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Performance evaluation and operating characteristics of a waveguide microwave applicator for space propulsion applications

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Perform ance evaluation and operating characteristics o f
a w aveguide m icrowave applicator for space propulsion
applications
Mueller, Juergen, Ph.D.
The Pennsylvania State University, 1993
UMI
300N.ZeebRd.
Ann Aibor, MI 48106
The Pennsylvania State University
The Graduate School
Department of Aerospace Engineering
PERFORMANCE EVALUATION AND OPERATING CHARACTERISTICS
OF A WAVEGUIDE MICROWAVE APPLICATOR FOR
SPACE PROPULSION APPLICATIONS
A Thesis in
Aerospace Engineering
by
Juergen Mueller
о 1993 by Juergen Mueller
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
May 1993
We approve the thesis of Juergen Mueller.
Date of Signature
fa t-.
/}
/9 7 3
Michael M. Micci
Associate Professor of Aerospace
Engineering
Thesis Advisor
Chair of Committee
Robert G. Melton
Associate Professor of Aerospace
Engineering
Charles L. Merkle
Distinguished Alumni Professor of
Mechanical Engineering
C i
/ F Ml J
Domenic A. Santavicca
Professor of Mechanical Engineering
b
Dennis K. McLaughlin
Professor of Aerospace Engineering
Head of the Department of
Aerospace Engineering
fU
Itj <113
ABSTRACT
A new electrothermal space propulsion concept using waveguide-heated plasmas
was investigated. Attention was focused on the understanding of basic operational
characteristics of this thruster concept. To this end, experimental testing of various
waveguide applicator configurations was conducted. Waveguide-heated plasmas are not
stable but tend to propagate toward the microwave power source due to heat conduction
or radiative processes. A rectangular waveguide applicator was used to measure plasma
propagation velocities. Plasma velocities in nitrogen were found to be around 10 cm/s.
In helium two propagation modes were observed, one ranging in plasma velocities
between 10 and 90 cm/s while the faster mode showed propagation velocities up to 2000
to 3000 cm/s. Inserting a bluff body made from boron-nitride material into the gas flow
enabled stabilization of the microwave discharge over given power ranges depending on
mass flow rates and gas pressure. For the stabilized plasma in the rectangular guide up
to 90% coupling efficiency, i.e. absorbed over total incident microwave power, were
measured. However, it was observed that rectangular waveguide plasmas sustained in a
TE10 electromagnetic field pattern touch the waveguide walls at two locations, possibly
resulting in problems of thruster erosion and efficiency loss. Therefore a circular TMm
mode applicator was investigated. The microwave discharge in this applicator could be
sustained well separated from the waveguide walls at coupling efficiencies up to 96%.
For a simple converging conical nozzle arrangement, using measured data on power,
pressure and mass flow rate and quasi-one dimensional nozzle flow theory, values for
such rocket performance parameters as thruster efficiency, specific impulse and thrust
were estimated to be 40%, 350 sec and 0.4 N, respectively.
iv
TABLE OF CONTENTS
LIST OF FIGURES....................................................................................................
ix
LIST OF TABLES ......................................................................................................xvi
ACKNOWLEDGEMENTS ....................................................................................... xvii
Chapter 1. INTRODUCTION.................................................................................
1
1.1. A Brief Introduction to Electric P ropulsion .........................................
1.2. Scope of the Thesis ..............................................................................
1
6
Chapter 2. MICROWAVE PROPULSION C O N CEPTS......................................
8
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
Introduction............................................................................................
Basic Characteristics of Microwave Electrothermal T h ru sters
The Resonant Cavity C o n c e p t..............................................................
The Coaxial A pplicator.........................................................................
The Waveguide Applicator - An Introduction......................................
Comparison of Microwave Thrusters and other Electrothermal
Propulsion Concepts .........................................................................
8
8
16
21
24
29
Chapter 3. PLASMA PROPAGATION AND STABILIZATION.........................
31
3.1. Introduction............................................................................................ 31
3.2. Plasma Propagation M o d e s.................................................................... 32
3.2. Plasma Stabilization .............................................................................. 37
3.2.1.
3.2.2.
3.2.3.
3.2.4.
Flow Stabilization.........................................................................
Magnetic Field Stabilization ......................................................
Bluff Body Stabilization..............................................................
Other Means of Stabilization......................................................
37
37
38
39
Chapter 4. ELECTROMAGNETIC THEORY OF WAVEGUIDE
COM PONENTS................................................................................. 41
4.1. Introduction............................................................................................ 41
4.2. Maxwell?s Equations.............................................................................. 41
V
TABLE OF CONTENTS (cont?d)
4.3. Rectangular Waveguides
.....................................................................
45
4.3.1. TE M o d e s ..........................
4.3.2. TM M odes..................................................................................
45
52
4.4. Circular Waveguides.............................................................................
56
4.4.1. TE M o d e s ..................................................................................
4.4.2. TM M odes..................................................................................
56
63
Chapter 5. THE STRAIGHT, RECTANGULAR WAVEGUIDE
APPLICATOR..................................................................................
66
5.1. Introduction.....................
5.2. Experimental System.............................................................................
66
67
5.2.1.
5.2.2.
5.2.3.
5.2.4.
5.2.5.
The Rectangular Waveguide Applicator ................................... 67
Gas Supply System ..................................................................... 71
Plasma Ig n itio n .......................................................................... 73
Photodiode A rray ........................................................................ 73
Bluff Body Experiment ............................................................. 75
5.3. Propagating Plasma Investigations........................................................
78
5.3.1. Experimental Procedures ........................................................... 78
5.3.2. Results ........................................................................................... 79
5.3.2.1. General Plasma B ehavior...................................................
5.3.2.2. Propagation Velocity Measurements...................................
5.3.2.3. Coupling Efficiencies ........................................................
79
80
88
5.4. Stabilized Plasma Investigations...........................................................
94
5.4.1. Experimental Procedure............................................................. 94
5.4.2. Results ........................................................................................... 95
5.4.2.1. General Plasma B ehavior...................................................
5.4.2.2. Plasma Stabilization behind Bluff Bodies...........................
95
97
vi
TABLE OF CONTENTS (confd)
5.4.2.3. Stability Boundaries .............................................................102
5.4.2.4. Coupling Efficiencies .......................................................... 105
5.5. Comparison of Propagating and Stabilized Plasmas ............................ 109
Chapter 6. THE CIRCULAR WAVEGUIDE APPLICATOR................................ 113
6.1. Introduction............................................................................................ 113
6.2. Design of the Circular Waveguide Applicator........................................ 114
6.2.1. Concept..........................................................................................114
6.2.2. Design Calculations .....................................................................121
..................................... 122
6.2.2.1. Circular Waveguide Section
6.2.2.2. Rectangular Waveguide S e c tio n ...........................................123
6.2.3. The Coupling P r o b e .....................................................................126
6.3. Experimental System ............................................................................... 131
6.3.1.
6.3.2.
6.3.3.
6.3.4.
Waveguide Circuitry.....................................................................131
Gas Supply System ....................................................................... 133
Bluff Bbdy Configurations .......................................................... 137
Plasma Ig n itio n .............................................................................141
6.4. Experimental Procedure.......................................................................... 142
6.5. Experimental Results............................................................................... 146
6.5.1. Electric Field Distribution............................................................. 146
6.5.2. General Plasma B ehavior............................................................. 157
6.5.3. Plasma Size and Location............................................................. 161
6.5.4. Stability Boundaries .....................................................................169
6.5.5. Coupling Efficiencies ..................................................
171
6.5.6. Nozzle Inlet Temperatures .......................................................... 177
6.5.7. Overall Efficiencies .....................................................................180
6.5.8. Specific Impulse .......................................................................... 184
6.5.9. T hrust
.......................
184
6.5.10. Specific P ow er.............................................................................187
6.5.11. Variation of other Thruster Param eters..................................... 189
vii
TABLE o f CONTENTS fcpnt?fl
Chapter 7. PLASMA SPECTROSCOPY.................................................................. 190
7.1. Introduction............................................................................................ 190
7.2. Equilibrium R elations.............................................................................191
7.2.1.
7.2.2.
7.2.3.
7.2.4.
Complete Thermal Equilibrium .................................................. 191
Local Thermal Equilibrium ( L T E ) ............................................. 194
Partial Local Thermal Equilibrium ( PLTE ) ..............................196
Non-LTE Plasmas: the Generalized Multithermal Equilibrium
Model (G M TE )....................................................................... 197
7.2.5. Non-LTE-Plasmas: Corona Equilibrium ..................................... 199
7.3. Spectroscopic Plasma Diagnostic Techniques........................................200
7.3.1.
7.3.2.
7.3.3.
7.3.4.
7.3.5.
7.3.6.
7.3.7.
7.3.8.
Absolute Line Intensities .............................................................201
Relative Line Intensities............................................................... 203
Absolute Continuum Spectroscopy................................................205
Relative Continuum Intensities.....................................................206
Relative Line to Continuum Intensities........................................206
Stark Broadening and S h if t..........................................................207
Doppler Broadening .................................................................... 215
GMTE Plasma Diagnostics.......................................................... 217
7.4. Plasma Temperature Measurements for the Rectangular and
Circular Waveguide............................................................................ 218
7.4.1. Selection of the Spectroscopic M eth o d ........................................218
7.4.2. Spectroscopic System and Procedure for the Absolute
Continuum M ethod..................................................................220
7.4.2.1.
7.4.2.2.
7.4.2.3.
7.4.2.3.
Spectroscopic System .......................................................... 220
Calibration............................................................................ 222
Abel Inversion....................................................................... 223
Experimental Procedure....................................................... 226
7.4.3. Spectroscopic System and Procedure for DopplerBroadening............................................................................... 230
7.4.3.1. Selection of the Spectral Line ........................................... 230
viii
TABLE OF CONTENTS (cont?d)
7.4.3.2. The Fabry-Perot E ta lo n .....................................
231
7.4.3.3. Spectroscopic System ..........................................................237
7.4.3.4. Discussion of the Method . . . . ......................................... 237
7.5. Spectroscopic Results .......................................................................... 240
7.5.1. Electron Temperatures measured for the Rectangular
W aveguide...............................................................................240
7.5.2. Electron Temperatures measured for the Circular
W aveguide..................................................................
242
7.5.3. Comparison of Electron Temperatures for Various
Applicators...............................................................................245
Chapter 8. CONCLUSIONS AND RECOMMENDATIONS ................................249
REFERENCES
.........................................................................................................256
Appendix A. TUNGSTEN WIRE-MICROWAVE FIELD
INTERACTIONS...............................................................................266
Appendix B. VARIATION OF BLUFF-BODY SIZE
.......................................... 270
Appendix C. PLASMA-BLUFF BODY INTERACTIONS .....................................278
Appendix D. THERMAL TRANSIENTS..................................................................285
ix
LIST OF FIGURES
Figure 2.1
Concept of a Microwave Electrothermal T hruster.......................
Figure 2.2
Resonant Cavity Thruster
..................................................................
17
Figure 2.3
Coaxial Microwave Thruster .............................................................
22
Figure 2.4
Principle of the Waveguide-Applicator .............................................
25
Figure 4.1
Geometry of the Rectangular W aveguide.....................................
Figure 4.2
Rectangular TEI0- (top) and TMn-modes (bottom) ..........................
Figure 4.3
Geometry of the Circular W aveguide..........................................
57
Figure 4.4
Circular TEU- and TMoi-modes.....................................................
62
Figure 5.1
Set-up of the Straight, Rectangular Waveguide Experim ent.......
68
Figure 5.2
Gas Supply System for the Rectangular Waveguide Applicator . . .
72
Figure 5.3(a) Tungsten-Wire Support directly mounted in the Quartz Tube . . . .
74
Figure 5.3(b) Tungsten Wire Support using HBC-grade Boron Nitride Mount . .
74
Figure 5.4
Amplifier-Circuit for the Photodiode Array
....................................
76
Figure 5.5
Stabilization of the Plasma by means of a Bluff Body ....................
77
Figure 5.6
Voltage-Peaks obtained from the Photodiode A rray .....................
Figure 5.7
Forward Power with respect to Time for a Propagating Plasma
Figure 5.8
Experimental Plasma Velocities for Helium and Nitrogen
at 1 atm Gas Pressure....................................................................
84
Comparison of Experimentally Obtained Plasma Velocity Data
at 1082 W with Batenin?s Data at 1100 W .................................
85
Figure 5.9
9
46
53
81
..
83
X
LIST OF FIGURES (cont?d)
Figure 5.10
Coupling Efficiency with respect to Time for a Propagating
Plasm a..................................
90
Figure 5.11 Absorbed Power with respect to Time for a Propagating Plasma . .
91
Figure 5.12 Reflected Power with respect to Time for a Propagating Plasma . .
92
Figure 5.13
Transmitted Power with respect to Time for a Propagating
Plasm a...................................................................................................93
Figure 5.14 Stabilized Plasma in the Straight, Rectangular Applicator.............
96
Figure 5.15 Stable Plasma Positions with respect to Bluff B o d y .............................98
Figure 5.16
Recirculation-Zone behind a Conical Bluff Body exposed to a
Low-Reynolds Number F l o w .............................................................100
Figure 5.17
Stability Boundaries of a Helium Plasma with respect to
Inlet Flow Velocity and Input Power................................................... 104
Figure 5.18
Coupling Efficiencies vs. Mass Flow Rate for Helium at various
Input Power L e v e ls ............................................................................ 106
Figure 5.19
Coupling Efficiencies vs. Input Power for Helium at various Inlet
Flow Velocities ..................................................................................107
Figure 5.20
Absorbed, Reflected and Transmitted Power for Helium vs. Input
P o w e r ................................................................................................. 108
Figure 5.21
Coupling Efficiencies for Helium at constant Mass Flow Rates
at various Pressures............................................................................ 110
Figure 6.1
TM0) Mode Generation in a Circular W aveguide.............................115
Figure 6.2
Schematic of the Circular Waveguide Applicator ( Drawn To
Scale) ..................................................................................................117
Figure 6.3
The Circular Waveguide Applicator.....................................................120
LIST OF FIGURES (cont?d)
Figure 6.4
Anticipated, "Ideal" Field Pattern in the Circular Waveguide
Applicator............................................................................................ 124
Figure 6.5
Coaxial-to-Rectangular Waveguide T ransition.................................... 130
Figure 6.6
Waveguide-Circuitry for the Circular A pplicator............................... 132
Figure 6.7
Experimental Set-up of the Circular Waveguide Experiment . . . .
134
Figure 6.8
Schematic of the Gas Supply System for the Circular Waveguide
Applicator.......................................
136
Figure 6.9
Bluff Body Designs (Material: HBC-Grade Boron N itrid e )
138
Figure 6.10 Bluff Body Support A dapter................................................................. 140
Figure 6.11 Measurement of the Electric Field Distribution by means of a
Coaxial A ntenna..................................................................................147
Figure 6.12 Electric Field Measurements (Power Equivalents) at the Wall of
the Empty Circular Waveguide A pplicator.....................
149
Figure 6.13 Field Distribution in the Empty Circular Waveguide Applicator
(Drawn to Scale)..................................................................................150
Figure 6.14 Electric Field Measurements (Power Equivalents) at the Front
Wall of the Filled Circular Waveguide Applicator ...........................151
Figure 6.15 Electric Field Measurements (Power Equivalents) at the Back
Wall of the Filled Circular Waveguide Applicator ........................... 152
Figure 6.16 Field Distribution in the Filled Circular Waveguide Applicator
(17 cm Bluff Body Position, Drawn to Scale) ...................................153
Figure 6.17 Plasma Formation in the Circular Waveguide Applicator
at Quartz Tube Dome (Drawn to Scale)............................................. 160
Figure 6.18 Plasma Size and Location for a Helium Plasma at 1.8 a t m
162
xii
LIST OF FIGURES (cont?d)
Figure 6.19 Plasma Size and Location for a Helium Plasma at 2.6 atm ............... 163
Figure 6.20 Plasma Diameter vs. Power at various Pressure Levels for
Helium ................................................................................................. 166
Figure 6.21 Plasma Length vs. Power at various Pressures for Helium ...............167
Figure 6.22 Plasma-Bluff Body Spacing vs. Power at various Pressures for
Helium ................................................................................................. 168
Figure 6.23 Stability Boundaries for the Circular Waveguide Applicator using
Helium ................................................................................................. 170
Figure 6.24 Coupling Efficiencies vs. Input Power for the Circular Waveguide
Applicator using H elium .....................................................................172
Figure 6.25 Coupling Efficiencies vs. Pressure for the Circular Waveguide
Applicator using H elium .....................................................................173
Figure 6.26 Absorbed, Reflected and Transmitted Power Levels vs. Input
Power for the Circular Waveguide Applicator using Helium . . . . 174
Figure 6.27 Absorbed, Reflected and transmitted Power Levels vs. Pressure
for the Circular Waveguide Applicator using Helium ........................ 176
Figure 6.28 Mass Flow Rates vs. Input Power for the Circular Waveguide
Applicator using H elium .....................................................................178
Figure 6.29 Calculated Nozzle Inlet Temperatures and Absorbed Power
Levels for the Circular Waveguide Applicator using Helium . . . .
179
Figure 6.30 Calculated Overall Efficiency vs. Power for the Circular
Waveguide Applicator using H elium ...................................................181
Figure 6.31 Calculated Overall Efficiency vs. Pressure for the Circular
Waveguide Applicator using H elium ...................................................182
xiii
LIST OF FIGURES (cont?d)
Figure 6.32 Calculated Specific Impulse vs. Power for the Circular Waveguide
Applicator using H eliu m .....................................................................185
Figure 6.33 Thrust vs. Pressure for the Circular Waveguide Applicator
v
using Helium . ..................................................................................186
Figure 6.34 Specific Power vs. Input Power for the Circular Applicator
using H elium ..................................
Figure 7.1
188
GMTE-Temperature P lo t...................................................................... 198
Figure 7.2. Spectroscopic System ........................................................................... 221
Figure 7.3
Geometrical Relationships between the Variables utilized in the
Abel-Inversion T echnique..................................................................224
Figure 7.4
Continuum-Emission Coefficient at 4250 A for Helium
vs. Electron Temperature ..................................................................227
Figure 7.5
Gaunt-Factor vs. Temperature
Figure 7.6
f-Value vs. Temperature......................................................................229
Figure 7.7
Principle of the Fabry-Perot Etalon ................................................... 233
.................................................228
fi.
t
Figure 7.8
Output of the Fabry-Perot Etalon irradiated by the 6328 A
He lin e ................................................................................................. 236
Figure 7.9
Optical Set-Up for the Circular Waveguide Experim ent....................238
Figure 7.10 Measured Electron Temperatures obtained with the Absolute
Continuum Method vs. Input Power at various Mass Flow Rates
and Pressures.......................................................................................241
Figure 7.11 Peak Electron Temperatures obtained with the
Absolute Continuum Method vs. Input Power
for the Circular Waveguide Applicator using Helium ........................243
xiv
LIST OF FIGURES (cont?d)
Figure 7.12
Electron Temperature Profiles vs. Input Power for the
Circular Waveguide Applicator using H e liu m .................................. 244
Figure 7.13
Impact of Variations in Bluff Body Size on the Electron
Temperature for the Circular Waveguide Applicator
using H elium .......................................................................................246
Figure 7.14
Comparison of Electron Temperatures obtained by Absolute
Continuum Spectroscopy for various Microwave Applicators . . . . 247
Figure A. 1
Coupling Efficiencies obtained for the case of a Tungsten-Wire
inserted into the Circular Waveguide Applicator ............................. 267
Figure A. 2
Microwave Power Absorption by a Tungsten Wire inserted into the
Circular Waveguide Applicator.......................................................... 268
Figure B. 1
Impact of Variations in Bluff-Body size on Coupling Efficiencies
for the Circular Waveguide Applicator using Helium ........................271
Figure B.2
Impact of Variations in Bluff-Body Size on Stability Boundaries
of the Circular Waveguide Applicator using H e liu m ........................272
Figure B.3
Impact of Variations in Bluff-Body Size on Absorbed Power and
Nozzle Inlet Temperatures for the Circular Waveguide
Applicator using H eliu m .................................................................... 274
Figure B.4
Impact of Variation in Bluff-Body Size on Thruster Efficiencies
for the Circular Waveguide Applicator using Helium ........................275
Figure B.5
Impact of Variations in Bluff-Body Size on Specific Impulse
for the Circular Waveguide Applicator using Helium ........................276
Figure B.6
Impact of Variations in Bluff-Body Size on Specific Power
for the Circular Waveguide Applicator using Helium ........................277
Figure C .l
Stability-Hysteresis for the Plasma in Interaction with the
Bluff-Body Flow Field in the Circular Waveguide Applicator . . . 279
XV
LIST OF FIGURES (cont?d)
Figure C.2
Plasma-Bluff Body Interactions affecting Coupling Efficiencies
for the Circular Waveguide Applicator using Helium ........................280
Figure C.3
Reflected and Transmitted Powers as affected by
Plasma-Bluff Body Interactions in the Circular Waveguide
Applicator using H eliu m .................................................................... 282
Figure D. 1
Effect of Thermal Transients on the Coupling Efficiencies of
a Circular Applicator using Helium ..................................................286
Figure D.2
Effect of Thermal Transients on the Absorbed, Reflected and
Transmitted Power Levels for the Circular Waveguide
Applicator using H eliu m .................................................................... 288
Figure D.3
Effects of Thermal Transients on Nozzle Inlet Temperatures
and Absorbed Power for the Circular Waveguide
Applicator using H eliu m .................................................................... 289
Figure D.4
Effect of Thermal Transients on Overall Thruster Efficiencies
for the Circular Waveguide Applicator using Helium ........................291
Figure D.S
Effect of Thermal Transients on Specific Impulse for the
Circular Waveguide Applicator using H e liu m .................................. 292
Figure D.6
Effect of Thermal Transients on Specific Power for the
Circular Waveguide Applicator using H e liu m .................................. 293
xvi
LIST OF TABLES
Table 1.1
Propellant Mass Fractions of ContemporarySpacecraft .................
2
Table 2.1
IEEE Frequency B ands.....................................................................
13
Table 2.2
Comparison of Microwave, ArcjetandResistojet Thruster
Performances..................................................................................... 30
Table 4.1(a)
q^-values for Circular TE M o d e s ..................................................
59
Table 4 .1(b) q^-values for Circular TM M o d e s.................................................. 59
Table 4.2(a)
K^-values for TE M odes.................................................................
60
Table 4.2(b) K^-values for TM Modes ............................................................... 60
Table 7.1
Line Widths due to Stark and DopplerBroadeningfor selected
Helium L in e s.......................................................................................231
ACKNOWLEDGEMENTS
I wish to thank Dr. Michael M. Micci, my thesis advisor, for giving me the
opportunity to participate in this interesting research project and for his guidance and
assistance throughout the project. I would also like to thank Mr. Philip A. Balaam, Dr.
In-Seung Chung, Mr. Anthony J. Colozza and Mr. Daniel J. Sullivan, my office mates
and friends, for their support and help throughout the years which extended far beyond
a merely professional level; Mr. Bob Dillon, Mr. Jim Fetterolf, Mr. Wayne Holmberg
and Mr. Rex Jacobs without their mechanic and electronic skills this project would not
have been possible; and Ms. Amy Myers who, in long hours, typed all of the
publications that have resulted from this work. Last but not least, I would like to thank
my parents, Elfnede and Karl Muller, for thirty years of continued support.
1
Chapter 1
INTRODUCTION
1.1. A Brief Introduction to Electric Propulsion
Interest in electric propulsion concepts is on the rise as their potential for
delivering a high specific impulse at a low fuel consumption meets the demands of more
sophisticated future space missions such as establishing orbits at high inclination angles,
orbit transfer and stationkeeping of heavier spacecraft having longer lifetimes,
deployment of whole spacecraft constellations, sophisticated interplanetary missions both
robotic and manned and moving large flexible space structures requiring low thrust but
high specific impulse propulsion systems. Since launch costs for boosting the spacecraft
from earth?s surface into low earth orbit (LEO) make up for a large portion of the overall
mission costs, smaller propellant mass fractions are able to greatly reduce the delivery
costs of such future spacecraft1, thus allowing easier and more flexible access to space.
On the other hand, propellant mass savings for higher specific impulse electric engines
can also be replaced by additional payload, thus enhancing the commercial or scientific
value of the particular mission. Contemporary inteiplanetary spacecraft show propellant
mass fractions as high as 70% (see Table 1.1) which is a dramatic increase over the 9%
propellant fraction of the historical Pioneer 10 and 11 probes, emphasizing demanding
future space mission profiles. Geostationary (GEO) satellites reveal similar propellant
mass fractions if the propellant necessary for GEO-transfer is taken into account1. Onorbit propellant mass fractions of 10-15% for today?s telecommunications satellites are
common1.
2
Table 1.1 Propellant Mass Fractions of Contemporary Spacecraft
On-Orbit
Propellant
GTO-Prqpellant
Reference
Intelsat VA
15 %
54 %
1
Satcom Ku3
10%
60%
1
Intelsat VI
11 %
50 %
1
CRAF
70 %
-
2
Viking
60 %
-
1
Mars Observer
57 %
-
2
Pioneer 10 & 11
9 %
-
1
Spacecraft
GEO-Satellites
Interplanetary
Spacecraft
The reasons for these large propellant masses can be found in the limited
specific impulse ability of current state-of-the-art chemical propulsion systems used on
these spacecraft. Typically, 400-N class bipropellant, hypergolic NTO/MMH engines are
employed for main propulsion applications and an array of 10 to 20-N class bipropellant
engines using the same propellant combination or less than 1-N class monopropellant
hydrazine thrusters are required for attitude control purposes.
Hydrazine engines, however, only achieve specific impulse values up to 200 sec
while corresponding values for NTO/MMH bipropellant engines may reach up into the
low 300 sec range3. The first pump-fed NTO/MMH space propulsion engine is the XLR132 thruster currently under development at Rocketdyne and Aerojet4,3. Despite a
chamber pressure of 1500 psia which is about 10 times the pressure of most storable
pressure-fed upper stage engines and about half the chamber pressure of the Space
Shuttle Main Engine (SSME) and a nozzle area ratio of 400:1, the specific impulse
remains limited at 342 seconds4,5.
Electric propulsion systems under consideration such as resistojets, arcjets,
magnetoplasmadynamic thrusters (MPD?s) and ion engines are capable of delivering
specific impulses in the 280-800 sec, 650-1500 sec, 1500-4000 sec and 2000-10000 sec
range, respectively1 and therefore offer the potential of significant propellant savings. At
the same time, power capabilities of future spacecraft will increase: the next generation
of commercial communication satellites in GEO-orbits are expected to provide 6 kW
electrical power thus enhancing the attractiveness of electric propulsion systems6.
Of the electric thruster hardware currently under development, ion engines show
very high specific impulses up to 5000 sec7, resulting in significant propellant savings
over chemical as well as other electric thrusters3,4,8*10. Although high specific impulse
values require high power inputs into the thruster, power requirements of ion engines
remain moderate for near-earth missions due to high overall thruster efficiencies,
exceeding 80 %7. However, performance data are envisioned to drop as future operational
thrusters might have to resort to more affordable and more readily available propellants
than xenon such as argon and krypton9. In addition, high thruster efficiencies in the
specific impulse range of 2000 sec and below, are not available with ion engines either.
This specific impulse range, however, is very interesting for near-earth missions since
it combines significant propellant savings with low thruster power requirements.
Furthermore, although offering the highest payload ratios available with today?s electric
engines3,4,8*10, low thrust values of only a couple hundred millinewtons will result in long
trip times with ion engines8 which might prove to be a major setback, in particular for
near-earth missions. Slow transfer through the Van-Alien radiation belts could cause
severe solar power cell degradation as well as damage to other semiconductor electronic
components onboard the craft.
Higher thrust values up to a few newtons are available with state-of-the-art
electric propulsion technology in the form of electrothermal resistojets and arcjets and
magnetoplasmadynamic (MPD) thrusters. The MPD thruster, however, currently does
not appear as a serious alternative to other electric propulsion devices due to severe
cathode erosion problems"'17, limiting lifetimes of current thruster configurations to only
a couple of hours16,17. Furthermore, thruster efficiencies remain fairly small and in most
cases rarely exceed 30% for steady-state thrusters14,17'23. Quasi-steady MPD thrusters,
although offering moderate thruster efficiencies in the 40 to 50% range13,14,26 show even
higher cathode erosion losses than steady-state engines and can therefore not be seriously
considered as options for space propulsion applications at this stage of their development.
Specific impulses obtained with current steady-state, self-field argon thrusters remain
limited around the 1000 sec margin14,17,21'23, although steady state thrusters augmented by
external magnetic fields have reached values in excess of 5000 sec in the past using
hydrogen as a propellant14,18*20.
Among the electrothermal devices, resistojets do offer high thruster efficiencies
in excess of 80% for hydrogen or helium propellants27,28, however, specific impulses are
low with the exception of high power ( > 3 kW ) hydrogen thrusters27and barely exceed
those values obtained with chemical devices2731. Contemporary resistojet thruster designs
fulfilling lifetime requirements on the order of 10,000 hours as envisioned for use on the
Space Station Freedom28 deliver specific impulses up to 500 sec for hydrogen, 425 sec
for helium and only 160 sec for nitrogen using a 500 W power supply28. Thus, potential
propellant mass savings are relatively small. Currently used resistojets on space missions
have been limited exclusively to stationkeeping purposes29.
Arcjets, on the other hand, have obtained specific impulses of up to 800 sec with
storable ammonia propellant at a power level of 30 kW32 and up to 2000 sec with
cryogenic hydrogen propellant at a power level of 200 kW27. Thruster efficiencies,
however, remain low to moderate, ranging around 30% for storable32'33 and up to 50%
for cryogenic propellants27. It has been estimated that heat losses due to anode attachment
account for 14 to 20% of the overall efficiency losses while cathode attachment adds
another 5 to 8% losses36. Problems associated with using the better performing cryogenic
arcjets, however, arise from problems related to long-term storage of the hydrogen
propellant37,3*. Short thruster lifetimes, currently not exceeding 573 hours of continuous
operation39, is an additional disadvantage of this thruster type, in particular since future
needs for electric orbit transfer vehicles (EOTV?s) have been estimated to a minimum
required lifetime of 10,000 hours for an electric thruster10,40. Thus, additional arcjet
thrusters would have to be carried along by an EOTV to replace thrusters that have failed
during the mission, increasing the overall propulsion system weight10.
Electrodeless thrusters would potentially avoid these lifetime problems. Laser
thrusters, which form an electrodeless plasma discharge by focusing a laser beam into
a region of the thrust chamber well away from any thrust chamber walls, might offer
these lifetime advantages4146. Separation of the power source from the spacecraft by
means of power beaming will also result in low spacecraft masses and high available
power levels, however, significantly increase the complexity of the overall system.
Thus, although even today?s available electric propulsion types do offer significant
payload increases over chemical systems3,4*'10, none of the systems offers ideal
performances with respect to all thruster parameters of interest, such as specific impulse,
thruster efficiency, thrust and lifetime. Reviewing several of the recently investigated
EOTV applications suggests the following performance as desirable in order to lead to
6
future improvements for electric propulsion over current concepts3,4,8*10,47: specific
impulses of at least 900 to 1000 sec should be obtained at thruster efficiencies of or
exceeding 50% in order to result in significant propellant savings over chemical thrusters
while still keeping power requirements low enough to result in a reduced spacecraft dry
weight over current electrothermal concepts. On the other hand, specific impulse values
should not exceed the 2000 sec margin in order to avoid excessive power requirements.
Thrust levels of a couple of newtons should be obtainable in order to reduce trip times
over contemporary electric thruster concepts. Furthermore, high thruster lifetimes on the
order of 10,000 hours or more are desirable.
It will be those performance requirements on a future electric propulsion system
by which the performance characteristics and the development status of new thruster
concepts, such as the herein investigated microwave thruster concept, will have to be
measured.
1.2. Scone of the Thesis
One advanced propulsion system currently under investigation is the microwave
electrothermal thruster (MET) and subject to further study in this thesis. Microwave
energy is transferred into an absorption chamber where the propellant gas is heated into
a plasma stage. By a careful choice of the generated electromagnetic field pattern in the
absorption chamber, the plasma can be sustained in a position away from the chamber
walls and kept in place by means of a combination of electrodynamic forces induced by
the microwave field and gasdynamic forces that can be introduced by such stabilizing
devices as bluff bodies. Thus, plasma and thruster structure are separated and the
propellant gas can be heated to a much higher temperature than wall material
constrictions would allow.
Several different microwave thruster configurations have emerged in the past and
will be reviewed in the next chapter. The objective of this thesis is to focus on the
investigation of one particular thruster configuration, the so called waveguide-mode
thruster concept, where the absorption chamber is simply formed by a waveguide section.
The research efforts undertaken to this end presented in this thesis will constitute the first
comprehensive examination of this thruster type to date.
The following chapters will therefore deal with the introduction of the various
common characteristics of microwave thrusters and discuss engine configurations that
have emerged so far. Attention will then be focused on the important physical phenomena
to be understood and design issues to be solved in order to arrive at a working waveguide
mode microwave thruster. Performance optimization of this thruster for space propulsion
applications is beyond the scope of this thesis and invesigations will rather concentrate
on proof-of-concept type studies, determination of general operating characteristics and
initial performance evaluations of the waveguide thruster concept in order to estimate its
potential for possible future use as a space propulsion device.
8
Chapter 2
MICROWAVE PROPULSION CONCEPTS
2.1. Introduction
This chapter will serve to discuss general microwave thruster behavior and the
basic concepts behind this new propulsion device in more detail. The thruster
specifications given in the last chapter to be met by an advanced electric propulsion
system in order to result in increased performances over currently existing systems can
be regarded as the design goal for microwave electrothermal thruster concepts. In the
present chapter, it will be investigated if microwave thrusters offer the potential of such
performance increases. To this end, several microwave thruster configurations currently
under consideration will be introduced and performance data obtained with these
configurations will be reviewed.
2.2. Basic Characteristics of Microwave Electrothermal Thrusters
Microwave propulsion systems show several advantages over other electrothermal
thrusters. The concept of this thruster type relies on the principle of absorbing microwave
radiation by the propellant gas (see Figure 2.1). Microwave power is transferred into the
thrust chamber or applicator by means of waveguides. Here, ignition occurs by means
of microwave breakdown: an initial, low concentration of electrons present in the
propellant gas due to random collisions of the higher energetic propellant atoms absorb
Applicator
Microwave
Power
Propellant;
V propellant
Propellant
Coupling
Probe
Electromagnetic
Field Mode
Plasma
Figure 2.1 Concept o f a Microwave Electrothermal Thruster
part of the incoming microwave radiation. Subsequently, higher energetic electron-atom
collisions occur and increase the electron concentration. This in turn results in increased
microwave absorption until breakdown takes place and a plasma is created. Microwave
absorption is almost entirely due to the interactions between the microwave field and the
electrons. Ions are too heavy and have too low of a mobility to be able to follow the
high-frequent microwave field and thus cannot absorb its energy. Typical plasma
temperatures reached with microwave absorption devices range around 10,000 K.
If chamber dimensions and coupling methods are properly chosen, electromagnetic
field patterns can be established inside the applicator which are able to sustain a plasma
in maximum field regions away from the chamber walls. Under ideal circumstances the
plasma remains positioned stably in the maximum field region and serves as a heating
element for the newly incoming cooler propellant. Heat is transferred from the plasma
to the remainder of the propellant by what is currently believed to be some combination
of heat conduction, forced convection and radiation. The heated propellant is then
thermally expanded in a nozzle to produce thrust while the plasma remains stationary in
the maximum field region inside the applicator. However, as will be discussed in Chapter
3, plasma instabilities may cause the plasma to move out of its original position toward
the microwave power source and therefore establish a need for plasma stabilizing devices
such as bluff bodies, for example.
Since the applicator walls are thermally isolated from the plasma by a relatively
cool propellant gas film flowing between the plasma and the walls, this allows the
propellant to get much hotter than the walls. Thus, propellant temperatures should exceed
those in resistojets, for example, and therefore microwave engines should allow for
higher specific impulses.
Furthermore, problems associated with electrode erosion as they occur in arcjets
11
are avoided thus enabling much longer thruster lifetimes and allowing for the choice of
a wider range of propellants, including the use of oxidizing ones.
Thirdly, the coupling of microwave energy into gases at pressures on the order
of atmospheric is extremely efficient. Coupling efficiencies up to 99% have been
obtained48,49, clearly exceeding values for electrodeless RF coupling in this pressure
range50.
Fourth, radiation losses from a microwave created plasma are believed to be small
due to the relatively low temperatures on the order of 10,000 K encountered, compared
to values about double as high for laser engines41. Zerkle et.al.41 point out that at
temperatures of 20,000 K, laser thrusters may suffer efficiency losses due to radiation
losses. At the considerably lower plasma temperatures observed for microwave thrusters,
those losses might be diminished accordingly.
Fifth, using magnetrons, microwave power can be generated at an efficiency up
to 85% and up to a peak power in the 10 MW range for a frequency of about 3
GHz51,52. This is also the frequency range of choice for microwave propulsion devices:
the 2.45 GHz, 5.8 GHz and 24.125 GHz bands have been assigned by international
regulating authorities for industrial, scientific and medical purposes, having the advantage
of not interfering with bands used for communication purposes53. The 24.125 GHz band,
however, is not applicable for microwave propulsion concepts since engines would have
to be scaled down in size to an extent which renders them impractical51. As will be
shown in Chapters 4 and 6, the geometrical size of a thruster scales inversely with its
operating frequency. Increasing the frequency from 2.45 GHz to 24.125 GHz, i.e.
roughly by a factor of 10, would result in a ten times smaller engine configuration. Since
for 2.45 GHz-thrusters waveguide diameters range between 10 and 20 cm depending on
the actual configuration chosen, engine dimensions would fall within the range of a
12
couple of centimeters and thus within the range of the plasma size, which is fairly
independent of frequency variations and mainly depends on pressure and power levels
chosensl. Thus, selecting an operating frequency that high might result in contact between
the plasma and the waveguide applicator walls and lead to erosion problems and thruster
efficiency reductions due to heat losses into the engine structure. However, Frasch
et.al.91 point out that in this frequency range other coupling methods than the
conventional standing field patterns are possible and plasma-microwave interactions can
be obtained by using quasi-optical methods to guide the microwave energy. These
coupling mechanisms are untested so far in view of space propulsion applications and
beyond the scope of this introduction.
An additional disadvantage of using frequencies higher than S- and C-band
frequencies52, i.e. frequencies in the range of 2 to 8 GHz (compare with Table 2.1) can
be found in the fact that microwave generation efficiencies at frequencies higher than 10
GHz drop below 50%51. Taking into account the high PCU efficiencies of other electric
thruster concepts, ranging as high as 90% and above, resorting to frequencies other than
found in the S- and C-bands would render microwave thrusters uncompetitive with
respect to those other systems. Onboard microwave energy generation in the S- and Cbands, however, appears to be practical and the complexity associated with power
beaming to the spacecraft, as necessary for laser propulsion devices is thus avoided
although this option remains open53.
Sixth, if it would be decided to beam microwave power to the spacecraft rather
than creating it onboard, microwave power beaming does offer certain advantages.
Microwave absorption in the atmosphere is small and transparencies of 90% are
obtainable in the 0.6 to 30 GHz range53. The main attenuation for microwave radiation
in the atmosphere is due to rain drops, in particular towards the higher frequencies53. At
13
Table 2.1
IEEE Frequency Bands
Designation
Frequency
Wavelength
30-300 Hz
10-1 Mm
300-3000 Hz
1-0.1 Mm
3-30 kHz
100-10 km
30-300 kHz
10-1 km
300-3000 kHz
1-0.1 km
3-30 MHz
100-10 m
VHF (very high frequency)
30-300 MHz
10-1 m
UHF (ultra high frequency)
300-3000 MHz
100-10 cm
SHF (superhigh frequency)
3-30 GHz
10-1 cm
30-300 GHz
1-0.1 cm
300-3000 GHz
1-0.1 mm
P band
0.23-1 GHz
130-30 cm
L band
1-2 GHz
30-15 cm
S band
2-4 GHz
15-7.5 cm
C band
4-8 GHz
7.5-3.75 cm
X band
8-12.5 GHz
3.75-2.4 cm
Ku band
12.5-18 GHz
2.4-1.67 cm
Kband
18-26.5 GHz
1.67-1.13 cm
Ka band
26.5-40 GHz
1.13-0.75 cm
40-300 GHz
7.5-1 mm
300-3000 GHz
1-0.1 mm
ELF (extreme low frequency)
VF (voice frequency)
VLF (very low frequency)
LF (low frequency)
MF (medium frequency)
HF (high frequency)
EHF (extreme high frequency)
Decimillimeter
Millimeter
Submillimeter
7 GHz, 10% of the transmission will be lost due to a 5 mm/h rain, 40% due to a 50
mm/h rain and up to 90% due to a severe thunderstorm. However, for wavelengths
greater than 10 cm (and frequencies smaller than 3 GHz), even attenuation due to rain
becomes negligible? Thus, once again the lower S-band frequencies are favored for
microwave thruster applications. Furthermore, microwave power beaming into orbit may
benefit from space defense related research currently being performed in this area? .
