction at constant pressure.

The sub-expression
ZviHoi = How) " H0(e) ' How = Ii (2.32)
1

determines the change in enthalpy that occurs during the ionization reaction at
a temperature of 0°K. l5, more commonly referred to as the ionization potential,
is the work’ required to remove an electron from its atomic orbit and place it at
rest an infinite distance.

The sub-expression
gvisou = 0001‘) 1' 500(0) ' 300m (2.33)

is used to determine the entropy changes that occur during the reaction.

The general form of the Saha equation can now be derived from

31

rearranging Equation 2.30 to give
1
Pum '5?“ - I: (2.34)
——-—- - BT e —
Pu, RT

where:

B = exp[%§:\l1(5001 ’ CP1)]

For the ideal gas in this investigation,

cm a -%R and -11—z;v1c,1 - g (2.35)

and the finalized expression for the Saha equation becomes

5 .1. - -11.
3:._P__ . T-sexpllni'x‘i“ av”) ..] . K m «a...»
P
where:

K,(T) = equilibrium constant for reaction
PM.) =- partial pressure of ions
PM . partial pressure of electrons
Pun :- partial pressure of unionized atoms
I, . ionization potential

Equation 2.36, along with some basic kinetics can be employed to
quantitatively solve the mass balance for the experimental investigation, which
includes helium gas. Helium is often used in plasma diagnostics since it is a
simple gas whereby only two electrons can be detached and consequently,

atomic data are widely available.

32

2.7.3 Degree of Ionization

To solve the mass balance, the plasma state must be further
characterized by the degree to which ionization occurs. Simply stated, this
quantity is the ratio of the number of moles of ionized atoms, ni, to the number

of moles of atoms before ionization begins, no, or

B 3 'I1:—: (2e37,

With the exception of atomic hydrogen, most gases will undergo multiple
ionization at temperatures in excess of 10‘ °K, therefore, a more general
expression must be used for the degree of ionization. The degree of k-fold
ionization, that is the number of electrons (k) leaving the electronic shell of the

atom, can be defined as

”I:

 

p . (2 . 38)
k n(tr-1)
The ionization of helium proceeds according to the scheme
He ‘ He. ‘1’ e- (2.3,)

He‘ '- He“ + e'

that is, the monatomic helium-atoms give rise to helium ions and electrons.
The resulting gas can then be treated as a mixture of proton gas and electron
gas, which are both treated as ideal gases. Since helium has two available

electrons to ionize, double ionization can also occur at sufficiently high

33

temperatures.

In general, the summation of the molar fractions within the gas must
equal 1. The number of ions in the plasma must be equal to the number of
electrons, since each is responsible for the other. These relations can be

written as molar fractions giving

xM) "’ x(A°l * xle) ’ 1 and x(A’l ' xlel 13"”

and the total and partial pressures can be defined as

P = Pun + PW, + Pr.) and P“, = Pm (2.41)
so
P = Pun " 2PM "' PIA) 1' 2pm., (2'12,
where:
Pun = me Pm = x(A°)P 13(0) = x(e)P

According to Equation 2.38, at equilibrium, Hemem out of Hem moles
of singly-ionized helium has become doubly-ionized, leaving the following

concentrations of species remaining in the gas

Hem " Hem (l-Dm) (2‘43,
Hem = Herman) ‘3'“)
e‘ = Hem (143(2)) (2.45)

The total number of moles of components in the helium plasma where

34

double ionization can occur is

N ‘ Hem * Hem * e‘
" Hem (173(2)) 1' Hemflm 1' Hem (1+B(2)) (2‘1"
' Hem (Ztflmi

The partial pressures of the individual components can be determined from

1'Pm

9(2) 1+B(2)
P P . ——P P . ——-P (2.47)
2+9“) (2) (O)

P a
(1) 2"”(2) 2*” (z)

 

Combining Equation 2.47 with Equation 2.36 (Saha equation) allows the

degree of ionization for helium to be expressed as

 

 

 

P P (1+3 )3
K = .43.).le = (3) (3) p (2.43)
p(2) Pm (2*Pm) (1'Pm)
which upon algebraic manipulation and rearranging gives
_ 1 l 2
Bur-3+ 7+“; (2.40)
KP

Using Equation 2.49, the degree of ionization for helium is plotted in
Figure 2.5 as a function of temperature and pressure. These results correspond
well to those obtained by Lick and Emmons, who used a statistical mechanics
approach".

The degree of ionization can be used to account for the primary
components of the helium plasma, which are the singly- and doubly-ionized
atoms and the electrons. The corresponding molar fractions can be relatively

determined from the above expressions to give Figure 2.6, which was

35

Helium Plasma Degree of Ionization
Functions of Temperature and Pressure

 

 

 

 

 

Deweeollonlzatlomfi

 

 

 

 

 

 

 

Figure 2.5 Helium Plasma Degree of Ionization Obtained from the Saha
Equation as Functions of Pressure and Temperature

36

Components of a Helium Plasma
chtion of Temperature. P I 76 mTorr

 

1 .00

0.40

Mole Fraction. X

0.20

 

 

 

0.00

 

Figure 2.6 Helium Plasma Molar Constituents at 76 mTorr Obtained from the
Saha Equation

37

computed at low pressure as a function of temperature.

As the temperature is increased, the singly-ionized atoms are ionized
further, thus producing more electrons to carry on the ionization process. It ‘
appears that equilibrium is achieved between the singly-ionized species and
electrons up to 20,000°l< and above 40,000°K between the singly- and doubly-
ionized species and electrons. Current investigations never exceed 20,000°l(,
so doubly-ionized species normally do not exist.

It is important to note that the Saha equation and thus the degree of
ionization is restricted to mOnatomic gases under conditions such that the
solution of unionized gas along with the products of its ionization may be
treated as an ideal gas. In accordance with the conditions for thermodynamic
equilibrium, all components of an ionized gas should, in the state of equilibrium,
be at the same temperature".

It is evident that plasmas can have a high degfee of ionization only at low
pressures, since the recombination of ions and electrons is directly proportional
to the number of molecular collisions and thus to the pressure. At low
pressures, and hence large interionic distances, the potential energy of the van
der Waals forces, which is inversely proportional to the sixth power of the
interionic distances, is negligible in comparison to the other components of the
internal energy.

The potential energy of Coulomb electrostatic forces which occur

between electrons and oppositely charged ions is another component of the

38

internal energy of the plasma. This energy is directly proportional to the first
power of the distance between ions and electrons. At high temperatures and
low pressures, that is, for low plasma densities, the energy of the van der
Waals attractions and of the Coulomb forces may be neglected and the plasma

treated as an ideal gas”.
2.8 Electromagnetic Theory

The theory behind electromagnetism as it relates to plasma formations
has been presented in detail by previous researchers". To avoid redundancy
and still maintain the topic thoroughness, only the finalized derivations of
important equations will be presented here.

The electromagnetic field is composed of the electric and the magnetic .
field vectors. These vector fields satisfy four classic equations known as

Maxwell's equations20

 

V'D-p 83
VXE.-§E (2.50)
VxF=3+gy - Mac?)
(I t
V°P=0

where:

39

D 8 electric induction
% 8 charge density

. electric field
B = magnetic induction
H a magnetic field
7 a current density
0 :- absolute permittivity

The electric induction is a function of the electric field, polarization
density, and the permittivity of free space (60)
D scoE+P (2.01)

where:

e, s permi tivitty of free space
'P :- polarization density

The polarization density can be eliminated from this expression if the electric
susceptibility (x,) is known. Furthermore, the dielectric constant (x,) is one
plus x,. The electric induction can be rewritten as
E = e,(1 + 1,)? =- e,x,2 . e'E' - (2-521
The magnetic induction is a function of the magnetic field, the
magnetization density, and the permeability of free space (”0)
E 3 "0(H‘FE‘) (2e53,

where:

permeability of free space

Po
5? magnetization density

Once again, the magnetization density can be dropped from this term if the

4o

magnetization susceptibility IXmI is known. The relative permeability (Km) is one

plus xm. The magnetic induction can be rewritten as

Psuo(x.+ HF:- poxfia (17! (2.54)

The current density is a scalar multiple of the electric field plus the
velocity of the media crossed with the magnetic induction. That scalar function

is the electrical conductivity (0). The current density is given as

JsoE+vx§=nV (2-55)

where:

o 2 electrical conductivity

V . velocity of media

n, as electron density

CHAPTER 3

 

Plasma Diagnostic System

3.1 Introduction

The plasma diagnostic system is designed to generate a stable plasma
in an isolated environment so various fundamental properties of the plasma may
be evaluated. These properties are studied through dimensional, calorimetric,
and spectroscopic analyses. In order to provide accurate and reliable
measurements, the system must allow for various parameters to be fixed
relative to one another and all active experimental components must be
calibrated independently.

The current system has been significantly modified from previous
systems to allow for flexibility in the research program along with the physical
enhancement of data measurements. The majority of the system components
are now digitalized or integrated to the computer data acquisition. These
changes will be explained in detail in the appropriate sections of this chapter.

An overview of the current plasma diagnostic system is illustrated in Figure 3.1

41

42

 

.\\\l IIIIII lull
: xii
. . . \lill.
. . . _
. . 1 u
o _ . _.
a u n L
cuaaozhzou

 

’04.; moz:m<1

 

 

 

 

o @ 3:3

 

 

 

 

 

) I s + @ 25.0.35.
.
u n . u z. 5»; -iI
:i _ :
lllll Is . . Uh
T IIIIII |\\ \- .. 0
T IIIIIII I‘ _ _ _ _ _ _
320 @ Q _ ®
hmozm
< :6 9A 02.9.5 5.. .23
® @ «0:32:86:
293:2
.Zzofizuxa 32... @
GU 02358 G

bm3<1xu

‘I IIIIIIIIII

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.... 55113
N 5
So «2 IILI r .I- .0. So «2
\IIL
I. ...... JO IIIIII 2
So 96 Sana

 

 

 

U @ 3138025.:

Experimental Configuration

Figure 3.1

43

and summarized below.

High-purity experimental gases (A) are volumetrically regulated into the
system by a digital controller (B). This control system maintains constant gas
flow rates and mixture ratios. The gas or mixture flows axially through a.
specially designed collar (C) and into the quartz containment (D) which is closed
to the environment. A second quartz tube (El surrounds the containment and
air is passed through the annulus to provide cooling and to enable convective
heat losses to be measured. The quartz tubing is positioned within a brass
resonant cavity (F) that can be mechanically altered to produce the desired
resonance. A sliding short (G) allows the cavity height to be varied from 6 to
16 cm. The coupling probe (H) transfers the electromagnetic energy from a
bidirectional coaxial cable connected to the power source to the cavity by
means similar to that of an antenna. Resonant mode TM012 is maintained
throughout these experiments. The source of microwave power is a Micro-Now
4208 oscillator capable of providing 400 watts of stable, well-filtered power
at a fixed frequency of 2.45 GHz.

The electromagnetic fields generated within the resonant cavity cause
free electrons in the gas to be accelerated to energies sufficiently high to ionize
other atoms by collisions. The resulting chain of collisions caused by the
released electrons produce the plasma, which is a collection of electrons, ions,
and neutral species. In order to initialize the plasma, the system must be

evacuated to pressures less than 1 Torr. This creates the large mean free paths

44

and thus, the sufficient electron energies required for ionization. An NRC
vacuum pump (l) provides a low pressure environment but is limited to 1 Torr.

The resonant cavity contains two Open ports (Jl positioned 90° on either
side of the coupling probe. These ports allow photographic and spectroscopic
investigations to be conducted. The size, shape, and color of the plasma are
macroscopically characterized by photographic techniques (K) over various
operating conditions. These measurements provide necessary data used in heat
and mass transport models.

The optical spectroscopy system is used to measure the line intensity
and widths of the plasma emission. A fiber optic cable (L), specially designed
to withstand the heat and microwave interactions, is positioned within the
cavity at various points along the plasma. The fiber optic is connected to the
spectrosc0pic system (M), which consists of a monochromator, photomultiplier
tube, power supply, and electrometer. The processed output is sent to a data
acquisition system where it is recorded on an AT computer (N). The electron
density, plasma frequency, percent ionization, atomic electronic temperature,
and molecular rotational and vibrational temperatures of the plasma are
determined as functions of absorbed power, pressure, and flow rate.

The experimental system is designed to allow for calorimetric
investigations to accurately measure energy inputs, outputs, and distribution
within the cavity. Energy lost to the cavity walls is calculated by measuring

temperature changes of water (0) circulating around the cavity. At low

45

pressures, wall recombination processes dominate the system and
consequently, convective heat transfer from the discharge tube well back into
the plasma occurs. Convective heat losses out of the plasma is calculated by
measuring the temperature difference of the air (P). Type T thermocouples
connected to an Omega 4008 Digicator (0) measure the inputs and outputs of
the air and water streams. The rate of energy that is transferred to the
experimental gas as it flows through the plasma system is determined as a
function of absorbed power, pressure, and flow rate from an energy balance
around the system.

The highly thermalized gas exits through the top collar (R) and is
exhausted through the pump. The top collar allows for the radial placement of
four additional thermocouples (S). This design enables temperature profiles of
the exiting gas stream to be made over various operating conditions. It also
allows for the time measurement of thermal equilibrium when parameters are

adjusted.
3.2 Microwave Source

The microwave source assembly is illustrated in Figure 3.2. The
microwave frequency oscillator is a Micro-Now Model 42081 (A) that provides
50 to 400 watts of stable, well-filtered microwave power at a fixed frequency

of 2.45 GHz to the cavity input probe. The maximum rating for the source is

46

©

Reflected
Fever

 

® ®I

Microwave
Fever

Didireeilenal]—_-®;*:E<:D

Coupler

j ' Cavity
© g @ Incident V

Pevrer ®

 

 

  
   

 

 

 

  
 

Coaxial
Reeleier

 

  

 

 

Figure 3.2 Microwave Source and Peripherals

47

500 watts but losses incurred from the microwave coaxial cable, circulator, and
bi-directional coupler reduces the maximum input to 400 watts. A Ferrite
2620 circulator (B) is connected to the oscillator and protects the magnetron
from reflected signals and increases the accuracy of the power measurements
(8). This is accomplished by providing the incident and reflected power sensors
with 20 Db of isolation. The system is further protected by reflected power
with a 500 Termaline 8201 coaxial resistor, or dummy-load (C). The incident
and reflected power levels are sampled by a 500 watt, 20 dB bidirectional
coupler (0). These power samples are further diminished by 20 dB attenuators
(E) and are measured by Hewlett-Packard Model 8481 A sensors (F) and. Model
435A analog power meters (G). The coaxial transmission line (H) transfers the

microwave energy to the microwave resonant cavity (I).

