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Microwave electrothermal thruster chamber temperature measurements and energy exchange calculations

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The Pennsylvania State University
The Graduate School
College of Engineering
MICROWAVE ELECTROTHERMAL THRUSTER CHAMBER
TEMPERATURE MEASUREMENTS AND ENERGY EXCHANGE
CALCULATIONS
A Thesis in
Aerospace Engineering
by
Silvio G. Chianese
© 2005 Silvio G. Chianese
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
May 2005
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UMI Number: 3172964
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The thesis of Silvio G. Chianese was reviewed and approved* by the following:
Michael M. Mice!
Professor of Aerospace Engineering
Thesis Adviser
Chair of Committee
Robert G. Melton
Professor of Aerospace Engineering
Deborah A. Levin
Associate Professor of Aerospace Engineering
David B. Spencer
Assistant Professor of Aerospace Engineering
Sven G. Bilen
Assistant Professor of Engineering Design and Electrical Engineering
Juergen Mueller
Member of Engineering Staff
Jet Propulsion Laboratory, Pasadena, CA
Special Signatory
George A. Lesieutre
Professor of Aerospace Engineering
Head of the Department of Aerospace Engineering
*Signatures are on file in the Graduate School.
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ABSTRACT
The microwave electrothermal thruster (MET) uses microwave frequency energy
to create and sustain a resonant cavity plasma to heat a propellant. It has been operated at
a variety of power levels with several propellants. The performance potential of the
device has not previously been ascertained because of complex physics involved in the
microwave heating, the relatively low thrust of the device, and difficulty in using
conventional diagnostics to study molecular plasmas. The objectives of this investigation
were to measure heavy particle temperatures and to understand gas heating processes in
the MET plasma chamber for representative molecular propellants, oxygen and nitrogen.
These molecules have well known thermochemical and structural properties, and they are
components of liquid-storable propellants. A 2.45 GHz aluminum cylindrical thruster
with converging copper alloy nozzles was used. A spectroscopic system was used to
collect light emitted through a window in the plasma chamber.
A Schumann-Runge
emission model was developed assuming anharmonically vibrating, non-rigid rotating
oxygen molecules. The commercially available LIFBASE software was used to model
ionized molecular nitrogen first negative system emission from nitrogen plasmas.
Experimental data were compared to models using least squared difference summation
schemes.
Steady and repeatable plasmas were formed with oxygen, nitrogen, and ammonia
for most operating conditions.
Strong coupling between fluid dynamics and plasma
geometry was observed for high flow rate nitrogen tests. Oxygen temperatures of 2,000
K were measured with no variation due to spatial location or pressure and a slight
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iv
increase in temperature with specific absorbed power. Nitrogen temperatures of 5,500 K
were measured with no variation due to location, pressure, or specific absorbed power.
Thermochemical calculations show the relationship between equilibrium enthalpy
addition, temperature, dissociation fraction, and specific impulse. Nitrogen was found to
be an excellent choice as a propellant component while oxygen was found to be a poor
choice.
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V
TABLE OF CONTENTS
LIST OF FIGURES
......
LIST OF TABLES
.......
vii
x
xi
NOMENCLATURE...........................
xvii
ACKNOWLEDGMENTS..............
1
CHAPTER 1 - INTRODUCTION.......................
1.1
Motivation for Use of Electric Propulsion
1.2
Microwave Electrothermal Thruster Development................
4
1.3
Research Motivation and Objective ................................
9
1.4
References................................
CHAPTER 2 - MET THEORY
................
......
1
12
16
2.1
.....
Resonant Cavity Theory
2.1.1 Maxwell’s Equations............
2.1.2 TM Cylindrical Cavity Solution ....
2.1.3 TMon Cavity Characteristics.................
16
16
18
21
2.2
Plasma Formation Theory......................
2.2.1 Gaseous Breakdown.....................
2.2.2 Electron Impact Ionization..............
24
24
26
2.3
Propellant Heating .......
2.3.1 Electron Impact Energy Exchange
................
2.3.2 O2 and N 2 Cross Sections and Rate Coefficients.......................
2.3.3 Thennochemical Effects
................
28
28
37
39
2.4
References
40
.............
CHAPTER 3 - EXPERIMENTAL APPARATUS AND PROCEDURES
3.1
Apparatus...............................
3.1.1 Microwave Energy Input...........................
3.1.2 Resonant Cavity
.....
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43
43
43
44
vi
3.1.3 Gas Flow Regulation ........
3.1.4 Spectroscopic System ...........
47
48
3.2
Testing Procedures................ ............................................................... .
3.2.1 Plasma Formation
.......
3.2.2 Spectroscopic Analysis....
.......................
51
51
56
3.3
References
57
......
CHAPTER 4 - SPECTRAL EMISSION MODELS
.....
58
4.1
Background
......
58
4.2
Transition Frequencies
.......
59
4.3
T ransition Probabilities.............................
62
4.4
Transition Lineshapes
63
4.5
Population Distributions
4.6
MET Plasma Chamber Emission Models
......
4.6.1 Oxygen Schumann-Runge Emission Model.................................
4.6.2 Ionized Nitrogen First Negative System Emission Model.
68
69
83
4.7
References
88
........................................
......
66
......
CHAPTER 5 - RESULTS AND CONCLUSIONS
.....
91
5.1
....................
Phenomenological Results
5.1.1 Plasma and Fluid Dynamics Interactions
5.1.2 Power Absorption Measurements
.......
5.2
Emission Thermometry
............
5.2.1 Oxygen Schumann-Runge Emission...
...............
5.2.2 Ionized Nitrogen First Negative System Emission
5.3
Thermochemical Calculations
5.4
Conclusions
5.6
References
91
.................. 91
100
......
............................ ....................................... .
....................
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.....
102
102
105
108
114
117
LIST O F F IG U R E S
Figure 1.1:
MET Operating with Nitrogen
......
5
Figure 2=1:
Cylindrical Cavity Geometry
Figure 2.2:
Instantaneous Axial Electric Field Distribution for T M qh Cavity
23
Figure 2.3:
Instantaneous Radial Electric Field Distribution for TM0u Cavity
23
Figure 2.4:
Instantaneous Electric Energy Distribution for T M qh Cavity...............