Specific masses of microwave propulsion systems employing power beaming have been
estimated as low as 0.03 kg/kW* and thus would range lower than corresponding values
for all other advanced propulsion concepts except laser thrusters.
Another advantage microwave propulsion systems may have over other electric
propulsion systems can be mentioned although it will be limited to very specialized
missions only. If a high power microwave source operating in an appropriate frequency
band is already onboard the spacecraft, for example for earth-remote sensing purposes,
the microwave propulsion system could use this power during orbit transfer or
housekeeping periods. Although the development of a microwave thruster with only these
specialized missions in mind might not be justified, certain future remote sensing
satellites might profit from a potentially available microwave thruster. An additional
advantage of such a system would be that not only the power source but also the power
conditioning unit of the payload could be used by the propulsion system. This would not
necessarily be the case for competitive electric thruster concepts, such as arcjets or ion
engines even if access to a payload power source would be available. Both of the latter
two systems require either high current or high voltage power supplies, respectively, not
necessarily in demand for the rest of the spacecraft.
Disadvantages of microwave thruster concepts over existing electric propulsion
devices may be found in the very early stage of their development, with a substantive
15
part of the research and development efforts still lying ahead. So far, only laboratory
prototypes have been tested and research has been directed entirely towards proof-ofconcept studies and demonstrating the performance potential of microwave thrusters,
rather than optimizing this system for space propulsion applications. In particular
problems concerning plasma positioning and plasma stability will have to be addressed
in the future: as will be discussed in more detail in the next chapter, microwave plasmas
are not stable towards higher power levels and tend to move towards the microwave
source due to heat conduction and resonant radiation processes and thus will have to be
stabilized. Furthermore, plasma location will have to be maintained as close to the nozzle
inlet as possible in order to yield high temperatures at the nozzle inlet and thus high
specific impulses and thruster efficiencies. Yet, the plasma should be positioned far
enough away from the nozzle inlet so as not to cause erosion problems. This requires a
careful selection of the field patterns to be established in the thrust chamber and therefore
creates a need for significant development efforts in this area in the future.
In the following sections, some of these problems will be discussed by reviewing
several different microwave absorption concepts that have been studied to date48,54. Three
different configurations have evolved over the years which are the resonant cavity
applicator, the coaxial applicator and more recently, the waveguide applicator. Initial data
and operational characteristics that have been obtained will be used here to evaluate the
performance potential of these three microwave applicator concepts, to point out their
advantages and disadvantages and to motivate the introduction of the waveguide-mode
concept as the subject of investigation through the remainder of this thesis.
16
2.3. The Resonant Cavity Concept
Resonant cavity configurations have been studied extensively for space propulsion
applications at the Michigan State*5'*7 and The Pennsylvania State Universities5840 and at
the Aerojet Company61. The concept of a resonant cavity thruster is shown in Figure 2.2.
Here the absorption chamber consists of a cylindrical cavity of 17.8 cm inner diameter
for a microwave frequency of 2.45 GHz. The cavity length is adjusted by a movable
shorting plate and chosen according to the field pattern to be established inside the
cavity. Microwave energy is coupled into the cavity via a coaxial probe. Adjusting the
location of the probe and the movable end shorting plate allows tuning the system for
given microwave modes.
The TM0n and TM012 modes are frequently used field
configurations. Both modes allow one to keep the plasma located along the cavity axis
away from the walls. Under laboratory conditions, the propellant gas itself flows through
a quartz container positioned along the cavity axis, isolating the test gas from the
surrounding air.
Coupling efficiencies, being the ratio of the power absorbed by the plasma and
the thruster input power, in excess of 99% were obtained for helium49,55. Whitehair
et.al.55 obtained thruster efficiencies, being the ratio of thrust power to input power, up
to 45% with helium at specific impulses of 600 sec. Gas pressure was around 0.5 atm
resulting in a fairly low mass flow rate of only 8.9 mg/s. Power levels ranged between
400 and 500 W. Maximum specific impulses for nitrogen were obtained around 300 sec
but at thruster efficiencies of only 10 to 15%. Power was varied between 400 W and 1
kW. Raising the mass flow rate from 37 mg/s to 150 mg/s, however, raised thruster
efficiencies up to 35% while specific impulses dropped accordingly to about 200 sec55
following basic electrothermal thruster characteristics: increasing the mass flow rate and
17
Boron-Nltride_
Bluff Body
Propellant
Flow
t
Resonant
Cavity
Sliding
Short
Coupling Probe
Plasma
(high Power)
Quartz Vessel
Boron-Nitride
Plasma
(low Power) Orifice Plate
Figure 2.2 Resonant Cavity Thruster
18
inlet pressure will decrease the specific impulse since now more propellant gas has to be
heated, decreasing the available kinetic energy per individual gas particle. On the other
hand, heat conduction from the plasma to the propellant gas is increased at those higher
pressure levels and thruster efficiency values are thus higher.
Balaam49 recently obtained helium data for the resonant cavity thruster showing
specific impulses as high as 540 sec at 44% thruster efficiencies and 280 kPa gas
pressure yielding a mass flow rate of 70 mg/s and a thrust level of 0.37 N. A microwave
power level of 2 kW was coupled into the cavity. Again, increasing the mass flow rate
to a higher value of 140 mg/s resulted in much higher thruster efficiencies of 69%,
however, specific impulse values dropped to only 290 sec. Thrust values obtained for
these higher mass flow rates were 0.4 N.
Comparing these values with the performance requirements identified in the
previous chapter, which future electric propulsion systems have to face in order to result
in better overall performances than current systems, large discrepancies between the
design goal and the actually obtained data so far can be noted. However, the cavity
configurations used in both experiments were not devices optimized for space propulsion
applications and merely served the purpose of proof-of-concept studies and initial
performance demonstrations. Whitehair et al.55 used a simple quartz nozzle during their
investigations, leading to melting problems towards higher power levels, limiting their
performance data. Balaam49 used only a converging rather than a converging-diverging
nozzle. A difficulty in Balaam?s experiment was further that the plasma did not form in
the maximum field region that was present just above the nozzle inlet for the TM0U mode
used but in the only other maximum field region located just at the opposite cavity end.
Thus, distance between plasma and nozzle was fairly large, on the order of a couple of
centimeters depending on plasma length. This fact might have reduced performance
19
values due to heat losses from the propellant gas to the thruster walls as it was flowing
from the plasma towards the nozzle inlet. Forced air cooling of the quartz tube might
have enhanced this effect49-55.
Therefore, better plasma positioning might result in increased performances.
Recent, very preliminary observations62 seem to indicate that plasma formation in that
maximum field region of the TM^, mode close to the nozzle inlet is possible if the
nozzle orifice plate, which is located just inside the cavity at this location, is removed
and placed just outside the cavity. Although the orifice plate was manufactured from
HBC-grade boron nitride which is a dielectric material and should therefore only have
limited effects on the field distribution, later investigations discussed in this thesis will
show that boron nitride material present in a waveguide does indeed have a strong impact
on the local field distribution.
Further performance increases are possible if hydrogen instead of helium would
be used as a propellant. Using high temperature nozzle materials shaped into nozzle
contours particularly taking into account the low-Reynolds number characteristics of the
flow should also raise thruster performances. Such special nozzle types have been
developed for resistojets, taking on a so called "modified trumpet" shape30: a flared,
circular arc nozzle contour ("trumpet-shaped") serves to offset boundary layer growth in
the low-Reynolds number nozzle flow. However, since a circular arc profile would have
a very narrow and long throat region, possibly rendering the entire flow field viscous,
this part of the nozzle has been replaced by a 25░-half angle conical contour. Such nozzle
types currently being used for resistojet configuration have obtained area ratios as high
as 2500: l 30.
Other problems that will have to be overcome in order to raise performance data
are of a nature more specific to the cavity design itself. Using a spherical quartz
20
container rather than a straight tube, Balaam and Micci5**60 could show that the plasma
location is not symmetrical with respect to the cavity dimensions, rather, the plasma is
"pushed" sideways, away from the coax coupling probe that is penetrating the sidewall
of the cavity (compare with Figure 2.2). This effect is in particular noted towards higher
power levels. Such "free-floating" plasmas could be stabilized by inserting a boronnitride bluff body into the gas flow along the thruster axis. Gasdynamic forces were then
able to "suck" the plasma into the recirculation region right behind the body, relocating
it along the thruster axis60. However, towards power levels exceeding 2 kW, the plasma
started forming a "tail" that bent towards the coax probe. Further increases in power
could even result in the plasma leaving the recirculation zone behind the bluff body
entirely and moving towards the probe49. Attempts to keep the plasma from moving
sideways by means of narrow quartz tubes aligned with the thruster axis have led to
melting of the tubes as the plasma is forced into close contact with the tube walls due to
its lateral motion61.
This plasma propagation phenomenon has been observed for all microwave
applicators and will be discussed in greater detail in the next chapter. Here, it remains
to be pointed out that these plasma instabilities can severely degrade cavity thruster
performances towards higher power levels and that a change in the coupling design might
be necessary for the cavity applicator.
Future cavity configurations should also explore the possibility of being operated
without a quartz container, i.e. the cavity itself will serve as a gas container. This will
avoid cooling problems of the quartz tube and reduce thruster efficiency losses associated
with forced air cooling of the tube. However, technical problems to be overcome with
such a configuration will be sealing problems along the movable shorting plate. Thus,
a fixed cavity length might have to be chosen and tuning be accomplished externally
21
using stub tuners, adding to the weight and complexity of the system and possibly
lowering overall thruster efficiency63.
Summarizing, advantages of the cavity are its tuning capabilities resulting in
almost perfect microwave absorption. Disadvantages, however, may be found in system
complexity associated with tuning of the system as well as its relatively inflexible control
of plasma position and plasma stabilization in particular towards the more interesting
higher power levels. Future performance increases for the cavity will therefore depend
on the successful solution of those problems.
2.4. The Coaxial Applicator
The coaxial microwave thruster concept has been developed at Michigan State
University and although being the oldest concept63,64, has recently found renewed
attention63. In the latest experiments the coaxial absorption chamber consists of a 6.5 cm
i.d. outer conductor and a 2 cm o.d. brass inner conductor having a tip manufactured out
of Inconel. This configuration is shown in Figure 2.3. The plasma is formed and
sustained at the tip of the center conductor since a maximum field region exists here.
For helium, specific impulses up to 450 sec could be obtained at a power level
of roughly 750 W. However, thruster efficiency at this operating condition was only
30%. In order to obtain those performance data, a mass flow rate of 26 mg/s was
maintained at pressure levels between 576 and 865 Torr63. For nitrogen, thruster
efficiencies in excess of 60% could be obtained when the pressure level was raised above
2 atm. The power level was 500 W. Specific impulses, however, dropped just below 200
sec at these conditions. Maximum specific impulses obtained for nitrogen were around
Microwave
Power
Coaxial
Waveguide
Propellant
Sliding
Short
Cooling
Water
Thrust Chamber
r
Nozzle
^ Thrust
Plasma
Coaxial Waveguide
Transition
(sliding)
Figure 2.2
Spacer
(insulating)
Coaxial Center
Conductor
Coaxial Microwave Thruster
Coaxial Outer
Conductor
23
300 sec at mass flow rates of 65 mg/s and 500 to 900 Torr gas pressures. Thruster
efficiencies, however, dropped accordingly to 17%, following typical electrothermal
thruster characteristics.
Once again, actually obtained performance data are lower than the desired design
goal defined. Shifting the operating conditions to higher gas pressures in order to obtain
better thermal conduction from the plasma to the propellant gas and thus consequently
higher thruster efficiencies, while at the same time maintaining high power levels in
order to keep the specific impulse high, might still offer the possibility for further
performance improvements. As for the cavity, using hydrogen as a propellant rather than
helium or nitrogen and resorting to specially designed low-Reynolds number nozzles
might also result in thruster performance increases.
In general, advantages of this concept are its compact size of 9 cm total outer
diameter and 12 cm length of the thruster section. In particular it was shown that plasma
formation is possible even though the inner diameter of the outer conductor was below
the cutoff frequency for 2.45 GHz. Furthermore, control of the plasma location can
easily be obtained by moving the center conductor. Disadvantages can be found in the
fact that the plasma is attached to the center conductor tip and no method has been found
to detach it yet54. This fact will lower the thruster efficiency due to heat losses and
possibly lead to erosion problems. However, after a total testing time of 30 hours, no
erosion was noted63. Since the coax probe in this configuration does not carry an arc
current but only serves to set up the desired electromagnetic field pattern, erosion
problems will most likely not be as severe as for other thruster types, such as arcjets or
MPD?s. Finally, external tuning of the engine increases system complexity and lowers
overall efficiency of this thruster concept as well63.
The future success of this thruster type, although offering good control over
24
plasma positioning will therefore depend on progress made regarding plasma detachment
from the center conductor and further increasing overall thruster efficiencies.
2.5. The Waveguide Applicator - An Introduction
The most recent of all microwave thruster concepts simply uses a waveguide
section as the absorption chamber (Figure 2.4). A systematic research program is being
undertaken at The Pennsylvania State University to investigate waveguide applicators for
space propulsion purposes6*-69. Here, only a brief introduction to this thruster type
will be given in order to explain the motivation behind exploring this design. A more
detailed description of the overall research project, the actual designs involved and a
discussion of the performance data obtained with those configurations will be given
throughout the remainder of this thesis.
Attention to this thruster concept was first drawn by the fact that the highest
experimentally measured gas temperatures were obtained in a waveguide mode of
operation thus possibly providing higher specific impulses than other investigated
microwave propulsion concepts. Batenin et al.70 reported temperatures up to 11,000 K
for 4500 W incident power at a microwave frequency of 6 GHz in helium. The
significance of raising specific impulse values for microwave electrothermal thrusters in
view of the still limited performances available with coaxial and cavity thruster concepts
helped to overcome initial apprehension towards this concept caused by the fact that
plasmas created in waveguides are inherently unstable, tending to move towards the
microwave source due to various physical mechanisms described below.
Initial research was therefore mainly directed towards
understanding the
Microwave Power out
Microwave Power in
Rectangular
Waveguide
E-Plane Bend
Test Gas
Quartz Tube
E-Plane Bend
Plasma
Plasma-Quartz
Contact
E-Field Lines
( TE-| g-Mode)
Figure 2.4 Principle of the Waveguide-Applicator
26
propagation mechanism and proceeding from there in logical steps: numerical results
obtained by solving the governing energy equation63'*7were compared with experimental
flow velocity data67 in order to allow for conclusions regarding the actual propagation
mechanisms involved. The numerical scheme used throughout those calculations was
adapted from a model developed by Kemp and Root71 in order to investigate propagating
laser-heated plasmas. The model is one-dimensional and the pressure is assumed to be
constant throughout the flow field, allowing the energy equation to be decoupled from
the momentum equations. The solution of the energy equation is then treated as an
eigenvalue problem using a Runge-Kutta scheme and yields mass flow rates as the
eigenvalues from which the propagation velocities follow.
However, extensive simplifications have raised doubts in the applicability of the
model to the problem of waveguide-heated plasmas. Besides the constant pressure
assumption as well as the assumption of inviscid, 1-D flow, the microwave field
distribution was not accurately predicted by the model. Although a truly propagating field
pattern in the guide was assumed, actual field distributions show standing wave patterns
emerging in the guide due to microwave power reflections off such waveguide circuitry
components as bends and terminations. Consequently the plasma velocity is not constant
but varies with the local field intensity, the plasma tending to remain longer in the
maximum field regions. This effect might have lead to an additional error in the
numerical prediction of the plasma velocities.
In the case of helium even larger discrepancies between experimental and
numerical velocity data than in the case of molecular gases were observed67*61. Those
differences were attributed to a propagation mode change between heat conduction and
radiation dominated modes to be discussed in the next chapter. Since the numerical model
only included heat-conductive processes, this transition could not be predicted accurately.
27
Although modeling radiative propagation processes yielded data on the radiative
conductivities of helium, including those data in the propagation model failed as stability
problems with the code were encountered68. Furthermore, differences between
numerically determined and experimentally measured temperature values were noted
ranging up to a few thousand degrees67. Thus, confidence placed in the numerical results
was low.
In addition, radiative losses from the plasma were determined numerically and
estimated to be negligible for microwave created plasmas due to their relatively low
temperatures67. This latter point, however, remains to be an issue of further discussion
due to the doubts placed in the numerically obtained results mentioned above.
Despite the shortcomings of the numerical model, however, order of magnitude
agreement between the theoretical data and experimental data provided preliminary,
rough plasma velocity estimates which later on helped in the design of the waveguide
experiment.
These experimental investigations of the waveguide applicator were more
successful. Stabilization of the plasma by means of a blunt body followed66 and the
stabilized plasma was then studied to give information about stability boundaries,
coupling efficiencies and electron temperatures and their dependence on such parameters
as input power, pressure and mass flow rate68. Coupling efficiencies reached values in
excess of 90% while electron temperatures of up to 13,000 K were obtained, exceeding
comparable data for the resonant cavity by 2000 K.
All initial experiments had been performed using a 7.214 x 3.404 cm cross
sectional rectangular waveguide in the TEt0 mode. Although using this rectangular
waveguide mode was sufficient for proof-of-concept studies, operational waveguide
thrusters would suffer heating and erosion problems using this waveguide type. The
28
reason is that in this mode the electric field lines are perpendicular to the waveguide axis,
extending straight from wall to wall. Thus, the plasma which aligns itself along these
field lines, takes on a cylindrical shape and touches the waveguide walls at two locations.
Consequently, a circular waveguide applicator was then designed69 and tested.
This guide provides a field pattern much like in the cavity TM0U- and TMo,2-modes,
allowing the plasma to align itself along the waveguide axis, separated from the
waveguide walls and thus avoiding the severe erosion and heat loss problems encountered
with the rectangular waveguide. As will be discussed in later chapters, coupling
efficiencies for the circular guide could be raised to 96%. Thermal expansion of the test
gas through a conical converging nozzle allowed for the first time the calculation of
thruster performance parameters such as thruster efficiency, specific impulse and thrust
for a waveguide applicator. Electron temperatures measured for this applicator, however,
ranged lower than for the rectangular guide and reached values of only 10,500 K which
are comparable to those obtained in resonant cavities.
In the following chapters, a detailed description of the previously outlined
experimental investigations of waveguide heated plasmas will be given in order to further
illuminate this space propulsion concept and draw attention to its development potential.
This thesis is the first comprehensive study of a waveguide-mode microwave thruster
concept to date.
29
2.6. Comparison of Microwave Thrusters and other Electrothermal Propulsion
Concepts
At this point, a comparison between microwave thrusters and other electrothermal
thrusters might be appropriate in order to evaluate present microwave engine
performance in relation to already existing electric thruster hardware. Since for
microwave engines only limited thruster data are available to date, this comparison will
be restricted to nitrogen test data only.
According to Table 2.2, recent nitrogen arcjet tests33 revealed a specific impulse of
252 sec at a thruster efficiency of 20.8% for a mass flow rate of 45.4 mg/s and 654 W
input power. Resistojets obtained 145 sec specific impulse at 21 % thruster efficiency at
495 W input power level and a nitrogen flow of 105 mg/s31. These values compare to a
thruster efficiency of 24% and a specific impulse of roughly 255 sec for a coaxial
microwave thruster operated at 650 W and 62.5 mg/s mass flow rate63. The
corresponding values for a 104 mg/s mass flow rate and 500 W input power are 44%
thruster efficiency and 217 sec specific impulse^3.
Thus, despite the early development status, microwave thrusters can already be
considered as very competitive to already existing electrothermal thruster hardware.
Microwave thrusters do outperform resistojets clearly with respect to both specific
impulse and efficiency at comparable operating conditions and yield almost exactly the
same performance as arcjets. Note, however, that considering the laboratory-prototype
status of the microwave thruster concept, microwave thruster performance can still be
expected to increase, encouraging further development efforts in this area.
Table 2.2. Comparison of Microwave, Arcjet and Resistojet Thruster Performances
ih
(mg/sec)
*лp
(sec)
1JT
(%)
Propellant
Ref,
654
45.4
252
21
n2
33
Resistojet
495
105
145
21
n2
31
Microwave
650
62.5
255
24
n2
63
Microwave
500
104
217
44
n2
63
Thruster
Power
<W)
Arcjet
31
Chapter 3
PLASMA PROPAGATION AND STABILIZATION
3.1. Introduction
While previous chapters dealt with an overview of electric propulsion technology
in general and an introduction to microwave propulsion devices in particular in order to
establish a basis for the motivation behind the development of this new electric thruster
type, the present chapter will lead to the primary thesis objective of an investigation of
a waveguide-mode microwave thruster. As an important first step in this direction, it is
essential to understand that microwave-generated plasmas in general and in particular
waveguide-heated plasmas are not stable, but tend to propagate towards the microwave
power source. This effect will greatly influence the design of microwave thrusters and
will make itself felt in the operational characteristics of such a thruster. Under certain
circumstances, in particular towards higher power levels, where this effect is strongest,
it might even limit thruster performance.
After discussing the fundamentals of plasma propagation, several methods of
plasma stabilization will be reviewed briefly. Plasma stabilization can be regarded as an
important and crucial element in investigating the feasability of waveguide-heated plasmas
for space propulsion applications and as a prerequisite to arrive at a working waveguideн
mode thruster design.
32
3.2. Plasma Propagation Modes
Observations of microwave induced ionization fronts in waveguide components
were initially made by Beust and Ford in 196172. It was noted that arcs created in high
peak power transmitters tended to travel towards the microwave source.
In air,
propagation velocities of 0.25 m/s to 6 m/s and a dissipation of 75% of the incident
power were measured. Bethke and Ruess73 then conducted detailed investigations of
plasma front propagations in heavy inert gases. Here, propagation with considerably
different propagation velocities dependent on pressure and input power level were
observed, ranging between 10 and 10,000 m/s. Batenin et.al74 could confirm these large
velocities for noble gases, however, recorded much smaller values in the case of
helium70,75 where propagation velocities below 1 m/s for pressures greater than 0.7 atm
and 1200 W input power were reported. All experiments showed a dependence of the
propagation velocity on gas pressure, incident power and gas composition.
Explanations for this behavior for the different propagation modes suggest five
different propagation mechanisms which will be described in detail below:
(a)
heat conduction
(b)
radiative ionization due to resonant radiation
(c)
electron ionization due to aresonant radiation precursor discharge
(d)
electron diffusion
(e)
microwave breakdown
The two resonant radiation and the electron diffusion modes were given by Bethke
and Ruess73 to explain the propagation modes in heavy inert gases. At lower pressures
(< 3 Torr) and relatively low incident power levels (1 W - 60 W) the radiative
33
ionization process was dominant: resonant radiation from the already existing plasma is
emitted in all directions causing photoionization in the colder parts of the gas (wall
photoionization where ionizing electrons are created by the photoelectric effect at the test
section walls was observed to be negligible in this case). The microwave power is
therefore absorbed in a sheath in front of the original plasma towards the microwave
source, creating a new ionization front here and extinguishing the plasma behind the
sheath. The result is a plasma wave travelling towards the microwave source. Due to
higher gas densities at the line center of the plasma the resonance quanta have lower
mean free paths here and the resonant radiation will therefore diffuse faster towards the
boundaries of the plasma, creating a filamentary shape which was also observed by
Batenin75. The actual ionization process is a multistep reaction, which requires less
energy per reaction step and follows the reaction equation
hpv
Z
hpv
X -----? r? ?A*? *X+ + e'
(3.1)
where X is the inert gas atom, Z any other atom including X, l y is a photon, X* an
excited atom, Xm an atom in a metastable state and e' being an electron. Thus, two
reactions are possible: a purely radiative two-step ionization and a three-step ionization
involving heavy particle collisions.
For higher pressures (> 1 Torr) and relatively high power levels (20 to 2000
W), the ionization process is provided by another multistep reaction, leading to the
propagation mode with the highest velocity magnitudes: electrons are created by resonant
radiation emission from the already existing plasma; however, due to the high incident
power level and lower electron mean free paths, these electrons are now largely
responsible for the ionization process since electron collision frequency and energy
transfer per collision are now largely increased. This mode may lead to a maximum
propagation velocity as soon as the collision frequency of the electron-atom interaction
equals the microwave frequency, providing maximum ionization rate.
Since this
maximum is dependent on the collision frequency it depends on the gas species. The
process of creating a plasma wave, which travels towards the microwave source is the
same as before. The governing reaction equation according to Bethke and Ruess73 is
e
e* or h.p
(3.2)
e
e or hfv
using the same notation as before and e* being a high energy electron. These electrons
are generated by photoionization obeying a reaction mechanism according to Equation
(3.1). Once enough electrons have been created and energized by the microwave field,
plasma propagation continues with the reaction according to Equation (3.2). According
to that reaction equation, several possibilities exist to arrive at ionization. First, electron
collisions can lead to a metastable state, from where further electron collisions or
resonant absorption may result in ionization of the gas atom. Secondly, electron collision
could create a normally excited atom, rather than producing a metastable atom. If this
excited atom undergoes heavy particle collisions, it can transfer into a metastable state
and be ionized from there on as before. Thirdly, the excited atom can directly be ionized
due to electron collisions or resonant quanta absorption.
Both resonant radiation processes could be verified by Bethke and Ruess by
placing solid windows in the gas containing glass tube.
windows allowing transmission of wavelengths >
By using LiF and Tedlar
1100 A and >2000 A respectively and
observing that the plasma wave was not stopped by the LiF but by the Tedlar window
35
yielded a resonant radiation between 1100 A and 2000 A, which passes through the LiF
window and causes photoionization on the other side. However, Bethke and Ruess73
noted that in this case wall-photoionization is dominant compared to gas photoionization
due to the significantly increased wall surface area by placing the window inside the
guide.
The third propagation mode common in heavy inert gases resulting in propagation
velocity magnitudes between the two mentioned modes occurs at lower pressures (< 1
Torr) but high incident microwave power (20 to 2000 W)73. The underlying process in
this case is electron diffusion from the plasma, causing ionization by impact on gas
atoms. In case of very high power levels electrons may also create secondary electrons
by collisions with the test section walls as well, causing a very strong increase of plasma
velocity with increasing power in this range. In this case the propagation velocities may
even exceed the ones obtained by the electron ionization with a resonant radiation
precursor. Again a plasma wave travelling towards the microwave source is created.
Investigations of helium, nitrogen and air by Batenin et al70,75,76 and air by Beust
and Ford72, however, showed much lower propagation velocities than in all the cases
reported for heavy inert gases.
Explanations for processes contributing to this
propagation mode have been given by Raizer77, Batenin et al. 70,78 and Meierovicti? ; the
dissipation of the incident microwave energy heats the plasma resulting in thermal
conduction to the colder gas sheath surrounding the plasma. This heated gas sheath
containing excited atoms now becomes ionized by randomly emitted electrons from the
already existing plasma resulting in a ionization front travelling towards the microwave
source.
No radiation dominated propagation modes form in molecular gases since
molecular gas temperatures are lower than those observed for inert gases because a
36
significant amount of energy is stored in form of vibrational and rotational energy modes
within the molecule. Additional energy is dissipated due to the dissociation of the
molecule. Lower gas temperatures will lead to lower degrees of excitation and thus
reduce the amount of resonant quanta present in the gas. In the case of helium, excitation
is difficult to accomplish even for higher temperatures due to the relatively high lying
excited levels. Significant degrees of excitation can therefore only be expected at high
power levels or low gas pressures where electron mean free paths are long and collision
partners can pick up sufficient amounts of kinetic energy between collisions.
Microwave breakdown will occur when for a low gas pressure the electric field
is strong enough to cause the ignition of a plasma at those places in the waveguide where
the E-field has a maximum. Due to the absorption of the electric field in those plasma
regions closer to the microwave source the discharge further downstream extinguishes
and the plasma seems to flash through the quartz tube towards the power source.
Theoretical models for the different modes of propagation have been developed
by Raizer77, Meierovich79, and Myshenkov and Raizer80. The analytical calculations by
Raizer and Meierovich for the heat conduction governed propagation mode in air show
relatively good agreement with the experiments, while an analytical model for resonant
radiation modes gives velocities by a factor of 4-7 too small80 due to simplifications in
the analysis. In particular, the different propagation modes could not be reproduced.
A purely numerical approach was attempted by the author and others6**7, however, as
was mentioned in the previous chapter, simplifications made in the numerical model led
to discrepancies between experimental and numerical velocity data. These differences
were particularly pronounced in the case of the inert gas helium, which might have been
caused by radiative processes not included in the model.
37
3.2. Plasma Stabilization
3.2.1. Flow Stabilization
Although stabilization of the plasma is possible in principle by establishing a
counter flow with a flow speed equal to the propagation velocity of the plasma, this
method is rather impractical, since the required match between the velocities has to be
absolutely accurate during the entire period of operation.
Pressure and power
fluctuations, however, will continuously change the plasma velocity, making this exact
match with the flow velocity virtually impossible. Therefore, this method of plasma
stabilization, although theoretically possible, has to be discarded, not only for space
propulsion applications but also for laboratory use.
3.2.2. Magnetic Field Stabilization
Early means of stabilization of the plasma were provided by magnetic fields81
created electromagnetically. The diverging transverse magnetic field towards the end of
the coil creates Lorentz forces acting on the electrons, which are randomly emitted by
the plasma. Since these electrons are important for the electron diffusion mode and some
of the radiation modes, these propagation modes may therefore be stabilized by a
magnetic field. However, strong magnetic fields cause splitting of the spectral lines due
to the Zeeman effect. Reabsorption of resonant quanta becomes therefore less likely
resulting in longer mean free paths for these quanta so that not only is stabilization for
the pure resonant radiation modes not achieved but larger propagation velocities may
38
actually be observed73. In addition, Batenin et al.74 noted that magnetic field stabilization
is only possible below a certain critical gas pressure. Once this pressure value was
exceeded in the experiment, magnetic field stabilization was no longer possible even
when increasing the field strength. Although Batenin et al.74 do not give a specific value
for the critical pressure, no magnetic field stabilization for pressure values higher than
60 Torr was ever recorded*1. Pressure values that low are absolutely impractical for
space propulsion applications of an electrothermal thruster concept, since they will
severely limit obtainable thrust values. Furthermore with respect to space propulsion
applications, magnetic coil stabilization would add to the weight of the propulsion system
as well as to its complexity.
3.2.3. Bluff Body Stabilization
A very simple and highly efficient way of stabilizing the plasma is the insertion
of a bluff body made out of a dielectric material such as boron nitride into the flow.
Bluff bodies have been used extensively as "flameholders" in combustion devices such
as jet engines and ramjets*2. The bluff body constricts the flow cross section thus causing
the flow speed to increase if the flow is subsonic. If the dimensions are properly chosen
this increased flow speed is larger than the plasma propagation velocity, so that the
plasma cannot travel upstream across the bluff body. Right behind the bluff body there
exists a recirculation zone. The plasma can therefore move easily upstream into the
recirculation zone and stays trapped there since further propagation across the bluff body
is not possible. This stabilization method has been chosen for the experiments to be
conducted in this study. In later chapters, this stabilization mode will be discussed in
39
more detail, revealing a rather complex behavior regarding the interactions between the
flow field around the body, the plasma, the microwave field distribution and Anally the
bluff body material itself.
3.2.4. Other Means of Stabilization
During operation of the waveguide experiment to be discussed in Chapter 5, it
was observed that two other mechanisms can enhance stabilization. The electromagnetic
field distribution along the waveguide axis is not uniform but shows maxima and minima
since a standing wave pattern is formed due to reflections from such waveguide
components as bends and terminations. The plasma tended to stay in the maximum field
regions. This mechanism is either similar to the magnetic coil stabilization where
stronger magnetic fields perpendicular to the plasma propagation tend to prevent electron
emission by the plasma due to Lorentz force action, thus enhancing plasma stabilization
or the plasma can simply not be sustained in regions of lower electric field since the
electrons cannot pick up enough energy required for the ionization process. The same
effects, however much stronger than in waveguide components, could cause the plasma
stabilization in resonant cavities.
Furthermore, restriction of the waveguide cross sectional area by inserting metal
pieces causes the energy density and therefore the field strengths to increase at those
points leading to the same stabilization mechanism as the maximum field regions show.
It should be pointed out that in conjunction with the bluff body stabilization those last
two methods could enhance the stabilization of the plasma. A third mechanism which
could be used to improve stabilization of the plasma was mentioned by Batenin et al.70:
40
small amounts of nitrogen added to helium caused a dramatic decrease of the propagation
velocity. This effect could be explained by superelastic or second order collisions
between helium and nitrogen atoms. The excitation energy of the helium atom is
transferred into additional kinetic energy of the nitrogen atom, therefore quenching the
excitation state and decreasing the number of excited atoms in the helium gas. Since the
density of excited atoms strongly influences the ionization rate, this will lead to lower
propagation velocities which in turn could simplify the stabilization process. The latter
point gains importance when the possibility of radiation dominated propagation modes
as observed for inert gases is taken into consideration, leading to very high propagation
velocities and difficult to stabilize plasmas.
41
Chapter 4
ELECTROMAGNETIC THEORY OF WAVEGUIDE COMPONENTS
4.1. Introduction
In the present chapter, some basic elements of the electromagnetic theory
governing the field distributions in waveguide components will be discussed. Starting
with the Maxwell equations and their boundary conditions, electromagnetic field patterns
in common waveguide configurations such as rectangular and circular guides will be
derived. Knowledge of these field patterns is essential both for the theoretical modeling
as well as the experimental design of waveguide experiments. It turns out that the
physical dimensions of a microwave thruster are entirely determined by the
electromagnetic field patterns to be established in the guide and that such important
design parameters as cutoff frequency and guide wavelength require the calculation of
the complete field distribution in the microwave applicator. Throughout the following
chapter, the physical explanation of the electrodynamic laws will be emphasized wherever
possible.
4.2. Maxwell?s Equations
The basic physical laws determining the electromagnetic fields in a waveguide are
given by the Maxwell equations83о4:
42
f S ?3S - J r gt iV
(4.1)
fB-3S = 0
(4.2)
f S - i . - f M . 3 s
(4.3)
fa -3 t.fJ - 3 S
(4.4)
+f M - 3 s
Here, D, B, E and H are the electric and magnetic flux density and field strengths,
respectively and are related to each other by
B = e, e j
(4-5)
S - n ,? . a
(4.6)
where ft, and г0 are the vacuum susceptibility and permittivity and pR and eR are the
relative susceptibility and permittivity, respectively, describing the magnetic and electric
properties
of the medium filling the waveguide and very closeto one
in the here
considered cases. Inorder to solve this system of coupled integral equations,
it is
furthermore necessary to know the dependence between the current density and the
electric field strength which is given by:
J - o B
a being the electrical conductivity and pc the charge density.
(4л7)
43
Assuming a periodic time dependence of exp(jwt), the Maxwell equations written
in differential form for free space environment, i.e. assuming no currents and electric
charges, become:
$ ?D =Q
(4-8)
^ ? fl = 0
(4-9)
% x i= -j< * S
(4-10)
fx 8 = j< a d
(4-n >
Note that charge and current free conditions do not hold at the metallic wall boundaries
of the waveguide, so that boundary conditions will have to be introduced that take this
fact into account. A discussion of these boundary conditions will follow below.
In order to solve for the fields in a waveguide, the Maxwell equations have to be
modified further. Using the vector identity
$ x % x A = % ( $ 'A ) - t f A
<4*12>
and the Maxwell equations (4.8) and (4.11) above, one arrives at the electromagnetic
wave equations
f
and
i
+ G>2
\lR VL0 ?* ?tf E = 0
(4-13)
44
V2 S
(4.14)
+ G>2 l l j H , ? * ? , # = < )
which are the required wave equations to be solved for the waveguide fields. This is
achieved by using the appropriate boundary conditions for the electric and magnetic fields
at the conducting waveguide walls. For the electric fields the boundary conditions can
be established by applying Faraday?s law, Equation (4.3), in integral form across the
boundary between the media considered as shown in standard texts83?84. The result is that
ETi = ETj
(4.15)
where the Ef are the tangential electric field components on both sides of the boundary.
For the case of a perfect or nearly perfect conductor such as the waveguide walls it can
be concluded based on physical reasons that the field inside the conductor has to be
close to zero since even a field of small magnitude would create a current density large
enough to immediately counteract any field producing charge separation and thus cancel
the original electric field distribution. Therefore, for a metallic conductor the boundary
condition at the wall reads
ETx = 0
i.e.
the electric fieldeitherterminates perfectly normal
(4.16)
to the surface orhas zero
magnitude here. Forthemagneticfield, applying Ampere?s law,Equation
(4.4), across
the boundary in a similar fashion as done for the electric field yields83*85
HTi = H T2 + K
(4.17)
where the HT are the tangential magnetic field components and K is the surface current
density in A/m, i.e. corresponding to current over width of the surface element. In the
45
case that medium 2 is a perfect conductor, such as the waveguide walls, no
electromagnetic fields can propagate inside the material. Therefore, HT can be assumed
zero here. Keeping the current density term in Equation (4.17) despite zero field
strengths for a perfectly conducting wall is no contradiction since the very large
conductivity values might still lead to a non zero current, as Equation (4.7) shows.
Mathematically, Equation (4.17) can now be written asо4,85
E l - o
dn
(4.18)
where the derivative is taken at the surface and normal to it. Equations (4.13), (4.14),
(4.16), (4.18), (4.10) and (4.11) can now be applied to obtain solutions for the field
patterns possible inside waveguides of different geometries. In the following, a distinction
is made between two basic types of propagation modes: transverse electric (TE) and
transverse magnetic (TM) modes. In the first case no electric field component along the
propagation direction is present, i.e. the electric field is entirely transverse while for TM
modes this is true for the magnetic field.
4.3. Rectangular Waveguides
4.3.1. TE Modes
In this section, transverse electric modes for rectangular waveguide components
are discussed. The geometry of a rectangular guide is shown in Figure 4.1. According
to the definition, for the TE modes one has to assume that Ez=0 and Hz^ 0 . For
propagation in the positive z direction it is further assumed that
46
Conducting Walls
Dielectric Region
( HR , e R )
Figure 4.1 Geometry of the Rectangular Waveguide
47
Ht = f y x y ) exp(-j'Pz)
(4.19)
i.e. the longitudinal magnetic field component has a sinusoidal distribution with respect
to the waveguide axis with 0 being the longitudinal wavenumber. Here, the so called
phasor notation83 has been used, the complete description of the field is obtained by
multiplying Equation (4.19) by the time dependent exp(jcot) term and then taking the real
part thereof. Since time dependency is not important in finding the geometrical field
pattern within the guide, the time dependent term has been omitted throughout the
derivation for simplicity. It will be reintroduced for the final result.
For the longitudinal magnetic field amplitude one can find from Equation
(4.14) written in cartesian coordinates that
j?
cte2
(4.20)
dy 2
where
kg = w2 p e - P2
(4.21)
and
(4.22)
and
(4.23)
were used. Writing
48
*? - г + 1$
(4.24)
Equation (4.20) can be solved using separation of variables. The following boundary
conditions according to Equation (4.18) and Figure (4.1) are applied
? = 0 at *=0 and x=a
a*
dH
= 0 at y=Q and y=b
(4.25)
(4.26)
This gives the result
Ht = Ho exp(-j'Pz) cos (? *) cos C ^ -y )
(4.27)
where due to the boundary conditions, kx and ky turn out to be
JK = ? x
a
(4.28)
and
(4.29)
7
b
The variables k* and ky can therefore be interpreted as the wavenumbers in the x- and
y-direction, respectively (see Figure 4.1). Using Faraday?s and Ampere?s laws, i.e.
Equations (4.10) and (4.11), all the remaining electric and magnetic field components can
be related to Hz and one finds using Equation (4.27)
49
г , ? iK , 2 $ 0 1 a j t - m
k? o
E , ? - ff l ,
for + z directed waves and
V
cos (2 5 * ) sin & )
a
o
(4.30)
? л P (-jP j) sin (2 5 * ) co s (г5.j)
o
a
o
(4.31)
H , - -E , 1 1 ?