3.3 Gas Flow System

Ultra-pure “five-9" gases (99.99996). including nitrogen, helium, and
argon, are used in these investigations. Contamination found in spectroscopic
analyses prevented the use of conventional ”four-9" gases (99.99%). The gas
flow rates and mixture ratios are controlled by Hastings 202A Flow Controllers
powered by a CPR-4A digital source. These gases flow axially through the
plasma containment assembly and are exhausted out of the building.

The pressure within the system is controlled with an NRC vacuum pump

48

from 0.25 - 1000 Torr. The pump was completely disassembled and
refurbished, including filter, oil, and fitting changes, to achieve the 250 mTorr
pressures. The flow system accommodates both low- and high-pressure
environments by means of a reduced pressure regulator for fine adjustments
coupled with a course adjustment for higher pressures. The high pressures are
measured with a Heise gauge (0—1600 Torr) and an analog Hastings SV-I

gauge (0-200 mTorr) accurately measures the low pressures.

3.4 Plasma Containment Assembly

The plasma region is sustained in a cylindrical quartz tube having an
outer diameter of 33 mm. This 'inner" tube is surrounded by a 50 mm O.D.
"outer” quartz tube which enables air to be passed through the annulus for
cooling and calorimetric studies (ie. T,“ ,m - Tair in = AT). Quartz is used for
the containment since it is transparent to microwave energy and to visible light,
thus enabling spectroscopic and photographic diagnostics to be performed on
the plasma. The plasma containment assembly is illustrated in Figure 3.3.

Aluminum collars are epoxied to the ends of the quartz tubing and have
historically simply provided the connections for the entering and exiting gas
streams. Design modifications of the collars have provided additional
diagnostic capabilities. The old collars prevented the quartz tubing from being

replaced or cleaned once inside the cavity. The modified collars can be easily

'I

'I

CASOUT «I ::
I

mm IN ——> C

 

OUTER OUARTZ TUIINC

 

 

 

COLLAR” ASSEMBLY

:3» wow

3 ——> vane out

QUARTZ TUBING DIMENSIONS

Inner: 0.0. 8 1 19/64"
Wall Thickness = 1/16"
Length =- 24"

Outer: 0.0. 8 1 61/64"
Wall Thickness II 5/64”
Length =- 22"

COLLAR MATERIAL: Aluminum
FITTINGS: Stainless Swagelok/Ulira-Torr

Figure 3.3 Plasma Containment Assembly

50

removed from the cavity. The design modifications for the top and bottom
collars are illustrated in Figures 3.4 and 3.5.

The modified bottom collar contains two radial inlet ports, positioned
180° from each other, in addition to the axial inlet port. These ports allow for
swirling gas flows through the containment, which has been determined to aid
in plasma stability”. Swirling gas flows also provide angular velocity terms to
the equations of motion. The top collar contains four 'Cajon" ultra-torr fittings
that allow solid Type K subminiature thermocouples to be lowered directly into
the exiting propellant stream. This configuration is used to determine radial, as
well as axial, temperature profiles of the thermalized gas. The top collar is also

water cooled to prevent the high temperatures from damaging the epoxy seal.

3.5 Microwave Cavity

As depicted in Figure 3.6, the plasma containment assembly (A) is
positioned vertically within a brass resonant cavity, which can be mechanically
altered to produce the desired electromagnetic field to maintain the plasma.
The cylindrical cavity has a fixed 178 mm inner diameter and a length, L,, that
can be adjusted with a sliding short from 60—160 mm (B). The sliding short
simply consists of an inner base plate that is connected to an adjustable screw
(0). The coupling probe, which actually directs the microwave energy into the

cavity, is also an adjustable parameter (D). The probe distance into the cavity

51

Inn-re- 1/10' m

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TOP COLLAR g 99
COLLAR uArERIAL: Aluminum , z i: :1 r; r
: W 4' :1 u {l : '1' I
FITTINGS: Stainless Svagelok and Ultra-Torr : I (II/('- : 3".
*_m ”It, ‘1 _____ |
m 1,1. m E E o
l I
I "“"'
seam Ilse I yr e-ss : : 814'
\I: t 1W '—I :
7 "'_ * i 0
/ l" i "
/ I "" I
‘ I
r (”4
u4-—4
*——— I Is/se- —-—4
2 SI/H' %
SIDE VIEW

 

BOTTOM VIEW

Figure 3.4 Top Collar Design

52

BOTTOM COLLAR :A I «N

I———Iww——.

 

 

COLLAR MATERIAL: Aluminum
FITTINGS: Stainless Svagelak and Ultra-Terr

1D

   

 

1 11M

  
 

 

 

 

 

 

 

 

'r
' V" I—-— i vu- -—
the-
: I "" I
I /~ 1 In.

E I O 1110- ‘t) i
1 3/10' : i 1 ; :
I IP-I 3100‘ I I I
l I I :I/rI V".
L I . I, I .

 

 

 

a

.,::=U U D

m I/Ie' an

 

 

 

n/u- .__. m I/4- an
I—— Isa/Isl- —--I
*fi 1 01/30” a
SIDE VIEW

Figure 3.5 Bottom Collar Design

53

 

 

 

I Q
I -9;
13:3 0 Q
I..—s

O
.0
rig-I I @110

.jj' '1
o it": 1&3

Figure 3.6 Microwave Resonant Cavity

 

 

 

 

 

 

 

 

 

54

is represented by L,. By adjusting the sliding short and coupling probe, several
resonance modes can be supported. The resonance modes represent
eigenvalues of the solution to Maxwell's equations”. The mom resonant
mode was exclusively used in these investigation.

The resonant cavity must be completely free from microwave leakage,
but must also contain ports for diagnostics. Two ports are positioned 90° from
the coupling probe to allow for photographic and spectroscopic investigations.
The photographic port (E) uses fine mesh screen to prevent the propagation of
microwave energy. The spectroscopic port (Fl consists of holes drilled within
a brass block that are small enough to stop microwave leaks but large enough
for the fiber optic placement. These ports are designed to allow for visible
access to the plasma region (0) in the TMmz mode. Copper tubing is welded
around the top, bottom, and sides of the cavity for calorimetric inveS'tigations

(H).

3.6 Spectroscopic System

The spectroscopic system consists of a 1 m fiber optic cable, illustrated
in Figure 3.7, with a specially fabricated Macor ferrule to withstand the heat
and microwave interactions. This termination is 15 mm from the plasma region
(separated by annulus), which produces approximately 3 mm of plasma cross-

section to be observed. The exiting termination is stainless steel and is

55

 

 

 

 

 

 

 

 

Figure 3.7 Fiber Optic Cable with Terminations

56

connected to the monochromator by a 'Cajon' ultra-torr fitting. The sheath is
made from Silverflex and contains a 1 mm active area of quartz fibers. The
cable can be positioned at various radial and axial points within the cavity. This
fiber optic system greatly improved spectral resolution and sensitivity over the
glass lenses previously used to focus the emissions by reducing signal noise.
A comparison of a helium plasma spectra obtained with and without the fiber
optic system, found in Figure 3.8, illustrates the noise reduction.

As illustrated in Figure 3.9, a port (A) within the microwave cavity
houses the Macor termination of the fiber optic (B). The stainless steel
termination is connected to a McPhearson Model 216.5 Half Meter Scanning
Monochromator (CI and photomultiplier detector (D). The entrance and exit
slits were optimized at 0.1 and 0.15 mm, respectively. Most of the spectral
observations were made between 3000-7000 A. A Hewlett-Packard Model
6110A DC power supply (E) provided a high voltage of 900 volts to the
photomultiplier tube. The PMT output was processed through a Keithly Model
616 digital electrometer (F), sent to a Metrabyte data acquisition and control
system (6). and recorded on an AT computer (H).

The spectroscopic system was calibrated by two different methods. The
proper alignment of the monochromator is critical for the desired spectral
resolution and location of obscure emission lines. This was accomplished with
a mercury source whose spectrum is accurately known. A second calibration

procedure was required to develop a numerical constant for the photomultiplier

 

57

Helium Plasma Spectra Generated
With and Without Fiber Optic Attachment

2.90

 

with Fiber Optic
2.00 -

1.60 " fl

1.00 '

Relative Intensity

0.90 "

 

 

0.00 AA ' A ‘fi—A‘u‘

3790 ~ 3330 3970 3910 3950 3990
2.50

 

 

III/out Fiber Optic
2.00 -

1.50 '

1.00 '

Relative htenelty

0.30 '

 

 

 

 

 

0.00 i
3790 3830 3870 3910 3960 3990

Wavelength

Figure 3.8 Helium Spectra Obtained With and Without the Fiber Optic Cable

58

km..- smfl ©

[Electrometerj ® J

/ g @ __
H0n:::r:r£1ater 9! ~ %-

— © : O

Q ma.
4L4:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.9 Spectroscopic System

, 59

response. The constant is referred to as the spectral response function and
requires the use of a precisely calibrated tungsten source.

An NBS calibrated tungsten lamp was borrowed from the chemistry
department as a standard of spectral irradiance. The lamp, made by Optronics
Laboratories, Inc. Model 245C, was calibrated in 1989 and had only 10.5 hours
of use. The tungsten lamp normally used contained hundreds of hours of use
and was last calibrated in 1982. The older lamp had a significantly different
response function than did the new lamp. The chemistry department also
provided a dedicated power supply that maintained a current of 6.5 _+_ 0.0001
amps.

The response calibration was conducted over a wavelength range of
2500-8000 A. The spectral response function, R A, was determined by the non-
dimensiOnalized equation

12, a [___I'“'"!“] x [————I*D°'" (3.1)
1-590011’

Iknovn Inasured 1

The spectral response function was extended with linear interpolation

P1(x) = f, + (x -x,)[£1—-—1-:3] (3-2)
x1 '- x0

to calculate the spectral response function for specific wavelengths. The
results of this calibration procedure are listed in Table 3.1. The wavelength,
A, is in angstroms and the known and measured intensities, IK and IM, are in

nanoamps. This function is incorporated into all spectroscopic calculations.

5!“.

v‘

Table 3.1 Tungsten Calibration Data for Spectral Response

60

 

 

 

 

 

A IK IM R .4 A IK IM R,_
2500 0.389 489 0.1405 5300 303.6 227571 0.2358
2600 0.684 489 0.2470 5400 326.8 184259 0.3134
2700 1.190 734 0.2865 5500 ‘ 350.0 146331 0.4227
2800 1.950 979 0.3521 5600 375.0 125042 0.5300
2900 3.010 1468 0.3623 5700 400.0 109870 0.6434
3000 4.430 2447 0.31 99 5800 425.0 9421 0 0.7973
3100 6.750 4405 0.2708 5900 450.0 79528 1.0000
3200 9.070 7341 0.21 84 6000 475.0 64846 1.2945
3300 13.21 10767 0.2168 6100 497.2 50898 1.7264
3400 17.36 15906 0.1929 6200 519.4 38173 2.4046
3500 21.50 23002 0.1652 6300 541.6 27162 3.5239
3600 27.85 32056 0.1535 6400 563.8 18353 5.4292
3700 34.20 42578 0.1420 6500 586.0 11501 9.0047
3800 43.83 56036 0.1382 6600 607.2 7096 15.122
3900 53.47 72187 0.1309 6700 628.4 4160 26.697
4000 63.10 87847 0.1269 6800 649.6 2447 46.916
4100 77.28 108647 0.1257 6900 670.8 1468 80.744
4200 91.46 131649 0.1228 7000 692.0 979 124.94
4300 105.6 152693 0.1222 7100 709.0 489 256.03
4400 119.8 175695 0.1205 7200 726.0 489 262.17
4500 134.0 196494 0.1205 7300 743.0 489 268.31
4600 154.0 21 1910 0.1284 7400 760.0 489 274.44
4700 174.0 225369 0.1364 7500 777.0 489 280.58
4800 194.0 231976 0.1478 7600 788.8 489 284.84
4900 214.0 238093 0.1 588 7700 800.6 489 289.1 1
5000 234.0 242742 0.1704 7800 812.4 489 293.37
5100 257.2 242498 0.1874 7900 824.2 489 297.63
5200 280.4 243232 0.2037 8000 836.0 489 301.89

 

 

CHAPTER 4

 

Plasma Dimensional and Quality Analysis

4.1 Photographic Method of Analysis

One of the simplest and most useful methods of observing plasma
behavior is through photography. Conventional snapshot photography is
particularly useful in the study of plasmas where rapid changes in luminosity,
size, and shape occur. These measurements can aid in the modeling of heat
transfer and chemical processes within the plasma region”.

The plasma dimensions and quality (which refers to the plasma stability,
shape, and color) were determined by photographing the discharge at a known
distance with 35 mm color slide film. The image was then projected against
a 100x100 mm grid, also photographed from the same distance, and analyzed
for size, color, and shape.

A Pentax MX 35 mm camera, mounted on a tripod, was used in these
investigations. It was found that low-speed film (100 ISO) combined with a

rapid shutter speed (1/250 5) and f1.7 aperture, produced the clearest slides.

61

 

62

Further improvement was made by mounting three Hoya dioptric lenses (sizes
+1, + 2. and +4) to the camera lens. The total distance from the end of the
dioptric lenses to the plasma was 88 mm. Each analysis was conducted in

triplicate for improved accuracy.

4.2 Plasma Overall Volume

Previous researchers have devoted considerable effort to understanding
deviations in the size and shape of single-component plasmas with pressure,
power, and gas flow rate. These characteristics have been monitored in both
the inner and outer regions of the plasma which are referred to as the strong
and weak ionization regions, respectively. Leonard and other researchers,
however, suggests that caution be exercised in this interpretation of the
luminosity gradients of the plasma as distinct boundaries“.