24
Figure 2.5:
Maxwellian Electron Energy Distribution Function ........................
30
Figure 2.6:
Momentum Transfer Cross Sections vs. Electron Energy
Figure 2.7:
N 2 Electron Impact Cross Section and Electron MaxwellianPopulation 39
Figure 3.1:
Microwave System Schematic........................
43
Figure 3.2:
Cavity Nozzle Plate with Insert...............................
45
Figure 3.3:
Resonant Cavity Schematic
Figure 3.4:
Picture of Resonant Cavity Thruster System
Figure 3.5:
Optical System Schematic
Figure 3.6:
Variation of Experimental FWHM with Slit W idth
51
Figure 3.7:
(a) Low Pressure and (b) High Pressure Oxygen Plasma................
53
Figure 3.8:
(a) Low Pressure and (b) High Pressure Nitrogen Plasm a...............
54
Figure 3.9:
(a) Low Pressure and (b) High Pressure Ammonia Plasma
55
........
18
..............
........
46
......................
47
......
Figure 3.10: He-Ne Laser Alignment Check Plot
38
49
.........
.....
56
Figure 4.1:
B 3Eu_ State Relative Rotational Population Distribution at 300 K
73
Figure 4.2:
B 32M Initial Relative Rotational Population Distribution at 1,000 K .
73
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viii
Figure 4 3 :
Initial Relative Rotational Population Distribution at 5,000 K .
Figure 4.4:
Calculated Schumann-Runge Emission Spectrum at 300 K
Figure 4.5:
Calculated Schumann-Runge Emission Spectrum at 1,000K .
73
.....
76
........
76
Figure 4.6:
Calculated Schumann-Runge Emission Spectrum at 5,000K ..............
77
Figure 4.7:
Schumann-Runge v' = 0 Modeled Spectral Output..
78
Figure 4.8:
Schumann-Runge v' = 1 Modeled Spectral Output......................
79
Figure 4.9:
Schumann-Runge v' = 2 Modeled Spectral Output
79
......
................
79
Figure 4.11:
Peak Intensity Variations with Temperature.........................................
80
Figure 4.12:
Peak Intensity Ratios vs. Temperature
....
80
Figure 4.13:
Least Squared Difference Summation vs.
O2 Temperature.............
81
Figure 4.14: Normal Probability Plot of O 2 Temperatures for Repeatability T ests..
82
Figure 4.15:
LIFBASE N 2 + FNS Emission Spectrum......................
85
Figure 4.16:
Least Squared Difference Summation vs.
86
N2 + Temperature
.
Figure 4.10: Schumann-Runge v' = 3 Modeled Spectral Output................................
Figure 4.17: Normal Probability Plot of N 2 + Temperatures for Repeatability Tests.
87
Figure 5.1:
13.6 mg/s Oxygen Plasma with 1.0 kW Absorbed Pow er
92
Figure 5.2:
94.9 mg/s Oxygen Plasma with 1.37 kW Absorbed Pow er
92
Figure 5.3:
15.6 mg/s Nitrogen Plasma with 0.85 kW Absorbed Power..................
93
Figure 5.4:
73.1 mg/s Nitrogen Plasma with 1.06 kW Absorbed Power
.........
94
Figure 5.5:
93.7 mg/s Nitrogen Plasma with 1.06 kW Absorbed Power..................
95
Figure 5.6:
150.0 mg/s Column-Like Nitrogen Plasma
96
Figure 5.7:
150.0 mg/s Ball-Like Nitrogen Plasma with Large Plum e....... .............
......
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97
Figure 5.8:
150.0 mg/s Ball-Like Nitrogen Plasma with Small Plum e...............
Figure 5.9:
0.95 mg/s
Ammonia Plasma with 1.2 kW Absorbed Power
.
ix
97
98
Figure 5.10:
9 .50 mg/s
Ammonia Plasma with 1.40 kW Absorbed Power.......
99
Figure 5.11: Percent Power absorbed vs. Oxygen Propellant Flow R ate.................
101
Figure 5.12: Comparison of Modeled and Measured Schumann-Runge System
102
................... 103
Figure 5.13: Squared Difference Sum for Two Locations
Figure 5.14: Temperature vs. Pressure for 20.1 MJ/kg Specific Absorbed Power.... 104
Figure 5.15:
Temperature vs. Specific Power at 17.0 p sia.....
Figure 5.16:
Comparison of Modeled and Measured N2+ FNSSystem ......
106
Figure 5.17:
Variation in N 2 + Temperature vs. Chamber Pressure..........................
107
Figure 5.18:
Variation
...................... 105
in N2+ Temperature vs. Specific Absorbed Power........ 108
Figure 5.19: Equilibrium Enthalpy Addition to Heat Propellants vs. Temperature.. 109
Figure 5.20: Percent Dissociation of Propellants vs. Temperature
.....................
110
Figure 5.21: Percent Enthalpy Lost to Dissociation vs. Temperature .....................
Ill
Figure 5.22: Isp vs. Temperature for 0 2, N2 andNH 3
Ill
..............
Figure 5.23:
Equilibrium Enthalpy vs. Isp for 0 2, N2 and NH 3
Figure 5.24:
Equilibrium Thermal Conductivity for 0 2, N 2 and NH 3
.................... 112
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.....
113
X
L IS T O F T A B L E S
Table 1. 1:
Performance Characteristics of In-space Propulsion Devices...
Table 3.1:
5 SLM UNIT Instruments UFC 2050A Full-scale Mass Flows
Table 3.2:
Detailed Procedure for MET Plasma Testing..................
52
Table 4.1:
Electromagnetic Frequency and Associated Energy Change Process ..
59
Table 4.2:
Molecular T ransition Appearance.................................
69
Table 4.3:
Schumann-Runge X3Sg_ Ground State Constants
....................
70
Table 4.4:
Schumann-Runge B 32L Excited State Constants
............................
70
Table 4.5:
B 32L Initial State Relative Vibrational Population Distribution
74
Table 4.6:
Schumann-Runge Oxygen Natural, Doppler, and Collisional FWHM.
75
Table 4.7:
O2 Example Experimental Conditions..............................