(4.32)
л , - г ? / Zra
(4.33)
is the wave impedance for TE waves, given by
z re = ^
(4.34)
The m and n are integers describing the corresponding TE*, mode. Using Equations
(4.24), (4.28) and (4.29) one can now write
jfc2 = (" ?L)2 + ( f E ) 2
a
b
(4.35)
Since K has the dimensions of a wave number, one should also be able to write
i
=
c
(4.36)
Xc
where K is a wavelength whose meaning will become apparent shortly. Using Equation
(4.21), the longitudinal wavenumber can now be determined by
so
p *
O)2 H? -
(4.37)
Xc
It is therefore obvious that field propagation along the waveguide can only occur for
U2 lie > ( г ) *
Xc
(4.38)
since only then is 0 real and the exponential factor in Equations (4.27) and (4.30)
through (4.33) remain complex. \ is therefore called the cutoff wavelength above which
wave propagation is no longer possible. It is related to the corresponding cutoff
frequency by
/. ? , ' i
y i* * * .
(4.39)
where c is the vacuum speed of light. The value for \ follows from Equations (4.35) and
(4.36) as
\
_______
(4.40)
The necessary condition for field propagation is now f > f e or X<XC. As an additional
characteristic behavior for wave propagation along a waveguide it has to be pointed out
that the free space wavelength
is not the same as the wavelength of the field
propagation inside the waveguide which will be denoted by X,, rather, one can find from
P? ^
and Equation (4.37) with
(4.41)
51
(4.42)
0) = 2%f = 2 * 4 0
that
K
K
i
*
(4.43)
Equation (4.43) is an extremely important relationship regarding waveguide component
design in particular if resonance conditions are to be established. Since for propagation
f > f c or X < \ c, respectively, it follows that \ will always be bigger than the free space
wavelength for the considered medium, \ j
For the most common TE mode, the TE,0 mode, which according to equations
(4.39) and (4.40) has the lowest cutoff frequency and is therefore the so called dominant
mode for rectangular waveguide propagation, one finally obtains83
(4.44)
s
(4.45)
H = H cos(?x) cos(uf-Pz)
1
a
(4.46)
and Ez=Ex=Hy=0, \.= 2 a and Eo=H o2^e. These equations clarify the problems
associated with this mode previously alluded to in Chapter 2: at a given axial location
z the electric field shows an x variation but no y variation, i.e. according to Figure 4.2,
the electric field impinges unweakened onto the waveguide walls, the maximum field
region located at x=a/2 therefore allows the plasma sustained by it to touch the
waveguide walls, resulting in possible erosion problems and efficiency losses due to
conductive heat losses into the structure.
4.3.2. TM Modes
The derivation for TM modes is similar to the one for TE modes and will
therefore only be outlined briefly. Knowing Hz=0 for TM waves and assuming again a
sinusoidal distribution of the E field with respect to the guide axis
Ez = f y x y ) exp (-j'Pz)
(4.47)
Equation (4.13) can be written for Ez in cartesian coordinates as
(4.48)
where the expressions (4.21) through (4.23) have been used again. Further assuming for
k, an expression as in Equation (4.24) and using separation of variables as well as the
following boundary condition for the z-component of the electric field:
53
/
?
?N o
-----
- N о '| й I й / ?
lojй io \
?' йI й I й,."?
J \
7
N\ /
??*y 0 10 10 f "
j оIо}о j
? ' л J о( о ?
/ г \ ----
f lines
a
H lines _
i
0 Outward directed lines
0 Inward directed lines
\\
?
T -о
-*------ p о
--------- л
'
---------- rH 3
о -r ?
о - p -------?
1 -0
о -- -
________ _
о "T
о - - i ------ ?
,
й -?
\\
0 y ?
i i t 'u
> -tй }й-:
й
E lines
t?
o ! й |?t
t t t
|
H lines
й Outward directed lines
▒
0 Inward directed lines
y
I
ml
uZ j
""
I J
<?> /й
j
t
Figure 4.2 Rectangular TEI0- (top) and TM,,-modes (bottom)83
54
Again, as indicated before, using Ampere?s and Faraday?s laws given by Equations
(4.10) and (4.11), expressing the results in terms of E*83 yields
л , ? A , t ! I T ? J W W sto(? *) cos(H y)
k c* ?>
a
q
H , ? -JE.
kC
?
a
exp (-j'Px) co sO ^ x ) sin (H y )
a
o
? Z? H,
E} = - Z ? Hx
(4.51)
(4.52)
(л?╗>
(4.54)
for waves propagating in the + z direction. Z ^ , the wave impedance for TM modes is
given by83
Zn =
2
- .
(i)?
(4.55)
and Equations (4.35) through (4.43) still hold. This allows Equations (4.50) through
(4.54) to be written for the lowest order mode, the TMU mode as
X2
1
- sin(?*) cos(^-y) sinful-Pz)
2 \g b
a
b
(4.56)
12 .
H = - $ ? cos(?x) sin(^y) sin(ul-pz)
7
2Xg a
a
b
(4.57)
H =
55
(4.58)
= Z jy Hy
E - E sin(?x) c o s A ) cos(uf-Pz)
a
(4.59)
(4.60)
b
and Hz=0.
The field pattern of the TMU mode at a given instant in time is depicted in Figure
4.2 and the advantage of this mode regarding plasma positioning can clearly be seen
since the maximum E-field region is now aligned with the waveguide axis thus not
allowing the plasma sustained by it to touch the restricting walls. There are more, higher
order modes which would allow for interesting plasma configurations. Creating these
higher order modes, however, would mean that lower order modes, in particular the
undesired TEI0 mode, would have to be suppressed by means of mode filters83 which are
metallic grids with a certain symmetry to them which are inserted into the waveguide to
reflect those lower order modes. This, however, would increase system complexity and
reduce the coupling efficiency of the waveguide configuration which are both setbacks
for space propulsion applications. Thus, higher order modes are not considered here.
However, using circular waveguide components, two other interesting field
configurations, the circular TEn
therefore be discussed next.
and TMot modes are easily obtainable and shall
56
4.4. Circular Waveguides
4.4.1. TE Modes
Circular waveguide modes can be derived similarly to rectangular modes. The
circular waveguide geometry is shown in Figure 4.3. Again, TE modes are characterized
by a zero longitudinal E-Held component, i.e. E*=0. The corresponding magnetic Held
component must obey the relationship
Ht =
exp W Pz)
(4.61)
Now, however, Hz is a function of the radial coordinate r and the azimuthal coordinate
<f> as indicated in Figure 4.3 . The corresponding wave equation written in those
coordinates is therefore
and k,2 is given by Equation (4.21). The wave equation can be solved by the standard
method of separation of variables again using the boundary condition for the magnetic
Held at a conductive boundary surface
(4.63)
Requiring finiteness at the origin and single valuedness with respect to <t>one arrives at
Ht = H0 exp ( - m J n (* /) cos /лt>
where the J? are Bessel functions of the first kind.
(4.64)
Conducting Wall
Dielectric Region
( H r , eR )
Figure 4.3 Geometry of the Circular Waveguide
58
In order to satisfy the boundary condition, Equation (4.63), one finds that
kc = л =
(4.65)
where the q^,? are given as the roots of the J?' and tabulated in Table 4. 1. The integers
n and m are describing the corresponding T E ^ mode. In a similarfashion as before one
can express the remaining field components in terms of Hz83 andfinds
Er = JHo 7 T exp(-./pz) JH(kcr) sin iлt>
K r
(4.66)
E* = W o - f 1 exp(-jPz) J nXkcr) cos n<J>
(4.67)
fff = - A7
(4.68)
TE
H. = A
?
(4.69)
z
with Ztb being the wave impedance for TE waves, given again by Equation (4.34), and
all other symbols as defined before. The integer m is hidden in the expression for k,..
Using Equation (4.65) one can express the cutoff wavelength in terms of the waveguide
diameter D=2a as
K ?T
? Km D
(4.70)
are tabulated in Table 4.2 . The expressions for
fc and
c
where the values for the
Qnm
59
Table 4.1(a) q^-values for Circular TE Modesо3
m
n
1
2
0
3.832
7.016
1
1.841
5.331
2
3.054
6.706
Table 4.1(b) q^-values for Circular TM Modesо3
n
1
2
0
2.405
5.520
1
3.832
7.016
2
5.135
8.417
I
60
Table 4.2(a) K^-values for TE Modes83
m
n
i
2
0
0.820
0.448
1
1.706
0.589
2
1.029
0.468
Table 4.2(b) K^-values for TM Modes83
m
n
'
1
2
0
1.306
0.569
1
0.820
0.448
2
0.612
0.373
61
/8 are the same as before using the modified value for
Employing these and the
relation for Z ^, multiplying by expflut) and taking the real part, transforms Equations
(4.64) and (4.66) through (4.69) for the dominant, lowest order TEu mode into
Er - -E?
X
X
(^ )
E, - -E . i
Jl&l)
sin* 8ln(o╗-pz)
(4.71)
sin(or-Pi)
(4.72)
co s*
X, ? H. J , A C03л cos(u(-Pz)
(4.73)
ff = - i t
(4.74)
TE
╗? - y -
<4-75>
TE
where E0=H0ZrE and
is given by \
=1.706D according to Table 4.2 . The TEn
mode is shown in Figure 4.4 . Although the TE? mode obviously allows sustaining a
plasma away from the waveguide walls due to the concentrated maximum field region
close to the guide axis, there areproblems with using this modefor spacepropulsion
tasks.The E-field
lines areparallel to a plane normal tothe guide axis. A potential
nozzle opening would most likely also be located in this plane and lead to large radiation
losses through this opening since the E-field lines are oriented parallel to it and since
radiation losses reach a maximum in a direction normal to the electric field vector.
62
TE n mode
\ e = 1.7060
E lines
H lines
Figure 4.4 Circular TEn- and TM01-modes*3
O
Outward
directed
lines
й
Inward
directed
lines
63
4.4.2. TM Modes
For circular TM modes, Hj=0 and г z follows the relationship
Et = гz(r,<J>) exp(-j'Pz)
with
(4.76)
now being a function of the polar coordinates r and <f>. Inserting this in the wave
equation for E* gives
i l (r El) ? 1
r dr
= -kl 6
r> ^
dr
(4.77)
?
where k,.2 is given as before. One can solve this to obtain
Ez = E0 exp(-yPs) J n( k /) cos n<t>
(4.78)
Using the boundary condition
Et = 0
at r = a
(4.79)
gives
J H (kca) = 0
(4.80)
from which follows
ke .
(4.81)
and the cu, are now the roots of the Bessel function of the first kind, Jn, and listed in
Table 4.1 . From this, X* follows to be
where the K,*, for the TM modes are given in Table 4.2 . The further solution process
is similar to the ones outlined before and given in detail by Rizzi83. The final results are
Hr =-JH0 n г
1
( A ) expf-ypz) J H( k /) sin n*
= -jH0 i
exp(-j'Pz) j'H(ker) cos л4>
Er =
= -Z TJ i r
(4.83)
(4.84)
(4 ?85)
(4.86)
with Ei as given by Equation (4.78). 2^Mis once again the wave impedance for TM
waves as given before. For the TM^ mode the time dependent, propagating fields are
Hr = 0
? ╗ . - r 4 * / ) s? (? <-Pz)
Et = E0 J 0( k f) cos(cof-pz)
(4.87)
<4-88)
(4.89)
(4.90)
65
(4.91)
and Hz is zero. The values for Xg and /? remain the same as above, however, they have
to be modified using the new expression for X,., Equation (4.82). The field pattern of the
TMqi mode is shown in Figure 4.4 and indicates that this mode obviously resembles the
rectangular TM,, mode.
66
Chapter 5
THE STRAIGHT. RECTANGULAR WAVEGUIDE APPLICATOR
5.1. Introduction
In order to evaluate the applicability of waveguide-heated plasmas for space
propulsion purposes, the following approach was taken for the first set of experiments
conducted. First, plasma propagation velocities in waveguides were measured as
functions of gas species, power and pressure levels. The data on plasma velocity
magnitudes were then used to design an experimental set up allowing the plasma to be
stabilized by means of a bluff body inserted into the gas flow. Plasma stabilization was
regarded as a crucial step towards the utilization of waveguide applicators for space
propulsion applications. Finally, the stabilized plasma was studied regarding its general
behavior in interaction with the microwave and flow fields and initial performance
measurements were taken. The latter investigations focussed in particular on the
measurement of coupling efficiency, being the ratio of absorbed to incident power, and
its dependence on such parameters as input power, pressure and mass flow rate.
A straight, rectangular waveguide applicator was selected to perform this initial
set of experiments because of the simplicity and low cost of its design. Helium was used
as a test gas for most of the experiments performed. Although helium is not well suited
for space propulsion applications due to problems related to storability, it is cheap and
easy to handle in the laboratory environment while offering the opportunity to investigate
all basic plasma characteristics. Only for the measurements of the propagation velocities
was nitrogen used in order to expand the data base to molecular gases as well.
67
Spectroscopic measurements performed with the rectangular waveguide applicator will
be discussed in Chapter 7.
5.2.
Experimental System
5.2.1. The Rectangular Waveguide Applicator
The experimental set-up for the straight, rectangular waveguide experiment is
shown in Figure 5.1. The microwave power source is a 3000 W variable power
magnetron manufactured by Gerling Laboratories (GL131). It uses a Gerling GL103A,
208V/3phase, 20 Amp/phase power source at 60 Hz, yielding an overall efficiency of
roughly 80%**. The microwave circuit is composed of rectangular waveguide sections
with a 7.214x3.404 cross sectional area. The EIA (Electronic Industry Association)
designation for this guide is WR284 since its corresponding dimensions in inches are
2.84x1.34 inch52. The cutoff frequency for this guide is 2.079 GHz and it is therefore
well suited for tests conducted at 2.45 GHz which was the operating frequency used
throughout the experiments.
Before the microwave power enters the test section, it is transferred through a
ferrite-based three-port circulator (Gerling GL401A) which protects the generator by
diverting high reflected power levels into a dummy load. The dummy loads used were
Gerling GL402A terminations of the step-load type*3. The same type of load is used to
terminate the circuit after the microwave power has been transferred through the test
section. Three power meters register the forward, reflected and transmitted power levels.
For both, the forward and reflected power, a dual-loop Gerling GL204 wave coupler is
68
Quartz
Tube
Tungsten Plasma
Wire
k
Bluff
Body
o
Direction of
Electric Field
j
i
Slotted Waveguide
Test Section
Power
Meter
Dummy
Load
A
Power
Meter
Fiber
Optic
(╗vw
n
\
Dummy
Load
Three-Port
Circulator
Microwave
Power
Source
Figure 5.1 Set-up of the Straight, Rectangular Waveguide Experiment
69
used. The wave coupler is an integral part of the circuit and flanged between
corresponding rectangular waveguide sections. Transmitted power is measured via a
single-loop Gerling GL205 wave coupler. Attenuations of these couplers have been
calibrated by Gerling Laboratories to 55.57 dB, 55.62 dB and 55.61 dB for the forward,
reflected and transmitted power couplers, respectively. The actual power metering is then
performed electronically by a Hewlett-Packard HP478A thermistor mount attached to the
wave couplers via standard 50 Ohm coaxial connectors. Variations of resistance of a
thermally sensitive semiconductor resistor are detected by a Wheatstone-bridge circuit
and transformed into an analog current signal. This output signal can either be displayed
on an analog, Hewlett-Packard HP432A-power meter or be transferred from this meter
via an A/D board into a PC-computer for processing and storage. Power levels coupled
out of the circuit did not exceed 10 mW even for maximum forward power levels of 2.5
kW. Various E- and H-plane bends have been placed throughout the circuit to
accommodate for changes in the direction of wave propagation as required by the
experimental set-up.
The plasma is generated in the straight, slotted test section allowing one to view
the plasma. Like the other waveguide components, it consists of a WR284 waveguide
with a 7.214 x 3.404 cm cross sectional area and roughly 0.5 m in length. The
waveguide was operated in the TE,0 mode. Flanged at the ends of this straight waveguide
section are two modified E-plane bends allowing a quartz tube to be supported running
the length of the guide and intersecting the knees of both bends. The purpose of the
quartz tube is to contain the test gas and separate it from the laboratory environment. In
order to support the tube at the E-plane bend locations, tube sections aligned with the
waveguide axis had been welded to the bends (not shown in Figure 5.1). Diameters of
those tubes were chosen such that cutoff frequencies were higher than the operating
70
frequency of the guide and thus no microwave radiation could leak out. The tube is
manufactured from clear fused quartz of 1.5 mm wall thickness with an inner diameter
of 20 mm. The length of the tube is roughly 1.2 m.
Of particular concern were radiation losses from the slots manufactured in the
waveguide walls in order to view the plasma as mentioned. These slots were located in
the wide waveguide wall where the electric field is perpendicular to the wall (compare
with Figure 4.2). Since a time-varying electric Held does not radiate electromagnetic
energy in the direction of the electric field vector, radiation losses through the slots
should therefore expected to be small. However, due to the presence of the slots, the
electric field distribution in the vicinity of the slots is perturbed and differs somewhat
from the distribution shown in Figure 4.2. The electric field lines, rather than impinging
perfectly perpendicular onto the wide waveguide wall section, curve in the vicinity of the
slots and attach to the edges of the slots. Thus, an E-field component tangential to the
slots has been induced able to radiate.
Radiation measurements at the slots using a HI 1501 microwave radiation leak
detector
manufactured by Holaday Instruments revealed radiation losses up to 20
mW/cm2. Since 10 mW/cm2 are widely regarded as the upper limit for microwave
radiation doses that can be absorbed by humans without leading to health risks, an
aluminum window screen was wrapped around the rectangular test section, covering the
slots and lowering the radiation losses just below 10 mW/cm2 at those slots. At the
location where the experimental observer was located, radiation leakage was too small
to be detected.
71
5.2.2. Gas Supply System
The gas supply system for the experimental set-up of Figure 5.1 is shown in
Figure 5.2. The test gas, either helium or nitrogen, is released by the pressure storage
tank and enters a 1/4-inch Swagelok piping system. Valve VI has been installed for
safety reasons while the precision valve serves to regulate the flow rate. Two mechanical
pressure gauges are installed just in front of the quartz tube inlet to measure vacuum and
gauge pressure, respectively. The former pressure meter was necessary, since in
particular in the early stages of the experiment during the propagation velocity
measurements a substantial amount of data was taken at subatmospheric pressures. Valve
V2 protects the vacuum pressure gauge at pressures higher than atmospheric.
Due to the location of the pressure meters at the entrance of the flow tube only
inlet pressures can be recorded. The obtained pressure data do therefore not account for
pressure losses in the tube or local pressure variations due to the presence of the plasma
or the bluff body.
Stainless steel quartz tube adapters provide the transitions between the 1/4-inch
piping and the tube. These adapters are glued to the tube with epoxy. The outlet adapter
shown in the left of the figure consists of two parts which are flanged together and sealed
by a conventional O-ring. Unbolting the flange allows access to the inside of the tube,
required for the installation of a bluff body for example. At the outlet of the tube, the
gas passes through a rotameter-type, Omega FL-223 flowmeter using a stainless steel
float and is finally pumped away by a vacuum pump or released to the atmosphere via
valves V3 and V4 or V5, respectively. By adjusting valve V3 and the precision valve
simultaneously, the mass flow rate can be kept constant for varying inlet pressures.
72
Valve V5
Vacuum
Pump
Mass Flow
Meter
Valve V4
Adapter
?
D
Valve V3
Adapter
Gage Pressure
Gauge
Quartz Tube
Precision Valve V1
Valve
Gauge
Valve V2
Pressurized Tank
Figure 5.2 Gas Supply System for the Rectangular Waveguide Applicator
73
5.2.3. Plasma Ignition
Plasma ignition is provided by a tungsten wire installed inside the quartz tube.
The wire is heated due to absoiption of microwave radiation and therefore will emit
electrons which in turn are accelerated by the microwave fields to pick up additional
energy. Electron-heavy particle collisions will then lead to excitation and subsequent
ionization of the propellant gas until breakdown is accomplished. Tungsten was chosen
as the wire material because of its low work function.
Initially, this wire was installed inside the tube by bending it into a helix shape
with the diameter of the helix almost equal to the tube diameter as shown in Figure
5.3(a). However, this configuration led to repeated quartz tube breakage at those
locations where the wire touched the tube. Thus, a tungsten wire support made from
HBC-grade boron nitride was installed, keeping the wire away from the quartz tube
walls. The boron nitride support was held in the tube by means of three fins pressing
against the walls of the tube and thus kept the configuration in place by means of friction
forces only (see Figure 5.3(b)).
5.2.4. Photodiode Array
Parallel to the waveguide slots, five photodiodes were mounted to record plasma
velocity data. Whenever the luminous plasma passed by a photodiode, a voltage peak was
generated by this diode that could be measured. Knowing the distance between the
photodiodes and the time elapsed between the individual voltage peaks allowed the
determination of the plasma velocity. The voltage signals were fed into a PC via a
74
Quartz Tube
Tungsten Wire
Figure 5.3(a) Tungsten-Wire Support directly mounted in the Quartz Tube
Quartz Tube
Tungsten Wire
Wire Support ( Boron Nitride)
Figure 5.3(b) Tungsten Wire Support using HBC-grade Boron Nitride Mount
75
DT2801 series A/D-board manufactured by Data Translation. Since the distance between
the actual experimental site and the PC location was rather large, the voltage signals had
to be amplified first. A simple amplifier was constructed for this purpose and is shown
in Figure 5.4. HP-PIN-5082-4203 photodiodes were used and the amplifier chip was a
LF353N/TL082 Dual BIFET or a Dual 741 chip, respectively. Voltage levels on the
order of 1 to 2 Volts were obtained with this configuration.
The diodes themselves were mounted to an aluminum U profile that could be
stuck on the waveguide. Five hollow, cylindrical studs welded onto the U profile and
aligned equidistantly along the waveguide slots served to hold the diodes. This way, the
photodiodes were always well positioned at known distances from each other.
Furthermore, welding aluminum grids in front of the cylindrical studs holding the diodes
protected the latter from damage due to microwave irradiation, which had occurred
during the earlier stages of the experiment.
5.2.5. Bluff Body Experiment
The insertion of the bluff body in the quartz tube is shown schematically in Figure
5.5. Boron nitride was used as the bluff body material since it shows low microwave
absorption and high thermal conductivity thus avoiding thermal stresses within the body.
The conical bluff body was kept in place by three fins which pressed against the quartz
tube walls. The fins were insert into grooves manufactured into the cone surface and held
in place by epoxy glue. Due to the high temperatures involved, however, the epoxy
would melt and the fins were kept in place by friction forces only. Two different size
bluff bodies were used. The larger body had a diameter of 15 mm at the base of the
76
out
Figure S.4 Amplifier Circuit for the Photodiode Array
77
SIDE VIEW
Quartz Tube
Bluff Body
Plasma
Fins
FRONT VIEW
Quartz Tube
Bluff
Body
Fins
Figure 5.5 Stabilization of the Plasma by means of a Bluff Body
78
cone, corresponding to 3/4 of the quartz tube inner diameter. The cone height was 30
mm, resulting in a cone angle of 43░. The smaller body had a diameter at the cone base
of 10 mm and was of the same height, resulting in a cone angle of 14░.
5.3. Propagating Plasma Investigations
5.3.1. Experimental Procedures
The experimental set-up as shown in Figure 5.1 was used for the propagation
velocity measurements with the bluff body removed and the photodiode array aligned
along the slots in the waveguide test section as described above. In order to perform the
measurements, a certain gas pressure was adjusted in the quartz tube at zero mass flow
rate. The microwave power level was preset and the microwave source switched on
afterwards. The tungsten wire located at the downstream end of the tube ignited a plasma
in its vicinity which then moved upstream past the photodiodes which registered its
passage by giving off a voltage peak. These signals were fed into a microcomputer via
an A/D board for processing and storage.
Immediately after the plasma had travelled past the diodes, coupling efficiencies
were read and the power turned off since the plasma located itself in the upstream
portion of the flow tube intersecting the E-plane bend attached to the waveguide test
section. Here, the plasma was in touch with the quartz tube walls and could possibly
have caused melting of the tube.
Alternatively, coupling efficiencies could also be fed into the PC via the A/Dboard directly, allowing the monitoring of the efficiencies vs. time.
79
5.3.2. Results
5.3.2.I. General Plasma Behavior
The experimental investigations of the propagating plasma showed a plasma of
ellipsoidic shape propagating along the quartz tube towards the microwave source for
both helium and nitrogen. However, in both cases, the propagation was not steady and
in particular towards higher pressures a movement consisting of accelerations and
decelerations was observed. The reason for this behavior was believed to be due to the
field distribution along the waveguide which shows maxima and minima due to a standing
wave field pattern caused by reflections of the dummy load and waveguide bends as was
discussed earlier. There is a tendency for the plasma to stay in those maximum field
regions such as in the microwave cavity propulsion configuration33,38,39.
This unsteady plasma motion deserves a more careful consideration. According
to the discussions made in Chapter 3, the plasma moves faster through maximum field
regions than through node regions of the field distribution. Thus, while the plasma moves
into a maximum field region rather quickly due to progressively higher electric field
strengths, it leaves it at a much lower speed since it now enters a low-field region.
Furthermore, parts of the plasma remain longer in the maximum field region despite the
fact that the main plasma has already moved on towards the minimum field region. This
is due to the fact that in the maximum field regions a plasma can be sustained longer than
in the minimum field regions since locally more microwave power is available. The
overall appearance is therefore a plasma that tends to remain in the maximum field
regions over a longer time period than in the minimum field regions.
It was further observed that the same effect was responsible for breaking the
80
plasma apart:
smaller portions of the discharge remain longer in the regions of
maximum E-field strength then follow the larger initial plasma, however, due to
microwave absorption in the larger discharge, they extinguish and are reformed in the
next maximum field region.
S.3.2.2. Propagation Velocity Measurements
This section describes the experimental investigations to determine plasma
velocities in the rectangular waveguide test section. A typical plot of the output signal
from the photodiode array is shown in Figure 5.6. Here, the signal obtained from a
propagating helium plasma at 1 atm gas pressure and 1550 W incident power is shown.
Five signal peaks can clearly be identified; however, the first two peaks follow each
other much closer in time than the rest of the peaks. This may be attributed to either one
or a combination of the following reasons. First, a higher propagation velocity in the
vicinity of the tungsten wire may be caused by a higher electron concentration in this
region due to thermal electron emission from the wire, resulting in larger ionization rates
and thus larger plasma velocity values. Another reason may be found in the experimental
procedure for the propagation velocity measurements. Rather than ramping up the
microwave power value from zero to its desired value, this value was preset in the
microwave power control and the generator turned on afterwards. This way it was hoped
to avoid a transient between the zero and final power value at the beginning of the
measurement due to the relatively time consuming manual adjustment. This transient
would have allowed the plasma to propagate partially upstream the test section at lower
power values than the desired value and induced an error in the measurements. However,
81
FHOIODICDE SIGNAL VS TINE
HELIUM 1 AIN
1S5B.SU INC. POWER
POWER ABSORBED (4.84V.
Figure 5.6 Voltage Peaks obtained from the Photodiode Array
82
as can be seen from Figure 5.7, there is a considerable power overshoot over the preset
power value just after turning on the microwave generator which could have led to higher
plasma velocity values at the beginning of the test section immediately following ignition
of the plasma. Therefore, since the plasma velocity was obtained by averaging the four
velocity values between the five diodes, the first value was disregarded in case it was
significantly different from the other three velocity values.
The results of the propagation velocity measurements are shown in Figures 5.8
and 5.9. Figure 5.8 gives the measured plasma velocities for helium and nitrogen at 1
atm. Although a line has been drawn interconnecting the experimental data points, it
appears that there are really two groups of propagation velocity data for helium,
corresponding to two different modes of propagation, the group consisting of the first
five data points up to 1550 W input power might thus be attributed to a different
propagation mode than the last two data points obtained at power levels exceeding 1550
W. A preliminary interpretation of these results based on the numerical investigations
illuded to in Chapter 2 and discussed in References 65 through 67 would suggest a
propagation mode change between a heat conduction mode at power levels below 1500
W and a radiation mode at power levels exceeding 1500 W. However, since no high
confidence has been placed in those numerical calculations, any discussions on what
propagation modes actually have taken place remain rather speculative.
Propagation mode changes similar and as dramatic as depicted in Figure 5.8,
however, are well known and have been observed before by Bethke and Ruess73 for other
inert gases, such as argon, krypton and xenon. However, those mode changes were
obtained at pressures much lower (< 3 Torr) than the ones considered here and at
correspondingly lower power levels (around 50 W). Under those experimental conditions,
Bethke and Ruess73 identified the mode changes to have taken place between radiative
83
< r\
t
I-
\
!
i
'
BT5
Irt
time (
mm)
m i ) ] ) POHEE VS TIKE
B lTT
?
HELIUM, 1 AIM
ANALOG SIGNAL : 1442.23 N, 69.25X ABS.
Figure 5.7 Forward Power with respect to Time for a Propagating Plasma
84
P
L
A
S
Mo d e l
M
Ex p e r i m e n t
A
V
E
L
0
C
I
T
Y
1( H
C
M
/
S
500
?1000
1 500
2000
2500
POWER (W )
Figure 5.8 Experimental Plasma Velocities for Helium and Nitrogen
at 1 atm Gas Pressure
3000
85
10
P
L
A
S
Hel iu m
10
4
?
Ex p e r i m e n t ,
O
Ba t e n i n
1082 H
e t a l 1*,
1100 H
U
A
V
E
L
0
C
I
T
Y
2
10 '
C
K
/
S
10
0.2
0 .4
0.6
0.8
PRESSURE ( ATM )
Figure 5.9 Comparison of Experimentally Obtained Plasma Velocity Data
at 1082 W with Batenin?s70 Data at 1100 W
1.0
86
modes due to electron ionization with a radiative precursor and purely radiative modes
or electron diffusion modes, respectively (compare with Chapter 3). Propagation velocity
"jumps" up to one order of magnitude have been observed in those cases, comparable
to the velocity increases noted here.
As can be seen on Figure 5.8, no indications for propagation mode changes were
found for the molecular gas nitrogen. An explanation for this behavior may be found in
the fact that radiation modes require high gas temperatures to allow for sufficiently high
degrees of electronic excitation of the gas atoms. In molecular gases, however, energy
is also dissipated by dissociation, not allowing the gas particles to obtain the high kinetic
energies required to result in energetic collisions producing strongly excited heavies.
Figure 5.8 also shows two curves representing the theoretical velocity values
determined by the numerical model of Reference 67. As can be seen, there exist large
differences between numerical and experimental velocity data. While in the case of
helium this might be due in part to the propagation mode change discussed above,
differences exhibited between the nitrogen curves demonstrate the inaccuracies of the
model that have already been alluded to in Chapter 2.
Figure 5.9 shows the behavior for the plasma velocity in helium with respect to
changes in gas pressure and compares the data with that obtained by Batenin for a similar
power level70. As can be clearly seen, for both data sets plasma velocities increase with
decreasing pressure. Note that, although a good agreement for the propagation velocities
is found with data reported by Batenin et al.70 for pressures greater than 0.4 atm, the
sharp velocity increase of roughly one order of magnitude below that pressure had not
been found by Batenin et al.70. The same authors, however, reported velocity increases
of the same order of magnitude for argon and xenon at almost exactly the same pressure
value as observed for helium during these experiments. Thus, higher confidence was
87
placed in the here obtained velocity data. It seems possible, that plasma propagation in
the case of helium is dominated by heat conduction towards higher pressures and then
a mode change takes place around 0.4 atm, resulting in a radiative propagation mode
toward lower pressures. Since Batenin et al.70 reported possible nitrogen impurities in
helium, which could have quenched the radiation mode (see Chapter 3), this could
explain the discrepancy between the two data sets toward the low pressure end.
It is interesting to note that Bethke and Ruess73 found that for purely radiative
modes in heavy inert gases such as argon, krypton and xenon, where ionization is due
to photon impact only, plasma velocities decrease slightly with decreasing pressures.
Assuming a similar behavior for helium, this would suggest that purely radiative modes
have not been observed under the experimental conditions encountered here.
On the other hand, radiative propagation modes where the final ionization reaction
steps are due to electron collisions and photon impacts are only important for the
precursor discharge producing those electrons, lower pressures result in increased
ionization rates due to the longer electron mean free paths, enabling the electrons to
acquire more energy from the microwave field73. It should be noted, however, that
propagation velocities obtained with this mode go through a maximum if the collision
frequency equals the microwave frequency as was discussed in Chapter 3. For lower
pressures, the propagation velocity decreases again. However, pressures required for this
condition to be established range around 1 Torr and are thus significantly smaller than
the pressures encountered here73. These observations would therefore suggest that if a
radiative propagation mode was encountered in the lower pressure range shown in Figure
5.9, it is more likely due to an electron ionization mode with radiative precursor, rather
than a purely radiative mode.
Once again, any discussions on the actual propagation mechanisms involved
88
remain fairly speculative at this stage of the experimental investigation and only future
experiments, such as the ones performed by Bethke and Ruess73 previously discussed in
Chapter 3 for example, involving the placement of windows into the path of plasma
propagation or applications of magnetic fields, might give further clues beyond the rather
preliminary conclusions made above. However, since the goal of this investigation was
to study microwave waveguide applicators for space propulsion applications and since
helium is a fairly uninteresting propellant due to problems related to storability, any
further investigations in this direction have been ended in order to allow efforts to
concentrate on other development issues to be discussed in Section S.4 of this chapter and
in Chapter 6.
S.3.2.3. Coupling Efficiencies
Coupling efficiencies, being the ratio of absorbed to incident power levels, for
freely propagating plasmas ranged from the mid 60 to low 70% for helium at 1 atm and
from the low 60 to high 60% for nitrogen at the same pressure. For helium at 1080 W
input power, the coupling efficiencies dropped from approximately 63% at 0.23 atm to
about 60% at 1 atm gas pressure.
By feeding the analog signal obtained from the power meter via an A/D board
into a PC, the behavior of the coupling efficiency with respect to time and thus, for a
propagating plasma with respect to axial location along the waveguide, could be resolved.
A total of 4000 data points was taken at a sampling frequency of 4 kHz. The input or
forward power was preset at 1442 W, yielding an average coupling efficiency of 69%
for helium at 1 atm gas pressure. Fluctuations in the coupling efficiency as shown in
89
Figure 5.10 are due to several reasons. The first peak is due to the power overshoot
when the microwave power source, preset at the mentioned power level, is turned on.
This power overshoot can also be seen clearly on Figure 5.7, lasting roughly half a
second before an equilibrium power value is reached. This power peak at the beginning
was also successfully used in igniting plasma under conditions where the equilibrium
power value to be reached later was not sufficient for breakdown.
Subsequent peaks are believed to be a consequence of the standing wave pattern
present in the waveguide. According to Chapter 4, the guide wavelength in the
rectangular WR284 test section is 23 cm, i.e. there is a field maximum every 11.5 cm,
not taking into account any effects of the quartz tube on the guide wavelength. Since the
test section consisted of a 2 foot long rectangular guide with the length over which the
photodiodes were distributed being roughly 50 cm, this would allow for 4 to 5 field
maxima within this section of the guide depending on their actual location with respect
to the diode array. As can be seen on Figures 5.7 and 5.10 through 5.13, 4 peaks can
be identified for the forward, absorbed, transmitted and reflected power as well as the
coupling efficiency, apart from the initial power surge. As has been observed during the
experiments, the plasma does not only accelerate and decelerate as it moves through the
standing wave pattern, it also varies in size and brightness, appearing larger and brighter
in regions to be believed of maximum field strength and smaller and dimmer in minimum
field regions. Assuming that the absorbed power reaches its maximum in the maximum
field regions where the plasma is relatively large, overlapping Figures 5.11 and 5.13
reveals that the transmitted power goes through a minimum at those locations. The larger
plasma seems to be able to shield the incoming microwave power better and less power
gets transmitted.
The reflected power, on the other hand, reaches its maxima just between the
90
\
/
е 5 - - - - - - - - - - - - - - - - BT75"
iiHErmn
?
?
PERCEHIAGE ABSORBED M R (IS TIKE
HELIUM, 1 AIN
ANALOG SIGNAL : 1442.23H FORWARD, 6 9 .2 5 '/ ABS.
Figure 5.10 Coupling Efficiency with respect to Time for a Propagating Plasma
91
S>\
!
V
I
I
hr
bit
TINE < S H )
ABSORBED FOUER VS I I I
HELIIIH, 1 ATH
ANALOG SIGNAL : 1442.23H FORMARD, 6 9 .2 5 I DBS,
Figure 5.11 Absorbed Power with respect to Time for a Propagating Plasma
92
T500
? ?a m
i
? "? VlM
m
REFLECTED POHER VS TIHE
HELIUM, 1 AIN
ANALOG SIGNAL I 218.85 H
Figure 5.12 Reflected Power with respect to Time for a Propagating Plasma
93
IRANSNIITB POHER VS TIHE
HELIUM, 1 ATM
ANALOG SIGNAL : 224.59 H
Figure S. 13 Transmitted Power with respect to Time for a Propagating Plasma
94
minima and maxima observed for the absorbed power. This is surprising, since one
would expect the reflected power to reach its maxima whenever the plasma is largest in
size, i.e. when the plasma is located in the maximum field regions where the absorbed
power is largest. A satisfactory explanation for this phase shift has not been found. The
fluctuations in forward power are believed to be due to impedance matching fluctuations
of the microwave circuit to the microwave source due to variations in plasma size,
changing the impedance of the circuit.
5.4. Stabilized Plasma Investigations
5.4.1. Experimental Procedure
For the investigations of stabilized plasmas, the experimental set-up as shown in
Figure 5.1 was used, i.e. the photodiode array had been removed and a bluff body had
been inserted into the quartz tube. In order to ignite the plasma, a moderate gas pressure
was adjusted, usually around 1 atm or lower, and the plasma was ignited by means of
tungsten wire ignition. By regulating the precision valve and the downstream valve V3
( see Figure 5.2), the proper mass flow rate and pressure were adjusted. The microwave
power level was then varied keeping mass flow rate and pressure constant and forward,
reflected and transmitted power were recorded. Keeping the pressure constant, a new
mass flow rate was adjusted and the process repeated. Eventually, all the measurements
were repeated for a different pressure level.
95
5.4.2. Results
5.4.2.I. General Plasma Behavior
The plasma was observed to have a hot, white-glowing, cylindrical core that is
aligned along the E-field lines of the TE10 mode present in the guide and is thus oriented
perpendicular to the waveguide axis, with the plasma touching the quartz tube walls at
two locations (compare with Figure 2.4). The core is surrounded by a bluish, ellipsoidal
shaped, cooler plasma. Figure 5.14 shows a photograph of the straight waveguide
experiment. The slotted waveguide test section can clearly be seen. Running the axis of
this waveguide section, just behind the slots is the quartz tube that contains the bluff body
and the plasma, both visible in fairly close proximity. Some of the fins holding the bluff
body in place inside the quartz tube can still be made out. The finestructure of the
plasma, i.e. the separation between the hot, white-glowing core and the cooler ellipsoidic
plasma surrounding the core are not visible in this photograph, however, the plasma
clearly shows a filamentary tail stretching in the direction of the flow, entering the quartz
tube from the right side of the picture. The hoses inserted into the slots of the waveguide
test section provide compressed air in order to cool the quartz tube that is being heated
by the plasma.
The fact that the plasma touches the quartz tube walls in this configuration, has
to be viewed very critically in view of potential space propulsion applications, since this
circumstance would lead to heat losses and thruster efficiency reductions as well as
erosion, or in this particular case, melting problems.
Figure 5. 14 Stabilized Plasma in the Straight, Rectangular Applicator
97
5.4.2.2. Plasma Stabilization behind Bluff Bodies
Plasma stabilization, i.e. keeping the plasma localized in a certain position inside
the waveguide applicator, preferably close to a potential nozzle inlet, was considered of
particular interest and of crucial importance in evaluating the concept of waveguideheated plasmas for space propulsion applications. Three different stabilization modes
were observed during operation of the waveguide, some overlapping each other.
The plasma would sit stable in the recirculation region right behind the bluff body
as has been described earlier in Chapter 3 and shown in Figure 5.15. Although a great
amount of literature has been published on sizes and shapes of recirculation regions
behind bluff bodies (see Reference 60 for a survey, for example), only very few sources
deal with the particular problem of recirculating flows behind bluff bodies in plasma
systems.
Venkateswaran and Merkle89 recently performed a numerical study of bluff body
stabilized plasmas in a circular waveguide configuration. The recirculation zone behind
the bluff body was observed to be greatly affected by a variety of flow and plasma
parameters, causing the length of the zone to vary between zero and one bluff body
diameter. Higher mass flow rates caused by either increasing flow velocity or gas
pressure tended to increase the length of the recirculation zone while increasing the input
power reduced the length.