The dimensional analyses conducted most recently have utilized the
single-component gases used previously with additional emphasis directed
towards overall volumes compared to those of a binary mixture. The cavity
system, quartz containment, and dimensional measuring technique has also
been altered to improve sensitivity and accuracy.

The binary mixture used in these investigations consisted of 50% (by
volume) helium and nitrogen. All experiments were conducted by mixing the

gases prior to interacting with the microwave energy. Observations revealed

 

63

that when the composition was altered following plasma formation there was
only slight apparent volume change. This possibly indicates that the plasma
acts as a control volume with well-defined boundaries that allow little, If any,
mass transport into or out of the system.

The nitrogen and argon plasmas in these investigations were shaped
similarly to an oblate ellipsoid. Assuming axial symmetry the volumes were

easily found by the equation

41: L 3
-.- _ _ _ 4.1
v, 3 2x 2') I l
where:
V, = ellipsoidal volume
L = plasma length

W = plasma width

Helium plasmas exhibited an indentation at their center and the volume, V,,

was therefore calculated as two dumbbells connected to a cylinder or
- 2 1' 3 1! a A
V"2II3II2II”I2II2I “'2’
4.2.1 Pressure Dependence

Single component and binary mixture plasmas were generated and
evaluated as a function of pressure from 20 - 1000 Torr. The results are

illustrated in Figure 4.1. The parameters held constant are listed in Table 4.1

Plasma Overall Volume
Function of Pressure

 

 

 

 

 

 

 

 

13

‘1 '° I mm
8‘ 11 O , O “um
.5 10 ' V 80I80 “x
i . -

0

> . I-
E , P

‘ I

a I-

‘ J 1 1 l 1 1

0 200 400 300 800 1000

Presewe (Torr)

Figure 4.1 Overall Plasma Volumes for Helium, Nitrogen, and Mixture as a
Function of Pressure

65

below.

Table 4.1 Plasma Volume Conditions

If

 

 

Net Power Input = 240-250 W
Total Gas Flow Rate = 500 sccrn

Equilibration Time
Air Coolant Rate 2 scfm
Water Coolant Rate = 5.75 les

Film Speed = 100 ISO
Shutter Speed = 1/250 5
Aperture = f1.7
Resonance Mode = TMmz

15 min.

 

The overall volumes of the single-component plasmas coincide well with

previous work23'25.

A simple polynomial was used to represent the trends for
these plasmas. The volume decreases exponentially with increasing pressure.
This phenomenon is expected in theory since the mean free path at the lower
pressures is large enough to allow high-energy interactions between the neutral
and electron species. Though the collisional frequency increases linearly with
pressure, the mean free path decreases exponentially thus preventing sufficient
energy exchange at the higher pressures. Consequently, the rate of ion-
electron recombination and the percent of ionization decreases with the higher
pressures forming a smaller volume.

The nitrogen plasma decreases at a slower rate than does the helium

plasma. This is in part due to the sluggish nature of the larger molecule and

thus, shorter mean free path. The other reason for this slow response to the

grew-1

66

pressure change is the diatomic structure of nitrogen. The additional energy
modes require greater energy for ionization and the plasma is thus not as
susceptible to environmental alterations, with the exception of power input.
The binary mixture exhibited interesting characteristics indigenous to
both components and was fitted to a spline for better representation. At lower
pressures, the same abrupt change occurred as with helium but the volume
was slightly smaller than that of helium which contradicts logic for this mixture.
The slope approaches unity at moderate pressures and increases towards the
nitrogen curve at higher pressures. This unusual trend is difficult to explain
theoretically since the slow evolution of the nitrogen ions would be expected
to occur at the lower pressures where the mean free paths would be at their
maxima. Perhaps the helium species obstruct the collisional processes

necessary for the molecular dissociation of nitrogen.
4.2.2 Gas Flow Dependence

The Overall volumes were determined as a function of gas flow rate from
50 - 500 sccm maintaining the same parameters as those found in Table 4.1,
with the exception of power (275 W). The pressure was held constant at 400
Torr. As revealed in Figure 4.2, the flow rate has less influence on the volume
that does the pressure. The volume decreases with increased flow rate which

indicates that the smaller number of atoms allow greater energy and mass

67

Plasma Overall Volume
Function of Gas Flow Rate

 

12

 

l Heliun
1 1
0 Mtrogen

10 ‘I' v 00\00 sex

 

 

 

 

 

 

Plasma Volume (001')
e
0

 

 

‘ l l J 1 l l 1 1

60 100 150 200 260 300 380 400 480 600

Gas Flow Rate (scorn)

Figure 4.2 Overall Plasma Volumes for Helium, Nitrogen, and Mixture as a
Function of Gas Flow Rate

68

transfer due to fewer obstructions. In other words, fewer collisions take place
but each collision occurs with greater energy than would occur with an
increased number of atoms.

As with the pressure dependence results, the diatomic nitrogen plasma
undergoes a much more gradual volume change than does the monatomic
helium plasma. The mixture exhibited the same gradual change as that of the
pure nitrogen but the magnitudes in volume were closer to those in the helium

plasma.

4.2.3 Composition Dependence

Earlier experiments with mixtures of helium and nitrogen revealed an
inflection occurring at 70% helium suggesting that the 1:2 (33%l67%) atom
ratio was the cause. If this was indeed the case, then two monatomic
elements would fail to show this inflection. Argon was introduced into the
experiment to better assess the relationships between monatomic/diatomic and
monatomic/monatomic mixtures. These results are illustrated in Figure 4.3.

In general, the maxima occurred for the pure component extremes with
the minima in between. Pure argon exhibited the largest plasma volume,
followed by nitrogen and helium. The argon/helium mixture lost its definite
ellipsoidal shape at 70% and was transformed into a mass of filaments but its

trend seemed to be similar to that of nitrogen/argon.

 

69

Plasma Overall Volume
Function of Composition (by as volume)

 

 

 

 

 

 

 

 

Plasma Volume (cm'l

 

 

 

 

0 10 20 30 40 80 60 70 80 90 100

Gas Composition I! of first gas listed)

Figure 4.3 Overall Plasma Volumes as a Function of Composition (by volume)

70

The inner volumes of the plasma mixtures followed the same general

trend as the overall volumes. These volumes, along with the plasma color

transformations, are summarized in Table 4.2 for a helium and nitrogen plasma.

 

 

 

Table 4.2 Inner and Overall Volumes and Color Transformations for
Helium/Nitrogen Plasma
Gas V0 V. V, Plasma Color I
Composition (cm3l (cmal (%l Outer Inner
100% He 9.35 2.58 27.6 blue white
90% Hel10% N2 3.87 0.12 3.1 blue/pink white/pink
80% He/20% N2 2.91 0.17 6.0 bright pink light pink
70% Hel30% N2 2.03 0.24 11.8 bright orange light orange '
60% Hel40% N2 3.68 0.76 20.7 orange light orange
50% He/50% N2 3.81 1.17 30.8 orange light pink
40% He/60% N2 4.26 1.01 23.6 light pink light pink
30% Hel70% N2 4.81 1.02 21.1 light pink light pink
20% He/80% N2 6.08 1.32 21.7 light pink pink/white
10% He/90% N2 7.26 1.89 26.0 pink white
100% N2 7.96 2.31 29.0 pink white

 

The behavior of these mixtures suggests that the ionization potentials,

IA, for the three components do not contribute significantly to deviations of the

plasma volume (lm > I", > IAr > IN). The size of neutral species, however,

seem to be the controlling factor which again goes back to mean free path and

the collisional processes.

71

4.2.4 Power Dependence

The dependence of microwave power on plasma volume was determined
as a function of gas flow rate maintaining identical conditions as those found
in Table 4.1. This investigation was conducted on pure helium gas at a net
power of 200 and 300 W. These results are found in Figure 4.4.

Helium plasma volume decreases with increased flow rate at higher
power inputs as with above experiment. However, at lower power levels the
volume decreases slightly. This confirms the hypothesis that power
”saturation“ does occur with the helium plasma. This investigation confirms

that power levels have a significant influence over plasma size.

4.3 Gas-Surface Interactions

The effects of recombination greatly influence variations in the size and
shape of the plasma region. The recombination of ions can be catalyzed by
virtually all species and surfaces to which the ions are exposed. At low
pressures, this recombination is dominated by interactions with the
containment walls, which results in the plasma expansion of Figure 2.3. The
ability of a surface to catalyze recombination can be expressed as the fraction
of atoms striking the surface that recombine, known as the wall recombination

coefficient (WRC). Metals have the highest wall recombination coefficient with

 

72

Plasma Overall Volume
Functions of Gas Flow Rate and Power

 

 

 

 

 

Plasma Volume (0111‘)

 

 

 

 

 

0 100 200 300 400 800

Gas Flow Rate (eoaml

Figure 4.4 Overall Plasma Volume for a Helium Plasma at 200 and 300 W as
a Function of Gas Flow Rate

5

r.” ‘3"

If“

73

platinum equal to 1. Quartz and pyrex glass have a WRC of approximately 10‘3
and 10*, respectively“.

There are several expressions that describe the rate at which this wall
recombination occurs. Chapman, Finzel, and Hawley recommend the

following”:

r, = 1;,[c1 (moi/s) (4.3)

where the plasma surface area and molar concentration are represented by A,
and C, respectively. The surface reaction rate constant, k,, is related to the

wall recombination coefficient by

VII
k‘ = ”C [T] (‘0‘)

where Vm is the average velocity of the gas molecule. The WRC for fused
quartz can be accurately determined from a fit to an Arrhenius plot as a

function of wall temperature, Tw, by the expression

mac = 0.0566exp(;1—-1;-8—':1) (4.5)
'

Using this expression, the assumption of thermal equilibrium must be made so
that the wall temperature is the same as the gas temperature. Since the
temperature of the wall is primarily due to the highly exothermic recombination
reactions that occur at the wall, it is unlikely that the gas temperature equals

12

the wall temperature . It appears that the energy transfer due to these wall

reactions increase with an increase in pressure and a decrease in gas flow rate.

 

74

This is easily explained through the long residence times which creates a more
intense plasma.

The measured size of the plasma has been incorporated into Equation
4.3, which complicates the computations since the plasma area changes as a
function of pressure. The effects of the plasma area can be determined by
using a constant value in Equation 4.3 and comparing its results with those
obtained with another expression. This will be accomplished by using the
equation derived from Wareck for the wall recombination rate, which includes

the random velocity term from kinetic theory, V,,28

 

V
IV = WIN-{25] (collisions/s) “-6)
where:
.1.
VI = [M12 (m/S)
11m

Equation 4.6 excludes the wall temperature, so the assumption made in the
former expression that TW = T, is eliminated. Another advantage of Wareck's
equation is that it doesn’t incorporate the plasma area, so a comparative
analysis can be made between the various gases under evaluation. However,
Wareck's equation does place a strong dependence on the speed of the gas
molecules which is influenced by the pressure. The random velocity values are
only slightly different from the average velocities used in Equation 2.3. Figure

4.5 compares Equations 4.3 and 4.6 on the theoretical wall recombination rate

 

 

75

Wall Recombination Rate vs. Temperature
Effects of Area on WRR

 

 

 

 

2000
. D
2 i .e”
P .0
i 2000; .,.°'
; Area Included ,."
s »
a 1800 ' i e... aIL
I ’O a".-
g I ... .-....
i 1000; ’0’ 11"".
. .“
3 . ...° ._..-' Area Excluded
’ e. a'.
c ‘00 i:- ......-...
g ’ 133""
. I
0"“.Jl“l‘ll“All“‘J““
200 700 1200 1700 2200 2700

Temperance. ‘ K

Figure 4.5 Comparison of Wall Recombination Rate Equations for a Helium
Plasma as a Function of Gas and Wall Temperatures

76

for a helium plasma as a function of temperature. The curve marked “area
included" incorporates Equation 4.3 and assumes a constant pressure and
corresponding plasma area (A, = 20 cmzl. The other curve, marked “area
excluded', utilized Equation 4.6 where plasma area was irrelevant. This figure
reveals that the quantities do converge at lower temperatures. The
experimental gas temperatures are estimated to be approximately 1000°K

where the figure shows only a 25% separation difference.

 

CHAPTER 5

 

Calorimetric In ves tiga tions

5.1 Macroscopic Energy Balance

As mentioned earlier, calorimetric evaluations are conducted to describe
the energy absorption and distribution of the system. There are two systems
used in this evaluation. Macroscopically, the thermodynamic system is the
microwave resonant cavity found in Figure 2.1 which encompasses the quartz
containment. This system is used to quantify the energy distribution from the
microwave power source. Approximately 80% of the total microwave energy
is actually coupled into the plasma since a portion of the energy is reflected
back to the source and a portion is lost to the cavity walls through radiation.

The differential form of the general energy balance is15

2 . 3 . .
§EU+M(—‘;—+t)]=;lfi(fi+%-+')k+Q+W “-1)

For an open steady-state system and ignoring the kinetic and potential terms

since the gas velocity is much less than sonic, the energy balance becomes

77

78

Egkfik ‘1' Q. + w. I o (5.2)

Since no work is done to or from the system, the total heat is defined as

E 1.1km . -0 (5.3)
and upon rearranging yields the energy balance around the resonant cavity
system

E"source 3 Egas T 3.21: T Easter T Eradiation (5")
where:
Esource = P1 T Pr

1'
Eair T [Cp,airfiairdTair
To

1'
Enter = [CpmacezfivacerdTvacez
70

Pi and Pr are the power incident and reflected, respectively, measured by power
meters. The reflected power is the power lost due to improper resonant modes
that literally reflect a portion of the power back to the source. The incident
power is the net power that is transferred to the cavity. The air flows through
an annulus surrounding the inner quartz tubing and serves as a coolant to
prevent high temperatures from melting the discharge tube. The water

circulates around the resonant cavity and accounts for the energy lost to the

 

79

cavity wall. The flow rates of the air and water are controlled through
calibrated flow meters and their temperature changes are determined by
thermocouples positioned at the inlets and outlets.