82
Table 4.8:
O 2 Experimental Conditions for Repeatability T ests
Table 4.9:
N 2 Example Experimental Conditions
............
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2
.....
......
48
82
87
NOM ENCLATURE
Symbol
Description
A
magnetic vector potential
A
area
A
spontaneous emission coefficient
a
cavity radius
B
magnetic flux density vector
B
instantaneous magnetic flux density vector
B
modal constant
B
rotational constant
b
pressure broadening proportionality coefficient
c
conversion ratio
c
speed of light
D
electric flux density vector
D
instantaneous electric flux density vector
D
diffusion coefficient
D
rotational correction constant
D
sum of least squared differences
d
electrode gap distance
d
least squared difference
E
electric field vector
E
instantaneous electric field vector
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E
molecular energy
e
electron charge
F
electric vector potential
F
force
f
frequency
f
electron energy distribution function
G
total molecular vibrational and rotational energy
g
gravitational acceleration
g
degeneracy
g
transition lineshape
H
magnetic field intensity vector
H
instantaneous magnetic field intensity vector
h
cavity height
h
Planck's constant
I
impulse
I
moment of inertia
J
electric current density source vector
J
instantaneous electric current density source vector
I
energy flux
I
rotational quantum number
i
k
Boltzmann constant
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M
magnetic current density source vector
M
species molecular mass
m
mass
m
number of circumferential electric field full-period variations
j
m
mass flow rate
N
number density
n
number of radial electric field half-period variations
P
power
p
pressure
p
number of azimuthal electric field half-period variations
Q
partition function
q
volumetric flow rate
q
charge density
R
transition probability
S
triplet line transition probability
T
temperature
t
time
u
flow velocity
V
Voigt coefficient
v
electron velocity
v
vibrational quantum number
x
Cartesian spatial coordinate
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y
Cartesian spatial coordinate
z
Cartesian and cylindrical spatial coordinate
y
specific heat ratio
Av
spacecraft velocity change
Av
line full width at half maximum intensity
8
energy lost per collision
e
material permittivity
£
electron kinetic energy
"H
efficiency
0
characteristic temperature
e
cylindrical spatial coordinate
V
wavenumber
V
collision frequency
V
molecular vibration frequency
11
material permeability
n
electron mobility
P
cylindrical spatial coordinate
P
density
a
electrical conductivity
<y
collision cross section
I
thrust
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XV
T
c h a r a c te r is tic tim e
03
a n g u la r f r e q u e n c y
Subscript
Definition
0
standard
a
ambient
c
conduction
c
coilisional
ch
chamber
co
cutoff
D
Doppler
diff
diffusion
Earth
due to the Earth
e
electron
ee
due to electron-electron collisions
eff
e f f e c tiv e
el
due to elastic collisions
e le c
electronic
e le c t
e le c tr ic
eq
equilibrium
equiv
e q u iv a le n t
exit
nozzle exit plane
F
final
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F
due to electric field
I
initial
i
impressed
ion
due to electron-ion collisions
k
excited state
m
momentum transfer
m
upper state
mag
magnetic
N
natural
n
lower state
r
resonant
rot
due to rotational excitation and deactivation
s
species
T
total
V
vibrational
Superscript
Definition
TM
transverse magnetic
V
excited
f
upper state
tt
lower state
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ACKNOWLEDGMENTS
I would like to thank my parents and siblings for all their encouragement, support,
and love along this journey. My labmates and friends have provided answers to life's
questions along the way, technical and otherwise, and helped keep me smiling through all
the work. I couldn't have done it without them. I appreciate the advice, feedback, and
encouragement that Dr. Micci and the rest of my committee have given that kept me on
the right path. Mr. Bob Dillon's excellent machine shop work was indispensable.
I
would also like to thank the NASA Marshall Space Flight Center for funding this
research under the GSRP grant NGT08-52925.
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1-
C H A P T E R 1 - IN T R O D U C T IO N
The microwave electrothermal thruster (MET), or microwave arcjet, has been
studied under laboratory conditions for over twenty years.
The device has been
successfully operated with several different propellants at a variety of input power levels,
propellant flow rates, and chamber pressures.
To date, however, the true potential
performance of the device has not been ascertained.
This is due to several factors,
including the complex physics involved in the microwave heating, the relatively low
thrust of the device, and the difficulty in using conventional diagnostic techniques to
study high temperature chamber molecular plasma. The objective of this investigation
was to measure the temperature of representative molecular propellants within the device
at a variety of operating conditions and to determine the physical processes that control
the propellant heating.
This information can be used to ascertain if the potential
performance of the device is greater than other propulsion systems currently in use.
1.1
Motivation for Use of Electric Propulsion
Currently, over 180 satellites are in use that utilize electric propulsion and
research
and
development
continues
in
academia,
industry,
and
government
laboratories. 1' 5 In recent years, the percentage of satellites launched that use some form
of electric propulsion for a variety of tasks, from primary propulsion to delicate attitude
adjustment, has substantially increased.
Several types of electric propulsion systems
have been used on operational satellites, and even more have been demonstrated in
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laboratory environments.
There are three categories of electric propulsion devices:
electrostatic, electromagnetic, and electrothermal.6
Electrostatic devices, such as ion engines and Hall thrusters, use the energy from
static electric fields to accelerate charged particles. Electromagnetic devices use the
energy from a combination of either static or dynamic electric and magnetic fields to
accelerate charged particles. Some examples of this class of thruster are pulsed plasma
thrusters (PPT) and pulsed inductive thrusters (PIT). Electrothermal devices, such as
resistojets, DC and AC arcjets, and the MET, are the electric propulsion systems that
operate most like conventional chemical rockets. Electromagnetic energy is used to heat
a propellant to high temperatures and then the fluid is expanded through a nozzle.