The complexity of bluff-body stabilized plasmas in waveguides reveals itself even
more regarding a second mode of stabilization observed during the experiments: the
plasma was able to sit stable downstream of the recirculation region, sometimes
considerable distances (up to roughly
10
times the bluff body diameter) behind the bluff
body (see Figure 5.15). Considering a typical, low-ReynoIds number flow field behind
98
Quartz Tube
Gas
Bluff Body
Plasm a
(a) Plasma Located Stably in Recirculation Region
Quartz Tube
Bluff Body
Plasma1
i
---------
???????
-=-:-
^
^
^
(b) Plasma Located Stably Downstream of Bluff Body
N Quartz Tube
Gas
Bluff Body
Plasma'
(c) Plasma Located Stably at Bluff Body Tip
Figure S. 15 Stable Plasma Positions with respect to Bluff Body
:V f
99
a conical bluff body as shown in Figure 5.1690 indicates that the flow velocity changes
continuously behind the bluff body. At off-axis locations, the flow velocity decreases
from a maximum value next to the body to its original free-steam magnitude at large
distances downstream from the body. Therefore, there will be a region behind the bluff
body, where the plasma velocity exactly matches the flow velocity and plasma
stabilization is obtained.
Note, however, that along the axis the flow velocity decreases from its freestream value far downstream of the bluff body to zero right at the stagnation point at the
tip of the recirculation zone (see Figure 5.16). This would imply that a plasma
approaching the bluff body configuration along the axis would move into regions of
continuously lower flow velocity and could therefore not be stabilized until it reaches the
recirculation zone. Such a behavior, however, was never observed. A possible
explanation might be found in the fact that the plasma extends into regions far beyond
the axis location and thus into regions where "flow stabilization" is conceivable. It seems
therefore possible, that flow-stabilized plasma regions at off-axis locations prevent
portions of the plasma located along the axis to move upstream: once small portions of
the plasma at this location break off the main, stabilized plasma, they would immediately
extinguish due to a larger surface-to-volume ratio of the smaller plasma, resulting in
higher diffusive losses of charged particles. This explanation would obviously still allow
for the option of a cylindrical plasma core that is "bent" towards the bluff body at the
axis location. However, no such effect has been observed either, indicating that
electrodynamic effects seem to play a very important role in the stabilization of
waveguide-heated plasmas.
This latter point already became obvious during the measurements performed at
the propagating plasma. As was mentioned in Section 5.3, plasma motion was not steady
100
.000
.020
.040
.060
.080
.10
Figure 5.16 Recirculation-Zone behind a Conical Bluff Body exposed to a
Low-Reynolds Number Flow90
101
but tended to slow down in regions of maximum field intensity. In some instances, in
particular toward higher pressures (>
1 .2 S
atm), it was even observed that the plasma
would come to a complete halt in those regions. Similar observations were also made
during the bluff body experiments where the plasma would remain located in such a
maximum field region independent of its relative position with respect to the bluff body.
Moving the quartz-tube-bluff body configuration along the waveguide axis had no impact
on the plasma position relative to the guide. The reason for this "microwave field"
stabilization mode might be found in the fact that at higher pressures mean free paths of
the electrons between collisions become shorter and the electrons thus can no longer pick
up enough energy to cause ionization, unless, as in the maximum field regions,
sufficiently strong electric fields exist providing the necessary accelerations of the
electrons to higher particle energies. Therefore, the plasma remains restricted to the
maximum field regions of the standing wave present in the guide. The same effect,
although much more pronounced and observable even at much lower pressures is
routinely being observed for resonant cavity plasmas54*61.
Finally, a third mode of stabilization was observed. It was found that a plasma
located in the recirculation region behind the bluff body and in touch with the latter,
could creep upstream across the bluff body along the boundary layer adjacent to the body
surface. The plasma would take on the shape of a bluish, thin Him covering portions of
the cone surface and finally locate itself at the upstream bluff body tip. Here it could
cause severe and rapid heating of the body (see Figure S. IS). This stable plasma position
could be explained by strong heat transfer from the cone tip: since prior to moving into
the location at the cone tip the plasma was in touch with the bluff body, the body has
been heated significantly. Heat transfer from the body, however, has a local maximum
at the sharp cone tip, causing electronic excitation and subsequently a higher degree of
102
ionization in the immediate surrounding of the body tip than in other regions in the test
gas volume. Interaction with the microwave fields then lead to breakdown at the body
tip, creating a plasma at this location.
Of the stabilization modes encountered only the second mode discussed was
employed during waveguide operation. The other modes resulted in a plasma in touch
with the bluff body and severely heating it which could have led to erosion problems or
even its destruction. An additional concern regarding those stabilization modes was that,
upon heating, the bluff body would start to glow bright yellow. This continuum emission
might have interfered with the spectroscopic measurements, in particular the absolute
continuum method to be discussed later.
5.4.2.3. Stability Boundaries
Stability boundaries were given by the maximum and minimum input power levels
over which the plasma could be located stably behind the bluff body, not touching it. If
for a given mass flow rate and flow velocity the input power was too low, the resulting
plasma velocity could become smaller than the counter gas flow velocity so that "blowo f f occurred and the plasma was pushed down the waveguide. This was considered as
the lower stability boundary. On the other hand, if microwave power levels were too
high, the resulting plasma velocity might exceed the oppositely directed flow velocity and
the plasma could move upstream, causing the plasma to make physical contact with the
bluff body. The power level that could be maintained in the guide without having the
plasma touch the bluff body was considered as the upper stability boundary, since a
103
plasma touching the body could have lead to erosion problems or even the destruction
of the body.
Taking into account the stabilization mode in the recirculation zone as well would
have resulted in slightly higher upper stability boundaries. The changes were not large
because of the tendency of the plasma to creep up the boundary layer across the bluff
body causing severe heating problems at the upstream tip.
Between those stability boundaries, toward lower pressures, i.e. below 1.25 atm,
the plasma moved continuously into locations closer to the body as the power was
increased up to a point roughly one to two bluff body diameters downstream of the bluff
body. Here, the plasma performed a characteristic "jump" into the recirculation region
of the body.
Towards higher pressure levels, where "microwave field" stabilization was
observed in the maximum field regions along the guide, the plasma motion was rather
discontinuous and the plasma would "jump" from one maximum field region to another.
Just before reaching the bluff body, the plasma made another characteristic "jump" into
the recirculation region of the body.
Data for the stability boundaries are shown in Figure 5.17. Three pairs of curves
are displayed, each pair corresponding to different pressure levels ranging from 0.75 to
1.5 atm. The upper curve of each pair corresponds to the upper stability boundary while
the lower curve represents the lower stability boundary. The stability can be regarded as
good since the lower power level goes down to as little as about 60% of the upper power
level. This allows for the stability regions for different pressures to overlap thus allowing
stabilization of the plasma despite minor pressure fluctuations.
Note, however, that the highest obtainable power level shown in Fig. 5.17 lies
only just above 2 kW. If higher power levels are desirable in order to boost thrust and
104
2500
O 0.7S atm
A 1,00 atm
? 1.S0 atm
1500
INPUT
POWER
2000
1000
500
0.0
0. 2
0 .4
0.6
I NL E T F L O W V E L O C I T Y
0.8
( m /s
1. 0
1.2
)
Figure 5. 17 Stability Boundaries of a Helium Plasma with respect to Inlet Flow
Velocity and Input Power. Plasma stabilized downstream of Bluff Body
and not in touch with the Body. Each Pair of Curves corresponds
to upper and lower Stability Boundaries, respectively.
105
specific impulse values, a waveguide thruster would either have to be operated at higher
pressures as well or a different stabilization mechanism would have to be found.
5.4.2.4. Coupling Efficiencies
All coupling efficiency measurements, i.e. the determination of absorbed over
total incident power into the waveguide, were done using the second stabilization mode.
This means that the plasma was stably located downstream of the bluff body, not
touching it. As described before, the plasma took on an ellipsoidal shape with its major
axis perpendicular to the waveguide axis as indicated on Figure 2.4. Figure 5.18 shows
the coupling efficiencies with respect to incident power and mass flow. As can be seen,
the coupling efficiencies increase with mass flow. The reason for this is believed to be
due to the skin effect: cooling the plasma by increased forced convection due to higher
mass flows will lower its electrical conductivity. This increases the skin depth, which is
the distance up to which the electromagnetic fields can penetrate before having been
attenuated to 1/e of its initial strength, e being the Euler number. The bigger the skin
depth, however, the more energy can actually be dumped into the plasma since the
absorbing plasma volume increases. Maximum obtained coupling efficiencies ranged up
to 90% for the higher mass flow rates which compares favorably to those values obtained
in other microwave applicator configurations54.
On the other hand, coupling efficiencies decrease as the input power is increased.
This effect is most clearly seen in Figure 5.19. The reason for this effect can be
understood using Figure 5.20. This figure clearly shows that the absorbed power
increases at a smaller rate than the total input power. Since the coupling efficiency is the
106
COUPLING
E F F IC IE N C Y
100
60
4 0 ----O 1606.32
A 2028.56
? 2318.35
2 0 -----
20
30
40
50
60
MASS FLOW RATE
80
70
( mg/s
90
)
Figure 5.18 Coupling Efficiencies vs. Mass Flow Rate for Helium at various
Input Power Levels
107
100 -
COUPLING
EFFICIENCY
K
BO-
60*
0 42 cm/s
X 57.47 cm/s
A 6631 cm/s
? 75.62 cm/s
089.17 cm/s
09936 cm/s
1110.85 cm/s
+121.91 cm/s
? 13932 cm/s
A 146.74 cm/s
^ 159.16 cm/s
40-
20-
1200
1400
1600
1800
1
2000
POWER
( W)
1
1
2200
1
1---2400
2600
Figure 5.19 Coupling Efficiencies vs. Input Power for Helium at various
Inlet Flow Velocities
108
2000
1 5 0 0 -----
1000
^Absorbed
? Transmitted Power, 29.83 mg/s, 54.47 cm/s
O Reflected
A B S ..R E F .
AND
TRANS.
POWER
0 Absorbed
? Transmitted Power, 83.17 mg/s, 159.16 cm/s
? Reflected
5 0 0 -----
1400
1600
1800
INPUT POWER
2000
2200
( W )
Figure 5.20 Absorbed, Reflected and Transmitted Power for Helium
vs. Input Power
2400
109
ratio of these two values, its magnitude decreases. Furthermore, the power that is not
absorbed by the plasma is reflected by the plasma as can also be seen on Figure 5.20.
While the reflected power continues to increase, the transmitted power remains
essentially constant after an initial slight decrease. In particular in the case of a mass
flow rate of 83 mg/s, it can be noted that the absorbed power tends to level off after an
initially more pronounced increase while the reflected power continues to increase. This
effect is due to the fact that the plasma is a very good conductor, thus reflecting
incoming radiation. Therefore, in space propulsion devices using rectangular waveguide
applicators, the absorbed power would have to be increased by increasing the mass flow
rate rather than by raising the input power.
Figure 5.21 shows coupling efficiencies for constant mass flow rates but various
pressures. Although the coupling efficiencies change with pressure, variations are
relatively small compared to those with changing mass flow rate.
It should be noted that in all cases part of the microwave energy could have been
absorbed by the tungsten wire used to ignite the plasma. However, since the wire was
shielded from the incident microwave radiation by the plasma itself and was positioned
perpendicular to the electric field lines those losses should be small. Investigations in this
matter have been performed using the circular waveguide applicator confirming the above
made assumptions and are discussed in Appendix A.
5.5. Comparison of Propagating and Stabilized Plasmas
Comparing some of the results obtained for propagating as well as stabilized
waveguide-heated plasmas further emphasizes the complexity of the physical processes
110
100
COUPLING
E F F IC IE N C Y
80
60
4 0 ----1.00 atm, 58.00 mg/s
1.25 atm, 58.35 mg/s
1.50 atm, 57.68 mgIs
20
1600
1800
2000
POWER
2200
2400
2600
( W )
Figure 5.21 Coupling Efficiencies for Helium at constant Mass Flow Rates
at various Pressures
involved. One of the most striking results of this comparison is the fact that helium
plasma velocities measured for the freely propagating plasma significantly exceeded the
gas flow velocities which had to be maintained in the quartz tube to successfully stabilize
the plasma. For example, for a power level of 1600 W, from Figure 5.8, the plasma
velocity is roughly 20 to 30 m/s. Figure 5.17 indicates that the lowest inlet flow velocity
that is able to maintain the plasma in a stable position behind the bluff body is around
0.3 m/s at the same gas pressure of 1 atm. The maximum flow velocity obtainable at that
pressure before "blow-off occurs can be calculated using Figure 5.18 and is roughly 1.5
m/s. Even taking into account a maximum blockage of the flow cross sectional area of
the large bluff body, including the fins, of
66%
will not yield flow velocity values as
high as the measured velocities of the freely propagating plasmas at those pressure and
power conditions.
The reason for this discrepancy may be found in the fact that the oncoming
propellant gas flow over the stabilized plasma is cooling the latter at least in the outer
plasma layers. This will result in a local decrease in resonant photon and electron
concentration as well as their energies in the outer layers due to less energetic particle
collisions. Since for all propagation mechanisms considered, lower photon and electron
concentrations and energies will result in lower ionization rates the plasma velocities
obtainable will then be reduced.
Another observance made by comparing propagating and stabilized plasmas seems
to support the above assumption of plasma cooling due to propellant flow. As can be
seen in Figure 5.18, higher mass flow rates result in higher coupling efficiencies, which
was attributed to cooling of the outer plasma layers and a subsequent increase in the skin
depth. Note, however, that low mass flow rates resulted in coupling efficiencies between
60 and 70% which is in accordance with the values observed for propagating plasmas.
112
Thus, it seems that propagating plasmas are not subjected to cooling of their outer layers
since no propellant gas flow is providing forced convective cooling. This will result in
higher photon and electron concentrations and energies in those regions, resulting in
higher ionization rates and therefore higher plasma velocities for propagating plasmas
than for stabilized plasmas.
113
Chapter 6
THE CIRCULAR WAVEGUIDE APPLICATOR
6.1. Introduction
While experiments using straight, rectangular waveguides operating in the TE,0
mode such as described in the last chapter served to study basic principles of waveguideheated plasmas, that particular waveguide field configuration used suffers a major
disadvantage over other comparable microwave thruster concepts. As was pointed out in
previous chapters, in TE10 mode waveguides maximum field regions extend perpendicular
to the waveguide axis from wall to wall, thus allowing the plasma being sustained by it
to touch the thruster walls at two locations. This could lead to erosion problems and
thruster efficiency losses which could pose serious disadvantages to potential future space
propulsion applications of this concept.
Therefore, different waveguide configurations were investigated which would
avoid those problems and be able to sustain a plasma away from thrust chamber walls
in the center of the guide. Attention was also focused on the ease of generation of such
waveguides modes in the guide and as a result of this study, a circular waveguide
applicator using a TM0, mode was designed.
In the present chapter, the design process of the circular applicator will be
reviewed, followed by a description of the overall experimental apparatus including gas
supply system, ignition and bluff body design. Finally the experimental results obtained
with this waveguide type will be discussed, where for the first time for a waveguideн
mode microwave thruster data on such rocket performance parameters as specific
114
impulse, thruster efficiency and thrust will be presented.
6.2. Design of the Circular Waveguide Applicator
6.2.1. Concept
In this section the circular waveguide applicator as it was used throughout the
experiments is described. While this section is limited to a pure description of the
applicator, the following section will feature a discussion on how some of the waveguide
dimensions were determined. As a general introduction to the design of the circular
waveguide applicator, it should be noted that a major feature to all the waveguide
configurations considered in this thesis is that truly propagating field patterns as indicated
by the field equations discussed in Chapter 4 which had been derived assuming infinitely
long waveguides do not exist, rather, reflections from imperfect dummy loads or bends
cause a standing wave pattern to arise with a standing wave ratio ( SW R), i.e. ratio of
antinode to node of typically 1.1 to 1.2. This effect has been shown to be useful
especially at higher pressures for plasma stabilization purposes since the plasma tends to
stay in the antinode regions and standing field patterns are therefore not suppressed. In
the following, although field patterns for waveguide configurations will be shown, those
patterns can be assumed to be standing wave patterns.
The prime objection against a rectangular waveguide operated in the TE10 mode
is the fact that the plasma sustained by it touches the waveguide walls at two locations.
This problem could be avoided by generating a circular TM0] mode. According to Figure
6 .1,
a TMoi mode is excited by means of a coax probe in a circular waveguide section.
115
Side View
Xg/2 ------------ ?
Coaxial
Circular Waveguide
?
0* ?0
Electric Field Lines
Magnetic Field Lines
End View
Figure 6.1 TMqi Mode Generation in a Circular Waveguide
116
Propagation of the lower order TE? mode that would be allowed to propagate in the
guide since its cutoff frequency is lower than that for the TMW mode is avoided due to
the symmetry of the coupling mechanism. Comparing with Figure 4.4, the TE,, field
pattern cannot be established by the coax probe since it will force electric field lines to
originate or end at its tip at the center of the guide. TEU field lines, on the other hand,
originate at one wall section and end at the opposite one. Thus, an electromagnetic field
pattern has been established inside the guide that will allow a plasma to be sustained in
the center of the guide, away from thrust chamber walls.
The circular waveguide applicator as it was used throughout the experiments to
be described in this chapter, is shown in Figure 6.2. The circular pipe section was
welded onto a rectangular waveguide of sufficient size so as to allow for a transition
back to the TE ,0 mode. For the circular waveguide section a standard WC38S guide was
chosen according to the EIA (Electronic Industry Association) designation, i.e. 3.85" in
diameter. It was welded to a WR430 rectangular guide, i.e. a rectangular guide having
a broad wall width of 4.3". While the transition back to a rectangular guide will allow
reusing some of the waveguide components used for the rectangular waveguide
experiment, such as dummy loads and wave couplers, the reason for choosing this
transition was another. It was believed that now a cylindrically shaped maximum field
region of the rectangular waveguide part could be positioned over the nozzle inlet,
aligned with the nozzle axis. The plasma was therefore expected to be located along this
maximum field region, aligned with the nozzle axis and in immediate vicinity of the
nozzle inlet. The incoming propellant flow therefore would have had to stream along a
plasma extending in flow direction and good thermal coupling was expected to be
achieved.
However, the field configuration described here was not obtained in the actual
117
t
Bluff Body
I
Support Adapter-
To Microwave
Power Source
All Units
in mm
Top Flange with
Coaxial Port
Gas Inlet
Adapters
Coaxial Probe
Viewing Ports
-Front and Back
(3/32" Hole
Pattern)
Gas Inlets
Bluff Body
Plasma
Quartz Tube
To Power Meter,
Dummy Load
Conically
Converging
Nozzle
Circular Waveguide Section
(WC385)
Rectangular Waveguide Section
(WR430)
Orifice Plate
Sliding Short
Figure 6.2 Schematic of the Circular Waveguide Applicator (Drawn To Scale)
118
waveguide design. As will be shown in one of the following sections in this chapter,
inserting dielectric materials, such as the quartz tube, a bluff body and an orifice plate
into the guide distorted the field pattern. Also, according to electric field measurements
to be discussed later, the field configuration in the transition region is probably not
dominated by the rectangular TE 10 mode but by the circular TM0I mode extending from
the circular waveguide section into this portion of the rectangular guide. Full transition
to the rectangular TE10 mode appears only to happen further down the rectangular guide,
away from the region where the circular and rectangular guides are mated. Thus, the
actually obtained field configuration was different from the one expected and the plasma
formed in a maximum field region that was located further upstream in the center portion
of the circular guide, as shown in Figure 6.2. Measured field patterns inside the
waveguide configuration will be presented in one of the following sections.
The end flanges of the rectangular waveguide section are occupied by the dummy
load combined with a wave coupler/power meter-configuration so as to absorb and
measure the transmitted power and, on the other side, by a sliding short which allows
one to adjust the created field pattern in such a way that it is symmetric with respect to
the nozzle throat.
Inserted into the circular waveguide is a quartz tube needed for laboratory tests
in order to separate the propellant gas from the ambient air. The portion of the tube that
extends down into the rectangular part converges to a smaller tube diameter. The
motivation behind this design was to support close gas flow over the plasma that was
anticipated to be located in this region and thus enhance the thermal coupling. The quartz
tube has three inlets. All inlets are mounted at off-center positions to the tube in order
to enable the coaxial probe to be inserted into the circular guide. Through one of the
inlets a boron nitride blunt body was inserted into the tube so as to achieve the necessary
119
plasma stabilization in axial direction. The peculiar shape of the bluff body configuration
shown in Figure 6.2 was dictated by the requirement that the bluff body cone had to be
positioned along the waveguide axis, while the inlet provided for the bluff body assembly
was located off-center of the tube axis.
The two remaining inlets of the quartz tube allowed for injection of the test gas.
Two gas inlets were chosen in order to avoid flow non-symmetries due to the off-center
location of those inlets.
A hole pattern consisting of 3/32 "-holes was drilled in two opposite sides of the
applicator in order to be able to view the plasma. The hole diameters were small enough
to prohibit microwave radiation leakage.
An angled tube section was welded onto one side of the circular waveguide part
(not shown in Figure 6.2). This tube was supposed to allow a laser to be focused inside
the waveguide in order to ignite the plasma. The tube section was 80 mm in length and
20 mm in diameter. This dimensions were chosen such that its cutoff frequency was
higher than the operating frequency of 2.45 GHz and no microwave radiation could leak
out51.
Figure 6.3 shows a photgraph of the circular waveguide applicator. The plasma
can be seen at operating conditions of 1.6 atm gas pressure (helium gas) and 830 W input
power and is located just below the center point of the circular waveguide part as
mentioned above. Apart from the circular and rectangular waveguide components, the
sliding short flanged to the rectangular guide is visible at the right end of the picture. At
the left rectangular flange a waveguide transition from the larger WR430 type guide to
smaller WR284 guide is attached. This allowed for reusing various other WR284
components previously being used for the straight rectangular waveguide experiment,
such as an H-plane bend visible at the left side of the picture as well as the mentioned
Figure 6.3 The Circular Waveguide Applicator. Operating Conditions are 1.6 atm Gas Pressure and 830 W Input Power.
121
wave coupler and dummy load that were flanged to the bend. The thermistor power
sensor attached to the wave coupler is visible in the picture just above the bend. Clearly
recognizable on this photograph is also the angled tube that was supposed to serve as a
laser port at the left side of the circular waveguide portion. The top flange of the circular
section features the two gas inlets with flexible metal hoses attached to them and the inlet
for the bluff body configuration. The bluff body is barely visible just above the plasma
inside the applicator. The black rubber hose leading towards the back of the circular
waveguide section provides compressed air for cooling the applicator.
6.2.2. Design Calculations
Following the description of the circular waveguide applicator in the previous
section, this section will discuss the analysis that determined the sizes of some of the
components of the applicator. The analysis will be based on the waveguide theory
presented in Chapter 4. The herein introduced design procedure might also serve as an
example on how the basic electrodynamic laws govern the design process of a microwave
thruster and entirely determine its size and dimensions. Note, however, that the approach
chosen in this chapter, i.e. basing the design on analytical expressions derived for such
simple waveguide components as straight rectangular or circular guides, cannot
accurately account for the effects complicated configurations of dielectric materials
inserted into the guide or transitions between waveguides showing a three-dimensional
geometry might have on the electromagnetic field distributions. The applicator geometry
was therefore kept variable to a certain extent (i.e. variable coaxial probe length,
122
rectangular sliding short) in order to compensate for at least some portion of those
effects.
6.2.2.I. Circular Waveguide Section
The characteristic parameters determining the size of the circular waveguide are
cutoff wavelength (frequency) and guide wavelength previously described in Chapter 4.
Using Equation (4.82) shows that the usable range of guide diameters for a 2.45 GHz
power input lies between the margins
93.7 mm < D < 118.9 mm
For values smaller than that, the TM01 mode will experience cutoff. Bigger diameters,
on the other hand, will allow the next higher order TE^ mode to propagate. The chosen
standard circular waveguide is a WC385 according to the EIA designation, i.e. a 3.85"
or 97.9 mm i.d. tube. Cutoff frequency for this guide according to Equation (4.82) and
(4.39) is 2.35 GHz which is very close to the operating frequency of 2.45 GHz.
Although operating a waveguide so close to the cutoff frequency will result in increased
attenuation of the incident microwave power due to reflective losses83, these losses are
not severe in the case of space propulsion devices, since the lengths of the components
are small and range only in the tens of centimeters. On the other hand, operation close
to the cutoff frequency will result in large guide wavelengths
According to Equation
(4.43), in the case of the chosen WC385 guide the guide wavelength was determined as
X.o = 42 cm
123
not taking into account any dielectric materials placed into the guide. The length of the
circular waveguide was supposed to fit half a guide wavelength measured from the coax
tip which would allow one field maximum at the coax tip and another at the opposite
circular guide end where plasma formation was intended (see Figure 6.4). The actual
waveguide length was determined a little longer (23.5 cm) so as to allow for insertion
of the coupling probe. Note, however, that the actually field pattern obtained in the guide
was severely distorted as mentioned so that design modifications as discussed later will
become necessary.
Further, it seems noteworthy that according to Equations (4.82) and (4.43) the
length of the guide section is related to its diameter and cannot be chosen arbitrarily. The
reason for this lies in dealing with terminated waveguides not having infinite lengths.
Thus, reflections have to be taken into account as mentioned, leading to standing wave
patterns requiring the fulfillment of resonance conditions.
6.2.2.2. Rectangular Waveguide Section
The rectangular waveguide chosen had to be wide enough to physically allow
welding the circular guide to it. A standard WR430 guide was used, having a broad wall
width of 4.3" or 109.2 mm. The cutoff frequency of this guide is 1.372 GHz and thus
well below the operating frequency. Therefore, according to Equations (4.43), (4.39) and
(4.40), the guide wavelength is small and determined to be
Xg = 14.8 cm
and therefore only about 2 cm longer than the free space wavelength. Since it was
124
Coaxial Port
E-Field
Lines
/
I f'jiM
I 'Si'
/
!, i h 1
\
/ 11. tii n
11 " h i
I
Circular
Waveguide
(TM01 Mode)
\
'
i n i\v
///
>
v' \
V V*
\
s \\
\
nV
v
v
v
S
-
" __
f r sf ,
\ /// /
Y if /
V|;
lit!;
I |"l(
\ t e 1
╗ ii
'VI
?ml [<
if ta
ilW
Rectangular
Waveguide
(TEfQMode)
Figure 6.4 Anticipated, "Ideal" Field Pattern in the Circular Waveguide Applicator
(Note: Actual Field Pattern differs from Pattern shown)
125
originally anticipated that the plasma would form in a maximum field region just above
the nozzle entrance, the guide wavelength also has an influence on the length of the
rectangular section. The reason for this is the necessary condition for constructive
interference of forward and reflective waves from the sliding short in order to lead to a
maximum at the nozzle location. The distance from the nozzle entrance to the short
surface (compare with Figure 6.2), 1? therefore has to be :
*
2
4
(6-D
with m being an integer larger than or equal to zero. Only in this case, after a reflection
off the sliding short surface including a 180░ phase change, the reflected wave will arrive
at the nozzle location with the same phase as the forward wave and thus enhance the field
strength at this location. In order to keep enough spacing between the rectangular end
flange and the circular waveguide, m was chosen to be 2. With the variable short set at
mid-position, i.e. a quarter wavelength off the flange, the length of the rectangular
waveguide from the nozzle inlet to the flange was thus 148 mm. For the waveguide
short, a standard WR430 short manufactured by Gerling Laboratories was used (GL413).
In order to keep the waveguide configuration symmetrical, the distance from the nozzle
inlet to the second rectangular flange was chosen to be exactly the same distance,
resulting in an overall length of the rectangular waveguide of 296 mm.
However, as was mentioned above, the field configuration in the transition region
between circular and rectangular guide did not show the anticipated strong maximum and
tests revealed that changing the sliding short position had virtually no impact on the
plasma position in the center portion of the rectangular guide as shown in Figures 6.2
and 6.3.
126
6.2.3. The Coupling Probe
Coupling of the microwave power into the circular absorption chamber is obtained
by a transition from a rectangular guide to a coaxial line and from there into the circular
part. The latter transition seems simple and is rather intuitive from Figures 6.1 and 6.2,
however, the rectangular-to-coaxial part of the transition deserves a more detailed
consideration. According to the Poynting theorem describing the power flow associated
with an electromagnetic fieldо3 о5 о7
P
= f s (ExS) 3S
(6.2)
the power flux coming off the tip of the probe is much higher than the power flux
radiating off the sides of the probe, since the field strengths are lower here than at the
tip. The power being radiated off the sides of the coupling probe, however, will reflect
off the back wall and interfere with the main power flow off the tip. In order to ensure
constructive interference, a probe length of X,/4 would be necessary. Since in the case
of the here considered circular waveguide dimensions ( \ is 42 cm ) this would result
in an extremely long coupling probe, lengthening the entire thruster and adding to its
weight. However, consultation with Gerling Laboratories91 determined that a coax probe
length of 3 to 4 cm would be sufficient and not lead to notable losses based on practical
experiences with similar transitions.
The transition from the rectangular waveguide to the coax probe is governed by
impedance matching of the two different waveguide components. Several different
definitions for a waveguide impedance are possible107, here the following most common
is used:
where P is the microwave power input and V is the voltage corresponding to a specified
location across the waveguide cross section. For rectangular TE10 modes the x=a/2
position is usually chosen (see Figure 4.1), yielding
V -
(6.4)
- H ,Zw b ^
s
g
where b is the waveguide height according to Figure 4.1 and the rest of the terms
represent the electric field strength at this location according to Equation (4.44). The
power P can be obtained from the already mentioned Poynting theorem, Equation (6.2).
The only non-zero term
inthis equation is:
P =
J*J* Ey Hx
dxdy
(6.5)
Zre a b ^ f
(6 . 6 )
yielding
using the corresponding
expressionsfor Ey
and
Hx derived in Chapter 4 at the location
x=a/2. Therefore, Equation (6.3) upon insertion of Equations (6.4) and (6 . 6 ), using the
expression for
given in Equation (4.34) and employing Equation (4.41) yields one
possible expression for the impedance based on the chosen x location across the
waveguide cross section for the TE10 mode:
128
where
M2
\l- l/J
(6.8)
and X is the free space wavelength of the waveguide filling medium and is in the here
considered cases usually very close to the vacuum free space wavelength,
A similar
expression can be derived for a coaxial line and the result, using transmission line theory
isS3
1
^ojCceac ~ 60
Ji* in ?:
?Jt
(6.9)
$
where Rj is the inner conductor outer radius and R, is the outer conductor inner radius.
Due to the constant factor and the term X,/X> 1 in Equation (6.7), the waveguide
impedance of a rectangular guide is usually bigger than the one for a coaxial line, which
commonly have impedances around SO ohms, being 58.8 ohms for the particular coupling
probe used here. Matching two waveguide components with unequal waveguide
impedances, however, will lead to power reflections which can be significant and should
therefore be avoided.
Quantitatively, this is expressed using the expression of the reflection coefficient
r:
p - ReflectedVoltagejor E-Field or currenfytt p U
ForwardVoltagc(or E-Field or current)at p tz
,
Note that r is a function of axial distance z along the waveguide since the electric field
strength varies in this direction for all modes considered. In the case of a full reflection,
129
the reflection coefficient T will take on a value of one and in the case of no reflections,
T will be zero. If the waveguide has an impedance of Z0>Rand is terminated by a coaxial
waveguide acting as a load with impedance ZoiCotx, the reflection coefficient can be
expressed as83:
r = Zo^ .~ .Z░*
W
(6.11)
V
and T is taken at the interface between waveguide and the coaxial guide.
Reflected power levels can be calculated using Equation (6 .10) and the fact that
electromagnetic power is proportional to the square of the electric field strength:
P? -- P? | I f
where
(6.12)
is the incident power level.
Thus, in order to avoid reflective losses due to mismatch of waveguide
components, the impedances of the rectangular and coaxial guide, Z0>Rand ZotCotK will
have to be equal for T to be zero. This can be achieved by decreasing the waveguide
impedance by lowering its height b according to Equation (6.7). Practically this is
accomplished by inserting a plate parallel to the broad side of the waveguide at about half
the waveguide height, b, = b/2 (Figure 6.5). The lower half will therefore constitute a
guide of smaller height in connection with the now matching coax probe. This plate also
serves as a mechanical device to fix the center conductor of the coaxial line. The
rectangular waveguide is terminated about \ / 4 away from the coax insertion by a
shorting plate so as to allow for constructive interference with the reflections coming off
the short. Of course, now there exists a mismatch between the waveguide of the original
height b and the two guides of reduced height, b, and b-b, which can be interpreted as
switched in shunt ( parallel) with each other and in series with the original waveguide.
130
Electric
Field
Lines
L
\
rr
Rectangular
Waveguide
( shorted)
To
Microwave
Source
Coaxial
Waveguide
To
Applicator
V
Figure 6.5 Coaxial-to-Rectangular Waveguide Transition
131
In order to reduce reflections off the interface between these "three" rectangular
waveguides, a metallic screw is inserted into the broad wall of the waveguide just before
the split plate. Adjusting the length of the screw penetrating into the guide allows
impedance matching at the interface between these guides.
The physical principle behind this method is quite similar to the insertion of the
split plate since the screw locally reduces the waveguide height and thus decreases its
impedance. The proper screw position is found experimentally. Investigating this probe
transition therefore shows that not only the applicator itself and its power coupling
capabilities are of importance but the entire microwave circuit and its components as
well. Power losses associated with reflections of improperly designed transitions and
bends for example will severely limit the overall performance of the thruster despite all
efforts for increasing the power coupling into the plasma and from the plasma into the
surrounding propellant gas.
6.3. Experimental System
6.3.1. Waveguide Circuitry
The waveguide circuitry for the circular waveguide experiment is shown in Figure
6 .6 .
The circular applicator itself has been described in detail in the previous section. In
order to reuse waveguide components that were employed during the rectangular
waveguide experiments, a rectangular WR430-to-WR284 waveguide transition (Gerling
GL318) was flanged to one end of the rectangular waveguide part of the circular
applicator, allowing the installation of the WR284-based wave coupler and dummy load.
132
Flexible Waveguide
Coax
Transition
^ Coaxial
Waveguide
Quartz
Tube
Bluff
Body
A
Power
Meter C 7 \
<P|.PR>
Dummy
Load
^ Circular
Waveguide
Applicator
Three-Port
Circulator
7 v
Plasma
n
Sliding
Short
\
Dummy Power
Load Meter
( P T>
Microwave
Power
Source
Orifice Plate
Figure 6.6 Waveguide-Circuitry for the Circular Applicator
133
As mentioned, the sliding short at the other end of the rectangular waveguide part
was a WR430-based, Gerling GL413 model. In order to allow the coaxial coupling probe
to move, the coaxial guide together with the rectangular-to-coaxial transition was flanged
to a flexible waveguide which connected the applicator to the rest of the circuit,
consisting of the power source, power meters for the forward and reflected power levels
and the three-port circulator as described in Chapter S.
Figure 6.7 shows a photograph of the integrated experimental set-up. The circular
applicator that has already been described in Figure 6.3 can be seen in the center of the
picture. On top of the applicator, the mechanism to translate the coaxial probe can be
recognized, connected to the flexible waveguide section. The vertical waveguide sections
at the right end of the picture lead to the microwave power source located on the
laboratory floor. The flexible metal hoses that are attached to the gas inlets of the quartz
tube lead to the gas flow system that is installed in the foreground. The gas flow system
will be described in the following section. The three power meters measuring forward,
reflected and transmitted power can also be regognized located in front of the applicator.
Instruments visible to the left are spectrometer, photometer and current source required
for optical diagnostic investigations performed on the plasma to be described in Chapter
7. The entire set-up is located on an optical bench, allowing for easy mounting of optical
diagnostic equipment as well as the applicator and its gas flow system.
6.3.2. Gas Supply System
The gas supply system differs from the one used during the rectangular
experiments in that a nozzle was used during the circular waveguide tests, allowing
Figure 6.7 Experimental Set-up of the Circular Waveguide Experiment
135
expansion of the test gas to the atmosphere. As shown in Figure
6 .8 ,
the test gas
(helium was used exclusively during these experiments due to its easy and safe handling
capabilities in the laboratory environment) is released from the pressurized storage tank,
passing valve VI installed for safety precautions and then entering the precision valve
that controls the flow. After passing through the Omega FL-223 mass flow meter
described in Chapter 5, the flow is split up and enters the two gas inlets to the quartz
tube. The two particularly shaped gas inlets were necessary due to the overall geometry
of the circular waveguide configuration, requiring the coaxial probe inlet to be aligned
with the guide axis so that the inlets had to be moved to the sides. Transition from the
1/4 inch Swagelok piping to the quartz tube was again provided by stainless steel metal
adapters that were bonded to the tube by means of epoxy. Just prior to the gas tube
inlets, two pressure gauges were installed, allowing the measurement of the gas inlet
pressure in both gas inlets simultaneously. This configuration allowed the detection of
any flow non-symmetries, however none occurred.
The quartz tube itself consists of a fairly heavy main body of 80 mm inner
diameter at 5 mm wall thickness. The quartz tube dome, i.e. the top end of the tube,
features three inlets: the two angled gas inlets shown in Figure 6 .8 consist each of a 17
mm i.d. tube of 50 mm length, having a wall thickness of 2.5 mm and fused to the dome
at a 5░ angle. The straight part of those inlets are made from a 5 mm i.d. tube of 80 mm
length and 1.5 mm wall thickness. A third inlet is provided for the bluff body installation
and consists of a 200 mm, 9 mm i.d. tube having a wall thickness of 1.4 mm (not shown
in Figure
6 .8
but visible in Figure 6.2).
Towards the lower end the quartz tube main body goes over into a 45░ conical
section in order to channel the propellant flow towards the nozzle inlet. Overall length
of the main body including dome and conical section is 170 mm, with the cone having
136
Mass Flow
Meter
Precision
Valve
0
?
Valve V1
I? 0
Pressure r
Gauge
.^
/
Adapter:
Pressure
Gauge
Pressurized
Tank
Quartz Tube
Bluff
Body
Orifice Plate
Conically Converging
Nozzle
Figure 6.8 Schematic of the Gas Supply System for the Circular
Waveguide Applicator
137
a height of 20 mm. Attached to the cone section is a 40 mm i.d., 20 mm long tube
section of 2.8 mm wall thickness which also carries the tube flange, consisting of a 5 mm
thick, 75 mm diameter quartz plate having a central opening of 40 mm. This wide of an
opening was necessary in order to allow for the bluff body to be inserted and assembled
inside the quartz tube. All quartz tubing was standard size material provided by Quartz
Scientific.
A 1/4 inch thick, 75 mm HBC-grade boron nitride orifice plate is bonded to the
quartz flange by means of a silicon based, high-temperature RTV sealant. Soaking this
joint in gasoline-based products would dissolve this sealant and thus allow for opening
and closing of the tube. A 45░ conical opening was manufactured into the center of the
plate, having a throat diameter of 1 mm. This simple converging nozzle will allow
helium gas flow to choke at 2.08 atm gas inlet pressure, assuming standard pressure
conditions in the laboratory environment.
6.3.3. Bluff Body Configurations
The bluff body configurations used in the experiments are shown in Figure 6.9.
As in the rectangular waveguide experiment, the purpose of the bluff body is to provide
for plasma stabilization. Because of the possibility of plasma contact, high-temperature
resistant HBC-grade boron nitride was used as the bluff body material. T he peculiar
design of the body is a consequence of the overall thruster geometry, requiring a centered
coaxial probe inlet, so that all other inlets had to be moved to the sides. The long 200
mm rod is inserted through the straight, 9 mm i.d. quartz tube inlet as indicated on
Figure 6.2 and the horizontal rod as well as the cone are placed inside the tube through
138
\
Material: HBC-Grade Boron Nitride
All Units in mm
Vertical Rod
it
Horizontal Rod
Small" Bluff Body Cone
20
15
CM
I
i t
*
"Large" Bluff Body Cone
35
Figure 6.9
to
Bluff Body Designs (Material: HBC-Grade Boron Nitride)
in
CM
139
its large, 40 mm diameter exit flange. Assembly of the bluff body configuration had to
be performed inside the quartz tube itself. Due to the brittleness of the boron nitride
material and the complexity of the bluff body design, this process was extraordinarily
difficult to perform.
Several different cone shapes have been used throughout the experiments and are
shown in Figure 6.9. The standard cone was a 20 mm base diameter cone of 25 mm
height. Comparative measurements were made with a 35 mm base diameter cone of the
same height. A 35 mm base diameter cone of 50 mm height (not shown in Figure 6.9)
was used during the initial experiments. However, due to the greater height of this cone,
its weight was larger and placed greater moments on the rod support structure of the
configuration which eventually led to breakage in connection with excessive thermal
stresses in the structure. The large height of this particular cone and the fact that the
plasma was located in a maximum field region in the center part of the circular guide,
also caused the bluff body to be in touch with the plasma since the bluff body
configuration could not be moved any further upstream due to restrictions imposed by
the quartz tube dome (compare with Figure 6.2). Thus apart from some initial
experiments and electric field measurements (see Figure 6.16 of Section 6.5.1), this cone
was not used for any of the other measurements to be documentated later.