The flow rates have incorporated density corrections into their

calculations to account for changes in temperature”. For air this gives

H81! 3 0.01627F.12p.11 ‘SeS’

where:

 

273.13 s—.37eae g
I, = . 929 ,
p I 1 2 I 1' II 760 I L

with T, B, and e representing the temperature (°K), atmospheric pressure (mm
Hg). and moisture vapor pressure in air (mm Hg). respectively.

For water this gives

Mm“: 0.05551“ (0.0)

“COIP “ EDI

where:

0...,“ = 1.001826-0.00017T, 3%,.

with the temperature in degrees Celsius. Combining Equations 5.4 - 5.6 give
the following single-variable expression for the calculation of the amount of

energy actually transferred to the plasma:

Egas T Pi T Pr T fcp,airMairdTairT fcp ,vater'Mwaterd Twater (5'7)
T0

80
5.2 Energy Distribution

These experimental results represent the energy coupled to the plasma
region combined with the energy that was absorbed by the air coolant. Since
the air is moisture-free and thus, completely transparent to incident radiation.
all energy absorbed by the air can be taken as convective losses from the
plasma. The cavity system was polished with steelwool and the quartz
containment was replaced thereby improving the efficiencies by approximately
20% over previous experiments.

As with the dimensional investigations, the binary mixtures were mixed
prior to interacting with the microwave power since the well-defined boundaries
of the plasma allow little energy transport into or out of the system. The

maintained parameters for these investigations are summarized in Table 5.1.

Table 5.1 Calorimetric Conditions

 

 

Net Power Input = 275-300 W
Gas Flow Rate = 500 sccm

Equilibration Time = 30 min

 

Air Coolant Flow = 2 scfm
Water Coolant = 5.75 mL/s
Resonance Mode = TMou

81

5.2.1 Pressure Dependence

The energy distribution was determined as a function of pressure from
20 - 700 Torr for pure helium and nitrogen and their 50/50 mixture. These
results are found in Figure 5.1.

Pure nitrogen increases slightly with pressure due to the additional
energy modes which incorporates a “heat sink“ effect into the plasma once it
is initiated. The inverse relationship between energy absorption and volume
indicates that the available surface area is not the primary means of energy
transfer as once thought. Helium absorbs greater power at lower pressures.
At higher pressures, the decrease in ionization causes instabilities within the
plasma. The helium actually seems to become ”saturated" with power at the
higher pressures as opposed to the nitrogen which continues to absorb energy.

The binary mixture again exhibited similar properties as each of its pure
components. The energy absorbed decreases at lower pressures and begins to

increase towards that of nitrogen at higher pressures.
5.2.2 Gas Flow Rate Dependence
The calorimetric dependence of gas flow rate was evaluated at 400 Torr

under the conditions in Table 5.1. As illustrated in Figure 5.2, similar trends

were obtained with variations of the flow rate as with the pressure but much

 

82

Plasma Energy Absorption
Function of Pressure

 

80$

 

 

 

Energy Absorbed by Home

 

 

 

 

 

us
83% r - _-
. ‘
[- Heliun o Nitrogen v 50150 Mix]
'2‘ A L A 1 4 J A l n J n L
0 too zoo 300 400 soo 600 700

Promo (Torr)

Figure 5.1 Plasma Energy Absorption for Helium, Nitrogen, and Mixture as a
Function of Pressure

83

Plasma Energy Absorption
Function of Gas Flow Rate

 

   

 

    

 

0 lltrogen ' 60150 “x

 

 

 

85$ '

 

 

 

Energy Absorbed by Plume

 

 

 

81$
50 150 250 350 450 550 650 780 850 950

Flow Rate. eoom

Figure 5.2 Plasma Energy Absorption for-Helium, Nitrogen, and Mixture as a
Function of Gas Flow Rate

84

more dramatically. These results differ from previous researchers work for
helium who only took into account energy absorbed by the plasma and not its
convective/radiative losses into the air'9-25. The helium plasma again becomes
saturated with energy at higher flow rates but the nitrogen continues to absorb

energy.

5.2.3 Composition Dependence

Cubic splines, opposed to simple polynomials, were used to represent the
trends found in Figure 5.3 to draw attention to the various inflections that
arose. The argon/helium mixture exhibited an inverse relationship at 30%
compared to that of the helium/nitrogen mixture. This inflection was thought

to have occurred due to the diatomic/monatomic species.

85

Plasma Energy Absorption
Function of Composition (by 95 volume)

 

 

 

 

 

 

 

so;

r - Arle
5 saw 0 Arm:

v mm:
X
‘ sex-
3 “t V
a ' O
Q us-
I“
80‘ l l l l l l l l I

 

O 10 20 30 40 BO 60 70 80 90 100

ass Comesition (% of first gss listed)

Figure 5.3 Plasma Energy Absorption as a Function of Composition (by
volume)

 

CHAPTER 6

 

Spectroscopic In vestigations

6.1 Introduction

in order to optimize the thrust and improve nozzle designs and modeling,
a better working understanding of the plasma processes must be acquired.
Quantitative spectrosCOpic techniques are one of many diagnostic tools used
to explain fundamental behavior within the plasma”. Spectroscopy is a prime
technique, since it is nonintrusive to the plasma medium and can be applied for
the measurements of species temperature, species populations, and even
species velocities. Most of the spectroscopic techniques are conceptually
simple, reasonably accurate, and require little peripheral instrumentation.
However, when high degrees of sensitivity and spatial resolution are desired,
more sophisticated techniques, such as laser-induced fluorescence, must be
introduced.

The goal of these investigations is to use emission spectroscopy to

obtain temperatures and concentrations of pure gases; Several methods exist

86

87

for converting emission line intensities into more useful quantities, such as
temperatures and densities. These methods will be introduced along with the

general theory behind spectroscopy.
6.2 Theory

A hot solid or melt produces a continuous emission spectrum whose
simple characteristics are an attribute of the strong atomic coupling. A hot gas
or plasma contains weakly coupled particles and hence many more independent
degrees of freedom than does the solid or liquid. Consequently, the emission
spectrum of a hot gas is more complex consisting of a few spectral lines, many
lines arranged in band systems, continua, or combinations of lines, bands, and

confinua.
6.2.1 Spectroscopic Temperature Measurements

Temperature measurements obtained from spectroscopic analysis can be
grouped into radiometric and spectrometric methods. Radiometric methods
typically apply to “optically-thick“ gases where radiation is strongly absorbed
such as large flames and exhaust gases. These methods are primarily
thermodynamically based and involve little reference to the mechanisms of

radiation. Spectrometric methods apply to weakly absorbing or ”optically-thin"

88

gases and entail explicit use of the quantum theory of optical spectroscopy.
Spectrometric methods are commonly used for plasma diagnostics but
Herzberg has shown that these two methods are equivalent in the limit as the
radiative absorption goes to zero31 .

A plasma contains ions and electrons in addition to the monatomic,
diatomic, and polyatomic molecules that normally exists in a gas. Plasmas with
temperatures up to approximately 8000°K are composed mainly of atoms and
diatomic molecules, plus a few percent of ions (atomic and molecular) and
electrons. Most polyatomic molecules have been completely dissociated at
these temperatures.

The kinetic and internal degrees of freedom for a plasma can be regarded
as a thermodynamic system, and each such system has a temperature. The
kinetic or translational temperature is a measure of the mean kinetic energy of
the particles. The kinetic theory of gases states that each of these particles
has a velocity distribution given by the Maxwellian law, which assumes the

only interactions that occur among particles are elastic collisions. In practice

this condition only holds at low pressures”. The Maxwellian law is given by

-l-fl

3 (6.1)
N, a v’e H

The kinetic energy is related to the temperature by

89

3.1.7: .3. ,
E 2m (2)kT (‘2)

and the kinetic temperature is that temperature which satisfies Equation 6.2.
Statistical physics is used to define the internal degrees of freedom of
gas particles and the distribution of gas particles with respect to available
internal energy states is given by the Maxwell-Boitzmann formula”
8
Ngje 1*

N1 = (6.3)

;‘4

 

Since the internal degrees of freedom are nearly independent, there may
be one Maxwell-Boltzmann distribution for each one. That is, one Ei may
represent the energy due to internal vibration, another for rotation, and another
for the energy of orbital electrons. Consequently, there may be a
corresponding temperature for each energy distribution, such as vibrational
temperature, rotational temperature, or electronic temperature. These
temperatures are equivalent when the gas is in thermal equilibrium and are
equal to the kinetic temperature.

Penner and others question the importance of non-equilibrium in
spectroscOpic temperature measurements“. A spectroscopic errancy that may
be thought to have occurred due to non-equilibrium may turn out to be caused
by self-absorption, temperature gradients, or the use of incorrect spectroscopic

constants in calculating a temperature.

90

6.2.2 Degrees of Freedom

It is the internal degrees of freedom that give rise to the various kinds of
spectra observed. Equations 6.1 and 6.3 are used to characterize the
equilibrium state of each degree of freedom and each degree of freedom that
produces observable spectroscopic radiation provides a parameter to measure
temperature. The major internal degrees of freedom for an atom (or ion) with
a single orbital electron is illustrated in Figure 6.1. The optical behavior is
determined by the orbital electron which can be found in the ground energy
level or in one of the excited levels. Each of these energy levels contains a
cluster of atoms whose temperature-dependentdistribution is given by Equation
6.3.

The energy of an atom or ion is continually being changed by radiation
and by collisions with other particles. The absorption of radiation into an atom
forces its orbital electron to make a transition to a higher energy level.
Conversely, when an atom emits radiation, its orbital electron makes a
transition to a lower energy level. The "excitation“ transition refers to the
occurrence of radiant emission or radiant absorption at a particular spectral
wavelength. Combining all such transitions occurring in a gas produces the
observed line spectrum of the atomic species.

The transition labeled "ionization” occurs when the energy imparted to

an orbital electron by a collision or by absorption of radiation causes its total

Energy

91

ATOMIC ENERGY LEVELS

Free Electrons

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Free/Bound Electrons

 

 

 

 

 

Bound Electrons I

f ionization
excHa

tion

 

Ground Level

Figure 6.1 Atomic Energy Levels

92

energy to exceed the ionization potential of the atom. The excess energy
completely removes the electron from the atom, leaving behind an ion, which
has a different set of energy levels, and hence a different line spectrum, from
the neutral atom. The stripped electrons may recombine with the ions to form
neutral species, or they may remain free in the gas. The recombination causes
a continuous frequency band in the emission spectrum to be observed”.
Radiation observed in the uv-visible region is the result of electronic transitions.

The energy levels of a diatomic molecule are complicated by a potential
energy curve representing the electronic state for each configuration instead of
a constant energy as for the atoms. As two molecules approach each other
they first attract and then repel. In discussing molecular interactions it is
convenient to use plots of potential energy, V, versus intermolecular distance,
r. The interaction energy is zero when the molecules are infinitely far apart.
As they approach, the potential energy becomes negative because the system
has a lower energy than if the molecules were completely independent. At very
close distances molecules repel each other and the potential energy increases
rapidly. Potential energy curves for various diatomic gases are illustrated in
Figure 6.2. These curves were generated using the Lennard-Jones 6-12
equation and show that a minimum intermolecular distance exists where dV/dr
= 0. These potential energy 'wells" are more dependent on the size of the
molecule than the collisional process.

The complexities of the energy levels of a diatomic molecule are detailed

93

Typical Potential Energy Curves
for Diatomic Species

 

50
Oslculsted from the
40 '- Lennsrd-Jonss Sit: Emstlon
20 P
0

 

 

 

 

Potentlsl Energy
I
D
o

 

 

 

 

 

 

 

0.25 0.3 5 0.45 0.55 0.55 0.15

Distance Between Molecdes. nm

Figure 6.2 Potential Energy Curves for Diatomic Species

94

in Figure 6.3. The molecule has a vibrational degree of freedom along the
internuclear axis, and the vibrational potential energy varies with the separation
between the nuclei. In any electronic state, the molecule can vibrate along the
internuclear axis and rotate about an axis perpendicular to the internuclear axis.
A different set of energy states corresponds to each of these degrees of
freedom.

The observed spectra for the rotational, vibrational, and electronic states
are found in widely different regions. This is the result of the relative spacings
between the states, with vibrational states more closely spaced than electronic
states, and rotational states even more closely spaced. The energy difference
between the sates in a transition is proportional to the frequency of radiation.
Consequently, the rotational spectra is found at the longer wavelengths of the
far infrared and microwave regions, vibrational spectra in the near infrared, and
the electronic in the visible and ultraviolet regions.

The kinetic degrees of freedom contributes directly to the finite width of
the spectral line. Indirectly, the kinetic energy affects the spectroscopic
radiation by determining the gas temperature and thereby the populations of the

different energy states”.

Energy

 

95

Degrees of Freedom for
Diatomic Species

 

--------- i Rotstlcnsl stste

°°°°°° ’I

 

lnternuclesr Separation

Figure 6.3 Degrees of Freedom for Diatomic Species

 

 

96
6.3 Methods of Analysis

A variety of methods exist for the spectroscopic determination of
temperatures and populations within a plasma. These methods are based on
kinetic theory and statistical physics using the Maxwell-Boltzmann formulas.
Experimental investigations were conducted using the Single-line, Two-line
ratio, and atomic Boltzmann methods to obtain electronic temperatures. These
experimental temperatures were compared to those obtained from theory and

used to estimate the constituent species within the plasma.
6.3.1 Single Atomic Line Method

When self—absorption is negligible, that is, the reabsorption in one part
of a hot gas of radiant energy emitted by another part, the integrated radiance

of an atomic emission line is33
I = __c 1 (“A (6 4)
n- 4“ P 1.th ’

The transition probability, Am, referred to as Einstein's coefficient, can be
found in numerous referenceszs' 35. The number density, p“, is given by the

Maxwell-Boltzmann relation

97

a.
pin) z 90%;}? (5.5)

Combining Equations 6.4 ~ 6.5 and substituting v“m allm“, gives the radiance
of a single atomic line
In. s hc4p;éifme-% (6.6)

Once the line and wavelength have been identified, the values of gn, D, and En
can be found in published tables'o' 29. Values of Am, are known accurately for
relatively few lines but the dependence of In,“ on T is much greater than its
_ dependence on Am, so that only moderate accuracy in A"m is needed. The
empirical value I is the dimension along the optical path. This method is
commonly applied by preparing a plot of Inm vs. T for each line to be used. The
actual temperature of a species is found by relating the measured In"n value to
the corresponding temperature on the plot.