Equation 1.1 shows the relationship between nozzle exit exhaust velocity, uexit, and
chamber gas temperature, T Ch, for thermal thrusters.
f
(m
^
V
\ ^y~ X N
r exit
2cpTch 1 -
Pch )
Table 1.1 gives the typical performance characteristics for some chemical and
electric devices currently in use or under development. 7 As shown in the table, the major
Table 1.1: Performance Characteristics of In-space Propulsion Devices
Type
Propellant
Liquid Monopropellant
H2Q2, N 2 H4
N 2 0 4 and N 2 H4
Liquid Bipropellant
Resistojet
n h 3 , n 2h 4
Conventional Arcjet
n h 3, n 2h 4
Ion Engine
Xe
Hall Effect Thruster
Xe
Pulsed Plasma Thruster
Teflon
ISp (s)
150-225
300-340
150-300
450-600
2 ,0 0 0 -6 , 0 0 0
1,500-2,500
800-1,500
T hrust (N)
0.05-0.5
5.0-5 x 106
0.005-0.5
0.05-5
5 x 10"6 -0.5
5 x 10'6 -0.1
5 x 10"6-0.005
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3
performance difference between chemical and electric propulsion devices is the relatively
low thrust and high specific impulse of electric thrusters compared to chemical rockets.
Thrust, x, is simply the propulsive force exerted by a rocket, and the specific impulse, Isp,
is a measure of the amount of propellant flow rate, m, needed to produce the thrust. 8
X = r i l U CTit + ( p exi, - p a ) A exi,
11
—11 ... Pexit Pa
equiv uexit
^
exit
a
j
»
U
Earth
g E a tth
T
SP
(L 2 )
( 1.3)
equiv
•
(L 4 )
For many missions, an Isp greater than that possible from chemical rockets is desired to
reduce the propellant mass carried onboard, or even needed to enable the mission to be
possible at all. This can be shown by a consideration of the "rocket equation,” which
relates the ratio of the spacecraft final mass, mp, and the initial mass, mj, to the ratio of
the total spacecraft change in velocity, Av, and the equivalent exhaust velocity, uequiV,
defined in Equation 1.3.
HIAp
m,
___
Av
e “,ulv
U
(1.5)
For example, if the equivalent exhaust velocity from the rocket used is the same as the Av
needed for the mission, more than 63% of the initial mass of the satellite must be
propellant mass. Using a rocket with a higher exhaust velocity, and thus larger Isp, allows
for a larger mission payload mass fraction. However, maximizing the Isp is not the only
mission constraint.
Electric propulsion devices with very high exhaust velocity, and
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correspondingly large Isp values, typically have very low thrust capability because of the
large amount of power, P, required to accelerate relatively high propellant flow rates, as
shown in equation 1.6. This means that momentum change is slow and in some cases,
such as drag make-up, not fast enough for the use of such thrusters at all.
2iq
Therefore, it is desirable for some missions to have a thruster that is capable of specific
impulse values greater than chemical rockets, while still having relatively high thrust
levels. Electrothermal thrusters are devices that can potentially meet these criteria.
Resistojets and arcjets have been used on satellites previously. However, both of
these systems have performance limitations.
temperature of the heating element used.
Resistojet Isp is limited by the melting
DC and AC arcjets do not have this heat
transfer limitation. However, because the arc in these systems comes in physical contact
with the electrodes, erosion can limit their useful lifetime. In addition, these devices are
both electrically and thermally inefficient. The microwave electrothermal thruster may
operate at a similar theoretical performance level as the conventional arcjet, but
potentially offers better practical performance because of better electrical and thermal
efficiency, and longer useful lifetime.
1.2
Microwave Electrotherm al Thruster Development
Research on the MET began in the early 1980’s at Michigan State University and
The Pennsylvania State University. 9 ,1 0 Figure 1.1 shows a MET operating in laboratory
conditions with a small visible exhaust plume with nitrogen as the propellant. This early
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5
Figure 1.1: MET Operating with Nitrogen
work focused on proof-of-concept studies and configuration optimization using 2.45 GHz
power sources. It was during this time period that the transverse magnetic (TM) mode
resonant cavity arcjet thruster design was selected as the best way to transfer electric
energy into the propellant, while isolating the walls of the rocket chamber from the high
temperature plasma.
Some early diagnostics work was completed that showed the promise of the
device as well as the difficulty in determining the performance o f the systems.
Electromagnetic probes were used to determine that the cavity electrical efficiency was
greater than 95% for helium and nitrogen discharges from 30-1000 torr. Probes could not
be used successfully for other performance measurements because they interfered with
the electromagnetic and fluid dynamic properties o f the cavity. Spectroscopic techniques
were employed that were able to estimate electronic temperatures on the order of
K with some confidence.
1 0 ,0 0 0
However, determination of heavy particle translational
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temperature and equilibrium state proved elusive. Early versions of the MET required
active impedance matching to improve performance characteristics. However, operation
with very high electrical efficiency (>98% input microwave power absorbed) was
demonstrated for a system with a fixed geometry and input power between 1.4-2.2 kW
using helium and nitrogen as propellants. 11
More recent experimental investigations have focused on determining the
characteristic temperatures within the plasma. Air discharges produced by a relatively
low power source (0-300 W) at low pressure (0.5-100 torr) were found to have
vibrational temperatures between 3700-7300 K and rotational temperatures between
1000-2500 K . 12 As the pressure was increased, the two temperatures came closer to
converging. Also, as power was increased, the vibrational temperature increased. These
results suggest that, at even higher pressures and powers, it may be possible to increase
the stored energy of the propellant further and approach thermal equilibrium.
Spectroscopic measurements conducted with helium plasmas showed electronic
temperatures between 10,200-10,900 K for low power testing (200-400 W) and between
12,000-12,800 K for high power (750-2150 W) testing.1 3 ,1 4 These temperatures were
very insensitive to operating conditions such as flow rates (0-83.2 mg/s) and chamber
pressure (30-270 kPa).
These early results were for spatially averaged temperatures.
However, spatially resolved emission spectroscopy has shown the radial profile of the
helium electronic temperature has a maximum of approximately 12,000 K in the center of
the plasma and decreases to about 11,000 K at the edge of the plasma. 15 These results
were insensitive to operating power (500-1000 W) and chamber pressure (125-250 kPa).
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7
In the late 1990's a significant research effort was initiated to explore the use of
the microwave electrothermal thruster at low powers (<100 W ) . 16' 18
This effort
demonstrated that the microwave arcjet could be operated at 7.50 GHz with excellent
electrical efficiency (>98% input microwave power absorbed) with helium, nitrogen, and
ammonia as propellants with as low as 65 W of input power.