Of practical interest is also the bluff body support adapter. This adapter,
manufactured from stainless steel, seals off the bluff body inlet while at the same time
supporting the whole bluff body configuration in place. Arriving at a design that allows
for a movable bluff body yet tightly seals the test gas in the quartz container even at
pressures several times the atmospheric pressure is not a trivial task. Because of the very
simple construction, yet excellent performance of this adapter, it will be briefly
introduced here. The design drawing of the adapter is shown in Figure 6 .10. The adapter
MATERIAL
STAINLESS STEEL
( all DIMENSIONS IN <naj
CLEARANCE
T
threaoed blnoholes
TAP 4-40
27.5
.
440
ft
m
25.
35-
10X10 THREAD OflING
10. IQ82 nvn
w id th 1.78 mm
Q
15
17.
s
i
V1
OWING
GROOVE*
10. 2.9 mm
width 178 mm
00* 14J9 mm
depth 127 m m
w idth 2.11 m m
-
r
y
V .
55
V_/
^
c 17.i
7
Figure 6.10 Bluff Body Support Adapter
iH
T
o Q_o
141
consists of three pieces. The actual adapter bonded to the quartz tube is shown on the
left. It allows the vertical boron nitride rod of the bluff body to be inserted into the tube.
A 1/8 inch stainless steel rod which is connected to the boron nitride rod by inserting it
into an axial boring manufactured into the rod and bonding both together by hightemperature RTV sealant, is able to penetrate the center piece of the adapter, which is
being screwed onto the part connected to the tube. A standard O-ring provides sealing
of these two parts. The top part of the adapter is bolted to the center piece and in so
doing, the O-ring placed between these two pieces is squeezed and presses against the
stainless steel rod, not only providing sealing but also keeping the rod from moving and
turning. Loosening the screws, however, will allow for readjustment of a new bluff body
position.
6.3.4. Plasma Ignition
Ignition of the plasma was obtained by inserting a tungsten wire into a maximum
field region. Heating the tungsten wire will cause electrons to be emitted. The electrons
will then immediately be accelerated in the surrounding fields causing breakdown and
thus creating a plasma sustained by the microwave fields alone. In this experiment, the
wire was inserted through the nozzle opening and removed after ignition.
As was mentioned in Section 6.2, the circular waveguide applicator featured a
particular port through which a laser beam could have been focused into the guide to
allow for ignition of a plasma (see Figure 6.3). However, the laser system available was
not ready for use and no laser ignition was attempted during these experiments.
In addition, ignition by microwave breakdown, as routinely established in resonant
142
cavities, was attempted. However, breakdown only occurred in one of the two gas inlets.
Upon inspection, it was found that the particular inlet in which ignition was observed ran
slightly closer to the waveguide wall than the other inlet due to a slight non-symmetry
of the quartz tube. It was therefore suspected that one of the field maxima present along
the wall in the TM01 mode at this location caused the breakdown. Field distortions due
to the non-symmetrical bluff body might have rendered the field maximum in the center
of the tube weaker than the field maximum at the wall, thus leading to preferred
breakdown in the inlet. Therefore, ignition due to microwave breakdown was abandoned
for this particular experiment, although this option remains open for future, redesigned
waveguide applicators of this type.
6.4. Experimental Procedure
In order to ignite the circular waveguide applicator, valve VI (see Figure 6 .8 )
was opened and a low pressure just above atmospheric adjusted in the quartz tube via the
precision valve. The tungsten wire was inserted into the guide with the microwave
generator still shut off for safety reasons. After the wire was properly aligned along the
waveguide center, the microwave power was turned on and increased up to roughly
1000
W where breakdown occurred.
Once a plasma was established, the tungsten wire was removed and pressure and
power levels were adjusted to the desired operating conditions. Since no downstream
valve was present in this waveguide configuration as was for the rectangular waveguide
experiment, adjusting a particular pressure level determined the mass flow rate
automatically as well.
143
Coupling efficiencies were determined by measuring forward, reflected and
transmitted power, respectively and pressure and mass flow rate could be directly read
off the instruments. Determination of accurate mass flow rates, however, was extremely
difficult due to the crude scaling of the instrument (Omega FL223) and the extensive
calibration process required for each data point. Depending on the magnitude of the mass
flow rates measured, errors introduced by this method of flow metering were estimated
to range between 4 and 5%.
Using the measured experimental data for power, pressure and mass flow rate,
nozzle inlet temperatures, specific impulses, thruster efficiencies, thrust and specific
power could be calculated based on the assumption of an ideal, quasi-one dimensional
nozzle expansion. Due to the latter assumption this method can certainly not be
considered as very accurate. However, in the here considered case, where a converging
nozzle is used, the flow is accelerated to sonic speeds only, so that viscous losses during
the fairly low-speed subsonic flow in the converging section should stay fairly small,
limiting errors associated with these type of losses.
The necessary condition to choke the nozzle flow can be determined by the
pressure ratio between chamber stagnation pressure po and ambient pressure p.92:
(6.13)
The ambient pressure pa is assumed to be 1 atm and the specific heat ratio for helium is
1.67154, constant over a temperature range up to 10,000k93. Thus, a stagnation pressure
of 208 kPa is required to choke a helium flow. The mass flow rate through a nozzle of
throat area A under choked conditions is92
144
(6.14)
Here, To, is the stagnation temperature at the nozzle inlet. Using Equation (6.14) and the
experimental data obtained for ih and po, To, can thus be calculated. Assuming an ideal
expansion to vacuum one finds
(6.15)
g
Using the input power P and the cold gas inlet temperature Toe* one obtains for the
overall efficiency of the system
(6.16)
Note, that the thruster efficiency of an electrothermal rocket engine is usually defined as
(6.17)
where ue is the exit velocity and uc the chamber inlet velocity. Even apart from the gas
flow term in the denominator, which can usually be neglected next to the electric power
term, expressions (6.16) and (6.17) are not necessarily equivalent. The reason is that
expansion through a nozzle is never ideal, in particular for the low-Reynolds numbers
considered here, i.e. the
1/2
ihue2 term usually does not equal the ihCpTo, term due to
thermal and friction losses in the nozzle and a finite exit temperature of the exhaust.
However, since ideal nozzle expansion was assumed in this particular case of a simple,
subsonic converging nozzle, insertion of Equation (6.15) into (6.17) will yield an
expression of the form of Equation (6.16) apart from the cold flow term in the
denominator that is negligible compared to the input power term P. Thus, the efficiency
calculated by means of Equation (6.16) can be considered as the thruster efficiency of
the system under the idealized assumptions involved and the expressions "overall" and
"thruster efficiency" are therefore being used synonymously throughout the remainder
of this chapter.
The thrust force can finally be calculated as
T = thglp
(6.18)
and the specific power is determined as the ratio of the absorbed power to the mass flow
rate, i.e.
(6.19)
where
(6.20)
and Pf, Pr and PT are the measured forward, reflected and transmitted powers,
respectively.
146
6.5. Experimental Results
6.5.1. Electric Field Distribution
One of the first sets of experiments conducted with the circular applicator tried
to determine the electric field distribution in the applicator. Controlling the plasma
position more effectively than in the rectangular guide by means of the electromagnetic
field pattern was, after all, the motivation behind the design of the circular applicator.
As mentioned, however, one of the most surprising observations made during the
operation of the circular waveguide was the fact that the plasma was not located in the
transition region between the rectangular and the circular waveguide part as expected but
much higher upstream in the center of the circular guide. The field configuration
therefore seemed to be very different from the one that had been anticipated (compare
with Figure 6.4). The reason for this behavior was believed to be due to field distortions
in the guide due to the presence of dielectric materials and waveguide transitions.
Therefore, electric field measurements were undertaken.
These measurements could only be performed along the waveguide walls, where
the hole pattern manufactured into the guide for viewing purposes allowed for the
insertion of a coupling probe to measure the fields. To this end, a coaxial antenna with
variable attenuation was placed into the holes. The signal from the antenna was then fed
into one of the analog power meters to determine the microwave power level picked up
by the antenna. Special care was taken that the antenna was inserted always at the same
distance into the guide, roughly 2 mm (see Figure 6.11). If the E-field lines impinge
perpendicularly on the wall, a maximum power output will be read since the center
conductor of the antenna is aligned with the electric fields. According to the nature of
147
Waveguide Wall
Insulator
Electric
Field
Coaxial Probe
Outer Conductor
Inner Conductor
Figure 6.11 Measurement of the Electric Field Distribution
by means of a Coaxial Antenna
148
the TMqj mode that was assumed to be present in the guide, this location will correspond
to a minimum field region along the axis. On the other hand, a minimum reading at the
wall will correspond to a maximum field region at the guide center. Therefore, while the
E-field measurements along the walls represent true measurements, the determination of
the entire field pattern, although based on the E-field measurements along the walls,
involved a crucial assumption regarding the field mode present in the guide.
Results from these measurements are shown in Figures 6.12 through 6.16.
According to the measurement technique, not the electric field strengths themselves but
their power equivalents proportional to the square of the electric field strength were being
measured. Measurements along the wall for the empty waveguide, i.e. the waveguide
applicator without the quartz tube, bluff body and the orifice plate, are shown in Figure
6.12. Notice that according to these measurements a quarter wavelength corresponds to
about 10 cm, resulting in a guide wavelength of 40 cm according to the design
specifications. However, the distance from the coax probe tip to the first field maximum
at the center axis of the guide is much less than a quarter wavelength, only on the order
of 2 cm. This deviation from the ideal TMq, mode behavior shown in Figure 6.4 had not
been taken into account in the design, since no information regarding this point was
available at that time. As a result, the field maximum at the center was found 14.5 cm
below the top flange, falling almost 9 cm short of the transition region between circular
and rectangular guide, where plasma positioning was desired.
Note also the high peak in the antenna signal at the transition, followed by a sharp
drop-off, a behavior that had also not been expected. The reason for this sharp E-field
maximum at the wall can be explained with the help of Figure 6.13: the edge between
the circular and rectangular part will locally increase the electric field strength, while in
the rectangular waveguide comer following the edge, the electric field strength will fall
149
E -Field Measurem ents ( Empty Waveguide )
C ircu lar W aveguide A pplicator
16
14
12
% 10
r
b
6
4
2
0
Axial D ista n c e ( c m )
Coax P robe Tip
^
Transition (c irc u la r-re c ta n g u la r)
Nozzle P osition
Figure 6.12 Electric Field Measurements (Power Equivalents) at the Wall of the
Empty Circular Waveguide Applicator
150
Coaxial Port
E-Field
Lines
/ / V \
f r
\
' 1! j
M
/
* Circular
Waveguide
,1
'll*
Mi l
h h
HI,
l'l|
ill;I'
ii
I*
l?
.? l
i ╗ it
M U
\ V
O n ,0 \ \ I /
I
I' |' I I'
II W
11/
Rectangular
Waveguide
? <*
Figure 6.13
Field Distribution in the Empty Circular Waveguide Applicator
(Drawn to Scale)
151
E -F ield Measurem ents (" F r o n t" -S id e )
C ircular Waveguide A pplicator, Q uartz Tube, O rifice P la te and Bluff Body
270
15
16
17
18
240
210
cm
cm
cm
cm
Bluff
Bluff
Bluff
Bluff
Body Position
Body Position
Body Position
Body Position
180
E 150
г
120
90
Axial Distance ( c m )
Coax Probe Tip
Transition (c irc u la r-re c ta n g u la r)
Nozzle P osition
Figure 6.14 Electric Field Measurements (Power Equivalents) at the Front Wall of
the Filled Circular Waveguide Applicator
152
E -F ie ld Measurements (" B a c k " -S id e )
C ircular W aveguide A pplicator, Q uartz Tube, O rifice P late an d Bluff Body
50
45
40
A
?
35
1
15
16
17
18
cm
cm
cm
cm
Bluff Body Position
Bluff Body Position
Bluff Body Position
Bluff Body Position
30
t- 2 5
4)
з20
a.
15
10
5
0
2^ 4
I
10
12 1 4
16 1 8
20
22
26
28'
Axial Distance ( c m )
C oax P robe Tip
Transition (c irc u la r-re c ta n g u la r)
N ozzle P osition
Figure 6.15 Electric Field Measurements (Power Equivalents) at the Back Wall of
the Filled Circular Waveguide Applicator
153
Coaxial
E-Field
Circular
Waveguide
Bluff Body
"Front"
Side
"Back"
Side
Quartz
Tube
Rectangular
Waveguide
?xy&wl'i'lAvi't
Orifice Plate
(Boron Nitride)
Figure 6.16 Field Distribution in the Filled Circular Waveguide Applicator
(17 cm Bluff Body Position, Drawn to Scale)
154
off to zero in order to fulfill the boundary conditions that all tangential electric field
components vanish at conducting walls.
Inserting dielectric materials into the waveguide was further observed to disturb
the field patterns. Figures 6.14 and 6.15 show the E-field measurements taken at the
front and back side of the guide when it was filled with the quartz tube, the bluff body
and the nozzle orifice plate. "Front"-side measurements were taken at that side of the
guide where the bluff body was inserted (compare with Figure 6.2 and Figure 6.16).
"Back"-side measurements refer to the data points taken at the opposite waveguide wall.
Both sets of data were taken, since due to the particular bluff body configuration used,
non-symmetries have been introduced to the applicator. The bluff body position was
varied during these measurements and the body was moved axially from a position where
its cone base was located 15 cm below the top flange to a position where it was 18 cm
below the flange.
An obvious impact of the insertion of dielectric materials into the guide is the
further reduction in guide wavelength that can be observed. The first field maximum on
the center axis of the waveguide, corresponding to a minimum along the wall shown in
Figure 6.14, was found only 8 cm below the top flange, compared to 14.5 cm for the
empty guide. A second maximum on the center line was found 16 cm below the flange
when measured at the front side, yet 20 cm below the flange when measured at the back
side. This difference obviously indicates non-symmetries in the field pattern which seem
to have been induced by the non-symmetrical bluff body: at the front side of the guide,
where the long 200 mm boron nitride rod and the horizontal rod are located, wavelengths
are even more reduced due to this additional dielectric material place inside the guide.
However, axial bluff body position did not have an impact on guide wavelengths. The
interdependence between field patterns and dielectric materials present in the guide is
155
sketched in Figure 6.16, based on the E-field data taken along the walls.
Reductions in guide wavelength had been anticipated, however not to this extent.
Previous measurements94 had indicated guide wavelength reductions of only fractions of
a centimeter. The reason for this behavior may be found by investigating Equation (4.43)
closer. This equation can be rewritten as
where \ 0 represents the guide wavelength in an empty waveguide. As can be seen from
Equation (6.21), the guide wavelength is proportional to the product of the guide
wavelength of the empty guide and a factor containing the dielectric constant and
permeability of the dielectric materials inserted into the guide. Thus, the larger the guide
wavelength for the empty waveguide, the larger are the absolute changes in guide
wavelength induced by insertion of the dielectric material. In the case of the here
considered circular applicator the guide wavelength was 42 cm vs. a free space
wavelength of only 12 cm, pronouncing the effect of guide wavelength shortening.
Another difference noted between the front and backside field measurements is
the fact that signals taken at the front side are much larger than those taken at the back
side. The reason for this behavior is not well understood. A possible explanation might
be that imperfect insulators such as the boron nitride material which the bluff body is
made of, scatters microwave radiation, resulting in higher measured power levels at the
front side of the guide, where a larger portion of the body configuration is located.
Finally, another unexpected phenomenon observed during the operation of the
circular waveguide applicator might be explained by the mentioned field distortions.
Adjusting the coax probe and the sliding short of the empty waveguide applicator allowed
tuning the system such that all the incident microwave power was being absorbed by the
dummy load terminating the circuit and none was reflected. This behavior is expected
for a properly designed waveguide. However, upon insertion of the quartz tube and the
bluff body configuration, it was noted that all the incident power was reflected and
virtually none transmitted through the applicator to be absorbed by the dummy load
although the tuning of the system had not been changed. Even readjusting the tuning
would not change this effect. It therefore seems possible that the distortion of the
microwave fields caused by the dielectric materials does not permit a TEt0 mode to be
set up in the rectangular waveguide section.
This effect was investigated a little further by placing a large cylindrical slab of
boron nitride material into the empty waveguide. The boron nitride piece was roughly
5 cm in diameter and 5 cm in height. When the empty applicator was tuned such that all
the incident microwave power was transmitted, placing the boron nitride piece in the
transition region between circular and rectangular guide resulted in full power reflection.
Pushing the piece into the rectangular portion of the guide away from the transition
region gradually reduced the reflected power levels in favor of higher transmitted power
levels until all the incident power was transmitted again. Since the guide wavelength in
the rectangular portion of the applicator is significantly shorter than in the circular part
(14.8 cm vs. 42 cm), according to the comments made in connection with Equation
(6.21), field distortions induced by insertion of a dielectric material in the rectangular
part should be smaller then when the material would be inserted in the circular part.
157
6.5.2. General Plasma Behavior
The plasma behavior in the waveguide was determined to a significant extent by
the electromagnetic field configuration in the guide discussed previously. The plasma was
ignited by means of a tungsten wire that was inserted into the guide through the nozzle
orifice. Upon ignition, the plasma detached from the wire and moved into a location at
the center of the circular waveguide section as indicated in Figure 6.2 and shown in
Figure 6.3 and 6.7. This was unexpected, since plasma location was anticipated in the
transition region between the rectangular and circular guides. This behavior could be
explained by the distorted field pattern discussed in the previous section.
The plasma took on an ellipsoidic shape with a white glowing, ellipsoidic core,
surrounded by a cooler, bluish gas layer and was symmetric. This "finestructure? of the
plasma, however, is not being revealed on the photographies taken of the experiment (see
Figure 6.2 and Figure 6.7). Several attempts to move the plasma out of its position in
the center portion of the circular guide in order to locate it further downstream failed.
Moving the coax probe deeper into the guide had no effect on the plasma location
although reflective losses increased due to detuning the guide. When the bluff body was
lowered in order to attempt to push the plasma downward, the plasma essentially
remained in place initially. Once the body came into touch with the plasma and was
lowered further, the plasma shape appeared distorted and "compressed" in its axial
direction. The lower plasma boundary had moved downward slightly, however not to the
same extent as the bluff body had been lowered and thus the upper boundary had moved
into the same direction. Severe heating of the bluff body resulted from this procedure,
causing the bluff body to glow red even at power levels as low as 1000 W. Therefore,
all attempts to move the plasma out of its position in the center of the circular portion
158
of the applicator downstream toward the nozzle inlet had to be abandoned.
Consultation with Gerling Laboratories91 led to the suggestion of decreasing the
entire height of the circular guide rather than just inserting the coax probe deeper.
Merely moving the probe will have no effect on that part of the fields that are reflected
off the top flange. Thus, by reducing the entire guide length, it might be possible to
move the field maximum further downward towards the nozzle. Due to financial
constraints, however, these design changes could not be effected.
It was further observed that with the bluff body in its uppermost position just
below the quartz tube dome, i.e. the upper end of the quartz tube, and well separated
from the plasma, stability boundaries were encountered as with the rectangular guide
applicator. If for a given mass flow rate the microwave power was raised above a certain
level, plasma propagation velocities became high enough for the plasma to move
upstream until it touched the bluff body. Once in touch with the bluff body, plasma shape
changed significantly, taking on a filamentary, column shape, denser and hotter in
appearance due to a contraction in radial direction as well. At the same time, an
extension of the plasma in axial direction was noted. The plasma extended now from the
bluff body all the way down to its original position in the maximum field region. The
latter point seems to indicate that both gasdynamic and electrodynamic forces are acting
on the plasma. While gasdynamic forces tend to pull the plasma into the recirculation
region behind the body, electrodynamic forces try to maintain the plasma in the
maximum field region. Both effects result in the stretching of the plasma and give it its
long, filamentary shape. More quantitative results on both stability boundaries as well
as size and shape of the plasma will be given in Sections 6.5.3 and 6.5.4, respectively.
In the case that no bluff body was present in the waveguide or a gap existed
between the bluff body tip and the quartz tube dome, rather than moving upstream in a
159
continuous fashion, the plasma either "jumped" toward the quartz tube dome or a second
plasma formed at the dome surface. As was shown in Figure 6.16, a second field
maximum lies right above the quartz tube dome and could have caused the ignition of the
second plasma (see Figure 6.17). Furthermore, when the bluff body was present, yet a
small gap remained between the cone tip of the body and the dome, arcing was observed
at this location. Although not directly visible, a rapid cracking sound was heard and upon
inspection of the tube, "bum-marks" were visible at the inside of the dome at that
particular location. This indicates that boron nitride does not act as a perfect insulator,
a fact that later was confirmed during the E-field measurements. Arcing of the cone tip
in conjunction with the maximum field region at this location could have been responsible
for plasma ignition in this region.
A lower stability boundary was found for the circular waveguide applicator as
well, however, it was fundamentally different from the one observed for the rectangular
guide. Unlike in the straight, rectangular waveguide experiments, where "blow-off"
occurred towards lower power levels, here the plasma extinguished if the microwave
power was too low. "Blow-off, on the other hand, was never observed. This indicates
that "microwave field" stabilization as discussed in Chapter 5 is obviously very strong
in the case of the circular applicator using the TMq, mode. Reasons for stronger
maximum field regions in the circular applicator than in the rectangular guide may be
found in the fact that reflections in the circular applicator, in particular off the bottom
plate, are much more pronounced than in the rectangular guide, thus leading to stronger
standing wave patterns, having higher SWR ratios and therefore more intense maximum
field regions.
160
Circular Waveguide
Applicator
Quartz Tube Dome
Plasma
Figure 6.17 Plasma Formation in the Circular Waveguide Applicator
at Quartz Tube Dome (Drawn to Scale).
161
6.5.3. Plasma Size and Location
Plasma size and location were determined for various operating conditions.
Measurements were taken with a simple ruler that was hand held along the waveguide
wall and are thus only accurate to 1 or 2 mm. This error induced by the measurements
seems not critical, since another error of at least the same order of magnitude was
introduced by the difficulty to clearly define a plasma boundary. As was mentioned in
the previous section, the plasma consisted of a hot, white glowing core of ellipsoidal
shape surrounded by an ellipsoidal blueish gas layer. This blueish gas layer was very
diffuse, gradually getting dimmer toward the edges of the plasma so that it was difficult
to determine a defined plasma edge. On the other hand, the white core of the plasma
showed a much more marked edge which could be measured easier. Measurements were
reproducable within the above mentioned margin of error. Plasma diameter and plasma
length therefore refer to the corresponding dimensions of the white plasma core and the
distance between bluff body and the plasma, which was another quantity measured,
corresponds to the distance between the body and the white plasma core, accordingly.
The measurements of these plasma dimensions are therefore somewhat arbritrary and no
emphasis should be placed on the absolute values of these data, rather, their relative
changes should be considered as operating conditions are changed.
Figures 6.18 and 6.19 show plasma diameter, length and plasma-bluff body
spacing as defined above for two different pressure conditions, 1.8 and 2.6 atm. As can
be seen on these figures, the plasma diameter increases slightly with input power as does
the length of the plasma. Higher power levels therefore increase plasma size. The plasma
diameter, however, levels off and it seems that the bluff body, having a base diameter
of 20 mm, restricts the plasma from growing any larger in the radial direction.
162
Plasm a Size and Location
C ircular Waveguide A pplicator, Helium, 1 .8 a tm , 2 0 m m Bluff Body
0
?
&
V
?
?
0
D ia m e te r D
L e n g th L
S p a c in g S
L+S
D ia m e te r D, P la s m a in to u c h w ith B luff B ody
L e n g th L, P la s m a in to u c h w ith B luff B ody
______ ?______i______?______i______ _______ i______?______ i______ ?______ i______?______ i
600
700
800
900
1000
Input Pow er ( W )
1100
1200
Figure 6.18 Plasma Size and Location for a Helium Plasma at 1.8 atm
163
Plasma Size and Location
C ircular W aveguide A pplicator, Helium, 2 .6 a tm , 20 m m Bluff Body
D ia m e te r D
L e n g th L
S p a c in g S
L+S
D ia m e te r D, P la s m a in to u c h w ith B luff B ody
L e n g th L, P la s m a in to u c h w ith B luff B o dy
800
Input Pow er ( W )
Figure 6.19 Plasma Size and Location for a Helium Plasma at 2.6 atm
164
Spacing between the plasma and the bluff body decreases as the power is being
increased due to higher plasma velocities at higher power levels. As in the rectangular
guide, "flow stabilization" behind the bluff body might have played a role. The higherpower plasma experiencing higher plasma velocities therefore positions itself further
upstream, where flow velocities are higher due to the cross-sectional flow area
restrictions caused by the bluff body and are thus able to stabilize the plasma again
(compare with the discussions made in Chapter 5).
However, "flow stabilization" behind the bluff body seems not to be the only
possible explanation for the stabilizing mechanisms involved. As can be seen by plotting
the sum of plasma length and spacing between plasma and bluff body vs. input power,
this value remains fairly constant over the power range considered. This obviously means
that the lower plasma boundary remains in place in the maximum field region where the
plasma was originally located and the entire plasma merely "stretches" into the
recirculation zone behind the bluff body. Therefore, it can be assumed that "microwavefield stabilization" as discussed in Chapter S also plays a role in plasma stabilization. Due
to the higher electric field strengths in the maximum field region, electrons at this
location can pick up more energy from the microwave fields and thus cause higher
ionization rates. Thus, the plasma can be maintained longer in this region, although parts
of the plasma have already moved upstream.
An interesting variation of this effect was observed when the bluff body was
turned sideways out of its position along the center axis of the waveguide. The plasma
followed the bluff body away from the center axis to a certain extend, then jumped back
into the maximum field region located on the center axis, demonstrating again the impact
both gasdynamic as well as electrodynamic effects have on the plasma.
A slight pressure dependence was found regarding this effect as can be seen by
165
comparing Figures 6.18 and 6.19. For a gas pressure of 2.6 atm, the lower plasma
boundary did move upward towards the bluff body by about 1 cm. This effect was
reproducable. Thus, at higher gas pressures, gasdynamic forces induced by the bluff
body seem to become more important compared to electrodynamic mechanisms. On the
one hand, "suction" forces caused by the recirculation region behind the body increase,
while on the other hand electron collision frequencies increase as well towards higher
pressures. Thus, the electrons now cannot pick up sufficient amounts of microwave
energies between collisions to keep ionization rates at a level necessary to maintain a
plasma in the maximum field region.
Figures 6.20 through 6.22 demonstrate the pressure dependence of plasma
diameter and length as well as the plasma-bluff body spacing. Figure 6.20 indicates that
towards lower power levels, the plasma diameter decreases with increasing pressure
level. The reason is the same as given above: higher electron collision frequencies limit
the amount of energy the electrons can pick up between collisions and thus lower the
ionization rates. In particular in field regions off the guide axis, towards the boundaries
of the plasma, where field intensities are lower, this loss in electron energy can become
critical and portions of the plasma might extinguish in those regions so that the plasma
will appear smaller. Towards higher power levels, however, the plasma size is influenced
by the bluff body size which prevents plasma growth in radial directions beyond the bluff
body diameter, overcoming pressure effects.
Plasma lengths as well decrease with increasing pressure due to the reasons given
above. The increase in plasma length with respect to the power is not linear since as the
power is increased and parts of the plasma move closer to the bluff body, the plasma
does not only grow in size due to the larger power input but is also stretched due to
increased "suction" forces induced by the body.
166
Plasma Diam eter Variations
C ircular W aveguide Applicator. Helium, 2 0 mm Bluff Body
5 .0
4 .5
1 .4
1 .8
2 .2
2 .6
4 .0
a tm
a tm
a tm
a tm
3 .0
2 .5
2.0
0 .5
0.0
400
600
800
1000
1200
1400
1600
Input Pow er ( W)
Figure 6.20 Plasma Diameter vs. Power at various Pressure Levels for Helium
167
Plasm a Length Variations
C ircular W aveguide Applicator, Helium, 2 0 m m Bluff Body
8
7
E
o
_c
E3
(A
O
1.4 a tm
1 .8 o tm
2.2 a tm
2 .6 a tm
a- 2
0
400
600
800
1000
1200
1400
1600
Input Pow er ( W )
Figure 6.21 Plasma Length vs. Power at various Pressures for Helium
168
Variations in P la s m a -B lu ff Body Spacing
C ircular W aveguide A pplicator. Helium, 2 0 mm Bluff Body
5 .0
4 .5
1 .4
1 .8
2 .2
2 .6
a tm
a tm
a tm
a tm
2 .5
2.0
0 .5
0.0
400
600
800
1000
1200
1400
1600
Input P ow er ( W )
Figure 6.22 Plasma-Bluff Body Spacing vs. Power at various Pressures for Helium
169
For the same reason, the plasma-bluff body spacing shown in Figure 6.20 drops
off nonlinearly with respect to increases in microwave power. For a given power level,
the spacing is larger at higher pressure levels due to restrictions in plasma size and the
fact that plasma velocities are reduced so that the plasma experiences a decreased
tendency to move upstream.
6.5.4. Stability Boundaries
Figure 6.23 shows the upper and lower stability boundaries in the circular
waveguide applicator already discussed qualitatively in Section 6.5.2. As mentioned, the
upper stability boundary is given by that power level where the plasma moves in contact
with the bluff body due to an increase in plasma velocity. This operating condition is
undesirable, since it will lead to severe heating of the bluff body, possibly resulting in
erosion or even destruction of the latter. The lower stability boundary is given by that
power level where the plasma extinguishes. "Blow-off1was not observed for plasmas in
circular applicators. As can be seen on Figure 6.23, stability can be regarded as very
good since the lower power level corresponds to about 60% of the upper power level.
For a given operating point located somewhere between the upper and lower stability
boundaries in Figure 6.23, this will allow for substantial power and/or pressure
fluctuations without the plasma touching the bluff body or being extinguished.
170
Stability Boundaries
C ircular W aveguide A pplicator, H e -P ro p e lla n t
2000
1800
?
o
u p p e r stability bou n d ary
lower stability bou n d ary
1600
C -1 4 0 0
1200
2 1000
80 0
600
400
P re s s u re ( a tm )
Figure 6.23 Stability Boundaries for the Circular Waveguide Applicator using
Helium
171
6.5.5. Coupling Efficiencies
In this section investigations regarding the interaction between microwave field
and plasma will be discussed. Coupling efficiencies, being the ratio between absorbed
and total incident microwave power, are shown in Figures 6.24 and 6.25 and indicate
very high values in excess of 96%, considerably better than observed even for the
rectangular case and within the range of coupling efficiencies observed for resonant
cavities49,58'60. As can be noted in Figure 6.24, the coupling efficiencies go through the
same slight decrease towards the lower power levels as in the rectangular case. This
decrease may be explained by the fact that plasma conductivities and thus electron
densities decrease just prior to extinction of the plasma. Thus, the plasma is not able to
absorb as much power anymore.
On the other hand, the steady drop of coupling efficiencies, as it was observed
for rectangular waveguide plasmas towards higher power levels has not been observed
for circular waveguide plasmas. Explanation of the level of the coupling efficiencies
requires a look at Figure 6.26: unlike in the rectangular case, in the circular waveguide
absorbed power values continue to increase linearly with input power while reflected
power levels, known to increase for the rectangular case, stay fairly constant as do the
transmitted power levels. These differences between rectangular and circular case may
be explained by the respective guide dimensions in relation to plasma size.
In the circular case, it was observed that the plasma was able to grow in size as
the power level was increased. Since a larger plasma volume means that the plasma is
able to absorb more power, absorbed power levels keep increasing as increased input
power levels lead to increases in plasma size. On the other hand, in the rectangular case
discussed in Chapter 5, the plasma was confined to a 20 mm i.d. quartz tube, not
172
Coupling Efficiencies vs. Input Power
Circular W aveguide A pplicator, H e -P ro p e lla n t
100
90
^
80
~ 70
o'
|
60
0
?
vC 5 0
л.
LJ
^
40
1
30
░
20
o
?
?
k
0
O
3 .0
2 .6
2 .2
1 .6
1 .2
a tm
a tm
a tm
a tm
a tm
10
400
600
800
1000
1200
1400
Input P ow er ( W )
1600
1800
Figure 6.24 Coupling Efficiencies vs. Input Power for the
Circular Waveguide Applicator using Helium
2000
173
Coupling Efficiency vs. Pressure
C ircular W aveguide A pplicator, H e-P f.opellant
100
?
?
60
1.0
a
1.3
1.7
7 2 1 .1 6 W
9 3 7 .5 0 W
1 2 9 8 .0 8 W
2 .4
2.0
P re ssu re ( a t m )
Input P o w er
2.7
3.1
Figure 6.25 Coupling Efficiencies vs. Pressure for the
Circular Waveguide Applicator using Helium
3.4
174
Absorbed, Reflected and Transm itted Power
C ircu lar W aveguide A pplicator, H e -P ro p e lla n t
1800 r
1600
1400
k.
V
5 1200
o
CL
CO 1000
c
o
?
?
800
4)
600
CO
JO
400
tr
<
A
O
?
A
A bsorbed
R eflected
Power, 3 .0 a tm
T ra n sm itte d
A bsorbed
R eflected
Power, 2 .0 a tm
T ra n sm itted
200
700
900
1100
1300
1500
Input P ow er ( W )
1700
1900
Figure 6.26 Absorbed, Reflected and Transmitted Power Levels vs. Input Power
for the Circular Waveguide Applicator using Helium
175
allowing the plasma to expand significantly. Additionally provided microwave power
therefore could not be absorbed anymore, rather it was reflected by the plasma already
blocking a large portion of the waveguide section. Thus, in the rectangular case,
absorbed power values leveled off at the expense of increased reflected power levels.
As Figures 6.25 and 6.27 demonstrate, pressure dependencies of coupling
efficiencies and the various power levels measured are fairly insignificant over the
pressure ranges considered.
Measurements of coupling efficiencies are very accurate. In order to estimate
measurement errors, several sets of measurements were repeated for various power
levels. The deviations from the previously taken coupling efficiency data averaged at
about 0.5 percentage points, the lowest difference being 0.1 percentage points while the
highest deviation was 1.2 percentage points. These measurement errors can be considered
as "lumped" errors, not only taking into account reading errors off the instrument scale
but also the fact that in establishing the proper operating conditions for the microwave
applicator not always precisely the same input power level or operating pressure could
be adjusted.
The extreme accuracy of the coupling efficiency measurements were aided by the
versatility of the Hewlett-Packard HP432A power meter that allowed for a great variety
of different scale settings, enabling even very small power levels as encountered for the
reflected and transmitted powers to be measured with great accuracy. Further, it was
noted during earlier measurements not documentated in this thesis that the HP432A
power meter showed a zero drift that could have indeed led to much greater errors in the
coupling efficiency measurements. Once the cause for these errors had been determined,
great care was taken to continuously monitor and correct this zero shift, typically after
each set of data taken for a certain power level, every half hour or so.
176
Absorbed, Reflected and Transm itted Power
C ircu lar W aveguide A pplicator, H e -P ro p e lla n t
1400
.1200
fc 1000
i
800
c
0
?
o
г 600
A
4>
* 400
(0
< 200
1 .5
?
?
A
1.7
1.9
A bsorbed
R eflected
T ra n sm itte d
A bsorbed
R eflected
T ra n sm itted
Pow er, 1 3 7 0 .2 W Input Pow er
P ow er, 9 3 7 .5 0 W Input Pow er
H' . B i I , B i 0 J
2.1
2.3 2.5 2.7 2.9 3.1
I
L.
3.3
3.5
P re ssu re ( a t m )
Figure 6.27 Absorbed, Reflected and transmitted Power Levels vs. Pressure for
the Circular Waveguide Applicator using Helium
177
6.5.6. Nozzle Inlet Temperatures
No means were available to directly measure the nozzle inlet temperature during
the experiment, however ideal quasi-one dimensional flow calculations as discussed
before yielded at least some initial data in this regard. These calculations were based on
the measured mass flow rates through the choked, converging nozzle as described above.
As can be seen from Figure 6.28, mass flow rates drop slightly as the input power is
increased. This is due to the fact that more power is absorbed by the plasma as it grows
in size. The hot plasma surface area is therefore increased and more thermal energy can
be transferred to the propellant flow. Average propellant flow temperatures at the nozzle
inlet therefore increase and the propellant density decreases. As a result, the mass flow
rate is reduced. Note, however, that the changes in mass flow rates are only slight even
for large power changes. Combined with the already mentioned crude scaling of the
Omega FL223 rotameter-type flowmeter, determination of the mass flow rate was rather
inaccurate and estimated at least of the order of 4 to 5%. This error was transferred into
all the other rocket performance parameters via the calculations discussed before.
Figure 6.29 indicates a slight nozzle inlet temperature increase ranging from
roughly 950 K to about 1100 K if the input power level was increased from 800 to about
1750 W. For all pressure conditions considered, the temperature increase is rather small
compared to a much more pronounced increase in the absorbed power level also shown
in Figure 6.29 for comparison. The latter point demonstrates the large thermal losses the
current circular waveguide applicator is experiencing. A satisfactory explanation for the
heat losses within the applicator has not been found yet. It is possible that due to the
unfavorable plasma location roughly 14 cm above the nozzle entrance, a large portion
of the power absorbed by the propellant is given off again into the thruster structure
178
Mass Flow Rates vs. Input Power
C ircular W aveguide A pplicator, H e -P ro p e lla n t
130
120
>110
t/>
o>100
*
a '?
a
E
v?*
0
?
?
?
90
<D
O
O' 8 0
5
o
0
?
1 .2
1 .4
1 .6
1 .8
2 .0
2 .2
2 .4
2 .6
2 .8
3 .0
1600
1800
70
A
8 60
V
A
o
2
A
50
0?8 * 0 0 0
40
30
400
600
800
1000
1200
1400
Input P ow er ( W )
Figure 6.28 Mass Flow Rates vs. Input Power for the
Circular Waveguide Applicator using Helium
a tm
a tm
a tm
a tm
a tm
a tm
a tm
a tm
a tm
a tm
2000
179
Calculated Nozzle Inlet Tem perature and Absorbed Power
C ircular W aveguide A pplicator, H e -P ro p e lla n t
1800
1600
1400
1500
?
?
A
2.2 a tm
2 .4 a tm
3 .0 a tm
1400'
1300 г
1200
4>
'* 1000
O
Q.
"O
800
гV
>
1200 &
E
o
m 600
<
-
<v
1100*3
0)
c
1000 V
B
N
N
40 0
O
900
200
0
700
900
1100
1300
1500
Input P ow er ( W )
1700
z
? *800
1900
Figure 6.29 Calculated Nozzle Inlet Temperatures and Absorbed Power Levels
for the Circular Waveguide Applicator using Helium
180
by means of forced convection. Inspection indeed revealed a significant heating of both
the quartz tube and waveguide structure.
Another possible heat loss mechanism is radiation losses from the plasma.
Assuming the propellant gas is optically thin, radiation from the plasma would be able
to pass through the propellant flow without heating it and be absorbed by the thruster
walls. Although preliminary numerical calculations documented elsewhere6148 and
discussed in Chapter 2 seemed to indicate that radiative losses from a microwave-heated
plasma are negligible, no high confidence had been placed in those calculations and the
possibility of radiation heat losses remains open.
6.5.7. Overall Efficiencies
Increased thermal losses at higher input power levels are also demonstrated by the
behavior of the overall or thruster efficiencies shown in Figure 6.30. Overall efficiencies
have been calculated according to Equation (6.16), based on measurements of mass flow
rate and power and the calculated values for the average nozzle inlet temperature
discussed in the previous section. As can be noted, overall efficiencies of the applicator
configuration drop as the input power is increased and do not exceed 40% even for the
lower power levels.
Increasing pressure levels, on the other hand, have a favorable impact on overall
efficiencies. As shown in Figure 6.31, overall efficiencies increase with pressure as heat
conduction between the plasma and the surrounding propellant gas is enhanced as well.