The Single-line method is complicated by the number density of neutral
atoms since it is a function of temperature. If a pure gas is used at relatively
low pressures, the ideal gas law can be safely used to calculate no at
temperatures where ionization is negligible. An iteration procedure is required
where no is calculated from an assumed temperature and substituted back into
Equation 6.6 to calculate the temperature. Because no varies much more
slowly with T than does the exponential function in Equation 6.6 the iteration

converges rather quickly.

98

Any non-overlapping spectral line or group of lines with relatively
accurate values of Am, En, and A"m can be used with Equation 6.6 for
temperature measurement. A molecular band may be included in the group of
lines so AM, and En are band, rather than line, parameters, and perhaps even
a system of many bands, all part of one electronic transition of a molecule.
Due to the broadening of spectral lines caused by collisions between radiating
particles, overlapping of neighboring lines is more pronounced at higher
pressures. This overlap is harder to avoid for bands than for lines, because
bands are spread over a broad spectral region. Therefore, a safe practice is to
integrate the line radiance In,“ over the full width of the line to ensure Equations
6.4 and 6.6 to be valid.

The electronic partition function, 0, must be incorporated into any

diagnostic used to determine particle density or temperature and is defined as18

8n
o = Egne’TT (6.7)
n

This function is very close to 1 for most gases. particularly those with high
excitation energies, making the transition from the ground state under low to
moderate temperatures”. This condition also holds rigorously for an ideal gas,

but holds only at low pressures for real gases“.

 

99
6.3.2 Two-line Radiance Ratio Method

For a plasma in LTE, the internal degrees of freedom given by the
Maxwell-Boltzmann distribution, Equation 6.3, can be used to determine the
populations of different energy states. The temperature can be estimated by
measuring the relative populations of two or more states, and determining the
value of T for which Equation 6.3 fits the data best.

it Am, En, gn, and Am, of each of two atomic lines are known, it follows

from Equation 6.3 that33

 

3. 3 9.11.1. e- "I." (M)
I: 9213211

where the subscripts 1 and 2 refer to the two spectral lines. Griem modifies

Equation 6.8 by rearranging and introducing the absorption oscillator strength,

f, to give37

-1

"2123911:

(0 e 9)
”11139213

 

kT = El-Ez‘[1n

Griem also gives extensive tabulated values of the absorption oscillator
strengths for various systems”.

The advantage of this method over the Single-line method is the

elimination of the number density and path length. This method also allows

relative, rather than absolute, transition probabilities to be used. The

disadvantages of this method are the poor sensitivity for line intensities with

100

a small difference in upper energy states and its dependence on LTE.

When both lines are from the neutral atom, the two-line ratio method
yields an atomic excitation temperature corresponding to the equilibrium
population of neutral atom electronic energy levels. If both lines are from an

ion, the ionic excitation temperature is obtained.
6.3.3 Atomic Boltzmann Plot Method

The atomic Boltzmann plot is an extension of the two-line method to
many lines. Taking the natural logarithms of Equation 6.6 and making the
electronic partition function, 0, equal to unity gives”

In”). B
an = _ t1 6.
ln{ C — ( 10)

 

where:

 

c = 1n{ life]

Equation 6.10 reveals that the intercept on the ordinate axis, C, can be used

to determine the particle density Ir)0 if the path I is known.

101

6.4 Species Concentrations

In LTE, the Saha-Eggert equation can be applied for the calculation of the
particle distribution function for neutral particles and ions. The Saha-Eggert

equation is defined as10

3
3m . 2g. . Li. . “mm 3 $94.; (6.11)
pa Po h: 0,,

where 01 and 0,, denote the partition functions for the ion and atom,

respectively. Equation 6.11 assumes the reaction follows

M = M* + 9. “e12’

where M, M”, and e' represent the neutral atom, ion, and electron,
respectively. Consequently, the number of ions in the plasma must be equal
to the number of electrons, since each is responsible for the other. Equation
6.11 is most useful when the ionization is appreciable (> 5%) and p0 cannot be
determined from the ideal gas law. The partition functions often deviate
considerably from the statistical weight of the grdund state, especially at high
temperatures”.
Tabulated data is available for the “reduced“ Saha-Eggert equation1o

sm = iéis'm (6.13)

O

102

where:

3 -ss
541') =2.4125x10311‘=e 15, m"

Drawin lists values for S'IT I, as well as O, and 00, at various temperatures for

different elements and ionization stages.

6.5 Advanced Methods of Analysis

Though much information has been gained by these investigations, many
assumptions have also been made. In order to validate these assumptions,
advanced experimental techniques, including LlF and actinometry, must be
employed. Though current experimental equipment limitations, primarily failure
to maintain low enough pressures, prevented the use of these methods, they

are still introduced for the completion of this topic and for future research.

6.5.1 Laser-Induced Fluorescence Spectroscopy

Laser-induced fluorescence spectroscopy (LIF) can potentially provide
species concentration and temperature trends and also validate the existence
of the often assumed local thermal equilibrium. A recently acquired high-watt
laser will enable experiments to be conducted using LlF spectroscopy.

LlF utilizes a tunable dye laser to excite a transition of a molecule of

interest. The fluorescence emitted by the excited molecules can be sensitively

103

detected by photomultiplier tubes or optical multichannel detectors shielded
with the appropriate interference filters. By observing the fluorescence from
only a short length along the laser beam, good spatial resolution can be
achieved. Variable fluorescence excitation scans can be recorded by tuning the
monochromator to a particular emission wavelength of an atomic or molecular
species of interest“.

LIF is a prime method of diagnostics because it can yield spatially
resolved measurements with a high degree of sensitivity. This technique is
particularly ideal for the detection of constituent light atomic species in plasmas
where conventional optical detection is difficult”. Researchers at MSU will use
LIF to obtain quantitative measurements of, among other things, radical and
charged particle densities and velocity distributions, gas temperatures (including
rotational and vibrational), and electric fields.

This versatile technique will accurately describe populations of various
species, such as ions, neutrals, and free electrons, that have been previously
described by methods where dubious assumptions have been made. One
particular assumption that can be evaluated for its validity indirectly through LIF
is that of LTE. Easily accessible models can be developed with the information
obtained from LIF. There are only a handful of LIF experiments conducted with
plasma mediums worldwide so the work at MSU will continue to be on the

cutting edge of this technology.

 

1 04
6.5.2 Actinometry

Though LIF determinations can be obtained in most experiments, there
are instances where this technique is not applicable or practical and the use of
actinometry may be desirable. Inert-gas actinometry is a simpler technique than
LIF and measures the concentrations of the reactive ground state atoms or
molecules by comparison of their emissions with those originated by one or
more inert gases added to the discharge mixture. The concentration of the
inert gases. or actinometers, which normally includes N2, Ar, He, or their
combinations, are held constant at 2-3% of the overall concentration. The
mixtures of these reactive gases and various actinometers have been under
study at MSU in order to better understand their behavioral effects in a plasma.

Since the noble gas density is known, the excitation efficiency of any of
its levels is determined simply by dividing the emission intensity of that level
by the noble gas density. It the excited state responsible for a noble gas'
emission matches closely in energy with the level responsible for an emission
line from a reactive species, than the same group of electrons will be
responsible for the excitation of both levels. The excitation efficiencies of
these levels of the noble gas atom and the reactive particle will then have
similar dependence on plasma parameters. Thus, the reactive particle density
can be determined by combining its emission intensity with the excitation

efficiency of the noble gas. Under certain conditions, a simple actinometric

105

equation of the form

 

Ix [X]
—- =- x constant “.10
I, [A]
where:
I, . emission intensity of molecule X
I, 2 emission intensity of actinometer
[X] = concentration of molecule
[11] - concentzalon of actinometer

constant - preportlonality constant

can be used to evaluate the concentration trends of [X] from the variation of
lx/IA, since [A] is kept constant. In most cases, the constant used in the above

equation will not be solved for analytically since it is independent of the

discharge parameters and relative results can be easily generated.

Three conditions must be met in order to ensure that the emission

intensity ratio is proportional to the concentration ratio“:

0 The emission intensities, Ix and IA, must be produced by electron impact

excitation of the ground state species X and A.

0 IX and IA, must decay primarily by photon emission.

e The electron impact excitation cross sections for X and A must have a

similar threshold and shape as a function of electron energy.

These criteria make the selection of the actinometer a crucial parameter. But
even when the conditions are violated, in practice the emission intensity ratio

may be proportional to the concentration ratio over some limited range of

plasma parameters.

.-

106

Actinometry experiments will provide information on the densities of ion
and neutral species within the plasma. This technique could also be extended
in the determination of gaseous temperatures within the plasma. Actinometry
is a powerful nonintrusive diagnostic technique for understanding the role
played by stable and unstable species which are produced in various

discharges.

6.6 Electronic Temperatures

The electronic temperatures for a helium plasma were determined as a
function of pressure and gas flow rate using the atomic Boltzmann, Single-line,
Two-line methods. The experimental conditions are summarizes in Table 6.1

below.

Table 6.1 Spectrosc0pic Conditions

Net Power Input = 175 - 200 W
Spectrometer Scan Rate = 0.5 Almin

Entrance Slit Width = 0.1 mm

Exit Slit Width = 0.15 mm
PMT Power Supply = 900 volts
Resonance Mode = TM

 

Helium was chosen as an experimental gas due to its simple atomic nature in
which accurate atomic data are widely available and because of its chemical

inertness. The Two-line method resulted in high standard deviations and

107

therefore was inconclusive. This was possibly due to the narrow range of
wavelengths evaluated and consequently, the small energy differences between
the transitions.

The atomic Boltzmann plot method resulted in electronic temperatures
ranging from 3200 to 4600°K. A least-squares fit was used to determine the
slope and intercept for each temperature. The reproducibility for these fits
were all greater than 85% using 9-14 data points. Table 6.2 lists the most
prevalent transitions used in these calculations and Figure 6.4 shows where

these transitions appear on the helium energy diagram.

Table 6.2 Observed Transitions

 

A (A) Transition A (A) Transition
5015.7 2s‘s - 3p‘P° 4921.9 2p‘P° - 4610
3964.7 2s‘s - 4p‘P° 4387.9 2p1P° - 5610
3888.6 2s3s - 3p3P° 5875.6 2p3P° - 3d3D

 

 

3187.7 2s3s - 4p3P° 4471.5 . 2p3P° - 4630
5047.7 2p1P° - 4319 4026.2 2p3P° - 5d30
4713.2 2p3P° - 4s3s

 

 

The corresponding data for these lines necessary to apply the atomic Boltzmann
method were taken from Striganov and the CRC Handbook29'35. A portion of
these data points are summarized in Table 6.3.

These results match closely the electronic temperatures calculated by

previous researchers”. A plot of Te, calculated from the atomic Boltzmann

Energy

 

108

Helium Energy Level Diagram

 

 

 

 

 

 

‘F
I
I
1—7—
1 I
I I
I I
I I
I I
I ..
I
8:
. I
Q r a
I I
I I
I I
’ I
I I
I
2 '
*

‘D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I ,
‘—1—— I I I
\ I I I
'\ I ’I*——
d‘ _ I I I
’\ I I I I I
.\ ' g :I I I
\ I ' °I I I
\\ , , Q: ’I II
I
’ \,’ , I I I
\, , I I I
, IKI I
' I 1.! I
'\ , 0.! I
\ I I I
' \’ I I I
' )1 I I I
I I I 1.1
\ I I I
I I \ I IKI
I I \I I.I
I I \I I.I
I I s I I
:1 I I\I I
w '2
.I I
I I
r I
I .1
I :1
I .I
I I
I I
I ' '
A

 

Figure 6.4 Energy Level Diagram for Helium

109

Table 6.3 Spectroscopic Data for Helium

 

A En ' Am, 3‘

 

3187.7 191217 9 0.05639 0.2175
3354.6 196079 3 0.013 0.1843
3613.6 193943 3 0.039 0.1438
3819.6 195260 15 0.0636 0.1316
3888.7 185565 9 0.09478 0.1285
3964.7 191493 3 0.0719 0.1265
4026.2 193917 15 0.116 0.1257
4120.8 193347 3 0.0444 0.123
4387.9 193918 5 0.0894 0.1205

5

4471.5 191445 1 0.246 0.1239

4713.2 190298 3 0.0955 0.146
4921.9 191447 5 0.198 0.1697
5015.68 186210 3 0.1338 0.1852

 

 

5047.7 190940 1 0.0675 0.1904
5875.6 186102 15 0.7053 1.1414
where:

A=A

En = Upper energy level, cm'1

gn Upper statistical weight
Anm = Transition probability, 108 53'1

RA = Response Function

110

method, as a function of pressure is given in the top of Figure 6.5. The gas
flow rate was maintained at 500 sccm and the pressure was steadily increased
from 5 Torr to 800 Torr.

The bottom curve of Figure 6.5 shows the electronic temperatures of the
same emission line intensities used in the top, but calculated from the Single-
line method. The results of these measurements produced considerably
different temperatures than those obtained from the atomic Boltzmann Plots.
These temperatures range from 10,000 to 14,000°K but the overall trend is
maintained. Each data point represents an average of the temperatures
obtained over all the measured transitions. The error in these measurements
was 1500°K. A sample graph used to obtain these results for the Single-line
method is illustrated in Figure 6.6. Based on classical statistical mechanics,
Lick and Emmons have estimated the electron temperatures for a helium plasma
under these conditions to be approximately 11,OOO°K‘3.

Both plots in Figure 6.5 clearly show the temperature increases with
pressure and slowly levels off at higher pressures. Experiments show that this
* leveling off is an attribute of microwave power limitations. The helium plasma
becomes “saturated“ with power and additional power input is reflected.
Gases with additional degrees of freedom, such as nitrogen, are capable of
absorbing greater amounts of power.