The mean chamber
temperature of the heavy particles was experimentally determined as a function of input
specific power by measuring chamber pressure and flow rate.
The maximum mean
chamber temperatures realized were 1,700 K, 2,100 K, and 1,200 K for helium, nitrogen,
and ammonia, respectively. The temperatures increased with absolute power input, but
showed a nonlinear trend with respect to specific power.
Two different spectroscopic studies were also conducted as part of these
investigations. Helium plasma electronic temperature measurements were made with a
relative line intensity method using four different spectral line intensity ratios at three
different operating pressures, 28 psia, 37 psia, and 50 psia. At the lowest pressure, there
was large variability in the temperature determined from each ratio (±75%).
As the
pressure increased, the temperatures measured from each ratio approached a selfconsistent value of approximately 4000 K (±18%). This indicates that as the pressure
was increased, the system was more likely near equilibrium. A possible reason for the
high electronic temperature measured compared to the gas temperature was that the gas
temperature measured was a mean temperature, and the electron temperature
measurements were made in the center of the plasma. Doppler shift experiments were
conducted to determine the helium propellant centerline specific impulse from the MET
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as a function of specific power, with an absolute input power of 80 W. The centerline
specific impulse increased nonlinearly with specific power, with a maximum measured
value of approximately 1,300 s at a specific power of 30 MJ/kg. Work on the low power
MET continues at Penn State with emphasis on vacuum thrust measurements. 19
Researchers in industry have begun to develop MET laboratory investigations as
well. Researchers at the Aerospace Corporation have recently completed a study on the
use of water vapor as a propellant for the microwave electrothermal thruster.
Initial
research focused on the development of a feed system and a mechanical thrust stand that
could be used for this work . 2 0
As part of the system characterization study, helium
propellant performance was measured and a maximum specific impulse of 410 s was
achieved. A maximum Isp of 210 s was measured with water vapor as the propellant. It
was hypothesized that the poor performance was due to the relatively low chamber
pressure that could be achieved (190 torr), with the available input power (1 kW) for this
study. A subsequent investigation showed much better performance with water vapor as
the propellant with a higher power magnetron (up to 4.1 kW ) . 21
momentum trap thrust stand was used.
For this work, a
Maximum thrust values of 250 mN were
measured, and a maximum specific impulse of 428 s was calculated from the knowledge
of flow rates and thmst values.
These values compares favorably to conventional
hypergolic chemical rockets used for satellite control and propulsion.
Investigators at Research Support Instruments have begun studying the use of the
MET operating with helium and nitrous oxide as propellants. 2 2 A pendulum-based thrust
stand was used to measure the thrust from the device while it was operating in a
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9
horizontal orientation.
Buoyancy effects have precluded accurate performance
measurements for most operating conditions to date. However, a helium propellant thrust
up to 50 mN and specific impulse up to 350 s were measured. Nitrous oxide propellant
thrust of over 70 mN and specific impulse of over 170 s were measured.
In addition to the experimental studies undertaken, several computational
investigations have been conducted to analyze the MET. Initial studies considered only a
single temperature model with helium as the propellant.23
This work showed
qualitatively the strong fluid dynamic control over plasma location. More recent work
incorporates a two-temperature model to examine the helium plasma flow.24’25 A fully
coupled fluid dynamic Navier-Stokes and electromagnetic Maxwell equations model was
used. The plasma was found to be highly non-equilibrium in nature with electron and
heavy particle temperatures that differ greatly. A test case with 4 kW input power and
220 mg/s of propellant flow was found to have a thrust of 0.721 N and an Isp of 334 s.
While the modeling effort is encouraging, only monatomic helium was modeled and the
fluid flow modeled was not similar to that used in experimental investigations.
In
addition, the calculations showed that maximum propellant heating did not occur on the
plasma centerline, as found experimentally.
1.3
Research Motivation and Objective
Previous experimental studies of the microwave electrothermal thruster have
shown that it can be operated at high electrical efficiency over a variety of power ranges
and flow rates, with several different propellants. However, it has not been shown how
the energy is absorbed by a propellant or that it can be converted efficiently to directed
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10
kinetic energy to provide thrust for a rocket.
The best way to assess the potential
performance of a thermal rocket is to measure the temperature of the gas in the chamber.
Knowledge of the temperature gives a measure of the potential specific impulse of the
rocket for a given operating condition. If the temperature is not high enough to produce
an Isp greater than a chemical rocket, or if the corresponding thrust is not as large as
another electric thruster can produce at a similar Isp, then the study of that particular
thermal rocket need not continue. However, if the temperature measured in the chamber
corresponds to a relatively high specific impulse for the mass flow rate of propellant
used, then the investigation should continue in earnest. Direct thrust measurements are
less instructive because of measurement uncertainties due to the buoyancy of the MET
chamber plasma in the laboratory environment and due to the relatively low thrust of the
device. In addition, measuring the chamber temperature directly allows for a measure of
potential performance, regardless of the type of nozzle used.
Measuring the temperature in the plasma chamber of a MET is not a simple
matter. The high temperature free floating plasma surrounded by tangentially injected
propellant potentially creates a strong temperature gradient within the chamber. This,
along with the electromagnetic energy present in the chamber, makes use of
thermocouples or other probes unfeasible. The plasma emits a significant amount of light
over a broad spectrum when molecular propellants are used.
Without careful
consideration, this light emission would cause interference with typical laser based
thermometry measurements, such as laser induced fluorescence (LIE) and spontaneous
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Raman scattering spectroscopy.
In addition, there can be several different molecular
temperatures corresponding to the different energy storage modes in molecules.
Using spatially resolved molecular emission spectroscopy with a quantum
mechanical and statistical thermodynamics model, it is possible to determine the
molecular rotational, and thus translational, temperature.
The physical processes by
which the microwave energy is transferred to the gas molecules in the MET plasma
chamber have not been investigated in the past, but are of critical importance in
propellant selection and performance evaluation. The first objective of this investigation
was to determine the spatially resolved rotational temperature of representative molecular
propellants in the microwave electrothermal thruster chamber while varying the chamber
pressure and absorbed specific power independently.
The second objective was to
understand the plasma heating physics within the MET plasma chamber. The results of
this investigation should be sufficient to determine whether this type of thruster offers
potential performance that is sufficient to warrant further study.