However, these overall efficiency values are considerably lower than those
recently obtained for a cylindrical resonant cavity applicator49,93. With that particular
181
Calculated Overall Efficiency vs. Input Power
C ircular W aveguide Applicator, H e -P ro p e lla n t
100
90
2 .2
2 .4
2 .6
2 .8
3 .0
80
60
a tm
a tm
a tm
a tm
a tm
50
40
30
20
10
0
700
900
1100
1300
1500
Input Power ( W )
1700
Figure 6.30 Calculated Overall Efficiency vs. Power for the
Circular Waveguide Applicator using Helium
1900
182
Calculated Overall Efficiency vs. Pressure
C ircular W aveguide A pplicator, H e -P ro p e lla n t
50
45
40
30
25
20
?
a
*
15
10
1 298.08 W
1 370.20 W Input P ow er
1442.31 W
5
0
2.0
2.2
2.4
2.6
2.8
3.0
3 .2
P re ss u re ( a t m )
Figure 6.31 Calculated Overall Efficiency vs. Pressure for the
Circular Waveguide Applicator using Helium
3 .4
183
cavity applicator, overall efficiencies of up to 70% have been obtained, using the same
approach to determine the efficiency as in this study. In both cases, the plasmas
generated in these applicators appeared very similar with respect to size and shape and
spectroscopic measurements performed on these plasmas to be discussed in Chapter 7
revealed temperature values between 11,000 K and 12,000 K in both cases as well.
However, while in the case of the here considered circular waveguide applicator the
lower boundary of the plasma was located roughly 14 cm above the nozzle entrance, the
entire height of the cavity applicator was only on the order of 12 cm. The plasma was
located in the upper field node49,95 with its lower boundary even closer to the nozzle
entrance. Depending on operating conditions, this distance varied and in some cases it
was observed that the plasma was forming a "tail" that virtually extended all the way
through the cavity to the nozzle inlet. These observations seem to give evidence to the
fact that the larger separation between nozzle inlet and plasma in the circular applicator
might have been the cause for the lower overall efficiencies obtained for this device,
resulting in increased heat losses from the propellant flow to the thruster walls. This
assumption, however, requires further validation through experiments. In order to allow
for a more conclusive determination on the effect plasma-nozzle entrance separation has
on the performance of a potential microwave thruster, measurements of rocket
performance parameters should be conducted using the same applicator at identical
operating conditions, varying only the distance between the discharge and the nozzle
entrance.
184
6.5.8. Specific Impulse
Specific impulses obtained for the circular applicator were found to be
disappointingly low as well. The specific impulse values were calculated according to
Equation (6.15) and are shown in Figure 6.32. As can be seen, maximum specific
impulses ranged only up to 350 sec with the current thruster configuration, even
assuming ideal expansion into a vacuum through the converging nozzle. The increase in
specific impulse with power is only slight and the gas pressure was not found to have a
noticeable impact on the specific impulse.
Comparing the here obtained data for the specific impulse with those of the
resonant cavity applicator mentioned above49,93 once again revealed that the corresponding
values obtained for the cavity ranged significantly higher, up to 600 sec. Taking into
account very similar operating conditions and plasma properties both in the case of the
circular waveguide applicator and the resonant cavity leads as in the case of the thruster
efficiencies discussed above to the assumption that the larger physical separation between
plasma and nozzle entrance for the circular waveguide applicator could have caused this
performance decrease. Heat losses from the propellant flow to the walls seem to increase
as the flow path between the plasma heat source and the nozzle increases. As mentioned
earlier, this assumption requires additional experimental validation.
6.5.9. Thrust
Calculated thrust data are shown in Figure 6.33 and were determined using
Equation (6.18) and data obtained for mass flow rates and gas pressure. No power
185
Calculated Specific Impulse vs. Input Power
Circular Waveguide Applicator, H e -P ro p e lla n t
450
400
J2.300
2.2
2 .4
2.6
2.8
3.0
700
900
1100
1300
1500
Input Pow er ( W )
a tm
a tm
a tm
a tm
a tm
1700
Figure 6.32 Calculated Specific Impulse vs. Power for the
Circular Waveguide Applicator using Helium
1900
186
Calculated Thrust vs. Pressure
Circular W aveguide Applicator, H e -P ro p e lla n t
0.40
0.35
0.30
0.25
0.20
0.10
0.05
0.00
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
Pressure ( a t m )
Figure 6.33 Thrust vs. Pressure for the Circular Waveguide Applicator
using Helium
187
dependence at all was found for the thrust. This observation is in agreement with
investigations made regarding the thrust behavior for resonant cavities49?95. Obviously,
the very weak effects of decreasing mass flow rates and increasing specific impulses with
increasing power cancel each other. A fairly strong pressure dependence for the thrust
was found, however (Figure 6.33). Increasing the mass flow rate by increasing the
pressure, combined with the almost pressure-invariant behavior of the specific impulse
led to the increase in thrust with pressure. Thrust values between 0.275 and 0.39 N were
calculated, comparing favorably with corresponding thrust values obtained for the
cavity49*95.
6.5.10. Specific Power
Specific power values, being the ratio of absorbed microwave power to mass flow
rate through the thruster, obtained with the circular applicator are depicted in Figure
6.34. Values ranged between
8
and 16 MJ/kg which is fairly low compared to other
electrothermal propulsion systems49. This performance loss may once more be explained
by the poor plasma positioning too far from the nozzle entrance for the circular
waveguide applicator.
As input power is increased, the specific power increases as well since absorbed
power increases almost linearly with input power, while the mass flow rate drops
slightly. Increasing the pressure, on the other hand, lowers specific power values, since
absorbed power is little affected by pressure changes (see Figure 6.27) while mass flow
rates increase sharply with pressure (see Figure 6.28).
188
Specific Power vs. Input Power
Circular Waveguide Applicator, H e -P ro p e lla n t
16 r
14
JM 2
lio
I
o
0
?
?
?
8
CL
.2
л-
6
о
4A
A
k
'o
a
to
400
V
?
O
?
600
800
1000
1200
1400
Input Power ( W )
1600
1.2
1.4
1.6
1.8
2 .0
2.2
2.4
2.6
2.8
3.0
a tm
atm
a tm
a tm
a tm
atm
a tm
a tm
atm
a tm
1800
2000
Figure 6.34 Specific Power vs. Input Power for the Circular Applicator
using Helium
189
6.5.11. Variation of Other Thruster Parameters
During the course of the investigations of the circular applicator several additional
experiments of a more preliminary nature had been performed. These experiments
concentrated on the measurement of the effects that bluff body size, thermal transients
and plasma-bluff body interactions had on the operation of the circular applicator. Except
for the variation of bluff body size these experiments had not been planned. Rather,
several unusual effects with respect to the measurement of coupling efficiencies or other
thruster parameters were observed during certain operating conditions of the circular
applicator that had not previously been noticed during other microwave-heated plasma
experiments and it was then decided to investigate these effects further. Unfortunately,
time constraints did not permit an exhaustive study of these phenomena and very often
the interpretation of the few obtained data was only very preliminary or not even possible
at all. However, because these effects have never been documentated before, it was
decided to list those preliminary data in Appendices B through D for future reference and
to provide a basis for more detailed research in those areas.
190
Chapter 7
PLASMA SPJEC.TRQSCQPY
7.1. Introduction
Besides thrust, overall efficiency and specific impulse, the plasma temperature
itself is an important parameter to characterize the performance of a microwave thruster.
Although nozzle inlet temperatures might be significantly lower than plasma
temperatures, the latter do give information regarding the coupling of microwave energy
into the plasma and the effectiveness of the plasma in serving as a heating element for
the propellant flow. Since nozzle inlet temperatures and subsequently all other thruster
performance parameters are in part determined by the amount of heat that can be coupled
into the plasma, knowledge of the plasma temperature can therefore give an indication
of the performance potential of a microwave thruster.
Plasma spectroscopy, i.e. the interpretation of the radiation emitted by the plasma
due to its internal excitation, here caused by the microwave heating process, is a nonintrusive diagnostic tool which does not require the presence of probes exposed to the
plasma possibly changing its properties. Comparisons of these experimental data with the
predictions made by the quantum mechanical laws governing the radiative behavior of
the plasma will give information on electron temperatures, electron densities and heavy
particle temperatures. In order to determine these quantities accurately, possible
deviations from thermal equilibrium behavior within the plasma have to be known as well
as their impact on the spectroscopical method studied. In the following, a closer look will
be taken at possible equilibrium relations governing the plasma behavior, available
191
spectroscopic methods to study the plasma will be discussed and finally, the spectroscopic
set-up used throughout the experiments will be introduced and results obtained will be
discussed. It should be noted that all the plasma diagnostic methods taken into
consideration here were solely based on emission spectroscopy.
7.2. Equilibrium Relations
7.2.1. Complete Thermal Equilibrium
The state of complete thermal equilibrium requires first of all that the electrons
are distributed over the bound levels following a Boltzmann distribution96
Nn
= 8n <*P i - t y y ?
8m eXP {-EJ W
(7.1)
where the Nn and Nmare the population densities, gn and gmthe degeneracies and E? and
the energies of the n?th and m?th state, respectively.
Secondly, these electrons have to be in equilibrium with the free electrons, i.e.
the bound electron temperature T has to equal the electron temperature Te. Thirdly, the
Saha equation describing the ionization process has to be valid and governed by the same
temperature T:
Qz
(27tffic)3/2(*7)5/2
(7.2)
where E,tZ., is the ionization potential of the less ionized particle, the Qz are the
192
corresponding electronic partition functions, the Nz are the particle densities and pe is the
free electron pressure.
Fourth, excitation of electrons due to collisions with free electrons and
deexcitation due to superelastic or second order collisions, where the excitation energy
is carried away by the collision partner in the form of additional kinetic energy have to
exactly balance themselves as well as, fifth, excitation and deexcitation due to radiative
processes which means that the radiation within the plasma can be described by the black
body Planck function.
Finally, both, electron and heavy particles have to follow a Maxwellian velocity
distribution, i.e. have to be in equilibrium among themselves and, furthermore, in
equilibrium with each other, requiring that Te = Tg, where T,, the heavy particle
temperature, is used for both the ion and atom temperatures since equilibrium between
those two species is usually easily accomplished.
Noting the extensive requirements for complete thermal equilibrium, it is
conceivable that this plasma state is very difficult to be accomplished. Especially in the
here considered case of microwave electrothermal thrusters, where the plasma is heated
by collisions with electrons, which in turn receive practically all the absorbed microwave
energy due to their electric charge and high mobility, non-equilibrium is bound to occur
between electrons and heavy particles. This is caused by the fact that the energy transfer
from the electrons to the heavy particles is of the order
The magnitude of this factor ranges around 10'3 which means that the electron has to
make on the order of
103 collisions
to transfer all its kinetic energy to the heavy particle.
Thus, equilibrium is not easily established and significantly different temperatures will
193
therefore result. More quantitatively, an energy balance can be performed between the
gained energy of the electrons from the microwave field, which is simply the electric
force, eE, times the distance between two collisions, written as one half times the
acceleration eE/me times the square of the time between the collisions, r. This can be
rewritten as96:
| *0; - rp ^
where
л. - \ & tv".
(7-4)
is the mobility
\ie = vJE
=x ejmt
(7.5)
Equation (7.4) is based on an expression given by Lochte-Holtgreven96 but was corrected
by a factor 1/2. Using the mean free path length, X, and
x = X/v, = U jm J2 kT t
(7-6)
where ve is the average ( root-mean-square) electron velocity, one obtains
Tr Tg
AT
T.
'
T-
(Xeг )2 M
(h r ?
2 #
8l╗.
(7'7)
Therefore, the temperature difference and thus the degree of non-equilibrium can only
be decreased at high pressures (small X) and low power levels (small electric field
strength E). Complete thermal equilibrium can therefore only be expected for high
pressure plasmas and in the case of microwave-heated plasmas this requirement becomes
even more important due to the particular electron-heating mechanism involved.
The above definition of complete thermal equilibrium can be relaxed if it is only
194
applied to each species alone, i.e. electrons and heavy particles separately. Both species
still follow Maxwell distributions but may now have different temperatures associated
with them.
7.2.2. Local Thermal Equilibrium (LTE):
The term "local thermal equilibrium" only refers to electrons as the species
dominating the transition rates between different bound levels. Due to their high
velocities they interact much more often with the bound electrons and can therefore
equilibrate faster97. LTE is achieved when the distribution function for the bound
electrons is still a Boltzmann distribution, the temperature associated with it being equal
to the free electron temperature Te, the Saha equation is still valid using the free electron
temperature Te, however, radiative equilibrium is no longer valid. This implies that
collision rates have to dominate radiative processes in order to establish these conditions.
Therefore, the required electron densities and pressures within the plasma are rather
high, especially if the plasma is optically thin, suffering higher radiation losses. In the
latter case, electron number densities of
1018 cm'3 are
usually required, quite independent
of the gas species96. In the case that black body radiation, i.e. radiative equilibrium is
found in the vicinity of resonance lines, lower electron densities ranging between
1 0 15
and 1016 cm*3 depending on the gas species are needed to establish LTE. The strong
dependence of this value on the absorption of spectral lines can be explained by the high
transition probabilities of these lines which in turn are caused by the high energy
difference between the ground and excited levels: for hydrogen for example, the lowest
excited level lies at around 10 eV over the ground level and only 3.6 eV below the
195
continuum. In case this resonance radiation is not reabsorbed, those levels would be
quickly depopulated faster than collisions could repopulate them since the probabilities
for collisional excitation out of the lower energy levels are small due to the required
large electron impact energy. This severe depopulation would disturb the equilibrium
distribution unless sufficiently high electron densities could provide for high enough
collision rates. Recognizing that collisional excitation across the highest energy gap is the
weakest point in order to achieve LTE, Griem, McWhirter and Wilson96 derived an
expression for estimating the required electron number density leading to LTE for purely
optically thin plasmas, i.e. assuming no radiative equilibrium at all, not even in the
vicinity of spectral lines:
Net 1012 T lt ft (Em - E f c m '3
(7*8)
where Te is given in degree K and Em-Eil, the largest energy gap, usually corresponding
to E rE ,, in eV. For electron temperatures ranging up to 13,000 K as were measured for
waveguide-heated helium plasmas and will be discussed later, Irmer98 gives electron
densities of 1015 cm'3, however, assuming complete thermal equilibrium. Using Equation
(7.8) and the fact that the largest energy gap between electronic states for the helium
atom is roughly 22 eV, the required electron number density to achieve LTE in an
optically thin helium gas is 1018 cm'3. This means that LTE might not have been reached
under the here considered experimental conditions. Therefore, the here encountered
plasma state might be better described by partial thermal equilibrium discussed next.
196
7.2.3. Partial Local Thermal Equilibrium (PLTE)
The term partial local thermal equilibrium96 refers to the plasma condition where
only the upper electronic levels can be regarded in equilibrium with the free electrons
while lower levels either do not follow a Boltzmann distribution at all or obey a
Boltzmann distribution governed by a different temperature value. As discussed before,
"fast" transitions between the lower levels overpopulate the ground level and
underpopulate the low lying levels just above the ground level. This is particularly the
case for optically thin, low density plasmas where reabsorption of spectral lines as well
as collisional excitation are small. For the higher levels, where transition probabilities
decrease, the collisional rates might still be sufficient to maintain an equilibrium
distribution with the free electrons, so that LTE is established over those levels. Typical
electron number density requirements for optically thin PLTE plasmas for hydrogen at
electron temperatures of 1 eV range between 1014 and 1010 cm'3 in order to establish LTE
above the 4th or 10th level, respectively97. An expression to estimate these density values
was given by Griem97:
л >7 ?
10 ?
?
n 'V
m -3
(7 .9 )
1% ,
n being the principal quantum number above which LTE is established, EIH is the
ionization potential of hydrogen and Z the nucleus charge number. For helium at 1 eV
electron temperature the value for Ne would give about 101Scm'3 for LTE above the 4th
and 10? cm'3 for LTE above the 10th energy level. Comparing this with the electron
densities in the helium plasma98 one should therefore at least expect PLTE for the high
levels despite the fact that the electron number densities have been calculated assuming
complete thermal equilibrium and are thus probably slightly lower in reality.
197
7.2.4. Non-LTE Plasmas: the Generalized Multithermal Equilibrium Model
(GMTE)
Eddy and coworkers99*101 recently applied non-LTE plasma diagnostics in order
to investigate arcjet and MPD thruster plumes. Here, not even an equilibrium between
the free electrons and the upper bound levels is assumed anymore, which, however, still
follow a Boltzmann distribution governed by a different temperature value. Lower levels
may or may not obey a different Boltzmann distribution or no Boltzmann distribution at
all. More quantitatively, upper levels are populated according to a temperature value Tex^:
N j s . - N Jg, rap [ -( E .-E J /k T ^ ]
(7.10)
If a Boltzmann distribution can be associated with the lower levels ( below n=m*,
compare with Figure 7.1) then this temperature is referred to as Texo. The temperature
Te? indicated in Figure 7.1 is of a more artificial nature: it is determined by the straight
line in the Boltzmann plot, Figure 7.1, connecting the ground level population density
with the highest excited level at the ionization point and thus is obtained from
N jg , = NJgl exp [-(г , - E, -AE;) /* T J
(7.11)
where A E, is the reduction of the ionization potential due to Debye shielding96: although
the here considered plasmas can be regarded as quasi-neutral as a whole, on small scales
this quasi-neutrality is not preserved. The electric field of the ions is only shielded by the
electrons beyond a certain radial distance from the ion. Within this so called Debye
sphere electric fields prevail. Thus, incoming electrons only need a lower energy than
the required ionization potential to cause ionization because they gain additional energy
in the accelerating ion field. The value for N,/g, is obtained from the extrapolation of the
198
exa
'exp
E, / k
Figure 7.1 GMTE-Temperature Plot
199
curve previously obtained for
The importance of Tew lies in its usage for
determining the ground level population:
Na I Q( T aa) - N l l g l
(7.12)
The reason why T ^ is used in the electronic partition function, although not explicitly
mentioned by Eddy, might be explained as follows: depopulation of the ground level, i.e.
the fact that Nt does not equal N, is not only governed by transitions into the lower
levels, which could be described using T ^ but also by subsequent transitions out of those
lower into higher states which in turn are described best by using
Tju, according
to Figure 7.1, provides an "averaging" process of these transitions obeying different
distribution functions and is therefore used in Equation (7.12).
7.2.5. Non-LTE-Plasmas: Corona Equilibrium
For very low-density plasmas, a case of even more severe non-LTE behavior as
described in the GMTE model can be observed, where the bound electrons do not follow
a Boltzmann distribution function anymore and definition of temperatures even for highly
excited states therefore becomes impossible. In these cases a different kind of equilibrium
is considered, taking into account the balance between collisional ionization and radiative
recombination in a steady, optically thin plasma state. The governing equation can be
written as96
3l
*x-i
=
(7.13)
W
The Nz are the number densities of the various ionization stages and a and S are the
200
radiative recombination and collisional ionization rates, respectively. Equation (7.13)
replaces Saha?s equation, which of course does not hold anymore either. In case
collisional three body recombination at rate Q is taken into account, this gives
Ni
_
*Z-1 "
* N eQ
W
In cases, however,wherethe plasma densities are small
rare,
(7 14)
and three body collisions are
the radiativerecombination process dominates the collisional recombination and
Equation (7.13) holds. Since these conditions are obtained in the solar corona96, Equation
(7.13) is often referred to as the corona equation. Difficulties regarding calculations
involving corona equilibrium are due to the inaccuracies involved in the determination
of a and S, in particular for elements other than hydrogen and higher ionization stages.
In these cases, corona calculations are therefore subject to a great deal of uncertainty102.
The conditions required for corona equilibrium to hold, however, are usually not
encountered in electrothermal space propulsion plasmas, where high densities are desired
and temperatures are usual moderate (< 13,000 K).
7.3. Spectroscopic Plasma Diagnostic Techniques
In the following, several spectroscopical methods will be discussed which are
appropriate for determination of such plasma parameters as electron temperature Te,
heavy particle temperature T( and electron number density Ne. In the first part only
approaches applying to LTE or PLTE are considered. Since LTE and PLTE only refers
to the electron temperature, these methods can only be used to determine either Te or Ne.
For the here considered plasmas obtained in microwave space propulsion devices,
201
however, PLTE can be assumed at best so that those methods will have to be reviewed
rather critically. The second part then involves spectroscopical methods which do not
involve LTE or even PLTE and are only limited by the fact that in order to define a
temperature, a Maxwell distribution is assumed for the electrons or the heavy particles,
respectively. This, however, is a relatively good assumption for plasmas even at
pressures significantly below the atmospheric value99. The diagnostic approaches applying
to non-LTE plasmas can therefore be viewed as proposed spectroscopic methods for
investigating microwave heated plasmas.
7.3.1. Absolute Line Intensities
The integrated line intensity is given by96,97,99
(7.15)
where I is a volumetric intensity given in W per cm3 and steradian, i.e. Abel inversion
of the surface intensity values obtained by comparison with a calibrated lamp, for
example has already been performed. From the upper level population density Nm and
Equation (7.1), it follows
N
N
In ? = In ? - (Ew - En)lkTt
(7.16)
from which a Boltzmann plot can be obtained so that the electron temperature can be
determined as the inverse slope of the straight line obtained by plotting ln(Nm/ g J vs.
E ^k presuming that the corresponding energy levels and statistical weights are known
202
and the LTE condition holds. Especially in the latter case, the lower level densities can
all be referred to one common ground state population via
? = ? л p [-(E , - E,Wtr j
S.
S,
(7.17)
where Nt/gt is in turn obtained from
NICKT') = N f a
(7.18)
with N being the total number density for the gas species considered. This approach is
of course not possible in PLTE . In that case all lines would have to be taken from the
same lower level N*D/g*Dabove which PLTE holds, in order to establish the Boltzmann
plot.
Since at low temperatures Nm and therefore I increases while at higher
temperatures the exponent in Equation (7.17) approaches one and the population density
of the lower level decreases, causing Nmto decrease as well, the integrated line intensity
goes through a maximum at a given temperature value, referred to as norm temperature,
values of which are tabulated for various elements and transitions96.
A major disadvantage of absolute line intensity measurements are the inaccurately
known transition probabilities A ^, especially for transitions between higher levels in
particular interesting for PLTE cases. Errors for A ? values may be as high as 100%*
resulting in significant inaccuracies regarding the determined temperature values.
203
7.3.2. Relative Line Intensities
In order to avoid determining the population density first so as to find the
temperature from a Boltzmann plot as required for absolute intensity diagnostics, relative
intensities can be measured to yield electron temperatures directly, provided that LTE
holds96,97. Using Equations (7.15) through (7.18) one obtains
! i = A ' *? v?
N*? л p [- E' ' E*]
h
^ 2 V2 <?, n A2
a
(7.19)
where I, and I2 correspond to the integrated intensities of two different lines with the
corresponding upper level energies E, and Ej, upper level statistical weights, gt and g2
and transition probabilities A, and A2 at frequencies vx and v2, respectively. If one
considers the same species and ionization stage, the partition functions as well as the
atom densities cancel, leaving
T =
( 7 *2 0 )
Differentiating Equation (7.19) yields further
AT _
kT
A (W
T ? E, - % (V /2)
(7.21)
which indicates that the inaccuracy of the measured temperature values grows as the
energy difference Ei-Ej decreases. Since this difference does not exceed 2 eV96 in most
cases and since transition probabilities are poorly known and forming their ratio may lead
to large errors, this spectroscopic method can be regarded as rather inaccurate.
204
Furthermore, in order to cancel the densities, LTE had to be assumed all the way
down to the ground level. In case of PLTE the population densities would have to be
referred to the same lower state sufficiently high enough to ensure PLTE.
In order to increase the accuracy of this method, one could consider lines of the
same species but different yet subsequent ionization stages. Now, the energy level
difference would be enhanced by the reduced ionization potential. Relating densities and
partition functions via Saha?s equation yields
- =2 d lilZ i
h
A2 82 V2
JL 7 * 2 ^
hI
+Et
- LEfflkBT
(7.22)
N*
where E, and AE, are the ionization potential and its reduction due to Debye shielding,
respectively. Obviously, in applying Saha?s equation using the electron temperature, LTE
had to be assumed, PLTE is not sufficient anymore. The electron density Ne could be
canceled if Saha?s equation would be employed once more together with the assumption
of quasi neutrality, leaving now the ratio of the partition functions in the equation.
A major disadvantage of this method is the fact that for typical space propulsion
plasmas the degrees of ionization are usually quite small and in the case of the here
considered microwave plasmas do not even exceed 1 %.
An even more temperature sensitive version of the relative line method can be
obtained by relating lines of different species of the first ionization stage. In the case that
ionization energies are significantly different for both species, there will be temperature
regions where one species is already strongly ionized while the other is not, yielding a
strong temperature dependence of the line ratio in this temperature regime. Disadvantages
of this method besides the assumption of LTE are that in the case pure gases are used
as propellants, a second species would have to be introduced to the propellant for
diagnostic purposes, possibly changing engine performance characteristics.
205
7.3.3. Absolute Continuum Spectroscopy
Absolute continuum spectroscopy relies on measuring the absolute intensity of a
pure continuum part of the emitted spectrum. For helium, a wavelength of 425 nm was
therefore chosen since no lines are present in the vicinity of this part of the helium
spectrum. In order to measure the absolute intensity of the continuum, the spectrometer
has to be calibrated with a calibrated tungsten lamp, for example, giving a relation
between spectrometer intensity units and the known intensity per unit solid angle and
wavelength interval of the lamp in W/ m2 St m. Thus, absolute continuum intensities can
be related to the measured spectrometer units. Abel inverting these data gives a
continuum emission coefficient in W/ m3 St m. Those data can now be compared with
an expression given by Bastiaans and Mangold103:
e' w
?
^
K( i
л * - ^
)]
< 7 -2 3 )
which gives the corresponding emission coefficient expressed in plasma properties. The
Gaunt factors ( G ) to be used are given by Berger104 and depend on wavelength and
electron temperature. The correction factor г has been plotted by Hofsaess105 for various
wavelengths and electron temperatures. To solve for the product of the electron number
density and ion number density the Saha equation has to be used, thus assuming local
thermal equilibrium95.
Errors can be introduced to this method by continuum radiation coming from ions
and unresolved spectral lines97 and the fact that the temperature dependence of the
continuum intensity in the visible spectral range is rather weak97.
Summarizing, it can be said that the LTE assumption is crucial for this method
which means that high electron number densities should be present in the plasma. Since
206
this is not the case towards lower pressures in microwave heated plasmas, the obtained
temperature values in this pressure range should be more carefully inteipieted as LTE
temperatures rather than electron temperatures.
7.3.4. Relative Continuum Intensities
Incorporating the Saha equation in the data reduction process for the absolute
continuum measurements can be avoided using the relative continuum method96,97. As for
the previously discussed relative line intensities, forming the ratio of the continuous
emission coefficients, Equation (7.23), cancels the density values if the same species and
ionization stage was considered. This method remains dependent on LTE since that
assumption was used during the derivation of the expressions for the emission
coefficients. Furthermore, as in the case of absolute continuum spectroscopy, errors can
be introduced by continuous radiation coming from ions and unresolved spectral lines97.
In addition, the temperature dependence of the continuum intensity in the visible spectral
range is rather weak97.
7.3.5. Relative Line to Continuum Intensities
As in the relative continuum measurements, determination of electron and ion
densities can be avoided if one combines line and continuum emission coefficients,
Equations (7.15) and (7.23), where in Equation (7.15) the integrated intensity already has
the dimensions of an volumetric emission coefficient since the Abel conversion was
207
assumed to have already been performed. Upper level population densities and
electron/ion densities can be interrelated by a combination of Boltzmann and Saha
equations. Since in both expressions the electron temperature is used, LTE has to be
assumed. It should be pointed out that employing the expression given by Griem97 for
line-to-continuum ratios has led to results orders of magnitude wrong. The reason might
be an error in the formula given by Griem. Indeed, comparing that expression with the
ones obtained by other authors, such as Lochte-Holtgreven* and Bastiaans and
Mangold109 indicates that Griem?s equation does not show a frequency dependence in the
exponential terms as given by the other authors and visible in Equation (7.23). Rather,
only a fixed ionization energy for hydrogen appears which seems to be physically wrong,
since ionization is possible from any photon energy greater or equal to the ionization
potential. Uncertainties regarding the line-to-continuum method come in again via the
errors attached to the transition probabilities for the line radiation.
7.3.6. Stark Broadening and Shift
Stark broadening is the first non-LTE spectroscopic method discussed here, only
assuming a Maxwellian velocity distribution of the electrons, thus allowing the definition
of an electron temperature. Since Stark broadening is a form of pressure broadening
where the perturbers are charged and in most of the cases are electrons, the electron
temperature enters the process via the electron velocity, having a severe impact on the
collisional cross sections. For the same reason, ion temperatures could be considered,
however, due to the low ion velocities and ion collision rates, their influence on the
Stark-broadening effect is of a different nature, related to spectral line splitting in their
208
electric fields rather than to collisional processes as will be discussed below.
The electric field surrounding the perturber coupled with the electric dipole
moment of the perturbed atom results in a strong interaction, with the interaction
potential given by106
V=
-
B? i
C7-24)
dominating all other pressure broadening mechanisms. In the case that the perturbed
particle has a permanent electric dipole, the Stark effect is linearly proportional to the
electric field strength and is referred to as the linear or 1st order Stark effect. Usually
only hydrogen atoms in states other than the ground state and hydrogen-like atoms such
as helium in its first ionization stage show this behavior. In the case that no permanent
electric dipole moment is present, it has to be induced by the perturber first according
to basic classical electrodynamic laws8147
p - a S
(7*25)
where a is the so called polarizability of the atom or molecule. Upon inserting in
Equation (7.24), this gives a square dependence of the perturbation potential on the
electric field strength and is therefore referred to as the quadratic or 2nd order Stark
effect. This is the common case for almost all species.
The terms 1st and 2nd order Stark effects originate from the quantum mechanical
treatment of this effect: time independent perturbation theory leads to zero 1st order
perturbation terms of the governing Hamilton operator of the system. In the case of
atoms and molecules obeying the quadratic Stark effect, the first non-zero terms in the
expansion are the
2 nd
order perturbation terms leading to much smaller energy
corrections than the 1st order terms would have given*07,108. For hydrogen and hydrogen-
209
like atoms in states other than the ground state, 1st order terms are non-zero and clearly
dominate all other energy correction terms of the Hamilton operator, indicating that 1st
order Stark effects are much stronger than second order effects.
The quantum mechanical treatment is also the only possible theoretical approach
to explain the second important effect of Stark broadening: besides merely broadening
spectral lines, they are also split in electric fields according to the above mentioned
interaction potential. Since this splitting is stronger for the 1st order Stark effect, spectral
lines of hydrogen for example take on the typical Holtsmark profiles: the lines, showing
a characteristic "double-hump", now consist of two separated and broadened Stark
components having a Lorentz-broadened profile each due to electron collisions,
overlapping however and smeared out by the statistical distribution of the ion fields
which contribute significantly to the Stark splitting and, as a matter of fact, are the only
electric fields considered in Griem?s calculations109. In the case of electric space,
propulsion plasmas, the electric fields applied to the plasma would also have to be taken
into account but are neglected for simplification and because of absorption processes in
the plasma.
In the case of 2nd order Stark effects, the separation of the lines is not that
emphasized and the "double-hump" Holtsmark profile is completely smeared out by the
random ion motions, yielding a profile much closer resembling a Lorentzian. As a matter
of fact, during the radiative plasma propagation calculations use was made of this
approximation which is known to hold relatively well97.
Temperature and density measurements in plasmas can now be obtained by trying
to curvefit the theoretically calculated profiles with the spectroscopically determined
lines. In the case of the first order Stark broadening, i.e. for hydrogen and hydrogen-like
profiles, the theoretical line shape is given by a normalized line profile S(a) with96*97
210
J"
S(a) da = 1
(7.26)
where o is given by97
(7 .2 7 )
a m A\ m_
2ncF?
and AX and Au being the wavelength and angular frequency distances from the line
center, respectively. F0 is the so called normal field strength caused by the ions:
(7.28)
F"
4 ne
and the relationship between S(a) and the line profiles in wavelength and angular
frequency scales, respectively, are
K ╗ ? 4 - лл>
*0
(7.29)
and
H.U) -
2 ncF0
m
C7.30)
S(a) has been tabulated by Griem97 for various hydrogen and ionized helium lines for
different electron temperatures and densities. The experimental procedure would
therefore consist of plotting various lines for different temperatures and electron densities
and comparing them with the experimentally obtained curves, normalized to the area
under the curve. If necessary, interpolation between the tabulated S(a) values for
different densities and temperatures would have to be performed. The best fit gives Te
as well as Ne.
211
For themore common second order Stark effect theprocedurebecomes more
complicated, since no line profiles have been tabulated. Here, thereduced line profiles
m .i r
*
j
* * <╗
. i * (,.(,л py
(7.3D
are related to wavelength or angular frequency intensity profiles by
7(<o) = - j(x)
w
(7.32)
/(*) ? ? m
(7.33)
and
respectively and w and wx are the line widths in angular frequency and wavelength units
tabulated by Griem97,110 for various lines and species at different electron temperatures
and densities, a is now given by
a =
(7.34)
w
with F0 as given above and Ca listed by Griem97 as well, x is a dimensionless variable
obtained from
x = -
to - to ~ d
A - 31 - d,
___
=
w
(7.35)
with d and dx being the Stark shifts in angular frequency and wavelength units,
respectively. The expressions u 0 and Xo stand for the angular frequency and wavelength
of the line center, respectively. Wr(0) is a distribution function given in tabular form by
212
Griem97 for values of 0=0.1 to (3=10, where larger values do not contribute significantly
to the integral of Equation (7.31). These 0 values are listed for different values of r
which in turn is the ratio of the mean distance between ions
p. ? H ^ r
1' 3
<7-36>
and the Debye radius
p?
(7.37)
-
i.e.
r =
Pm
(7.38)
Pd
The experimental procedure again consists of curvefitting the theoretical curves to the
experimental profiles, the best fit yielding Te and Ne. Interpolation for the values of
Wr(0), Co, w, d or wx and dK, respectively, may be necessary. Approximation of the 2nd
order Stark-broadened line profile by a Lorentzian profile may be good enough for the
radiative plasma propagation calculations, however is insufficient for accurate
temperature ( and density ) measurements. Thus, the method of curvefitting is rather
cumbersome and laborious.
A much quicker, however less accurate way of using Stark broadening for nonLTE temperature determination lies in using merely the HWHM ( half width at half
maximum) line widths. From the tabulated values the widths and shifts can be obtained
for arbitrary densities and temperatures via96,97
213
Wi = [1 + 1.75a (1 - 0.75r)] w
(7.39)
2
(7.40)
for neutral emitters where a and r were defined above. The second term in the brackets
accounts for broadening due to ion collisions which, however, only have a minor impact
on width and shift as can be seen from the rather small values of a tabulated by Griem97.
The value of Ne' is the electron density for which Griem calculated the widths and
shifts97,110 and, since they are linearly proportional to the density, can be obtained for
different densities by multiplication with a corresponding density ratio. In comparing
widths and shifts with the corresponding measured values, Te and Ne can be obtained.
The accuracy reported associated with this method varies: Berg et.al. 111 compared Stark
profiles in shock-heated plasmas of known electron temperature and density, where latter
were obtained by relative line and continuum intensities, respectively, with theoretically
determined Stark profiles based on those temperature and density data and found
deviations between experiment and theory of 10% for hydrogen HWHM widths and a
corresponding error of up to 20% for helium. Stark shifts on the other hand showed
errors exceeding 100% in particular for small shifts. Kelleher112 compared electron
densities and temperatures obtained from the determination of Stark widths of neutral
helium lines with the ones of the
Balmer line of hydrogen and found agreement for
electron densities within 15% and for electron temperatures within 20%. LochteHoltgreven96 reports 25 - 30 % accuracy for electron temperature and density
determination. Thus, although the experimental complexity using only the HWHM widths
rather than the entire profile is reduced, so is the accuracy of the obtained temperature
and density data.
214
Burgess and Cooper113 ,14 introduced a third method of determining electron
temperatures only, based on the Stark effect and avoiding the measurement of electron
densities. If ion broadening is assumed to be negligible, widths and shifts are directly
proportional to the electron density. Therefore the ratio of the shift and the width, listed
by Griem96 also, is independent of the density and thus the electron temperature can be
determined directly. Problems associated with this method are due to the relative
insensitivity of d/w with respect to Te towards lower temperatures in the range of 10,000
to 20,000 K. Furthermore, this temperature insensitivity is particularly noted for large
d/w values which are the only ones for which theoretical values of reasonable accuracy
are listed. Therefore, this method has to be considered rather skeptically regarding its
application to space propulsion plasma diagnostics. Finally, in all three cases of
employing the Stark effect, competitive broadening mechanisms, notably Doppler
broadening, have to be taken into account. This is either accomplished by considering
only such lines which show a strong Stark effect, rendering the Doppler-broadening
mechanism negligible, which, however, requires relatively high density plasmas. If such
a choice cannot be made, Doppler broadening has to be taken into account. If the Stark
profile can be approximated by a Lorentzian curve, superimposing a Gaussian Doppler
profile will result in a so called Voigt profile96,97,115 which are available in form of
computer subroutines169 or in tabular form1о2. Lochte-Holtgreven96 gives a table of
actually observed HWHM widths for various combinations of Doppler and Lorentzian
widths. If, however, an approximation of the Stark profile by a Lorentzian curve is
inappropriate, one has to go via the mathematical process of folding the two line shapes.
For a distance AX from the center of the Doppler profile one obtains for the distance AX'
from the center of the overall line profile:
I (AX') = / " 1
^
(AA) 1 ^ (AA'-AA) <?(AA)
(7.41)
where all integrated line profiles are normalized to one. Equation (7.41) means physically
that each intensity value of the Doppler profile at AX from the line center is smeared out
by the Stark broadening mechanism. The intensity at the point AX' from the center of the
overall line profile is then obtained by integrating over all intensities contributing to this
value. Thus, taking into account additional broadening mechanisms considerably
complicates spectroscopical measurements using the Stark effect even further.
7.3.7. Doppler Broadening
Doppler broadening is the only emission plasma spectroscopical method yielding
heavy particle temperatures directly, not limited to LTE plasmas and only requiring a
Maxwellian velocity distribution of the heavy particles. The intensity profile of a Doppler
broadened line is Gaussian and given by
/(Av) =
o p |A vJn
Av D
(7.42)
where I is the integrated line intensity:
/ = |" /(Av) d(Av)
and Av is the distance from the line center and Av0 is given by
(7.43)
216
with v being the most probable velocity and
p0
the frequency of the line center. From
Equations (7.42) and (7.44) one can determine the FWHM (full width at half maximum)
line width as96,57
2AXy2 = 2
yjba л \ 0
C7-45)
KC2
where M is the mass and kTg the thermal energy of the emitting heavy particles.
Therefore the heavy particle temperature can easily be obtained from the FWHM width.
Restrictions of this method are due to the fact that the width is only proportional
to the square root of the temperature limiting the sensitivity of Doppler broadening to the
gas temperatures. In addition, it has to be ensured that no other broadening mechanisms
affect the line shape: although natural line broadening is always negligible, Stark
broadening may become a competitor. Therefore, lines should be selected where Stark
broadening is known to be small. Corresponding data defining such lines can be found
by Griem97,110. In case Stark broadening is not negligible, superposition of both
broadening effects has to be taken into account leading to Voigt profiles or folding
processes as discussed in the previous section, severely complicating the temperature
determination. A good indication whether Stark broadening is negligible can be obtained
from a comparison of the far wings of the spectral line with the theoretical Doppler
profile: since the Gaussian Doppler profile decays with exp(-A\2) and thus much faster
than the nearly Lorentzian Stark profile which decays according to a AX*2 dependence,
the wings are much more dominated by Stark broadening.
Griem96 gives an accuracy of the Doppler broadening method of around 20%,
based on a 10% error for line width measurements and the quadratic dependence of T,
on the linewidth.
If besides the random motion of the heavy particles a directed motion is present,
217
this velocity can be detected by the Doppler line shift via116:
V -
-f
(7.46)
Ao
However, appreciable shifts are only achieved for supersonic flows. Detected shifts for
the nozzle flow of an arcjet engine investigated by Pivirotto and Deininger116 are only in
the range of 0 .1 A.
7.3.8. GMTE Plasma Diagnostics
The GMTE plasma model developed by Eddy et al.99' 101 described previously can
be used to yield the most comprehensive plasma diagnostics, providing data for Te, T,
and the upper bound level temperature
thus allowing a comparison with Te and
therefore giving a quantitative indication on the PLTE state of the plasma. Eddy
developed a general scheme for the spectroscopic procedure99: starting with the
determination of Te)W
? from absolute line intensities and a Boltzmann plot according to
Equation (7.10) and Figure 7.1, the electron temperature is initialized by this value.