The electronic temperature calculated by the atomic Boltzmann method

as a function of gas flow rate is illustrated in the top of Figure 6.7. The

111

Helium Plasma Electronic Temperatures
Emotion of Pressure

4700

 

4600

    
    

 

 

 

 

 

 

 

3700
3500 [Atomic Boltzmann Plot Methodj
8300 ‘ L 4 ' ‘ ‘ ‘ L ‘ 4 ‘ ‘ ‘ ‘
0 200 400 600 800
13800 I

 

[ Blngle-llne Method ]

 

 

 

J 1 A A A _L L A 4 4L A A A

o zoo Ioo ' coo aoo

Pressu'e. Torr

Figure 6.5 Helium Plasma Te as a Function of Pressure

112

Helium Plasma Electronic Temperatures
Single-line Method

1:: «stroll _ l/ )
g + I l
. ,0: :“" / / /
i .0: 0 4411 / /

: / /

10 11 12 13 14 16 16

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Termeratwe. ‘ K

Figure 6.6 Typical Graph Generated for Single-line Method

Temperature. ’ K

)

Temperetwe. ' K

113

Helium Plasma Electronic Temperatures
Function of Gas Flow Rate

 

4100

 

I Atomic Boltzmann Plot Method I
3900

3700
6600

3300

 

 

 

6100

 

 

1450

 

1350

 

1 2.60

1 1.60

 

 

1 0.60

 

0 300 600 900 1 200 1600

Gas Flow Rate. sccm

Figure 6.7 Helium Plasma Te as a Function of Gas Flow Rate

 

114

pressure for these measurements was maintained at 20 Torr. Here the
temperature suddenly drops off with an increase of gas flow and slowly levels
off as the flow rate approaches 1500 sccm. This result concludes that the
additional input of neutral species, at constant power, provides an obstruction
for the collisonal processes. The increased flow rates also allows for rapid
energy transport within the plasma and the additional cold species dampen the
temperature. Consequently, ionization, as well as T,, is minimized. The
corresponding electronic temperatures obtained using the Single-line method are
found in the bottom curve of Figure 6.7.

The same techniques and conditions used above, with the exception of
power (120 W) and pressure (0.5 Torr), were used on an argon plasma to
verify the general trends. The results illustrate a consistent trend in
temperature with gas flow rate. The results also confirm that the discrepancy
between the two methods do exist by approximately the same order of
magnitude as found for helium plasmas. The two curves in Figure 6.8
compares the atomic Boltzmann (top curve) to the Single-line method.
Compared to the work of Eddy and others, the top and bottom curves seem to
compare more closely to the temperatures of the gas and the electron,

respectively‘1 .

115

Argon Plasma Electronic Temperatures
Function of Gas Flow Rate

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

sooo f
' [Atomic Boltzmann Plot Method]
zsoo - 0 ’ ' *
' P - Os, Tm
.3 2000 P POVIOI O 120 W
.' .
‘3 1600 -
g 1000 -
. 0
soo -
o A A A A l A A A A l A A A l A A A A
o so 100 160 zoo
ioso
C . [ Single-line Method |
10.00 - P - 0.5 Torr
x ’ Power - 120 w
‘ I
i no .
r- I
s.oo -
s.so ‘ - .

0 60 1 00 160 200

Gas Flow Rate, scorn

Figure 6.8 Argon Plasma Te as a Function of Gas Flow Rate

116

6.7 Concentrations of Species

The concentrations of ions and electrons for the helium plasmas were
predicted from the Saha-Eggert equations using the two different sets of
temperatures obtained as a function of gas flow rate. The neutral atom
densities were determined from the ideal gas law and from the atomic
Boltzmann intercept. These two methods produced densities that were similar
in magnitude but their corresponding trends were surprisingly different. The
intercept method resulted in an initially rapid decay in neutral atom density with
increasing gas flow rate but it leveled off at 300 sccm. Conversely, the ideal
gas case steadily increased with increasing gas flow. These observations are
illustrated in Figure 6.9.

This trend observed with the ideal gas case is easily understood since the
electronic temperatures, which were assumed to be equal to the temperature
of the gas, decrease with gas flow and the neutral atom density is inversely
proportional to the gas temperature. A plausible explanation for this
discrepancy lies in the question of whether the electronic temperatures actually
do equal the temperatures of the gas. which would occur if the plasma was in
local thermal equilibrium. Since the electrons are the driving force of the
plasma, it is reasonable to expect their temperatures to be higher than the rest
of the species in the plasma.

The degree of ionization was determined using a combination of the

117

Helium Plasma Neutral Atom Density
Function of Gas Flow Rate

 

 

 

 

2.1«24 1.7a.”
Atomic Boltzmam
intercept
7 1.1”“ - . 1.4«23 2
a 6'— —-> ‘
5 Ideal Gee Law "
3 1.3«24 ’ t 1.0a.“ i
2 gauze i ‘ 6.8»22 2 '
e

Tn 1
8 8
3 4.2«23 _ 18.4”“ i

3.6e+21 ‘ ‘ ‘ ‘ ‘ ‘ 5‘ 1.6«20

0 300 600 900 1200- 1600

Gas Flow Rate. aocm

Figure 6.9 Helium Plasma Neutral Atom Density as a Function of Gas Flow
Rate

118

Saha-Eggert equations and tabulated data of the “reduced“ Saha-Eggert
equations“. The tabulated data was fit to a power-law equation maintaining
a 99.99% reproducibility value. As the degree of ionization approaches unity
(100%), these two methods produce equal results as illustrated in Figure 6.10.
The temperatures used in Figure 6.10 were those obtained from the
Single-line method, ranging from 10,000 to 14,000°I<. The resulting degree of
ionization rapidly drops from 46% to 0.1 96 with increasing gas flow. .
When the ideal gas law, used to determine the neutral atom density,
combined with temperatures obtained from the atomic Boltzmann plot are
applied to the Saha-Eggert equations, the plot found in Figure 6.1 1 is produced.
The overall trend remains the same as that found in Figure 6.10, but the degree
of ionization falls to 1.2 x 104%. Since no consistently detectable He+ lines
were observed in the spectrum under these conditions, this result seems
perfectly plausible. Furthermore, alternative methods used by previous
researchers and the data provided by Lick and Emmons suggests the degree of
ionization under these conditions to be of the same order of magnitude as those

in Figure 6.11“ 21.
6.8 Conclusions

The emission spectra of plasmas typically exhibit strong lines of gas

atoms and ions, therefore, spectroscopic methods are a potentially invaluable

119

Helium Plasma Degree of Ionization
Function of Gas Flow Rate

 

 

 

 

 

 

60
i 0 Bebe-Em
a ‘0 ’ 0 Data Flt
% 80" Derivationebaaedothde-Ine Method
-
° so
g
10
o A 1 A A 1 4 k
0 300 000 000 1200 1500

Gaa Flow Rate. aoom

Figure 6.10 Helium Plasma Degree of Ionization as a Function of Gas Flow
Rate - number 1

120

Helium Plasma Degree of Ionization
Function of Gas Flow Rate

 

 

 

 

0.13 f
* 0.10 ’
Derivations based on Atomic Boltzlnam
g picte' aiepe and ideal Gee Law appled
g o.os - to Baha-Eggert Equations
3
u
-3
° o.os -
8
s
3 . 0.03
0.00 L J ‘ ‘ ‘ ‘9—
0 300 600 000 1200 1500

Gas Flow Rate. accm

Figure 6.11 Helium Plasma Degree of ionization as a Function of Gas Flow
Rate - number 2

121

tool for the diagnostics of a plasma medium. The abundance of accurate
supplementary data is readily available once the particular transitions have been
identified. Though the methods are conceptually simple to apply, the reliability
in experimental technique and instrumentation must be without question for
these methods to be accurately used. It is also imperative that major
assumptions, such as the existence of LTE, be understood and experimentally
valid. An invalid assumption of LTE in these experiments provided the only
plausible explanation for the anomalies that arose, primarily the difference in'
temperatures calculated from the atomic Boltzmann and Singleoline methods.

The absence of LTE also explains the failure of the Two-line method,
which requires the system to be in LTE. It is possible that the narrow range of
threshold energies evaluated could have explained this failure, but previous
work has concluded that the plasma particle velocities are not Maxwellian
under these experimental conditions and that the electron densities range
between 1011 to 1013 cm“3 ‘3' 22' ‘2. Eddy determined the electron (or ion)
densities required for LTE to be about 2 x 1017 cm‘3, far above those obtained
in this investigation“. Pressures greater than 5 bar must be reached for these
densities to be acquired. Another explanation for the non-LTE existence could
lie in the particle relaxation times exceeding the particle residence times or the
lack of a microreversibility between the collisional processes.

The discrepancy between the results obtained with the atomic Boltzmann

plots and those obtained directly from the Single-line method proved to be

122

perplexing since each method has its valid points. Both methods are
theoretically applicable for the determination of electron, not electronic,
temperatures. However, the degree of ionizations obtained from the atomic
Boltzmann plots, combined with the lack of observable ionized atom lines
concludes that the atomic Boltzmann method produced the more reliable results
for the electronic temperature. Since the electronic temperature includes the
energy of the excited 'bound" electrons, it is reasonable to assume this
temperature to be equal to the temperature of the gas. Lick and Emmons have
concluded that helium is composed primarily of neutral species at temperatures 4
below BOOO°K, even at pressures of 10“ atm“.

The results obtained from the Singleoline method accurately reflect the
eiegjm temperatures of the plasma. Since the electrons are the driving force
of the plasma, it is reasonable to expect their temperatures to be higher than
the other species. These temperatures measured for the helium and argon
plasmas correspond well to the theoretical and experimental electron

temperatures obtained by others‘a' 25' 33' “.

Since the electronic (or gas)
temperatures are considerably lower than the electron temperatures, it confirms

that the plasmas in these investigations are not in LTE.

CHAPTER 7

 

Mo del Formula tion

7.1 Introd uction

The most concise method of consolidating the information acquired
through this research effort was found to be through the modeling of various
macroscopic quantities, namely the velocity and temperature distributions
around the plasma region. These models could provide additional insight on the
effects of convective and conductive energy losses from the plasma to the
surrounding gas. This information could then be used to better postulate the
diffusional processes and reactions that dominate the plasma, which has been
the basis of previous models. The advantages of modeling macroscopic
properties over microscopic phenomena is that the former can be
experimentally confirmed.

As described in Chapter 4, the influences of pressure on plasma
dimension is significant. The effects of pressure on energy absorption and

plasma temperatures was described in Chapters 5 and 6. Consequently, the

123

124

plasma size can be used to indirectly describe the energy absorption or
efficiency of operation and the temperatures within the plasma. It is therefore
critical that the proposed model be described as a strong function of plasma
dimension. These parameters, primarily plasma width and length are
summarized in Table 7.1. Since the helium plasma is complicated by a
dumbbell shape, the width was obtained by taking the average over the two
spheres and the connecting cylinder. This data is incorporated into the models

as WW9 a 2R, and L = A2.

Table 7.1 Helium Plasma Dimensions with Pressure

 

            
     

    

 

      
  

           
      
   

P(Torr) Wavgicm) L(cm) P(Torr) Waylicm)
0.5 2.97 5.19 400 2.47 3.67
1.0 2.91 4.74 500 2.43
10 2.69 4.29 600 2.40
50 2.63 4.04 700 2.38

 

 

            
  

  

1 00
200
300

2.61
2.57
2.52

3.97
3.81
3.77

800
900
1 000

2.36
2.36
2.34

 

   

    

      

                

     

 

 

The goal of this summary is to formulate a realistic model using
experimental observations that will describe the macroscopic properties of the
flowing gas around the plasma. Solutions of these models, which will be
sought by aid of a FORTRAN code at a later date, can then be coupled with

previously acquired information on the dynamic processes within the plasma“

125

‘9. Portions of the models can also be used to estimate, a priori, critical

properties of the plasma region. 0ne significant contribution lies in the
development of the theoretical pressure drop across the plasma. Since the
assumptions made in finding AP include that of an impenetratable plasma, the
experimental AP could be used to confirm or negate this assumption. It would
even be possible to determine the degree of neutral particle flow into the
plasma, which has been a widely debated topic. As described in Chapter 3, the
current experimental apparatus can also measure the axial and radial
temperature profiles downstream of the plasma. This data can be compared
to the theoretical profiles to further evaluate the modeling assumptions. The
various steps used to develop an accurate numerical representation for the

velocity and temperature distributions are outlined below.

7.2 Assumptions

Four models were considered to describe the velocity and temperature
distributions around a helium plasma and immediately downstream of the
discharge. The assumptions were initially oversimplified in order to grasp the
physics of the problem. These assumptions were progressively enhanced until
a final model, or combination of models, was developed that would accurately
describe the gas flow over the plasma.

All of the models assume cylindrical geometries for the containment and

ell-Ill I I... l'lll‘ l till

I." l ' l

126

the plasma region. Since the fluid is not highly viscous and the velocities are
much less than sonic, the viscous dissipation term, 0, is neglected from the
overall energy balance“. The models have also taken the thermal diffusivity,
a, and the gas viscosity, u, to be constant. A more realistic solution would
have taken a as a temperature~dependent variable since it is composed of It and
p, which are strong functions of T. However, the Prandtl number, which
compares the thermal diffusivity and the kinematic viscosity, appears to be
constant over the conditions of this analysis as illustrated in Figure 7.1“.

The assumption that the specific heat, CD, is constant and equal to 2.5R
at constant pressure is justifiable on the basis of the high excitation energies
of helium and the negligible existence of excited populations. Under conditions
where the degree of ionization was appreciably higher, the specific heat would
vary considerably due to the formation of a mixture and the energy needed to
ionize the neutral and singly-ionized species“. Uniform containment wall and
plasma temperatures were assumed and wall recombination and subsequent-
reaction effects were ignored.