The first objective was met by conducting experimental spectroscopic emission
thermometry studies on light emitted by the plasmas formed from oxygen and nitrogen
propellants within MET plasma chamber. These fluids could potentially be used as MET
propellants themselves, and they are also components of more complex liquid storable
propellants.
The thermochemical and structural properties of these representative
propellant molecules are well known. The second objective was met in two ways. First,
the energy exchange process between the input microwaves and gas particles was
investigated by reviewing experimental apparatuses with similar thermodynamic and
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electromagnetic conditions as the MET. This was done to determine the proximity to
local thermodynamic equilibrium within the plasma chamber.
The theory of
nonequilibrium electron impact energy mechanisms was also investigated, as it applies to
relatively high pressure molecular plasmas.
Second, representative equilibrium
thermochemical properties and performance values for the MET were calculated using
the CEA2 code with oxygen, nitrogen, and ammonia as propellants.26,27
This
investigation is the first to measure heavy particle temperatures within the MET plasma
chamber and to investigate the plasma heating mechanisms and performance for the
thruster at typical operating conditions.
1.4
References
1 Dunning Jr., J., Hamley, J., Jankovsky, R., and Oleson, S., "An Overview of Electric
Propulsion Activities at NASA," AIAA Paper 2004-3328, July 2004.
2
Saccoccia, G., "An Overview of Electric Propulsion Activities in Europe," AIAA
Paper 2004-3329, July 2004.
3
Tverdokhlebov, S., "An Overview of Electric Propulsion Activities in Russia," AIAA
Paper 2004-3330, July 2004.
4
Myers, R., "An Overview of Electric Propulsion Activities in U.S. Industry," AIAA
Paper 2004-3331, July 2004.
5
King, B., "An Overview of Electric Propulsion Activities in Academia," AIAA Paper
2004-3332, July 2004.
6
Jahn, R., Physics o f Electric Propulsion, McGraw-Hill, New York, 1968.
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
13
7
Sackheim, R., and Zafran, S., "Space Propulsion Systems," Space Mission Analysis
and Design, 3rd ed., Ch. 17, edited by I. Wertz and W. Larson, Microcosm Press, El
Segundo, CA, 1999.
8
Hill, P., and Peterson, C , Mechanics and Thermodynamics o f Propulsion, 2nd ed.,
Addison Wesley, Reading, MA, 1992.
9
Micci, M. M., "Prospects for Microwave Heated Propulsion," AIAA Paper 84-1390,
June 1984.
10 Hawley, M. C , Asmussen, J., Filpus, J., Whitehair, S., Hoekstra, C., Morin, T., and
Chapman, R.,
"Review of Research and Development on the Microwave
Electrothermal Thruster," Journal o f Propulsion, Vol. 5, No. 6, pp. 703-712, NovDee, 1989.
11 Sullivan,
D.,
and
Micci,
M.,
"Performance
Testing
and
Exhaust
Plume
Characterization of the Microwave Arcjet Thruster," AIAA Paper 84-3127, June
1994.
12 Passow, M., Brake, M., Lopez, P., McColl, W., and Repetti, T., "Microwave
Resonant-Cavity-Produced Air Discharges," IEEE Transactions on Plasma Science,
Vol. 19, No. 2, pp. 219-228, April 1991.
13 Balaam, P., and Micci, M., "Investigation of Free-Floating Resonant Cavity
Microwave Plasmas for Propulsion," Journal o f Propulsion, Vol. 8, No. 1, pp. 103109, Jan-Feb, 1992.
R eproduced with perm ission o f the copyright owner. Further reproduction prohibited w ith o u t perm ission.
14
14 Mueller, I., and Micci, M.,
"Microwave Waveguide Helium Plasmas for
Electrothermal Propulsion," Journal o f Propulsion and Power, Vol. 8, No. 5, pp.
1017-1022, Sept-Oct, 1992.
15 Balaam, P., and Micci, M., "Investigation of Stabilized Resonant Cavity Microwave
Plasmas for Propulsion,” Journal o f Propulsion and Power, Vol. 11, No. 5, pp. 10211027, Sept-Oct, 1995.
16 Nordling, D., Souliez, F., and Micci, M., "Low-Power Microwave Arcjet Testing,"
AIAA Paper 98-3499, July 1998.
17 Souliez, F., Chianese, S., Dizac, G., and Micci, M., "Low-Power Microwave Arcjet
Testing: Plasma and Plume Diagnostics and Performance Evaluation," AIAA Paper
99-2717, June 1999.
18 Souliez, P.,
"Low-Power Microwave Arcjet Spectroscopic Diagnostics and
Performance Evaluation," Masters Thesis, Department of Aerospace Engineering,
The Pennsylvania State University, University Park, PA, 1999.
19 Clemens, D., "Performance Evaluation of a Low-Power Microwave Electrothermal
Thruster," Masters Thesis, Department of Aerospace Engineering, The Pennsylvania
State University, University Park, PA, 2004.
20 Diamant, K., Brandenburg, J., Cohen, R„ and Kline, J., "Performance Measurements
of a Water Fed Microwave Electrothermal Thruster," AIAA Paper 2001-3900 July
2001 .
21 Diamant, K., Zeigler, B., and Cohen, R., "Tunable Microwave Electrothermal
Thruster Performance on Water," AIAA Paper 2003-5150, July 2003.
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
15
22 Sullivan, D., Kline, J., Zaidi, S., and Miles, R., “A 300 W Microwave Thruster
Design and Performance Testing,” AIAA Paper 2004-4122, July 2004.
23 Venkateswaran, S., Merkle, C , and Micci, M., “Analytical Modeling of Microwave
Absorption in a Flowing Gas,” AIAA Paper 90-1611, June 1990.
24 Chiravalle, Y., Miles, R., and Choueiri, E., “Numerical Simulation of MicrowaveSustained Supersonic Plasmas for Application to Space Propulsion,” AIAA Paper
2001-0962, January 2001.
25 Chiravalle, Y., Miles, R., and Choueiri, E., “A Non-Equilibrium Numerical Study of
a Microwave Electrothermal Thruster,” AIAA Paper 2002-3663, July 2002.