Using this, Ne can be determined from absolute continuum spectroscopy, which has been
modified by Eddy99 to take into account non-LTE behavior. Then the heavy particle
temperature is obtained. Eddy lists several different ways, the simplest being the
assumption of Te=Tf which, however, would severely restrict this method to only a few
special cases. The other methods to determine T( are based on an energy balance between
electrons and heavy particles, thus involving both electron temperature and electron
density. The neutral gas density can now be obtained from the equation of state, using
the assumption of quasi neutrality and the measured pressure of the plasma:
218
P = (Na * N ) kTg + NJcTt
(7.47)
Knowing Na one can proceed to find the temperature Tm from Equation (7.12) which in
turn can be used in the Saha equation, modified for GMTE99, in order to calculate an
updated value for Te. If the new and old value for Te differ, the last steps starting from
the determination of T( involving T? have to be repeated until convergence is obtained.
With this new value of Te, the modified absolute continuum relation is solved again for
a new value of Ne and the entire process is repeated until both Te and Ne converge to
final values. Weaknesses of this procedure may be found in the usage of absolute line
intensities which could lead to large errors in the cases of poorly known transition
probabilities and in the rather complicated iterative procedure. Modifications to this
method may be possible by determining the heavy particle temperature Tg directly by
means of Doppler-broadening measurements, thus simplifying the iterative process.
7.4.
Plasma Temperature Measurements for the Rectangular and Circular
Waveguide
7.4.1. Selection of the Spectroscopic Method
Two different spectroscopic methods, the absolute continuum method and Doppler
broadening, were used throughout the experiments. Howevere, only the absolute
continuum method lead to temperature data, the Doppler-broadening method failed.
Absolute continuum spectroscopy was chosen because of its relative simplicity.
Because of the LTE assumption involved, however, the obtained temperature values have
219
to be interpreted very carefully. During a recent investigation of argon arcjet plumes,
Eddy99 noted that for pressures greater than 1 atm, temperature differences between Te
and T, almost disappear at the center of the arc. Differences between the so called LTE
temperature, which is the actual temperature obtained by the absolute continuum method,
and the electron temperature Te drop below 500 K at those pressure conditions at
locations close to the arc center, virtually dissapearing at pressures of about 5 atm.
However, conditions at the edge of the arc are very different. Here, differences between
Te and Tf become negligible only at pressures of 5 atm or greater, the electron
temperature being almost 3000 K higher than the heavy particle temperature at 1 atm.
The LTE temperature lies by about the same value above the electron temperature at that
particular pressure. It is difficult to make any definite conclusions from a steady-state arc
discharge in argon to a high-frequency microwave discharge in helium in this matter, in
particular as the degree of non-equilibrium between electrons and heavies can be
expected to be larger in the high-frequency discharge due to the much higher mobility
of the electrons. It should be made clear at this point that any assumptions of thermal
equilibrium between heavy particle and electron temperature are premature and would
have to be thouroughly investigated using other spectroscopic methods. Even the obtained
electron temperature values may have errors attached to them, which, however, are
difficult to quantify without performing detailed non-LTE diagnostics. Temperature data
obtained for microwave-heated helium plasmas using the absolute continuum method
should therefore be carefully interpreted as a rough first estimate of the actual
temperature conditions holding in the plasma with the accuracy of this method remaining
to be determined.
The second spectroscopic method used in the experiments was Doppler broadening
since this method is able to directly deliver heavy particle temperatures without requiring
220
any assumptions regarding the equilibrium state of the plasma. However, in order to
increase the resolution of the spectroscopic system to be described below, a Fabry-Perot
etalon had to be placed in the optical path in front of the spectrometer used, requiring
very accurate beam collimation. These last two requirements led to significant decreases
in the signal-to-noise ratio of the spectroscopic configuration and in the end, no
temperature data could be obtained using the Doppler-broadening method. In the
following, details of the two spectroscopic methods used will be given and results
obtained will be discussed.
7.4.2. Spectroscopic System and Procedure for the Absolute Continuum Method
7.4.2.I. Spectroscopic System
The spectroscopic system used throughout the experiments is shown in Figure 7.2.
The spectrometer is a 0.5 m, f/6.9 Czemey-Tumer system with a dispersion of 16
A/mm. A 2400 lines/mm Bausch and Lomb ruled grating blazed at 300 nm is used.
Attached to the exit slit of the spectrometer is a Hamamatsu 1P28A photomultiplier tube
(PMT) with a detection range from 185 nm to 700 nm and a maximum spectral response
at 450 nm. The PMT serves to amplify the signal which is then further amplified and
converted into an electronic current analog signal by a Pacific Instruments Model 126
photometer. This photometer also supplies the PMT high voltage which was set at 9501100 V in order to optimize the signal-to-noise ratio. The filter required to dampen
signal fluctuations in the photon counting mode was usually set at 1 sec or less. The
analog signal for the spectrometer could be transferred via a Data Translation A/D board
221
Plasma
Discharge
Collimating Lens
/Fiber Optics Cable
^?Entrance
?Spectrometer
Diffraction
Grating ?
Exit
Slit
_
.Collimating
Mirrors
PMT
Amplifier/DiscriminatorH {
Spectrometer
Drive Unit
Personal
Computer
Photometer
Figure 7.2. Spectroscopic System94
222
(DT2801-series) into a micro computer where data could be stored and processed.
For the absolute continuum measurements, the optical signal was transferred from
the plasma into the spectrometer by means of a 2 m long fiber optic cable consisting of
a bundle of fused silica fibers. The useful spectral range over which signals can be
transferred through the fiber reaches down to about 400 nm, below which attenuation of
the signal increases significantly.
The cable was directly mounted to the entrance slit of the spectrometer. Entrance
and exit slits of the spectrometer were set at the same width and height and varied
depending on the experimental conditions. For spectroscopic investigations of straight
waveguide plasmas which emitted a rather bright signal, slit widths of 40 /t were
sufficient. The dimmer plasmas in the circular waveguide applicator required a 180 ft slit
width. Slit height was set at 2 mm in all cases.
7.4.2.2. Calibration
In order to perform absolute intensity measurements, the spectroscopic system has
to be calibrated first. To this end, a calibrated Optronics tungsten ribbon filament lamp
was used. The lamp was powered by a 15 A precision current source and calibrated at
an emittance of 10.27 ^W/St-mm2-nm. Taking into account tungsten filament area and
the beam area of the collected beam, the spectrometer "sees" an emission coefficient of
1.54 /iW/St-mm2-nm from the lamp. Comparing this value with the spectrometer units
registered and subtracting the dark current count of the PMT allows for calibration of the
spectroscopic system.
223
7.4.2.3. Abel Inversion
While the measured intensities are "surface" intensities, i.e. given per unit surface
area of the emitting plasma, the theoretical expression for the continuum coefficient given
by Bastiaans and Mangold103 shown in Equation (7.23) is a volumetric emission
coefficient, i.e. given per unit volume. Therefore, obtained and calibrated spectroscopic
signals have to be further processed in order to allow for a comparison with the
theoretical expression which ultimately will lead to the determination of the electron
temperature.
The procedure required to transform the intensity measurements from surface to
volumetric emission coefficients is known as Abel inversion. Figure 7.3 shows a slice
of a cylindrically shaped radiation source. From this figure it is evident that the surface
intensity I(y) is related to the volumetric emission coefficient e(r) by
(7.48)
and h is the height of the cylinder. Using the relation
(7.49)
substituting for x and exploiting the symmetry of e(r) with respect to the y axis yields
(7.50)
According to Abel?s inversion formula117, the volumetric emission coefficient turns out
to be
224
Direction of
Observation
Figure 7.3 Geometrical Relationships between the Variables utilized in the
Abel-Inversion Technique94
225
1
f* (<U(y)ldy) dy
r
(7.51)
'J(y2~r2)
According to Barr's summation technique, polynomial approximations of the integrand
lead to a numerical solution of Equation (7.51):
?
t t
E M
a-o
.
(7.52)
where the radius has been divided into N equal increments of length A and rk is the
location kA along the radius vector. ^ is the intensity measured at the point yn=nA and
the jSfa are the values resulting from the numerical approximation of the integral in
Equation (7.51) and are tabulated in References 94 and 117, for example. Barr?s
technique has been used exclusively throughout the spectroscopic measurements
performed here due to its simplicity and easy programming.
Note that with the fiber optic probe used for the spectroscopic set-up errors may
have been introduced to the Abel inversion technique. Since a collimating lens is placed
at the fiber entrance, light is not truly collected from a straight "slice" of the plasma as
shown in Figure 7.3, rather, from two light cones leading to and from the focal point of
the lens.
Furthermore, the lens diameter of the fiber-optic probe is roughly 1 cm in
diameter and although the spacing between the probe and the plasma results in an
intersecting cone cross sectional area somewhat smaller than that at the plasma surface,
the interval spacing, A, therefore has to be chosen rather large and the grid of
measurement points across the plasma is therefore rather crude since Abel?s inversion
technique does not allow for overlapping intervals. During the here performed
measurements, spectroscopic data were taken at the plasma center and at a location 5 mm
226
off center. The latter grid point was picked such that the intersecting probe area did not
extend beyond the plasma boundaries which would have resulted in erroneous results.
Finally, plasma configurations in cylindrical waveguide applicators or resonant
cavities are not truly cylindrical, rather reveal a more ellipsoidic shape. Since Abel's
inversion technique is based on cylindrically shaped light sources, an additional error
might have been introduced through this assumption.
It should further be noted that in the case of the rectangular waveguide plasma,
Abel inversion as discussed above was not necessary. Since the plasma had a truly
cylindrical shape and was aligned with the optical axis along which light collection was
performed, conversion between surface and volumetric intensities could simply be
obtained by dividing the surface intensities by the height of the cylindrical plasma, i.e.
20
mm.
7.4.2.3. Experimental Procedure
After calibrating the spectroscopic system, surface intensity values were measured
at two plasma locations in order to perform an Abel inversion. Intensities at the plasma
center and 5 mm off the center were registered. After subtracting the dark current of the
PMT, the intensity values were Abel inverted and compared with the continuum emission
coefficient according to Equation (7.23). This continuum emission coefficient is plotted
on Figure 7.4 for various pressures. For the graphical determination of the electron
temperature a more accurate linear plot was used. Both the Gaunt factor and the g-value
had to be interpolated for the temperature range considered and are shown in Figures 7.3
and 7.6 respectively, taken from References 104 and 105. As can be seen from Figure
227
Calculated Continuum Emission Coefficient
Helium
C*NJ
#
E
3 0 0 kPo
2 4 0 kPo
1 80 kPa
125 kPa
3
2
c
V
'u
'JZ
s0)
o
3
2
o
c
o
?55
w
E
u
3
2
10000.0 10500.0
11000.0
11500.0 12000.0 12500.0
13000.0
Electron Temperature ( K )
Figure 7.4 Continuum-Emission Coefficient at 42S0 A for Helium
vs. Electron Temperature
228
G a u n t-F a c to r
4 2 5 0 A ngstrom
1.161
1 .159
1 .1 5 7
1 .1 5 5
1 1.153
Y 1 .1 5 2
3 1 .1 5 0
1 .1 4 8
1 .1 4 6
1 .1 4 4
1 / 14 2
1 0 0 0 0 .0
╗
i
i
1 0 5 0 0 .0
i
i
...I? - i
1 1 0 0 0 .0
1 1 5 0 0 .0
T e m p era tu re ( K )
i
i
1 2 0 0 0 .0
Figure 7.5 Gaunt-Factor vs. Temperature
i
i
1 2 5 0 0 .0
229
г - Value
4 2 5 0 A ngstrom , He(l)
0 .4 6 5
0 .4 5 5
0 .4 4 5
0 .4 3 5
|
0 .4 2 5
> 0 .4 1 5
I
^ 0 .4 0 5
0 .3 9 5
0 .3 8 5
0 .3 7 5
-
0 .3 6 5 ^ ? 1---------1--------- 1---------1------------------ 11---------1---------1---------1--------- 1
1 0 0 0 0 .0
1 0 5 0 0 .0
1 1 0 0 0 .0
1 1 5 0 0 .0
1 2 0 0 0 .0
1 2 5 0 0 .0
T e m p e ro tu re ( K )
Figure 7.6 f-Value vs. Temperature
230
7.4, relatively small changes in the temperature yield relatively large changes for the
emission coefficient. Thus, errors in the intensity measurements or the calibration have
only a very small effect on the accuracy of the determined temperature values. On the
other hand, subtle changes in electron temperature can easily be detected using the
absolute continuum method.
7.4.3. Spectroscopic System and Procedure for Doppler-Broadening
7.4.3.I. Selection of the Spectral Line
Different line broadening mechanisms are active under typical plasma conditions.
The only broadening mechanism of interest here is Doppler broadening since it will allow
the determination of the heavy particle temperature. While natural line broadening due
to finite lifetimes of the excited states can almost always be neglected due to the small
line widths encountered, Stark broadening, i.e. collision broadening due to charged
perturbers, cannot be neglected in a plasma state in general. In order to avoid the
determination of complicated Voigt profiles or line folding processes, lines selected for
Doppler broadening measurements should be those where spectral line widths due to
Stark broadening are small compared to Doppler-broadened ones. Table 7.1 gives several
helium lines and their corresponding Stark97 and Doppler line widths49 at an electron
number density of 1016 cm'3. Since actual electron number densities in the here
considered plasmas are expected to be slightly lower, Stark widths can be assumed even
smaller by a factor corresponding to the ratio of the actual electron number density to
the density mentioned above.
231
Table 7.1
Line Widths due to Stark and Doppler Broadening for selected
Helium Lines
X(A)
Doppler Half-Width(A)
Stark Half-Width (A)
5000 K
1 0 ,0 0 0
K
5000 X
10,000 K
3188
0.007
0.007
0.080
0.114
3889
0 .0 0 2
0 .0 0 2
0.098
0.139
4121
0.017
0 .0 2 0
0.104
0.147
4713
0.007
0.009
0.119
0.168
5016
0.008
0.008
0.126
0.179
5876
0.003
0.004
0.148
0.209
|
As can be seen from Table 7.1, the 5876 A He line results in the largest Doppler
broadening while at the same time exhibiting only very small Stark broadening and was
therefore selected for the Doppler-broadening diagnostic. An additional advantage of this
line is that it is a fairly strong line with only the 3889 A line of comparable intensity11'.
7.4.3.2. The Fabry-Perot Etalon
In order to spectroscopically resolve the Doppler widths and in particular the
expected small Doppler shifts, a Fabry-Perot interferometer has to be used. This
interferometer serves as a very narrow band optical filter yielding a high spectral
resolution. This is achieved by repetitive reflections between two parallel reflective plates
232
resulting in destructive interference for most of the incoming spectrum while passing
through a very narrow frequency band due to constructive interference possible at those
particular wavelengths and geometrical conditions along the optical path of the incoming
radiation that satisfies the condition (Figure 7.7):
mX = 2 nR d cosO
(7.53)
where nRis the index of refraction of the medium between the mirrors, 6 is the internal
angle of incidence, d is the mirror spacing and m is an integer, indicating that this
condition holds for higher order harmonics as well and the signal peaks passed through
are repeated periodically. Tuning of the interferometer to different wavelengths is
commonly achieved by changing the mirror spacing using piezoelectric crystals that
transform a corresponding electric signal into the required mechanical displacement.
Further important parameters characterizing a Fabry-Perot interferometer are its free
spectral range (FSR), its bandwith (Av or AX) in frequency or wavelength units
respectively and its finesse ( F ). The FSR is given by the distance between the signal
peaks and can be expressed as119:
FSRk = XlJ 2 n j t
(7.54)
FSRV = c I 2 n г
(7.55)
or
in wavelength or frequency units, respectively. The bandwidth, i.e. the HWHM width
of the signal peak being the least resolvable wavelength (frequency) difference can then
be written as
Angle e
Plasma
Light
Source
Collimating
Lens
Fabry-Perot
Etalon
Focusing Spectrometer
Lens
Entrance
Slit
Figure 7.7 Principle of the Fabry-Perot Etalon
234
AA = FSRJF
(7.56)
Av = FSR, I F
(7.57)
or
where F is the finesse which therefore measures the ability of the interferometer to
resolve closely spaced lines. The finesse is limited by effects which reduce the strength
of interference, such as mirror reflectivity of less than
1 0 0 %,
a poorly collaminated
incoming beam and imperfections regarding the mirror flatness, i.e. lack of parallelism.
Accordingly, the finesse is made out of three parts:
(7.58)
F1
F1,
F}
F}
where FR is the reflectivity finesse and written as
(7.59)
F,
*
l-R
R being the reflectivity of the mirrors. FP is the flatness finesse
Fp = M J 2
(7.60)
with Mm the fractional wavelength deviation from true flatness of the mirror and finally,
FP, is the pinhole finesse
p
.
(7.61)
DH
with D as the beam diameter at the entrance of the spectrometer, or, if a limiting
235
aperture is used, the aperture diameter. fL is the focal length of the lens projecting the
image into the spectrometer. It should be noted that a spectrometer has to be used in the
optical path between the Fabry-Perot etalon and the detector so as to filter out
superfluous signal peaks.
As can be seen, the finesse depends on aperture and mirror separation and the
FSR on wavelength and mirror separation so that these parameters will affect the
bandwidth. If the bandwidth of the etalon is considerably smaller than the free spectral
range, a scan of the analyzed spectral line can be performed by continuously tuning the
Fabry-Perot etalon to the appropriate wavelengths along the line.
The Fabry-Perot interferometer to be used in these experiments was manufactured
by Burleigh and has a finesse range from 25 at full aperture (12 mm) to 35 at 3 mm
aperture and a variable mirror separation from 0.1 mm to 10 mm. A Burleigh RC-44
ramp generator provides for periodic changes in mirror separation with ramp durations
lasting between 20 ms and 10 s, usually set at 200 or 500 ms, allowing for scanning the
desired spectral line. The ramp generator is also used for the final electronic alignment
of the Fabry-Perot etalon following a more crude mechanical alignment requiring both
mirrors to be perfectly parallel to each other. The alignment of the etalon is performed
so as to yield a maximum finesse. Figure 7.8 shows the output of the etalon when using
a
2
mm spacer and irradiated by a 6328
A He-Ne laser line.
Spectrometer slit widths
were set at only 20 n for this purpose in order to avoid saturation of the PMT and a 500
ms ramp was used. Sampling rate of the data collection program was 5 kHz. The finesse,
i.e. the FWHM over the FSR obtained after a multitude of such measurements performed
during the alignment process averaged out to be roughly 25. At a wavelength of 5876 A,
which was the wavelength of the He line to be investigated, a spectral resolution of 0.035
A follows.
236
F a b r y -P e r o t A lignm ent ( May 2 ,1 991 )
U n exp an ded B eam , 5 0 0 m s R om p, 5 kHz S am p lin g , Filter off. P ro g ram on
0 .7 2 0
0 .6 4 8
0 .5 7 6
c 0 .5 0 4
D
г 0 .4 3 2
.9-0.360
> ,0 .2 8 8
c 0.21 6
-5= 0 .1 4 4
0 .0 7 2
0.000
0
100
200
300
400 500 600
D ata Point
700
800
900
Figure 7.8 Output of the Fabry-Perot Etalon irradiated by the 6328
1000
A He line
237
7.4.3.3. Spectroscopic System
The spectrometer and data-acquisition system are the same as used for the
absolute continuum measurements. The overall optical set-up is shown in Figure 7.9. The
optical signal is fed into a movable beam steerer and a stationary mirror through two
apertures set at 1 mm diameter and roughly 400 mm apart. These two apertures provide
for the necessary beam collimation. The signal is then guided into the aperture of the
Fabry-Perot etalon and then focused onto the entrance slit of the spectrometer. From
here, the signal was amplified by the PMT and fed into a PC via the photometer and
A/D board described earlier. It was also possible to display the signal on an oscilloscope
in real time. Although the scope was too inaccurate to actually perform line-width
measurements, this instrument allowed a rapid evaluation of the signal which was
particularly important during alignment procedures.
By means of a beam splitter, the optical path could be rearranged so that the
signal can be either taken from the relatively stationary plasma inside the applicator or
from the high velocity gas exiting the choked nozzle. Comparisons of both signals was
supposed to allow determination of the Doppler shift and thus allow measurement of the
gas velocity in case the latter would have been sufficiently large.
7.4.3.4. Discussion of the Method
Although numerous efforts were undertaken to measure the Doppler-broadened
line width, no line signal could be detected using the optical system as discussed. A
couple of facts may have contributed to this failure.
Applicator
I1! 1
k BS
tk
p
T
A1
FP
A2
BSP
M1
T
L2
M2
I
L1
?
KM3
Figure 7.9 Optical Set-Up for the Circular Waveguide Experiment
239
First, as already noted before, the plasma sustained in the waveguide was rather
dim. Even for absolute continuum measurements the spectrometer slit widths had to be
opened up to 180 p compared to only 40 n required for the rectangular waveguide
plasmas.
Secondly, using two 1 mm apertures set 400 mm apart reduced the signal strength
even further. Combining these two factors with the reflection losses in the Fabry-Perot
etalon and the various mirrors (four altogether) placed into the optical path, as well as
the transmission losses through the lens in front of the spectrometer entrance slit,
probably rendered the signal-to-noise ratio too weak in order to detect any spectral lines.
Furthermore, previous investigations using this diagnostic method49 have raised
doubts regarding the accuracy of the obtained temperature values. Spectroscopic
measurements using Doppler broadening resulted in temperature data up to 3000 K
higher than those measured using the absolute continuum method49. It is possible that the
spectral resolution of the etalon is smaller than expected due to insufficient collimation
of the beam. Poor beam collimation is taken into account by the pinhole finesse that was
not included in the finesse measurements discussed earlier and performed elsewhere49.
Therefore, the attempt to measure heavy particle temperatures by means of the
Doppler broadening of the line was abandoned. It appears possible that similar
experiments could be repeated successfully in the future if a higher quality Fabry-Perot
etalon is used having a higher finesse.
240
7.5. Spectroscopic Results
7.5.1. Electron Temperatures measured for the Rectangular Waveguide
Figure 7.10 shows the measured electron temperatures for the rectangular
waveguide plasmas obtained with the absolute continuum method. As can be seen, they
all range between
1 2 ,0 0 0
and 12,800 K and are fairly constant with respect to incident
power, however, appear to increase slightly with mass flow rate and decreasing pressure.
The first two observations are easily explained in view of the coupling efficiency
measurements: increasing the input power level for a given mass flow rate will hardly
change the power absorbed by the plasma since any additionally supplied power is rather
reflected by the plasma than absorbed. This will cause the electron temperature to stay
fairly constant as well. On the other hand, increasing the mass flow rate results in larger
absorbed power values due to the skin effect which in turn can be used to raise electron
temperatures. While at 0.75 atm the latter effect is not as clearly seen, it seems that
lowering the pressure increases the electron temperature since the electron mean free path
is larger and thus the electrons can acquire more energy since losses due to collisions are
reduced.
It should be noted that the temperature values obtained at 0.75 atm have to be
interpreted more carefully. Due to the LTE assumption involved in the absolute
continuum method, the temperatures obtained for the lower pressure values should be
termed "LTE-temperatures" rather than electron temperatures. In order for them to be
interpreted as electron temperatures, LTE would have to be established, which might not
be the case at 0.75 atm. According to measurements made by Eddy99 on argon arcjet
plumes, electron temperatures in this pressure domain can actually range up to 1000 K
241
15000
A ? A --------- A ?A
ELECTRON
TEMPERATURE
x.
10000 -
-
0 0 .7 5 atm,
X 0.75 atm,
A 1.00 atm,
? 1.00 atm,
0 1.00 atm,
#1.00 atm,
5 0 0 0 --
0
i r
500
~l
750
i "i - i
i i
1000
I I
i l I l
1250
INPUT POWER
i l l
1500
8.75
28.32
10.33
21.67
52.00
83.17
mg/s,
mg/s,
mg/s,
mg/s,
mg/s,
mg/s,
22.55 cm/s
72.95 cm/s
19.89 cm/s
42.00 cm/s
99.36 cm/s
159.16 cm/s
i r iT
l
1750
2000
( W )
Figure 7.10 Measured Electron Temperatures obtained with the
Absolute Continuum Method vs. Input Power at various
Mass Flow Rates and Pressures
2250
242
lower than LTE temperatures determined by the absolute continuum method.
7.5.2. Electron Temperatures Measured for the Circular Waveguide
In Figure 7.11, the electron temperatures obtained for the circular waveguide
applicator using the absolute continuum method are shown. As can be seen, those
temperatures values are significantly lower than those obtained for the rectangular guide
and range between 10,000 K and 11,000 K. Furthermore, a slight yet barely noticeable
increase with respect to power can be noted for each pressure condition. This is in
agreement with the coupling efficiency measurements taken for the circular applicator.
Since in the circular guide the plasma is free to expand, increasing the input power leads
to an increase in plasma volume. Therefore, the temperature at the plasma center which
is the temperature depicted in Figure 7.11, might increase slightly since thermal
conduction from the plasma center outward decreases due to the fact that the plasma core
is surrounded by a thicker, hot plasma layer.
Over the pressure ranges considered, no pressure effect on the electron
temperature can be noted. Although higher pressures lead to higher mass flow rates as
shown in Figure 6.28, which, according to the observations made for the rectangular
waveguide, should result in increased coupling efficiencies due to cooling of the outer
plasma layers and increases in skin depth, higher pressures also decrease electron mean
free paths between collisions, so that the electrons can pick up less microwave energy
between collisions, reducing electron temperatures again. Since both effects are
adversary, a fairly constant temperature profile may result.
In Figure 7.12, two temperature values, one taken at the plasma center and the
243
Peak Electron Tem perature
C ircular W oveguide Applicator, He - P ro p ellan t
2000
1000
0000
9000
a>
3 8000
-*->
O
v. 7 0 0 0
0)
a
E
0)
6000
h- 5 0 0 0
C
o
1 .2 5
1 .8 0
2 .4 0
3 .0 0
4000
o
J0> 3 0 0 0
LU 2000
1000
0
a tm
a tm
a tm
a tm
*?
400
600
800
1000
1200
1400
1600
Input Power ( W )
Figure 7.11 Peak Electron Temperatures obtained with the Absolute Continuum
Method vs. Input Power for the Circular Waveguide Applicator
using Helium
244
Electron Tem perature Distribution vs. Power
C ircular W aveguide A pplicator, H e -P ro p ellan t, 1 .8 a tm
( K)
10500
Electron T em perature
11000
10000
9500
9000
o
?
C enterline T em perature
T em p eratu re 5 m m off C en ter
8500
8000
700
800
j _____ i_
900
1000
Input P ow er ( W )
1100
1200
Figure 7.12 Electron Temperature Profiles vs. Input Power for the
Circular Waveguide Applicator using Helium
245
other taken 5 mm off center, are plotted vs. input power for a gas pressure of 1.8 atm.
Only a very sght difference between these two values can be noted, indicating that the
electron temperature remains fairly constant across the entire plasma.
In Figure 7.13, the impact of variations in bluff body size on the electron
temperature were studied and no significant differences apart from a very minute
decrease in temperature for the 35 mm bluff body could be found.
7.5.3. Comparison of Electron Temperatures for Various Applicators
Figure 7.14 depicts various electron temperature data obtained for various
waveguide applicators at the same pressure conditions (1.25 atm). In all cases the fiber
optic diagnostic system described above was used and absolute continuum spectroscopy
was employed. Although the electron temperature data were taken over different power
ranges depending on applicator type, temperature profiles with respect to power have
been shown to be very flat in all cases and a comparison between those data sets
therefore appears valid.
As can be seen, the highest temperature values were found for the rectangular
guide while data for the circular cavity49 and the circular guide are within the same
range, the temperatures for the guide slightly exceeding those for the cavity. This seems
to indicate that it is not the applicator type (i.e. waveguide or cavity) that determines the
temperature as was suspected before48 but more specifically the actual field pattern
involved or the geometrical dimensions of the guide or a combination of both. In the case
of the circular waveguide using the TM0I mode and the resonant cavity using the TM012
mode, field configurations are very similar as are the temperature values. The rectangular
246
Variation of B lu ff-B o d y Size
Im pact on Electron T e m p era tu re , C ircular W aveguide A pplicator, Helium
12000
11000
,- .1 0 0 0 0
5
9000
з
8000
2
7000
|
6000
г
5000
o
o
4000
d
%
3000
w
2000
?
?
2 .4
3 .0
2 .4
3 .0
a tm ,
a tm ,
a tm ,
a tm ,
20
20
35
35
mm
mm
mm
mm
Bluff
Bluff
Bluff
Bluff
Body
Body
Body
Body
1000
n
800
900
1000
1100
1200
1300
Input Pow er ( W )
1400
1500
1 600
Figure 7.13 Impact of Variations in Bluff Body Size on the Electron
Temperature for the Circular Waveguide Applicator using Helium
247
Comparison of Electron Tem peratures
1 .2 5 a tm G as P r e s s u r e , H e - P ro p e lla n t
13000
* ? ?
12000
11000
sc 1 0 0 0 0
4)
u
9000
?4-1
oL_
8000
3
w 7000
cl
г 6000
4)
hC
oL.
?4-f
o
V
Ld
5000
4000
3000
?
?
o
Circular W aveguide A pplicator, 4 3 - 4 5 m g / s m a s s flow
R e c ta n g u la r W aveguide, 2 7 .5 m g / s m a s s flow
R e c tan g u la r W aveguide, 65.01 m g / s m a s s flow
C ircular Cavity ( P e n n S t a t e ), no flow
2000
1000
0
300
500
700
900
1100 1300 1500 1700 1900 2100 2300
Input P ow er ( W )
Figure 7.14 Comparison of Electron Temperatures obtained by Absolute Continuum
Spectroscopy for various Microwave Applicators
248
TE]0 mode, however, is completely different in its appearance.
Furthermore, the cross-sectional area of the rectangular guide is 24.56 cm2, the
circular guide applicator has a 75.2 cm2 cross section and for the cavity this area is
226.87 cm2. As a result, microwave field intensities are significantly higher for the
rectangular guide than for the circular guide, and significantly higher for the circular
guide than for the cavity which could have led to a similar trend for the electron
temperatures.
249
Chapter 8
CONCLUSIONS AND RECOMMENDATIONS
This investigation concentrated on the relatively new concept of using waveguideheated plasmas for space propulsion applications. An initial performance evaluation of
this new waveguide applicator type was performed and basic operational characteristics
of waveguide-heated microwave electrothermal thruster types were determined. To this
end, experimental testing of various waveguide applicator configurations was conducted.
Optimization of this new thruster concept for space applications, however, was beyond
the scope of this thesis. The thruster designs presented in this study can therefore only
be regarded as laboratory test devices and are very preliminary in nature, serving the
purpose of evaluating the potential future use of waveguide applicators for space
propulsion purposes rather than representing actual flight concepts.
Since waveguide plasmas are inherently unstable, attention was initially focused
on understanding and quantifying plasma propagation. Plasma velocities of up to 10 cm/s
were measured for the molecular gas nitrogen. For helium, what appeared to be a mode
change between two different modes of propagation was found. For power levels below
1550 W and 1 atm gas pressure, propagation velocities ranged between 10 to 90 cm/s.
For higher power levels, however, a very sudden increase in plasma velocity to values
ranging between 2000 to 3000 cm/s was found. It was assumed that this increase in
plasma velocity was due to a change in the driving propagation mechanisms from heat
conduction to possibly resonant radiation. This assumption could, however, not be
confirmed conclusively. In particular, no high confidence was placed in numerical
250
investigations performed to this end due to extensive simplifications in the numerical
model.
Next, a crucial step toward utilization of this waveguide concept for space
propulsion applications was made by successfully stabilizing the plasma by means of a
bluff body. Stabilization was reported to be easy to achieve and handle, however, was
limited by both an upper and a lower power value whose magnitude depended on the gas
pressure in the discharge vessel. Furthermore, a complex behavior of the stabilized
plasma, involving not only plasma-flow field but also plasma-microwave field and even
plasma-bluff body material interactions was noted. In particular the latter interactions are
not understood at all yet and require further investigation. Plasma-microwave field
interactions could successfully be exploited to enhance plasma stabilization. The reason
for this behavior was found in the fact that even for waveguides truly propagating field
distributions do not exist; rather, reflections of such waveguide components as
terminations and dummy loads cause standing wave patterns to arise with the plasma
locating itself preferably in the maximum field regions.
The rectangular waveguide applicator was further used to obtain an initial
performance evaluation of this thruster type. Coupling efficiencies up to 90% were found
for a stabilized helium plasma. Increased mass flow rates resulted in clearly increased
coupling efficiencies which was attributed to the skin effect: cooling the outer gas layers
results in local electric conductivity decreases which allows the electromagnetic wave
pattern to penetrate deeper into the plasma so that the absorbing plasma volume together
with the absorbed microwave power is increased.
On the other hand, raising input power levels has been found to have an opposite
effect for rectangular waveguide plasmas. Since the plasma is relatively confined in the
narrow rectangular waveguide, additionally provided microwave power will not lead to
251
an expanding plasma absorbing this power, but rather be reflected by the plasma due to
its high electric conductivity. Thus, raising input power levels for rectangular waveguide
plasmas will result in reduced coupling efficiencies.
Although rectangular waveguide investigations were sufficient for initial
performance evaluations and general studies of plasma behavior in a waveguide, the fact
that in the governing TE ,0 mode the plasma was allowed to touch the waveguide walls
at two locations could be regarded as unacceptable for later use in space propulsion
devices due to erosion problems as well as thruster efficiency losses caused by heat losses
into the thruster structure. During the experiments performed here, where a quartz tube
was used to confine the test gas, melting of the tube occurred at those locations if
pressure levels were raised to values equal or greater than 1.5 atm.
Therefore, a circular waveguide applicator was designed based on the TM^ mode.
Testing of this applicator resulted in a plasma sustained in the center of the guide well
separated from the waveguide walls. High pressure tests up to 3 atm were conducted and
coupling efficiencies could be raised up to 96% which was much higher than before. This
microwave applicator configuration also used a simple converging conical nozzle in order
to obtain initial data on such rocket performance parameters as thruster efficiency,
specific impulse and thrust. Using quasi-one dimensional expressions for an ideal nozzle
expansion and measured data for mass flow rates, pressure and power levels, up to 40%
thruster efficiency and 350 sec specific impulse were calculated assuming ideal expansion
into a vacuum. Thrust levels were determined as high as 0.4 N using the same approach.
Spectroscopic measurements performed for both, rectangular and circular
waveguide applicators using the absolute continuum method yielded electron temperatures
between 12,000 and 13,000 K for the rectangular waveguide plasmas and corresponding
temperature values of 10,000 to 11,000 K for circular waveguides. Obtainable
252
temperature values were determined to be possibly influenced by the mode Held pattern
present in the guide as well as the cross sectional area of the guide, determining the
intensity of the microwave radiation at a given power level. Future investigations,
however, are recommended to validate these preliminary conclusions.
Although it was one of the goals for the circular waveguide applicator design to
be able to sustain a plasma close to the nozzle entrance to yield high nozzle inlet
temperatures and to result in increased specific impulse and thruster efficiency values,
this attempt clearly failed. Microwave field distortions caused by insertions of dielectric
materials into the waveguide and non-ideal coaxial-to-circular guide transitions resulted
in a plasma position roughly 14 cm above the nozzle inlet. Comparing the performance
of this applicator with others lead to the suggestion that it was this increased separation
between plasma and nozzle entrance that might have led to the poor performance of this
thruster concept.
It seems possible that reducing the overall height of the circular waveguide
applicator might result in rearranged field patterns, allowing a plasma to form closer to
the nozzle inlet. Future experiments with the circular waveguide applicator should be
directed to this end.
These experiments could be supported by numerical calculations in order to
determine the actual field pattern present in the transition region. Due to the geometry
involved, however, these calculations would require the development of 3-D codes. A
working numerical model, however, allowing the determination of field configurations
or even plasma locations in such three-dimensional geometries could significantly benefit
the design process.
Although a proof-of-concept study had been attempted for the waveguide-heated
microwave electrothermal thruster, it could be argued that this goal has not been reached.
253
Although it could be proven that energy can be transferred from a microwave discharge
sustained in a waveguide applicator to the propellant and then be converted into thrust,
performances of the circular waveguide applicator were rather poor compared to other
electric propulsion devices, including other microwave applicators (compare with Table
2.2). It appears that in order to improve the performance of the waveguide applicator in
particular and microwave electrothermal thrusters in general four major areas of future
research can be identified: plasma stabilization, plasma positioning, boosting the specific
impulse and microwave discharge physics.
Plasma stabilization will be required in order to be able to operate microwave
electrothermal thrusters at power levels higher than 2 to 3 kW as possible today. Higher
power levels will be necessary to achieve larger thrust values required for sufficiently
fast orbit transfer missions, for example.
Proper plasma positioning appears to be a prerequisite for optimal heat transfer
from the plasma to the propellant flow. Preliminary investigations seem to suggest that
a plasma location close to the nozzle entrance is the most optimal position in this regard.
Both plasma stabilization as well as optimized plasma positioning will aid the third
requirement of boosting the specific impulse of microwave electrothermal thrusters.
While the circular waveguide applicator investigated in this thesis was capable of
delivering only 350 sec of specific impulse, other applicators such as the resonant cavity
also did not exceed specific impulse values of 600 sec. This performance is
unsatisfactory. Enhanced plasma stabilization could lead to higher thruster input powers
and improved plasma positioning to increased energy transfer from the plasma to the
propellant which should increase the obtainable specific impulse. Especially designed
low-Reynolds number flow nozzle configurations rather than using simple converging
conical nozzles as was the case throughout this investigation could further improve
thruster performance.
254
Finally, it appears absolutely necessary to gain a deeper understanding of
microwave discharge physics. If more than 90% of the microwave power is absorbed by
the plasma, yet only 40% of this power is converted into thrust, where does the power
go? What is the portion of the power that is lost due to conduction, radiation or viscous
losses? Although some investigations performed in the course of this study indicated that
radiative losses are minimal, considerable doubt in these results persists as these results
were obtained by extensively simplified numerical calculations only. Or is it possible that
a strong non-equilibrium exists between the electrons that initially receive all the
microwave energy due to their high mobility and the heavy particles and that energy
transfer between these two species is poor in the time that it takes the propellant to exit
the nozzle? Average heavy particle temperatures thus would remain low and performance
of the microwave thruster limited. For microwave thruster designs employing
converging-diverging nozzles the determination of frozen flow losses should be
incorporated in these investigations. Answers to these questions would help to address
key problems in the development of microwave electrothermal thrusters and result in a
more intelligent design process, benefiting the development of future microwave thruster
concepts.
In this context it should also be pointed out the need for more advanced optical
diagnostic methods required to better understand the ongoing physical processes in a
microwave discharge. So far, emission spectroscopy was employed throughout the
investigations performed here, suffering from poor signal strength as well as the fact that
assumptions on the equilibrium state of the plasmas had to be made. More advanced,
state-of-the-art laser diagnostic methods would improve plasma diagnostics and possibly
help to answer some of the questions mentioned above.
It therefore seems fair to say that this thesis has posed more questions than it has
255
answered as is the case in many new fields of research. Although in this study for the
first time a concrete effort was made to take control over the plasma location by
attempting to tailor an appropriate field distribution in the waveguide and despite the fact
that it was possible to stabilize a waveguide-heated plasma at least over a restricted
microwave power range, significant future research efforts will be necessary to optimize
the microwave electrothermal thruster concept for space applications. Controlling the
plasma position using the circular waveguide applicator essentially failed and there is a
definite need to stabilize plasmas in microwave thrusters at significantly higher power
levels than encountered here. If possible, plasma stabilization should be obtained by
means other than the insertion of bluff bodies into the flow as these will result in
microwave field distortions and possibly lead to erosion or heat loss problems. This
thesis should therefore be regarded as a starting point to extensive future research
required in this field.
Despite the very early stage of microwave electrothermal thruster development,
however, significant progress can be reported. In particular thruster efficiencies obtained
are very competitive compared with those obtained for arcjets, and other microwave
applicator types are currently able to compete with arcjets and resistojets in terms of
specific impulses (see Table 2.2). Recognizing the early development status of microwave
electrothermal thrusters, there still appears to be a potential for future performance
increases. Higher lifetime expectations based on the electrodeless discharge concept of
a microwave thruster, possible advances in plasma positioning and stabilization and
adapting specially designed low-Reynolds number nozzle configurations could further
increase the attractiveness of the microwave electrothermal thruster concept. Therefore,
future development efforts in this area appear desirable and justified.
256
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V.I. and Chimnov, V.F., "Experimental Study of a Quasi-CW Discharge in
Helium at High Pressure", Sov.J.Plasma Physics, 3(6), Nov.-Dee. 1977, pp. 759762.
71.
Kemp, N.H. and Root, R.G., "Analytical Study of Laser-Supported Combustion
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72.
Beust, W. and Ford, W.L., "Arcing in CW Transmitters", The Microwave
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73.