Model A begins the analysis with the assumption that the gas completely
penetrates the plasma with a flat velocity profile or plugflow. Model B also
assumes the complete penetration of the gas into the plasma but incorporates
a parabolic velocity profile. Model C assumes an impenetratable plasma
whereby the gas flows around the plasma with a parabolic velocity profile due

to no slip conditions along the plasma and the containment wall. Model D also

 

.l'IIIIIII-Ili I II’IIII 1 III! I .ll

Cpl/It

1.20

127

Prandtl Number of Modeling Fluid

 

 

 

 

 

 

, Data takenteuuekehens’ #
1.10 ' ’ ’
Helium Gas 1
‘.oo - 7 P - 1e° .m .
0.90 ’
_ e
0.80 l'
b e
. 18
0.70 _ 067 . e
aesesseeseseesessseessses e e e e e e e 0
0.60 A l L A A A 1 A L 1 AL A
0 2 4 6 8 10 12 14 16
(Thousands)

Figure 7.1 Prandtl Number of Helium with Temperature

I. i l! l I II. All I III. | lllll' III:

 

128

assumes an impenetratable plasma but assumes the existence of molecular slip
along the plasma boundary. Models C and D describe the effects of the plasma
on the flowing gas. Using the solutions of these models for the boundary
conditions of Models A or B would provide a suitable model for the distributions

immediately downstream of the plasma.

7.3 Characterizing Dominant Forces

To begin the analysis, the Reynolds number was computed to determine
the effects of inertial and viscous forces within the containment. Several
extremes of the temperature and pressure were considered to obtain maximum

and minimum limits.

Re = ch(T)Vb _ Inertial terms (7.1)

u (T) Vi scous terms

 

where:

dc a 3.1 cm
po 8 1.7859 x 10" g/cmr3
PoPTo
TPO
1.915 x 10" g/cm 3
4(500 an’hnin) 1 min
1t(3.1 cm)2 50 5

Po
= 1 . 104 cm/s

The Reynolds number for the various cases considered are summarized in Table

7.2.

‘ ‘ '1 III | . 4

1 29
Table 7.2 Reynolds Number at Varying Conditions

CASE P, Torr T, K um, 104 pm, 10'8
g/cm s g/cm3

17.9
.536
17.859
535.8

 

In all but the most extreme case (3). the Reynolds number is much less than
one. This indicates that the viscous forces dominate and the inertial terms can
be neglected. It is important to note that the apparent laminar nature of the
flow may still exhibit turbulent characteristics due to mixing attributed to
thermal mixing and density variation. In fact, this mixing may be desirable from
the viewpoint that it generates a homogenous process that can be analyzed as
a well-mixed or CSTR reactor” ‘4' ‘5.

The derivations of each model are based on the combined influences of

the differential momentum and energy balances. The general form of the

equation of motion in cylindrical coordinates along the direction of flow (2) is

8V, 6V, V. 6Vx 6V, _
6t+V’-67+760+V‘az 96X, paz

+“[1 8(raV.)+ 1 39V. +§§

 

 

 

 

?'§? '5? '13 602 622

and the energy balance is

130

3T 3T 9s 3T 3T
33+V.-5;+—;-5+V.-3; " 3)
__ 1 3 3T 1 air 332'
- a TE}? 1‘3?) + [3 m3 + 37,3

where the thermal diffusivity is defined as

J.

a 8
pC,

The equation of motion is solved for each model and incorporated into
the corresponding reduced energy balance. Analytical solutions are obtainable
for most of the models but complications resulting from Bessel functions would

force these solutions to be further evaluated numerically.
7.4 Model A - Penetratable Plasma with Plugflow

This model, whose boundary conditions are illustrated in Figure 7.2,

assumes a penetratable plasma region and a flat velocity profile.

- »
» .-

Figure 7.2 Plugflow through Plasma

 

 

 

 

 

 

 

 

 

 

 

 

The following assumptions, discussed in section 7.2, were made in the

131

analysis:
1 . steady-state
2. laminar flow
3. fully developed flow
4. axisymmetric
5. negligible pressure drop across small reactor length (dP/dz =
constant) and negligible compression effects
6. negligible entrance effects
7. 1:, C9, p, and p are individually constant
8. uniform wall temperature, inlet temperature
9. negligible body forces

10. Rodlike or plugflow, VI = Vb

The simplified form of the equation of motion becomes

 

 

 

i a a t = ._c. a - (7")
ITI(I 61‘) '1 3'2- - COHStant
01'

a D: 1 6" 9:: 3?

ar’ + r 6r ll 62 constant ( i

which is subject to the following boundary conditions:

0

R0 (no slip on wall)

u
o
m
n
H
ll

 

<.'
u
o
m
n
H
u

l. (Ill l I. I III lull. it" I ' III] .

132

Integrating twice and applying the boundary conditions gives

= -isfl 2 - 2 7.s
, 4;: dz (Ro r ) ( i
The maximum velocity, vm, occurs at r = 0, thus
.. - 9c £2 2 (1.7)

V'“- Til-dz

and the velocity becomes

2
v A V 1 - .1. (7.0)
. «I (12.))
This model assumes a flat velocity profile so VI = Vm = Vb.

Since the temperature distribution in the axial direction will be much less

curved than in the radial direction, the assumption can be made that

62T
= 0
622

 

The simplified energy balance becomes

 

$13T=L3T=Xefl 79‘

r a:(‘ 3r) a 3—2' a 82 ( )
or

627' + $.33 _ £3 = £2.37: (7.10)

Br: I 6r (1 62 a z

Upon separating variables, which is discussed below, this partial differential

equation gives two ordinary differential equations which can be solved by

133

conventional methods. One solution involves a simple exponential equation
while the other uses a Bessel function. The solution to this equation was first
obtained by Graetz“ and has since been verified by numerous other
researchers". The final solution to Equation 7.10, with the boundary
conditions of uniform wall and inlet temperatures, is
T.” T ,"i 2 Jd(3g_)e'3%%fl (1.11)
T. ' To n-1 an1(aa) Re

where:

T, a temperature at surface of containment
To =- temgperature at time-=0

T - temperature along tube

JO 2 Bessel function of zero order
J1 = Bessel function of first order
An = n '3’ root of Jena) = O

1'?o = tube radius

2 = distance along tube
Re = Reynolds number = M

116'

Pr = Prandtl number = —k£

The bulk temperature, which defines the temperature of the fluid at any
axial position, can be obtained by combining the velocity and the temperature

distributions to give

2-2.
Tb = 37 I Trdr '(7-12’
R0 r-o '

Since the temperature profile relies heavily on the temperature of the

containment and not on the internal heat source (plasma), this model would be

134

more suited when combined with another model. In fact, this model would be
ideal for the temperature distribution at any axial position downstream of the
plasma, assuming a negligible radial profile. it is unlikely that the distribution
is completely independent of the radial distance, therefore, an improvement

over this model is described in Model B.

7.5 Model B - Penetratable Plasma with Parabolic Velocity Profile

This model goes one step further than Model A since it considers the

contributions of varying velocity in the radial direction. Figure 7.3 depicts the

modeled region.

 

 

.’ \\‘\. \\\\‘ -
\ \
”- \ \ ’
:0 PLASMA ) ; Tb
- ’, I, ’
-—- x" x” ->-
I I
1’ 1”

A

 

 

 

 

Figure 7.3 Parabolic Velocity Distribution through Plasma

Using the assumptions of Model A, but with a parabolic velocity profile

gives

2
v8 = 2Vb 1-(731 (7-13’

Incorporating Equation 7.13 into the simplified energy balance, Equation 7.10,

 

135

becomes

1.(.Ff;)2 .33: (7.14)
2

Solving this equation requires the technique of separation of variables letting

 

GIT {riaT 8 fl
6:3 £3? a

 

 

T=0(r)9(z) (7-15)

that is, 0, is a function of r and 6 a function of 2. Substituting these variables

into Equation 7.14 and rearranging gives

 

 

7:72 ‘ "-m

 

Since Equation 7.15 must hold true for all values of r and 2, each side can be
taken equal to an arbitrary figure. Jakob suggests using -1/b2 as this figure

transforming Equation 7.16 into the following48

09 A «9
713 ' m "-1”
and
.d_"9 + $.99 + ._1-1 - (Lflg g o (7.1a)
drz r dz 1:3 R0

Equation 7.17 can be easily integrated to give

136

_u

1

 

where C1 is a constant of integration. This expression for 6 can be substituted

back into Equation 7.15 giving

 

T a o'clefufih] (7.20)

The integral of Equation 7.18 can be obtained by first making the substitution

r g 52. g
—5 lb and b p
to give
1 dze 1 d6 1 (b2
—— —— —— 7" —— = 7.
1:2 do? + b2<l> dd) + b2[1 (3)16 0 ( 21)
or

.42 $.99. -31 = 7.22
(“,2 + tbdQ +(1 pa}, 0 ( )

It is worthy to note that Bessel's differential equation replaces the term (Dz/.82
with flzl¢2. Equation 7.22 can be integrated to obtain

no.
Rio) . 2323’” (7.23)

n-O

where:

137

_ 1 _ 1 1
80 = 1 B: ' "2—2 32:1 ‘ EFL-37.8”“ " 8211-2)

Combining Equations 7.20 and 7.23 and introducing the boundary conditions

T=To at 2 =0 and T=T8 at r=Ro gives the final solution

T, - T ”" nix/awn»: (7 24)
7‘75; ' 2. 3”” '
e n-

Tabulated data is available for the first 10 terms in the series for the eigenvalue
3,, and other critical constants for the flow in a round tube". Upon combining
Equations 7.13 and 7.24, the bulk temperature of the fluid at any axial position

can be found by

x-n. 2-2.

2
2 f TV,rdr (7-25)
R0 Vb r-O

Tb = —£—f (pC'p'I'Vz) (2nr)dr =

1‘ R02 Vbcpp I-O

 

7.6 Model C - lmpenetratable Plasma with No-slip Boundary Conditions

The third model evaluated considers the plasma to be a completely
impenetratable medium. As illustrated in Figure 7.4, the flow assumes a
parabolic velocity profile around the annulus due to no slip conditions. The

assumptions stated in. Model A also hold for this analysis.

 

 

 

 

 

Figure 7.4 Parabolic Velocity Profile around Annulus, No-slip
Conditions at R0 and Hi

The simplified equation of motion becomes

(11’ _ 1 3 av: e
a; ‘ rat—a?“ ‘7 “’

Integrating Equation 7.26 twice and applying the boundary conditions

V=0 at I

Z

R,J (quartz tube radius)
R1 (plasma radius)

gives the velocity profile around the annulus

2 2
a 1 d? 2 _ 2 R0 R1 R0
V: HE” R“ * 7:171“? (1.27)
R1

If the flow of neutral species into the plasma were considered negligible,
then the velocity profile given in Equation 7.27 would hold rigorously and the
small pressure drop could be estimated under varying conditions. The pressure

drop was evaluated based on the definition of flow rate or

139

Q '3 (V)°Aannulus
2.

 

 

 

=- ZuIrV,(r)dr
i. (7.20)
. _1.._d£ 2- 3 RV”: fl
2n!4udz(rRa)+ Rolrdr
1 1n—
R1
which reduces to
_u_ 123-R
x 3 —
o ‘2‘); 75f“ -R§r)dr + 1223mm, rlnrldt (7,2,,
In—
R1
Integrating Equation 7.29 yields
dP R0 'R1 1 2 2
0 " 33““ ' “1’77 21 R, ”mt-2" ‘ (RM!) (7.30)

1

and the final expression for the pressure drop over the plasma discharge

becomes _1

8 QAz Roa'R} 1
AP 2 1“ (InRN'3) - “23”?” (7.31)

I (Kg-R3) 21115
R

1

The influences of pressure on the radius of the plasma was
experimentally measured and described in Chapter 4. Incorporating this data
into the final expression of Equations 7.31 resulted in the distribution found in
Figure 7.5.

The temperature distribution around the plasma discharge, assuming
cylindrical geometry and uniformly heated surfaces, has been treated by Jakob

and Rees”. The following differential equation was derived

| A . I II I Ail II I l | (1' 'IIII‘II 1‘1' I

140

Theoretical Pressure Drop Over Plasma
lmpenetratable Plasma Model (Cl

° _ i 4

 

 

 

I
Q
j

 

+110"...-
ant-.070 Yen

AP. Torr

I
O
V ‘I Y

+ ”0.10 Terr
-o- from Terr
-12 r + eon Terr

 

 

F + P-no Terr

 

 

 

 

1 L 4 1 1 1
-16

o 10 20 so 40 50 60 70
A z, cm

Figure 7.5 Theoretical Pressure Drop for Model C

141

 

 

a aT_ZQr 2_; _r_6T_ 6’T 7.2
32(I3? uaM[R1 I 4’ 3113 R1 3; [622 ( 3 )

where:

Q a rate of volume flow
Ms (R: -Rf)(R: +Rf-B)
B . logarithmic mean radius
123-R}
12,,

In—
R:

 

Assuming the temperature change per unit length is constant at sufficiently
great distance, 2, from the beginning of the plasma, the following boundary

conditions can be applied

_6_T = Cons tan t and 62 T

32 322 = O

 

Equation 7.32 can be reduced to the following conduction expression

.1 fl 829$ 2 - 3 _I_ 7.33
dr(rdr xaM[R1r r +BrlnR1 ( )

Jakob has transformed this one-dimensional, second-order ordinary differential

equation into the following‘8

To’Tl 0
AT ZnaL

 

 

where:

142

 

_ 1 _ , sing”) _ 1
- 1
x (1-y’) (1+y3-z) {( y )[ 4 z

+ y’lny(y’-z) + 1nJ/{1-y’(y’-z) - 21131}

 

and
R1
Y -R—o'
2-
z , (y 1)
lny
191 - ‘11
qi+qo
q‘ . hioAZ'Z'R1(T1-To)

q0 . hMAz-ZIRJTo-Ti)

The temperature change, AT, is over the plasma length, l. The quantities qi and
q0 denote the rate of heat out of the plasma and the rate of heat into the quartz
containment, respectively. Solutions of Equation 7.34 can be obtained
numerically using calorimetry data obtained experimentally once the individual
heat transfer coefficients have been found. The individual heat transfer
coefficient for the plasma, hi0, can be found through tabulated data obtained

by Lick and Emmons“.