26 Gordon, S., and McBride, B., "Computer Program for Calculation of Complex
Chemical Equilibrium Compositions and Applications: I. Analysis," NASA RP-1311,
1994.
27 Gordon, S., and McBride, B., "Computer Program for Calculation of Complex
Chemical Equilibrium Compositions and Applications: II. Users Manual and Program
Description," NASA RP-1311, 1996.
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16
CHAPTER 2 - M E T THEORY
This chapter is divided into three sections.
The first section details the
mathematical theory governing the electromagnetic resonance in the cylindrical cavity of
interest. The second section outlines microwave frequency gas breakdown theory. The
third section describes the physical processes that control propellant heating.
2.1
Resonant Cavity Theory
2.1.1
Maxwell’s Equations
The electromagnetic field distributions for boundary value problems can be found
by solving Maxwell’s equations.1,2
(2 . 1)
V •B
—q
*imag
( 2 .2 )
(2.3)
V ■D = q eject
(2.4)
In addition to Maxwell’s equations, there is a non-independent equation relating the
electric current density and the charge density.
(2.5)
The system of interest for this work involves harmonic oscillations of electromagnetic
fields in sinusoidal form. Thus, the equations describing the fields and quantities of
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17
interest
can be represented by a combination of instantaneous and
time varying
components. Equation 2.6 shows this representation of the electric fieldstrength.
E(x, y,z,t) = i?e[E(x,y,z)e/mt]
(2.6)
The instantaneous electromagnetic field vectors can be related to each other using the
constitutive relations.
D = eE
(2.7)
B = pH
(2.8)
Jc = cjE
(2.9)
Using these relations, the Maxwell curl equations can be written in the following coupled
frequency domain form.
V x E = -M , - ycofxH
(2.10)
V x H = J. + g E + j'coeE
(2 . 1 1 )
Assuming homogeneous, lossless, and source-free material, the equations can be written
in uncoupled wave equation form.
V 2E = -® 2£|iE
(2.12)
V 2H = -G)2£jiH
(2.13)
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18
2.1.2
TM Cylindrical Cavity Solution
The resonant cavity used in this work is a cyiindrical chamber with the geometry
shown in Figure 2.1. The solution for Maxwell's equations will be described here for this
configuration.
a
Figure 2.1:
Cylindrical Cavity Geometry
In cylindrical coordinates, the instantaneous electric and magnetic field
distributions can be written in the following manner.
E(p, <t>,z) = E p(p, <j), z)ap +
(p, (j>, z)a^ + E z(p, (j), z)az
H(p,(|),z) = H p(p,(j),z)ap + H 0(p,<j),z)ap + H z(p,cj),z)a2
(2.14)
(2.15)
Using the definition in Equation 2.15 the magnetic field vector wave equation can be
broken
up intothree scalar equations. The electric field distribution equations can be
written in a similar form.
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19
f
V 2H„ +
V 2H a +
hp
2
an,
P2
P2
H„
2 3H„ A
P2
P2 3p ,
(2.16)
= - o 2ep,H
(2.17)
V 2H z = —®2£|iH 2
(2.18)
The solutions of these equations can be found by making use of the magnetic and
electric vector potentials, A and F.
. 1
3
1 3 t
\
ap e 3p p 3 p
cope p 3<j>kp 3p
. 1 3 f1 3 / . \
(pA
E z = -j® A z - j
cope 3z ^p 3p
. 1
H
p
H9 = - j © a ^ - J
3
fl5 F z
3F^
3z V £ vp 3<j)
3z y
A + —
p 3<j)
1 3A*
dhA
p 3<j>
3z
1 1 3
E* = - j( o A * - j
dA
1 3A.
(pA p ) + - —
1 3A*
3A,
p 3(j>
3z
I1 I1 f
-♦ + —
CQjO-E 3p p dp
p 3<p
. 1 1 3
1 3
(p F
H z = -jcocq - jrape 3(p\^p 3p
1 3F„ 3F.
— + ■
p 3tp
3z
) + ~ ^ L
p 3cp
+ ^ S
3z
3
i f 1 3A,
dz
+ —
cops p 3(p^p 3p
3p
e p 3p
1 5Fm 3R 1
1 3
3z
3<t>
( 2 .20 )
(2.21)
3A(„ ^
p 3cp
V -
(2.19)
3z
f3 A p
3A ^
v 3z
3p ,
II
(2.22)
(2.23)
(2.24)
PP
The field configuration of interest for this investigation is one where the magnetic field
components lie in a plane transverse to the cylinder axis.
Modes of this type are
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20
designated the transverse magnetic (TM) modes. For these modes, the input magnetic
field must be transverse to the cavity axis at all locations and times. For this case, the
only non-zero vector potential is the axial component of the magnetic vector potential,
Az.
This result allows the electric and magnetic field distribution equations to be
simplified.
. 1 d 2A z
I--------------2
cojie 9p3z
(2-25)
. l 32a ,
= “J
TTT"
ffifiE 3<t>3z
(2.26)
E' “
e
<p
E z = - j- 1 —
cops
^
2 A
z
+ G>p£A z
2
A
"
(2.27)
1 dA,
H '
=w lT
< 2 ' 2 8 )
H * = ------ ^
(2.29)
n z=0
(2.30)
For a closed cylindrical cavity with perfectly conducting walls, several boundary
conditions can be assumed.
I.
E<|>(a,(j},z) = 0
II.
Ez(a,cj>,z) = 0
III.
The electromagneticfields are finite everywhere
IV.
The fields must repeat every 2n radians in <}>
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21
V.
The waves propagate along the z-axis
The enforcement of these boundary conditions allows for the determination of the final
form of the magnetic vector potential.
V a
)
\ h
( 2 . 31 )
It is also possible to determine the resonant frequency of the cavity in terms of the
chamber geometry.
(2.32)
Bmnp is a modal constant and Xmn represents the nth zero (n = 1,2,3,--•) of the
Bessel
function of the first kind of order m (m = 0,1,2,...). Physically, m refers to the number of
full-period variations of the electric field along the circumferential direction.
The
number of half-period variations in the radial direction is represented by n. The p index
refers to the number of half-period variations along the cavity length.