Bethke, G.W. and Ruess, A.D., "Microwave-Induced Plasma Shield Propagation
in Rare Gases", Physics of Fluids, Vol. 12, No. 4, April 1969, pp. 822-835.
74.
Batenin, V.M., Klimovskii, I.I. and Khamraev, V.R., "Propagation of a
Microwave Discharge in Heavy Atomic Gases", Sov.Phys. JETP, Vol. 44, No.
2, Aug. 1976, pp. 316-321.
75.
Batenin, V.M., Baltin, L.M., Devyathin, I.I., Lebedeva, V.P. and Tsemko, N.I.,
"Stationary Microwave Discharge in Nitrogen at Atmospheric Pressure", UDC
537.523, 1972, Consultants Bureau, Plenum Publ. Co., pp. 1019-1025.
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Batenin, V.M., Devyathin, I.I., Zrodnikov, V.S., Klimovskii, I.I. and Tsemko,
I.I., "Experimental Investigation of the Motion of an Ionization Front in a
Microwave Electromagnetic Field", UDC 537.56, 1972, Consultants Bureau,
Plenum Publ. Co., pp. 814-818.
77.
Raizer, Y.P,, "Propagation of a High Pressure Microwave Discharge", Sov.Phys.
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78.
Batenin, V.M., Zrodnikov, V.S., Klimovskii, I.I. and Khamraev, V.R.,
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Meierovich, B.E., "Contribution to the Theory of an Equilibrium High-Frequency
Gas Discharge", Sov.Phys. JETP, Vol. 14, No. 5, May 1972, pp. 1006-1013.
80.
Myshenkov, V.I. and Raizer, Y.P., "Ionization Wave Propagating because of
Resonant Quanta and Maintained by Microwave Radiation?, Sov.Phys. JETP,
Vol. 34, No. 5, May 1972, pp. 1001-1005.
81.
Batenin, V.M., Zrodnikov, V.S., Klimovskii, I.I., Ovcharenko, V.A. and
Tsemko, N.I., "Magnetic-Field Stabilized Microwave Discharge", UDC
537.525.1, Consultants Bureau, Plenum Publ. Co., 1972, pp. 1186-1187.
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82.
Hill, P.G. and Peterson, C.R., Mechanics and Thermodynamics of Propulsion.
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83.
Rizzi, P.A., Microwave Engineering-Passive Circuits. Prentice Hall, Englewood
Cliffs, NJ, 1988.
84.
Gandhi, O.P., Microwave Engineering and Applications. Pergamon Press, New
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85.
Greiner, W., "Klassische Electrodynamik". Verlag Harri Deutsch, Frankfurt am
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86.
Feynman, R.P., Leigthon, R.B. and Sands, M., Lectures on Phvsics. Vol. 2,
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Gerling, J., personal communication, August 1991.
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Venkateswaran, S. and Merkle,C.,"Numerical Modeling of Waveguide-Heated
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90.
Venkateswaran, S. and Merkle, C.,"Numerical Investigation of Bluff Body
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91.
Gerling, J., personal communication, Spring 1991.
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John, J.E.A., Gas Dynamics. Allyn and Bacon, Boston, 1984.
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94.
Maul,W.A.,"The Characteristics of a Stationary Free-Floating Nitrogen
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95.
Balaam, P. and Micci, M.M., "Performance Measurements of a Resonant
Cavity Electrothermal Thruster", IEPC Paper 91-031, 22nd
AIDAA/AIAA/DGLR International Electric Propulsion Conference, Oct. 14-17,
1991, Viareggio, Italy.
264
96.
Lochte-Holtgreven, W., Plasma Diagnostics. North-Holland Publ. Co.,
Amsterdam, 1968.
97.
Griem, H.R., Plasma Spectroscopy. McGraw Hill, New York, 1964
98.
Irmer, J., "Die Zusammensetzung thermischer Edelgasplasmen im
Temperaturbereich von 1000-20,000 K bei Drucken von 1-50 atm", Akademie
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99.
Eddy, T.L.., "Low Pressure Plasma Diagnostic Methods", AIAA Paper 89-2830,
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100. Eddy, T.L. and Sedghinasab, A., "The Type and Extent of Non-LTE in Argon
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August 1988.
101. Cho, K.Y., "Nonequilibrium Thermodynamic Models and Applications to
Hydrogen Plasmas", Ph.D. Thesis, Georgia Insitute of Technology, July 1988.
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Marr, G.V., Plasma Spectroscopy. Elsevier Publ. Co., Amsterdam, 1968.
103.
Bastiaans, G.J. and Mangold, R.A., "The Calculation of Electron Temperature
in Ar Spectroscopic Plasmas from Continuum and Line Spectra", Spectrochemica
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104.
Berger, J.M ., "Absorption Coefficients for Free-Free Transitions in a Hydrogen
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Hofsaess, D., "Emission Continua of Rare Gas Plasmas", J.Quant. Spectrosc.
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106.
Baranger, M., "Spectral Line Broadening by Plasmas", Atomic and Molecular
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107. Gasiorowicz, S., Quantum Physics. John Wiley & Sons, New York, 1974.
108. Greiner, W., Ouantenmechanik. Teil 1, Verlag Harri Deutsch, Frankfurt, 1989.
109. Griem, H. R., Kolb, A.C. and Shen, K. Y., "Stark-Broadening of Hydrogen Lines
in a Plasma", Phys.Rev., Vol.116, No. 1, pp. 4-16, October 1959,
110. Griem, H.R., Baranger, M., Kolb, A.C. and Oertel, G., "Stark-Broadening of
Neutral Helium Lines in a Plasma", Phys.Rev., Vol. 125, N o.l, pp. 177-195,
Jan. 1962.
2 (5
111.
Berg, H.F., Ali, W, and Griem, H.R., "Measurement of Stark-Profiles of
Neutral and Ionized Helium and Hydrogen Lines from Shock-Heated Plasmas in
Electromagnetic T Tubes", Phys.Rev., Vol. 125, No. 1, pp. 199-206, January
1962.
112.
Kelleher, D.E., "Stark-Broadening of Visible Neutral Helium Lines in a Plasma",
J. Quant.Spectrosc.Radiat.Transfer, Vol. 25, pp. 192-220, 1981.
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Burgess, D.D., "Electron Temperature Measurements using the Stark-Effect?,
Physics Letters, Vol. 10, No. 3, June 1964, pp.286-287
114.
Burgess, D.D. and Cooper, J., "A New Method of Measuring Electron
Temperatures in Plasmas in Absence of Local Thermal Equilibrium",
Proc.Phys.Soc., Vol. 8 6 , pp. 1333-1341, 1965.
115.
Armstrong, B.H., "Spectrum Line Profiles: The Voigt
J.Quant.Spectrosc.Radiat.Transfer, Vol. 7, pp. 61-88,1967.
116.
Pivirotto, T.J. and Deininger, W.D., "Velocity Measurements in the Plume of
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117.
Barr, W.L.,"Method for Computing the Radial Distribution of Emitters in a
Cylindrical Source", Journal o f the Optical Society o f America, Vol.52, No.8 ,
August 1962, pp.885-888.
118.
Atomic Transition Probabilities, Hydrogen through Neon, Natl.Bureau of
Standards, NSDRS-NBS 4, Vol.l.
119.
Hecht, E. and Zajac, A., Optics. 2nd edition, Add. Wesley, Reading, 1987.
Function",
266
APPENDIX A
TUNGSTEN WIRE-MICRQWAVE FIELD INTERACTIONS
Ignition of waveguide plasmas was obtained by means of tungsten wire ignition
throughout the experiments. In particular for the rectangular waveguide, where the wire
could not be removed out of the guide upon ignition but remained exposed to microwave
irradiation, questions arose on how much microwave power was absorbed by the wire
rather than the plasma. A significant power absorption by the wire could have resulted
in much higher measured coupling efficiencies than could have actually been obtained
with the plasma alone.
Since in the case of the circular waveguide applicator, the wire could be removed
through the nozzle opening after ignition, comparative measurements could be made with
the wire either present in the guide or not. Figure A .l shows the impact of the tungsten
wire microwave absorption in the circular guide. As can be seen, the difference in
percentage points for the coupling efficiency increase with input power, however, level
off around 2 to
6
percentage points, depending on pressure conditions. Higher gas
pressures result in larger differences in coupling efficiencies. In Figure A.2 the
corresponding absorbed power levels for the wire are depicted. In the higher pressure
case, up to 45 W were absorbed by the wire while in the lower pressure case only up to
10 W were absorbed.
In the case of the rectangular waveguide, the wire was located perpendicularly to
the electric field lines while in the case of the here performed measurements with the
circular applicator the wire was aligned with the electric field lines. Therefore, the here
obtained results can be considered as an upper limit regarding the errors in coupling
267
Tungsten-W ire Effect
Im pact on Coupling E fficiency,C ircular W aveguide,Helium ,W ire parallel to Field
100
- 20
95
18
90
16
85
u
c 80
0)
u
75
LJ
CT
?C
70
O
?
?
A
A
1.2 atm , w /o Tungsten-W ire
1.2 atm , with Tungsten-W ire
1.5 atm , w /o Tungsten-W ire
1.5 atm , with Tungsten-W ire
Difference in Coupling Efficiency, 1.2 atm
Difference in Coupling Efficiency, 1.5 atm
14
K
>N
o
c
<u
o
H?
12
llJ
a>
c
10
a.
8
O
o
6
at
3
4
o
c
0!_)
0)
2
n
500
600
700
Input P ow er ( W )
900
Figure A .l Coupling Efficiencies obtained for the case of a Tungsten-Wire inserted
into the Circular Waveguide Applicator
268
Tungsten-W ire Effect
Im pact on A bsorbed Pow er, C ircular W aveguide,Helium,W ire parallel to Field
200
BOO
180
700
160
600
140
*500
o
CL
120 "8
1.2 olm , w^o Tungsten -Wire
1.2 otm , with Tungsten-W ire
1.5 otm , w /o Tungsten-W ire
t .5 atm , with Tungsten-W ire
Difference in Absorbed Power, 1.2 o tm
Difference in Absorbed Power, 1.5 a tm
a- 4 0 0
100 o
< 200
100
300
400
500
700
600
Input P ow er ( W )
800
900
Figure A.2 Microwave Power Absorption by a Tungsten Wire inserted into the
Circular Waveguide Applicator
efficiencies induced by the wire in the rectangular applicator.
270
APPENDIX B
VARIATION OF BLUFF-BODY SIZE
In order to determine the impact of variations in bluff-body size on thruster
performance parameters of the circular applicator, two different bluff body cones shown
in Figure 6.9 have been used for testing. The cones compared were a 20 mm base
diameter cone of 25 mm height and a 35 mm cone of the same height. As shown on
Figure 6.9, the "cones" consisted of a 15 mm long cylindrical section of 15 mm in
diameter providing the joint to the horizontal mounting rod. The cylindrical section then
went over into a conical section of 10 mm height. Thus, the 20 mm cone resulted in a
flow deflection angle of 14░ and the 35 mm cone in a flow deflection angle of 45░.
Comparisons made for these two cones are shown in Figures B.l through B.6 .
Figure B.l demonstrates that coupling efficiencies obtained for the circular
applicator are virtually identical for both bluff bodies. Remaining differences in coupling
efficiencies for both cases are well within the margin of error of 0.5 percentage points
established in Chapter 6 . Stability boundaries for the two different bluff body cases are
shown in Figure B.2. As can be seen, stability boundary values have shifted to lower
power values for the larger body. In the case of the upper stability boundary this may
be associated with the larger recirculation region behind the bluff body, imposing greater
gasdynamic forces on the plasma, trying to "suck" it into the larger recirculation zone.
However, a satisfactory explanation for the shift of the lower stability boundary could
not be found. Although statistical uncertainties are common regarding gas breakdown and
therefore extinction processes, in this case a definite trend towards extinction at lower
271
Variation of B lu ff-B o d y Size
Im p a c t on Coupling Efficiency, Circular W aveguide Applicator, H e -P ro p e lla n t
100
90
^
0>N
70
1
60
UZ
50
i▒j
1
2.2
3.0
2.2
3 .0
40
з? 3 0
o
░
o tm ,
a tm ,
a tm ,
a tm ,
20
20
35
35
mm
mm
mm
mm
Bluff
Bluff
Bluff
Bluff
Body
Body
Body
Body
20
600
800
1000
1200
1400
Input Pow er ( W )
1600
1800
2000
Figure B.l Impact of Variations in Bluff-Body size on Coupling Efficiencies
for the Circular Waveguide Applicator using Helium
272
Variation of B luff-B od y Size
Im p a c t on Stability B oundaries, C ircular W aveguide Applicator, Helium
2400
2200
2000
1800
?
o
?
?
Upper Stability Boundary, 20 mm Bluff Body
Lower Stability Boundary, 20 mm Bluff Body
Upper Stability Boundary, 35 mm Bluff Body
Lower Stability Boundory, 35 mm Bluff Body
^1600
4)
1400
$
O 1200
a.
3 1000
a
c
800
600
400
200
1 .0
1.3
1.6
1 .9
2 .2
Gas P re ssu re ( Atm )
2.5
2.8
3.1
Figure B.2 Impact of Variations in Bluff-Body Size on Stability Boundaries
of the Circular Waveguide Applicator using Helium
273
power values, was observed.
Surprising are also the decreased performances of the thruster with respect to
nozzle inlet temperature ( Figure B .3), overall efficiency ( Figure B .4), specific impulse
( Figure B .5) and specific power ( Figure B.6 ) for the larger bluff body. A satisfactory
explanation for these effects has not yet been found.
Thus, selection of bluff body size not only has an anticipated impact on the
stability behavior of the plasma but influences overall thruster performances as well. In
the here considered case, the smaller diameter bluff body performed better than the
larger body although a satisfactory explanation for this behavior has not yet been
discovered.
274
Variation of Bluff -B o d y Size
Absorbed Power and Calculated Nozzle Inlet Temperature, Circular Waveguide, He
2000
2000
2.2
3.0
2.2
3.0
1800
16 0 0 h
atm ,
atm ,
atm ,
atm ,
20
20
35
35
mm
mm
mm
mm
Bluff
Bluff
Bluff
Bluff
Body
Body
Body
Body
18002
5 1400
1600
1 1 200
o
a. 1000
?o
0)
nu 8 0 0
O
to
a>
a
p
5
14001
h-
aj
1200 =
0)
?O 6 0 0
<
N
400 -
200
?nooo-i
-
800
0
600
800
1000
1200
1400
Input P ow er ( W )
1600
1800
2000
Figure B.3 Impact of Variations in Bluff-Body Size on Absorbed Power
and Nozzle Inlet Temperatures for the Circular
Waveguide Applicator using Helium
275
Variation of B lu ff-B o d y Size
Im pact on C alculated Overall Efficiency, C ircular W aveguide, Helium
50
N
>s
O
4>
U
Ld
O
L.
2 .2
3 .0
2 .2
3 .0
V
>
o
600
800
1000
a tm ,
a tm .
a tm ,
a tm ,
20
20
35
35
mm
mm
mm
mm
Bluff
Bluff
Bluff
Bluff
1200
1400
Input P ow er ( W )
Body
Body
Body
Body
1600
1800
2000
Figure B.4 Impact of Variation in Bluff-Body Size on Thruster Efficiencies
for the Circular Waveguide Applicator using Helium
276
Variation of B lu ff-B o d y Size
Im pact on C alculated S pecific Im pulse, C ircu lar W aveguide, Helium
500
450
SI 3 0 0
9 -250
o 200
2 .2
3 .0
2 .2
3 .0
150
100
600
800
1000
a tm ,
a tm ,
a tm ,
a tm ,
20
20
35
35
mm
mm
mm
mm
Bluff
Bluff
Bluff
Bluff
1200
1400
Input P ow er ( W )
body
Body
Body
Body
1600
1800
2000
Figure B.5 Impact of Variations in Bluff-Body Size on Specific Impulse
for the Circular Waveguide Applicator using Helium
277
Variation of B lu ff-B o d y Size
Im p act on Specific Pow er, C ircular W aveguide A pplicator, H e -P ro p e lla n t
16
14
8
6
v
a
o
?
?
?
4A
2
л600
2 .2 a tm , 2 0 m m
3 .0 a tm , 2 0 m m
2 .2 a tm , 3 5 m m
3 .0 a tm , 3 5 m m
Bluff Body
Bluff Body
Bluff Body
Bluff Body
0
800
1000
1200
1400
Input Pow er ( W )
1600
1800
2000
Figure B.6 Impact of Variations in Bluff-Body Size on Specific Power
for the Circular Waveguide Applicator using Helium
278
APPENDIX C
PLASMA-BLUFF BODY INTERACTIONS
Plasma-bluff body interactions are not only limited to plasma stability
considerations but also reveal a very complex nature once the plasma is in touch with the
body. As shown in Figure C .l, when the spacing between the plasma and the bluff-body
is plotted vs. power, the plasma goes through a hysteresis in the spacing-input power
plane. Increasing the power level will cause the upper stability boundary to be reached,
where the plasma is in contact with the body and the spacing is zero. Further increases
in power will not change the plasma position next to the body any further.
However, if the input power is reduced, the plasma will not detach immediately
at the power level defined by the upper stability boundary, rather, it will remain in touch
with the body down to a power level roughly 2 0 % below the upper stability boundary.
In some cases, the plasma breaks up into two smaller plasmas just before this power level
is reached, one at the original plasma position in the maximum field region and a smaller
plasma still in contact with the bluff body. Thus there exists a range of power levels
where the plasma may exist separated as well as in contact with the bluff body depending
on the history of changes of the input power level.
The phenomenon observed during the comparison of data obtained from these two
plasma states are complex and not at all understood yet. The coupling efficiencies shown
in Figure C.2, for example, are higher for the plasma in contact with the bluff body at
pressures of 1.8 and 2.2 atm. For the 20 mm bluff body, differences in coupling
efficiencies for the 1.8 atm curves ranged from roughly 1 to 4 percentage points and for
279
Stability?Hysteresis
?3 10
c
3
L.?
D.
L.
o
CP
c
?u
o
Q.
V)
>*.
?O
o
CD
_D
CD
I
O
E
(0
_o
Bluff Body
CL
Input P ow er ( arb rita ry u n i ts )
Figure C .l Stability-Hysteresis for the Plasma in Interaction with the
Bluff-Body Flow Field in the Circular Waveguide Applicator
280
P la s m a -B lu ff Body Interactions
Im pact on Coupling Efficiency, Circular Waveguide Applicator, He-P ropellant
100
K
95
4 ^
X
o
c
a> 9 0
o
o
a
A
v
O
o> 85
Q.
3
O
░
?
?
50
A
V
?
1.8 atm, 20 mm Bluff Body, Plasma n o t in to u c h
2.2 atm, 20 mm Bluff Body, Plasma n o t in to u c h
2.6 atm, 20 mm Bluff Body, P la s m a n o t in to u c h
1.8 atm, 35 mm Bluff Body, Plasma n o t in to u c h
2.2 atm. 35 mm Bluff Body, Plasma n o t in to u c h
1.8 atm, 20 mm Bluff Body, Plasma in to u c h
2.2 atm, 20 mm Bluff Body, Plasma in to u c h
2.6 atm, 20 mm Bluff Body, Plasmo in to u c h
1.8 atm, 35 mm Bluff Body, Plasma in to u c h
2.2 atm, 35 mm Bluff Body, Plasma in to u c h
-L .
75
700
800
900 1000 1100 1200 1300 1 400 1500 1600 1700
Input Power ( W )
Figure C.2 Plasma-Bluff Body Interactions affecting Coupling Efficiencies
for the Circular Waveguide Applicator using Helium
281
the 2.2 atm curves from less than 0.5 to about 1.5 percentage points. Differences of less
than 0.5 percentage points are within the margin of error for the determination of
coupling efficiencies, however, for most of the data points shown differences in coupling
efficiencies are clearly exceeding this margin.
It could be noted, however, that at even higher pressures coupling efficiencies of
the plasma in contact with the bluff body are lower than those obtained for the separated
plasma. As can be seen from Figure C.2, for the 2.6 atm curves coupling efficiencies
are up to 1.5 percentage points lower for the plasma being in touch with the body than
for the separated plasma. Toward higher power levels, however, these differences in
coupling efficiencies shrink below the margin of error of 0.5 percentage points. The
cross over observed between the 2 .6 atm curve pair at these power levels therefore might
be associated with measurement errors.
The bluff body size seems to have an impact on this effect as well. As indicated
in Figure C.2, a larger diameter bluff body ( 35 mm ) shows significantly enhanced
differences between the coupling efficiencies obtained for both cases while following the
same trend. For gas pressures of 1.8 and 2.2 atm these differences now amount to
considerable 4 to
6
percentage points where the coupling efficiencies are higher for the
plasma in touch with the body than for the separated plasma.
In an attempt to explain this behavior of the coupling efficiency with respect to
the plasma-bluff body interactions, absorbed, reflected and transmitted power values were
measured individually. Figure C.3 proves that it is the behavior of the reflected power
that dictates the observed changes in coupling efficiency, while transmitted powers
remain fairly unchanged. At lower pressures, for both the 20 mm as well as the 35 mm
bluff body, reflected power levels drop as the plasma approaches the bluff body. At
higher pressures, on the other hand, reflected power levels increase for a plasma in
282
P la s m a -B lu ff Body Interactions
Im pact on R eflected an d T ra n sm itte d Pow er, Circular W aveguide, Helium
200
o
?
й
,1 8 0
l.
a> 160
*
o
0. 140
X)
a)
120
E
in 1 0 0
c
1.8 atm , 2 0 m m Bluff Body
2 .6 atm , 2 0 m m Bluff Body,
2.2 atm , 3 5 m m Bluff Body
1.8 atm , 20 m m Bluff body
2 .6 atm , 20 m m Bluff body,
2.2 atm . 35 m m Bluff Body
1.8 atm , 20 m m Bluff body
2 .6 atm , 20 m m Bluff Body,
2.2 atm , 3 5 m m Bluff Body
1.8 atm , 20 m m Bluff body
2 .6 atm , 20 m m Bluff body,
2 .2 atm , 35 m m Bluff Body
Reflected Power, Plasm a not in touch
Reflected Power, Plasm a in touch
Transm itted Power, P lasm a not in touch
Transm itted Power, P lasm a In touch
г
80
?a
c
o 60
?o
-й
f 40
o
й
s?
й
20
(X
0
800
900
1000
1100
1200
1300
Input Pow er ( W )
1400
1500
1600
Figure C.3 Reflected and Transmitted Powers as affected by
Plasma-Bluff Body Interactions in the Circular Waveguide Applicator
using Helium
283
contact with the bluff body. Changes in reflected power levels of up to SO % for the
small body and exceeding 90 % for the larger body could be observed, making these
effects easily observable and reproducable.
Trying to understand the physical mechanisms involved in these processes seems
difficult considering the preliminary nature of these measurements. Both plasma
conditions as well as bluff body size seem to influence the interactions between the
plasma, the bluff body and the microwave field. It is possible that an explanation for this
behavior may be found in possibly temperature-dependent microwave field-boron nitride
interactions, noting that the heat load to the bluff body increases as the gas pressure is
raised. Here, only the experimental data shall therefore be presented, a more detailed
explanation of this phenomenon will have to be postponed until more comprehensive
measurements have been performed, varying such parameters as gas pressure, gas
species, bluff-body material as well as the geometrical shape of the body, for example.
Plasma-bluff body interactions are even further reaching and have a peculiar effect
on the mass flow rate. Using the 20 mm diameter bluff body, a very slight drop in mass
flow rate was observed whenever the plasma moved in touch with the body. This mass
flow rate drop occurred at the exact moment when the plasma touched the body. No such
effect was noted for the 35 mm bluff body. Even for the 20 mm body the effect was very
small, reaching the margin of error of 5 % associated with the mass flow measurements.
The change in mass flow rate would therefore most likely have escaped attention if the
movement of the stainless steel ball in the Omega FL 223 rotameter-type flowmeter
would not have been observed at the moment the plasma made contact with the body.
This allowed for a relative mass flow measurement between the flow rate where the
plasma is separated from the body and the one where it is in touch with the body,
making the small difference between these flow rates apparent.
284
No obvious explanation for this behavior could be found. Although it is
theoretically possible to interpret the drop in mass flow rate by an increase in nozzle inlet
temperature according to Equation (6.14), it would be very difficult to find a plausible
explanation for such a sudden temperature increase. At least initially the much cooler
bluff body should act as a heat sink for the plasma, resulting in thermal losses rather than
in a performance increase for the thruster which would follow according to Equations
(6.15) and (6.16). It would also remain unclear why this effect could not be noted for
the larger bluff body. Nevertheless, the effect of a drop in mass flow rate upon the
plasma touching the bluff body was repeated many times for the
20
mm body and the
probability of an experimental error can therefore be considered as very small in this
case. More detailed, future experiments, however, are necessary to find a conclusive
answer to explain this phenomenon.
285
APPENDIX D
THERMAL TRANSIENTS
A thermally transient behavior was noted upon ignition of a plasma in the circular
waveguide applicator. For a period of 2 to 3 minutes, the plasma was observed to
undergo severe oscillations and displacements out of its normal position in the center of
the guide. In some instances, these displacement were so significant that the plasma, now
far removed from the maximum field region it is usually located in, extinguished again.
After this time period, from now on referred to as "warm-up period", these the
instabilities died down. A more detailed investigation of this warm-up period revealed
that not only nozzle inlet temperatures and subsequently all the other rocket performance
parameters were affected, but also the interaction processes between the microwave
radiation and the plasma.
In Figure D. 1, coupling efficiencies are shown for various pressures for both cold
starting conditions right upon ignition and thermal equilibrium which was determined by
observing the performance parameters measured. If no further changes for these
parameters could be noted, thermal equilibrium was said to be reached. As mentioned,
this period was usually reached after roughly 2 to 3 minutes. As can be noted on Figure
D. 1, coupling efficiencies are lower for the cold starting conditions than for the thermal
equilibrium state. However, for the case of 1.8 atm and the higher power levels of the
2.2 atm case these changes are within the margin of error of 0.5 percentage points found
for the coupling efficiency in Chapter 6 . For the lower power values of the 2.2 atm case
and the
2 .6
atm case, however, the trend of reduced coupling efficiencies during the
286
Thermal.Transients
Impact on Coupling Efficiency, Circular Waveguide Applicator, He-Propellant
100
95
N
s?^
O
c 90
a>
o
lii
o> 85
c
a.
3
O
o 80
75
600
0
1.8 a tm
2.2 a tm . Therm al Equilibrium
2.6 a tm
1.8 a tm
2.2 a tm , Cold S ta rtin g Condition
2.6 a tm
?
A
?
?
A
_l
700
I
800
I
I
900
I
-I I I l_
1000 1100 1200 1300 1400 1500 1600
Input P ow er ( W )
I
I
I
I
I
L.
Figure D. 1 Effect of Thermal Transients on the Coupling Efficiencies of a
Circular Applicator using Helium
287
warm-up period has clearly been established.
In an attempt to explain this behavior of the coupling efficiency, the individual
power levels were monitored. As Figure D.2 demonstrates, those differences in measured
coupling efficiencies can once again be explained by the corresponding behavior of the
reflected power levels. The transmitted power level again is rather unaffected, while
reflected power levels, on the other hand, are slightly higher just upon ignition. The
differences in reflected power levels amount to about 10 W or roughly 20% of the
reflected power level in thermal equilibrium. Changes in reflected power levels that high
could easily be measured with the available diagnostic equipment. As a result of the
increase in reflected power levels during the warm-up period, a slight decrease in
absorbed power can be noted. An explanation for this behavior of the reflected power
value under the changing thermal conditions of the applicator could not be found after
these preliminary investigations. It seems possible, however, that temperature dependent
electrical properties of the dielectric materials inserted in the applicator as well as the
bulk of the propellant gas might have played a role. This assumption, however, is merely
speculative and would require validation through further, more detailed measurements
of this effect.
Figure D.3 shows that although absorbed power values are only reduced slightly,
the nozzle inlet temperatures show a rather pronounced decrease during the cold starting
conditions, resulting in temperature differences greater than 100 K towards the higher
input power levels. This seems to indicate that a significant heat transfer from the heated
propellant gas to the still cold thruster structure occurs just upon ignition.
As a result of the nozzle inlet temperature decrease due to assumed heat losses
into the thruster structure during the warm-up phase, other thruster performance
parameters suffer losses as well.
288
Thermal Transients
A bsorbed, R eflected an d T ransm itted Pow er, C ircular W aveguide. Helium
1500
L
4) 1 3 5 0
5
O
CL 1200
T4>>
1050
г
(0 9 0 0
c
oL_
750
T3
4)
4-> 6 0 0
o
4J
o
?
H4)
?
?
450
CL
?D 3 0 0
4)
J3
i_ 1 5 0
O
V)
г>
<
800
A bsorbed
R eflected
Pow er, 2 .6 a tm , T h erm al Equilibrium
T ran sm itted
A bsorbed
R eflected
Pow er, 2 .6 a tm , Cold S tartin g C ondition
T ra n sm itted
a
a
J ==at
900
1000
1100
1200
1300
Input P ow er ( W )
111
0
0
1400
1500
1600
Figure D.2 Effect of Thermal Transients on the Absorbed, Reflected and
Transmitted Power Levels for the Circular
Waveguide Applicator using Helium
289
Thermal Transients
A bsorbed Power ond C alculated Nozzle Inlet T e m p e ra tu re , C ircular W aveguide, He
1600
i t 800
1400
1700
1600^
?1200
1500
a> 1000
?
o
CL
s
800
2.2 atm , Thermal Equilibrium
2.6 atm , Thermal Equilibrium
2.2 atm , Cold Starting Condition
2.6 atm , Cold Starting Condition
T4J)
J2
k. 6 0 0
o
m
n
< 400
3
1 400 з
a
1 3 0 0 j=
|2
1200^
nooj
1000з
? ?? *? *? i
200
700
800
900
z
900
800
1000 1100 1200 130 0 1 4 0 0 150 0 1 6 0 0 17 0 0
Input Pow er ( W )
Figure D.3 Effects of Thermal Transients on Nozzle Inlet Temperatures
and Absorbed Power for the Circular Waveguide Applicator
using Helium
290
As shown in Figures D.4 through D .6 thruster efficiency, specific impulse and
specific power values are lower just upon ignition and the effect on thruster efficiency
and specific power is particularly noted.
For actual future thruster operation, this performance degradation during start-up
will have to be taken into account. Note, that similar thermally transient behavior is
found for arcjets and resistojets. While arcjets show thermal transients lasting roughly
2
minutes, corresponding to the time periods measured here, resistojets, relying
completely on heat transfer from the platinum heat exchanger to the propellant,
experience thermal transients on the order of 2 0 to 60 minutes.
291
Thermal Transients
Im pact on C a lcu lated Overall Efficiency, C ircular W aveguide, Helium
50
i
25
=
20
2 .2
2 .6
2 .2
2 .6
600
700
800
900
a tm ,
a tm ,
a tm ,
a tm ,
T herm al Equilibrium
Therm al Equilibrium
Cold S ta rtin g Condition
Cold S ta rtin g Condition
1000 1100 1 2 0 0 1300 1400 1500 1600
Input Pow er ( W )
Figure D.4 Effect of Thermal Transients on Overall Thruster Efficiencies
for the Circular Waveguide Applicator using Helium
292
Thermal Transients
Im p a c t on C a lc u la te d Specific Im pulse, C ircular Waveguide, Helium
500 r
450
_400
$350
| 300
1 250
o
?
?
?
o 200
v 150
a
</)
2 .2 a tm ,
2 .6 a tm ,
2 .2 a tm ,
2 .6 a tm ,
Therm al Equilibrium
Therm al Equilibrium
Cold S tartin g Condition
Cold S tartin g Condition
100
50
600
700
800
900
1000 1100 1200 1300 1400 1500 1 600
Input Pow er ( W )
Figure D.5 Effect of Thermal Transients on Specific Impulse for the
Circular Waveguide Applicator using Helium
293
Thermal Transients
Im pact on Specific Power, Circular Waveguide Applicator, H e-Propellont
16
14
10
8
6
atm
2.2 atm , Thermal Equilibrium
2 . 6 atm
1 . 8 atm
2.2 atm , Cold Starting Condition
2 . 6 atm
1 .8
4
2
0
600
700
800
900
1000 1100 1200 1300 1400 1500 1 6 0 0
Input Pow er ( W )
Figure D.6 Effect of Thermal Transients on Specific Power for the
Circular Waveguide Applicator using Helium
m A
Juergen Mueller was bom on December 24,1961 in the town of Bremerhaven in
the former West Germany as the son of Elfriede and Karl Muller. He graduated high
school in Bremerhaven in December 1980 and enrolled at the Justus-Liebig Universitat
in Giessen, Germany, in 1982 where he participated in research on ion propulsion
systems during his thesis project. In August 1987, he graduated from Justus-Liebig
Universitat with a Diploma in Physics. During the same month, he joined The
Pennsylvania State University as a Fulbright-Scholar to pursue a Ph.D. degree in
Aerospace Engineering. Juergen Mueller is currently a Member of Technical Staff in the
Advanced Propulsion Technology Group of the Propulsion and Chemical Systems Section
at the Jet Propulsion Laboratory (JPL) in Pasadena, California.
Input Power at various
Mass Flow Rates and Pressures
2250
242
lower than LTE temperatures determined by the absolute continuum method.
7.5.2. Electron Temperatures Measured for the Circular Waveguide
In Figure 7.11, the electron temperatures obtained for the circular waveguide
applicator using the absolute continuum method are shown. As can be seen, those
temperatures values are significantly lower than those obtained for the rectangular guide
and range between 10,000 K and 11,000 K. Furthermore, a slight yet barely noticeable
increase with respect to power can be noted for each pressure condition. This is in
agreement with the coupling efficiency measurements taken for the circular applicator.
Since in the circular guide the plasma is free to expand, increasing the input power leads
to an increase in plasma volume. Therefore, the temperature at the plasma center which
is the temperature depicted in Figure 7.11, might increase slightly since thermal
conduction from the plasma center outward decreases due to the fact that the plasma core
is surrounded by a thicker, hot plasma layer.
Over the pressure ranges considered, no pressure effect on the electron
temperature can be noted. Although higher pressures lead to higher mass flow rates as
shown in Figure 6.28, which, according to the observations made for the rectangular
waveguide, should result in increased coupling efficiencies due to cooling of the outer
plasma layers and increases in skin depth, higher pressures also decrease electron mean
free paths between collisions, so that the electrons can pick up less microwave energy
between collisions, reducing electron temperatures again. Since both effects are
adversary, a fairly constant temperature profile may result.
In Figure 7.12, two temperature values, one taken at the plasma center and the
243
Peak Electron Tem perature
C ircular W oveguide Applicator, He - P ro p ellan t
2000
1000
0000
9000
a>
3 8000
-*->
O
v. 7 0 0 0
0)
a
E
0)
6000
h- 5 0 0 0
C
o
1 .2 5
1 .8 0
2 .4 0
3 .0 0
4000
o
J0> 3 0 0 0
LU 2000
1000
0
a tm
a tm
a tm
a tm
*?
400
600
800
1000
1200
1400
1600
Input Power ( W )
Figure 7.11 Peak Electron Temperatures obtained with the Absolute Continuum
Method vs. Input Power for the Circular Waveguide Applicator
using Helium
244
Electron Tem perature Distribution vs. Power
C ircular W aveguide A pplicator, H e -P ro p ellan t, 1 .8 a tm
( K)
10500
Electron T em perature
11000
10000
9500
9000
o
?
C enterline T em perature
T em p eratu re 5 m m off C en ter
8500
8000
700
800
j _____ i_
900
1000
Input P ow er ( W )
1100
1200
Figure 7.12 Electron Temperature Profiles vs. Input Power for the
Circular Waveguide Applicator using Helium
245
other taken 5 mm off center, are plotted vs. input power for a gas pressure of 1.8 atm.
Only a very sght difference between these two values can be noted, indicating that the
electron temperature remains fairly constant across the entire plasma.
In Figure 7.13, the impact of variations in bluff body size on the electron
temperature were studied and no significant differences apart from a very minute
decrease in temperature for the 35 mm bluff body could be found.
7.5.3. Comparison of Electron Temperatures for Various Applicators
Figure 7.14 depicts various electron temperature data obtained for various
waveguide applicators at the same pressure conditions (1.25 atm). In all cases the fiber
optic diagnostic system described above was used and absolute continuum spectroscopy
was employed. Although the electron temperature data were taken over different power
ranges depending on applicator type, temperature profiles with respect to power have
been shown to be very flat in all cases and a comparison between those data sets
therefore appears valid.
As can be seen, the highest temperature values were found for the rectangular
guide while data for the circular cavity49 and the circular guide are within the same
range, the temperatures for the guide slightly exceeding those for the cavity. This seems
to indicate that it is not the applicator type (i.e. waveguide or cavity) that determines the
temperature as was suspected before48 but more specifically the actual field pattern
involved or the geometrical dimensions of the guide or a combination of both. In the case
of the circular waveguide using the TM0I mode and the resonant cavity using the TM012
mode, field configurations are very similar as are the temperature values. The rectangular
246
Variation of B lu ff-B o d y Size
Im pact on Electron T e m p era tu re , C ircular W aveguide A pplicator, Helium
12000
11000
,- .1 0 0 0 0
5
9000
з
8000
2
7000
|
6000
г
5000
o
o
4000
d
%
3000
w
2000
?
?
2 .4
3 .0
2 .4
3 .0
a tm ,
a tm ,
a tm ,
a tm ,
20
20
35
35
mm
mm
mm
mm
Bluff
Bluff
Bluff
Bluff
Body
Body
Body
Body
1000
n
800
900
1000
1100
1200
1300
Input Pow er ( W )
1400
1500
1 600
Figure 7.13 Impact of Variations in Bluff Body Size on the Electron
Temperature for the Circular Waveguide Applicator using Helium
247
Comparison of Electron Tem peratures
1 .2 5 a tm G as P r e s s u r e , H e - P ro p e lla n t
13000
* ? ?
12000
11000
sc 1 0 0 0 0
4)
u
9000
?4-1
oL_
8000
3
w 7000
cl
г 6000
4)
hC
oL.
?4-f
o
V
Ld
5000
4000
3000
?
?
o
Circular W aveguide A pplicator, 4 3 - 4 5 m g / s m a s s flow
R e c ta n g u la r W aveguide, 2 7 .5 m g / s m a s s flow
R e c tan g u la r W aveguide, 65.01 m g / s m a s s flow
C ircular Cavity ( P e n n S t a t e ), no flow
2000
1000
0
300
500
700
900
1100 1300 1500 1700 1900 2100 2300
Input P ow er ( W )
Figure 7.14 Comparison of Electron Temperatures obtained by Absolute Continuum
Spectroscopy for various Microwave Applicators
248
TE]0 mode, however, is completely different in its appearance.
Furthermore, the cross-sectional area of the rectangular guide is 24.56 cm2, the
circular guide applicator has a 75.2 cm2 cross section and for the cavity this area is
226.87 cm2. As a result, microwave field intensities are significantly higher for the
rectangular guide than for the circular guide, and significantly higher for the circular
guide than for the cavity which could have led to a similar trend for the electron
temperatures.
249
Chapter 8
CONCLUSIONS AND RECOMMENDATIONS
This investigation concentrated on the relatively new concept of using waveguideheated plasmas for space propulsion applications. An initial performance evaluation of
this new waveguide applicator type was performed and basic operational characteristics
of waveguide-heated microwave electrothermal thruster types were determined. To this
end, experimental testing of various waveguide applicator configurations was conducted.
Optimization of this new thruster concept for space applications, however, was beyond
the scope of this thesis. The thruster designs presented in this study can therefore only
be regarded as laboratory test devices and are very preliminary in nature, serving the
purpose of evaluating the potential future use of waveguide applicators for space
propulsion purposes rather than representing actual flight concepts.
Since waveguide plasmas are inherently unstable, attention was initially focused
on understanding and quantifying plasma propagation. Plasma velocities of up to 10 cm/s
were measured for the molecular gas nitrogen. For helium, what appeared to be a mode
change between two different modes of propagation was found. For power levels below
1550 W and 1 atm gas pressure, propagation velocities ranged between 10 to 90 cm/s.
For higher power levels, however, a very sudden increase in plasma velocity to values
ranging between 2000 to 3000 cm/s was found. It was assumed that this increase in
plasma velocity was due to a change in the driving propagation mechanisms from heat
conduction to possibly resonant radiation. This assumption could, however, not be
confirmed conclusively. In particular, no high confidence was placed in numerical
250
investigations performed to this end due to extensive simplifications in the numerical
model.
Next, a crucial step toward utilization of this waveguide concept for space
propulsion applications was made by successfully stabilizing the plasma by means of a
bluff body. Stabilization was reported to be easy to achieve and handle, howeve
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