7.7 Model D - lmpenetratable Plasma with Slip Conditions Around the Plasma

The final model evaluated considers an impenetratable plasma region but

assumes slip along the plasma/flowing gas interface. This is a more reasonable

approximation since friction losses arising along a two-fluid interface would be

143

negligible compared to those along a fluid/solid interface. The modeled region

is illustrated in Figure 7.6.

 

 

 

 

 

Figure 7.6 No—slip along Containment Walls, Slip along Plasma

Incorporating the following boundary conditions

V1 2 O at r
dV,

R0 (quartz tube radius)

=0 at I

 

R1 (plasma radius)

into Equation 7.26 and integrating twice gives the velocity profile
= i2 2 - 2 2 i (7.35)
v2 4" dz[r R0 + 2R,1n( 1)]
The theoretical pressure drop was determined for this model to determine
if the slip/no-slip assumptions made in Models C and D would significantly alter
the pressure drop. Following the derivation outlined in Equations 7.28 - 7.31 ,

the AP was computed for this velocity profile to be

 

 

_ BpQAz 2 2 n( R0 ] 2 [1
AP- R ~4R 1 -R- (7.36)
1:02: - Rf)[ O i Ro’Ri 1

The results of Equation 7.36, illustrated in Figure 7.7, closely resemble the

distribution of those obtained for Model C. However, the significance of

aP, Torr

144

Theoretical Pressure Drop Over Plasma

0.00

-O.40

-0080

-1.00

U

1

I

I

 

‘\ t .1

hnpenetratable Plasma Model (D)

 

 

 

   

 

-0- lie Home
-*- #370 Terr
+ ”0.10 Torr
-O- P-T.‘ Terr
-t- P-TO Terr
+ P-uo Torr

 

 

 

 

l l l L l l

 

10 20 so 40 so so 70
AZ, cm

Figure 7.7 Theoretical Pressure Drop for Model D

145

pressure drop with distance has decreased by an order of magnitude for Model
D due to the reduced friction losses associated with slip conditions.

A comparison of the AP: for Models C and D at various pressures, using
identical parameters, is illustrated in Figure 7.8. The maximum difference
between the two models occurs as the pressure approaches 0, which is where
the plasma radius approaches the quartz tube radius. The order of magnitude
difference is estimated to be beyond the experimental error in measuring the
pressure drop so these two approximations can be regarded as virtually
identical. Consequently, either models can be used to predict the amount of
flowing neutral species that penetrate the plasma region. The temperature
distribution for Model D can be derived from the same equations used for Model

C.

7.8 Summary

The foregoing discussion has presented the development of several
models that can be used to describe the velocity and temperature distributions
around and downstream of the plasma. The assumptions used were initially
oversimplified in order to quantitatively grasp the physics of the problem and
to provide a foundation of models to build upon.

It can be concluded that the most realistic representation of the flowing

gas around the plasma must consist of a combination of models; one model to

AP (Model 0)
AP. (Model 0)

 

 

146

AP Comparison Between Models 0 I. D

 

 

 

 

Figure 7.8 Comparison of AP Obtained for Models C and D

lsllllnlll ll 1". I'll-I. Ill '1. I'll] l 1.1.}
III]! III." III). III
Ill. .

147

describe the distributions immediately around the plasma and another to
describe the distributions downstream. The final modeled region of the plasma

is illustrated in Figure 7.9 below.

 

Tlnlef Troll Tbulk. out

 

\‘ —II. I,
\ #l’
\ A

’

’-

- ‘

—- I' l ) PLASMA ) rpm,“
” J1 \

-

lllllll

 

 

 

Figure 7.9 Final Modeled Region

Since Model D best describes the gas around the plasma, it would be beneficial
to incorporate its solutions into Model B in order to describe the distributions
downstream. This generates a complicated analysis, but one which could be
numerically solved using finite elements in a supercomputing environment. It
should be noted that these models exclude the effects of radiation and, more
importantly, the diffusional effects of species out of the plasma. These two
effects, which have been evaluated by previous researchers“, will be
incorporated into the model at a later date.

The equations used to estimate the pressure drop over plasmas of
varying dimensions (Equations 7.31 and 7.36) will play an important role in
understanding the gas/plasma interactions. This theoretical pressure drop can
be compared to the experimental pressure drops in order to better assess the

degree to which the gas permeates the plasma surface. Improved models can

If It. '4' Illa-lull I‘ll III II 1" (ll'lll'll‘llul' ' all It'll

148

then be developed to describe the diffusion of species along the interface. The
same procedure can be followed to experimentally evaluate the temperature
distributions downstream of the plasma using thermocouple probes positioned
at various radial and axial points. These temperature profiles or mixing cup
temperatures can be used to evaluate nozzle performance and optimize the

proximity of the plasma in relation to the expansion placement.

 

I. l' I] ll Jill. II III .11 .1". 1"! III. I." II I! i l I i | 1. I. ll: 1' Ill-1' I! II- II I '11] 1|

CHAPTER 8

 

Summary and Conclusions

The microwave electrothermal thruster has been demonstrated to be a
viable substitute over systems involving electrodes and this work has
contributed to its development and realization. The diagnostic techniques used
in this investigation have provided significant insight towards the macroscopic
influences a microwave generated plasma has on its surroundings and vice
versa. This data is critical for the design and optimization of an efficient
thruster system.

The effects of various gases, mixture ratios, gas flow rates, pressure,
discharge power, and containment geometry on the plasma size, energy
absorption, and temperature has been evaluated in order to better assess these
macroscopic properties. The phenomenon occurring within the plasma has also
been better explained through these investigations, though much less
quantitatively than the macroscopic phenomenon. The physical and theoretical
effects that the above parameters have on the atomic processes, interactions,

and reactions have provided useful hypotheses on plasma formation and

149

l. 1' III III] In." 1' 'I. (III! I! I! I. 'IIIIII'III' I: ' ll. '1'! ill-Ill llllll"l IIIIIII .l'll‘ a) l l

150

sustainment. These effects have also better identified the dominating
interactions that occur within the plasma and how these interactions influence
plasma shape, size, energy absorption, and temperature.

The experimental configuration has been significantly modified to
accommodate these diagnostics by the most accurate and efficient means,
which includes computer-aided data acquisition and control techniques. The
configuration also possesses the flexibility for future alterations, which includes
increased power capacity, additional cooling, improved temperature
measurements, swirling flows, and cavity maintenance.

The analysis of plasma dimensions and quality has been conducted on
individual gases and their mixtures to better understand the transport
mechanisms and trends with parameter changes. Mixtures were emphasized
in this investigation in order to better understand the effects of contamination
and to determine relationships between monatomic and diatomic molecular
interaction. The detailed microscopic explanation of these results can be found
in Chapter 4, but in general it was observed that

e helium plasmas exhibit a ”dumbbell" shape while nitrogen and argon
plasmas exhibit an ellipsoidal shape

0 argon plasmas are transformed into a mass of elongated filaments at
pressures in excess of 100 Torr

0 plasma volume decreased exponentially with increasing pressure

0 helium plasma volume decreased with decreasing flow rate at low power

151

levels but decreased with increasing flow rate at high power levels due
to “saturation"

nitrogen plasma volume decreased with decreasing flow rates

plasma volume decreased with decreasing power

maximum volumes for mixtures were obtained at the pure component

extremes

Energy distribution investigations provided information on general trends

with individual gases and their mixtures at various conditions. They also

demonstrated the importance of a well maintained cavity and containment

system. It was observed that the energy losses due to convection and

radiation could be significantly reduced if the cavity and containment walls

were carefully cleaned, thus eliminating the absorption of energy by foreign

molecules. Efficiencies in excess of 80% were obtained under contamination

free conditions. Other trends observed in energy absorption include

pure nitrogen continues to absorb energy with increasing pressure due
to additional energy modes

pure helium fails to absorb energy with increasing pressure due to the
effects of “saturation"

mixtures of helium and nitrogen absorb the greatest amounts of energy
at their pure component extremes

pure nitrogen continues to absorb energy with increasing flow rates

152

0 pure helium fails to absorb energy with increasing flow rates

0 variations in power input contributes insignificantly to energy absorption

The presence of local thermal equilibrium within the plasma was
evaluated spectroscopically using several line—intensity conversion methods
whose dependence on LTE varies. The high standard deviations generated
using the TwoJine Ratio method, which is strongly dependent on LTE,
concluded that the plasma under these experimental conditions, summarized In

Table 8.1, is not in LTE.

Table 8.1 Experimental Conditions used to Evaluate LTE

Gas Flow Rate 100 sccm
Pressure 100 Torr
Net Power Input 300 Watts

 

Containment Geometry cylindrical

Containment Diameter = 31 mm

Resonance Mode = TMO1 2
Coolant ' = Air
Coolant Rate = 2 scfm

Gases = He, Ar, N2

 

A possible explanation for the non-LTE existence lies in the particle relaxation
times exceeding the particle residence times or the lack of a microreversibility
between the collisional processes.

It was determined through the various spectroscopic methodologies that

153

the atomic Boltzmann plot method is most suited for the estimation of
electronic temperatures, which includes the energy of the bound electrons.
Conversely, the Single-line method provided approximations for the electron
temperatures, which includes the energy associated with the free electrons.
Since the electrons are the driving force of the plasma it is reasonable to expect
their temperatures to be higher than the other species. The large deviations
between the electronic and electron temperatures also confirm the absence of
LTE. These temperature measurements were incorporated into the Saha-Eggert
equations to estimate the degree of ionization under these experimental
conditions. Other observations made through these experiments with helium
plasmas include
0 electronic and electron temperatures increase with increasing pressure
but tend to level out at high pressures due to "saturation"
0 electronic and electron temperatures decrease sharply with increasing
gas flow rates (similar trends observed with argon)

0 the degree of ionization decreases sharply with gas flow rate

Several models were formulated to describe the macroscopic influences
the plasma has on a flowing gas, primarily velocity and temperature
distributions and bulk temperature. The models are based on experimental data
that consists of plasma dimension, plasma temperature, plasma heat transfer

coefficients, gas flow rate, and containment geometry. It was concluded that

 

 

[Ill Ill Ill III I. all-Ir Ill-l1 I'll. 1' II. [.1
I III! lulll ,l
I II 1| I I1 ‘11.. ill‘ I [1.11

154

the combination of two models, one to describe the distributions immediately
around the plasma and another to describe the distributions downstream, would
most accurately represent the actual process. These models, however, make
no attempt to describe the effects of species diffusion on the velocity and
temperature distributions.

The pressure drop was also estimated from these models, assuming an
impenetratable plasma. This theoretical pressure drop can be compared to
experimental observations to determine the degree of neutral particle flow into
the plasma. The temperature distributions downstream of the plasma can also
be compared to experimental observations in order to better assess the validity
of the modeling assumptions.

Significant progress has been made over the past decade in developing
the fundamentals of microwave generated plasma behavior as applied towards
spacecraft propulsion. Advanced research methods must now be employed to
fill the gap between theory and experimental observation and to establish the
validity of major, and often dubious, assumptions. It is imperative that these
macroscopic investigations be coupled with the microscopic theory obtained
through this and previous research in order to establish a complete picture of

the overall plasma process and its role in spacecraft propulsion.

CHAPTER 9

 

Recommendations for Future Research

'All things I thought I knew; but now confess
the more I know I know, I know the less“

[Owen - Works, Bk. VI]

The old adage seems to have provided a central theme for this entire
humbling investigation since every answered question brought about two more
questions. Though it would be impossible to address every recommendation
in detail, it would be beneficial towards the continued progression of the project
to follow-up on a select few. Listed below are a few recommendations that

should be considered for future research.

1. It is highly recommended that future experiments be conducted with
pressures approaching 1 mTorr or less. This can only be accomplished
by incorporating a diffusion/roughing pump system into the experimental
apparatus. As discussed in Chapters 2 and 6, the degree of ionization

becomes significantly greater at lower pressures. Consequently, low-

155

156

pressure experiments would produce much higher concentrations of
singly-, possibly even doubly-, ionized species that could be
spectroscopically analyzed with greater accuracy. As illustrated in Figure
2.5, higher degrees of ionization can be achieved with lower pressures
at any given plasma temperature. These concentrations could also be
achieved by higher power input levels, but this modification would be at
the expense of higher plasma temperatures that could potentially melt
the quartz containment. This low-pressure environment is also a criteria

for LIF-based experiments.

Confirm the theoretical radial and axial temperature distributions
downstream of the plasma using experimental methods. The modified
collar system will allow the various placement of up to four subminiature
thermocouple probe assemblies to measure these profiles. The collar
system has been fabricated and the probes have been purchased to
conduct these experiments, however it is suggested that the current
data acquisition system be expanded to include temperature

measurements.

Incorporate sensitive pressure transducers around the containment
system to accurately measure the pressure drop over the plasma region.

This experimental data can be compared to. the theoretical pressure to

157

measure the degree of neutral particle penetration into the plasma.

Completely integrating the thermocouple wire and probes to the
computer DAS would allow the exact time needed to reach thermal

equilibrium within the containment to be measured.

Generate and analyze the effects of swirling flows on plasma formation
and sustainment. This addition of an angular component would also
provide another means of measuring whether the gas flow penetrates or
by-passes the plasma region. The modified collars contain radial inlet
ports to provide the "helix' formation and point velocity measurements

could be conducted with the aid of laser doppler velocimetry.

Develop FORTRAN code to obtain solutions for the combination of
models outline in Chapter 7. These models should be appended to
models previously formulated to describe the microscopic processes and
transport phenomenon within the plasma region. This final model would
account for the transfer of individual species to and from the plasma
region. This model would provide the most realistic description of the

entire plasma process used to predict nozzle performance.

11') ill I'll. (IIIIIIII.II'II|"III(II,I|I|‘IJ

10.

158

Relocate the current experimental system to within close proximity of

the tunable dye laser and begin LIF experiments.

Incorporate a nozzle assembly onto the experimental apparatus to

measure nozzle performance for varying plasma locations and conditions. '

Address the nonequilibrium status of the plasma including the
responsible elementis) and reasonable methods to place the plasma in

LTE.

A final recommendation would be to address whether these low pressure
diagnostics would apply to actual thruster performance operating at

pressures in excess of 5 atmospheres (ie. Do the mechanisms change?).

 

10.

11.

12.

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