2.1.3
TMo11 Cavity Characteristics
To obtain the highest possible exhaust temperature, the plasma position should be
as close to the exit nozzle of the thruster as possible. Plasma formation occurs in areas of
maximum electric energy density. For that reason, a resonant mode and cavity size with
electric energy density peaks only in the vicinity of the cylinder ends was chosen. The
amplitude of electric energy density is proportional to the square of electric field strength
at each location and time. Substituting Equation 2.31 into Equations 2.25 through 2.30, it
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22
is possible to show the final form of the electromagnetic field vectors for the TMJ„
mode.
„
„ , ( Xn.P
|cc
xss
Ez —E0UI0
V a J
v
11
j
E*=0
Tta
E „ = E 011—
Xoih
(2.34)
f XoiP ] sin ' ..HZ—^
V
(2.33)
a
J
IhJ
Hz =0
/ XoiPN:os
H
E*—'At
A q> = ■
oilJ i ^ - SJJ |
(2.35)
(2.36)
(2.37)
Xoi
Hp =0
(2.38)
Eon is the normalized electric field operating at the cavity resonant frequency. Figures
2.2 and 2.3 show the variation of the instantaneous electric fields in a plane along the
cavity axis for the TMon mode. The electric fields vary cosinusoidally with time. The
cavity modeled has a radius of 2.0 inches and a length of 6.2 inches.
The cavity
dimensions were chosen for 2.45 GHz frequency operation and to limit the toroidal
region of high electric energy density around the center plane of the cylinder. Figure 2.4
shows the variation of the instantaneous electric energy density in a plane along the
cavity axis. The TMon mode is clearly a good choice for operation where regions of high
electric energy density are desired, near the ends of the cylinder along the cavity
centerline.
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23
TS
0 .5
Axial Location, inches
R a d ia l Location, inch es
Figure 2.2: Instantaneous Axial Electric Field Distribution for TMon Cavity
E
Axial Location, inches
Radial Location, inches
Figure 2 3 : Instantaneous Radial Electric Field Distribution for TMoi t Cavity
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24
HI 0 .4 ,
02
Axial Location, inch es
R a d ia l
Location, inch es
Figure 2.4: Instantaneous Electric Energy Distribution for TMon Cavity
2.2
Plasma Form ation Theory
2.2.1
Gaseous Breakdown
The first step in creating stable resonant cavity microwave plasmas is to create
free electrons in the ambient gas by initiating gaseous breakdown. Gaseous breakdown
occurs when electrons are stripped from neutral molecules using an applied electric field.
The breakdown characteristics of a gas are a function of the gas composition, the gas
pressure, the electric field magnitude, the electric field frequency, and the method used to
•5
apply the electric field.
Under the influence of a constant electric field created between
two electrodes, the molecular electrons and positive nuclei are forced in opposite
directions due to Lorentz’s Law.
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25
F = qE
(2.39)
If the electric field is strong enough, the force pulling the negatively charged electrons
and positively charged nucleus in separate directions can overcome the electrostatic force
between them. The electrons are then separated from the nucleus and become “free
electrons,” capable of interacting with other neutral and ionic molecules.
The situation is similar for a neutral gas under the influence of a low frequency
harmonically varying electric field. The gas breakdown process takes on the order of IQ'8
to 10'6 seconds to complete. For a low frequency field, the polarity of the electrodes will
change more slowly than this. Therefore, the alternating voltage will not have enough
time to change the direction of the electrons before breakdown occurs and the electrons
attach to the anode. Thus, the only difference will be that the electrode attracting the
electrons will change as the frequency varies. It is assumed that the molecular ions do
not move appreciably under the influence of the electric field because they are much
more massive than the relatively light electrons.
The situation changes for high frequency harmonically varying electric fields.
Once the frequency increases to a certain level relative to the gap length between the
electrodes, called the cutoff frequency, fco, the electrons do not have enough time to reach
the anode before their direction is reversed.
_
fieE
f» = * r
<2-40)
This means that when the applied electric field frequency is greater than the cutoff
frequency, the electrons initially liberated by the electric field will be free to oscillate
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26
perpendicular to the electrodes until coming into contact with neutral or ionic molecules,
or cavity walls. When the rate of production of electrons is just greater than the rate of
electron loss due to diffusion and recombination, breakdown occurs.
electron lifetime with respect to the diffusional loss time,
The average
is a good measure of how
rapidly electrons need to be stripped from molecules to continue the breakdown process.
(2.41)
(2.42)
If gas pressure drops below atmospheric pressure, the electrons become more
mobile and more energy can be absorbed per electron, allowing for a lower breakdown
voltage.
If the pressure falls too close to a true vacuum, there may not be enough
molecules available for electrons to strike before hitting the cavity walls. Breakdown
occurs in larger cavities with a significantly weaker applied field, especially at low
pressures. This is because of the larger volume for electrons to travel before impacting
walls. For microwave frequency range plasmas, the breakdown electric field strength is
proportional to the operation frequency. Once breakdown occurs, and a small number of
electrons are released into the gaseous mixture, a much larger number of free electrons
can be released as a process known as electron impact ionization takes place.4
2.2.2
Electron Impact Ionization
When an electron collides with an atom or molecule, kinetic energy is exchanged.
If no excitation or ionization occurs because of this collision, it is considered to be an
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27
elastic collision. The collision is inelastic if excitation, deactivation, or ionization of the
impacted molecule is a result of the collision. Therefore, it seems logical to assume that
if the kinetic energy of the incoming electron is less than the ionization energy of the
impacted molecule, ionization will not occur. However, experiments have shown that the
energy needed to ionize molecules of gas can come from electrons with kinetic energy
less than the ionization energy of those molecules.
There are several possible explanations for this phenomenon. First, it is possible
that an initial electron collides with the molecule and raises it to a metastable excited
state. Before the molecule has emitted a photon and returned to the ground state, another
electron impacts it. This could occur until the total energy added to the molecule is large
enough to ionize it. It is also possible that an electron that does not have enough kinetic
energy to cause ionization could collide with a neutral atom and actually gain kinetic
energy and be traveling faster after the collision than before. The high-speed electron
then colliding with another neutral atom may have enough energy for ionization. Third,
two electrons not having enough kinetic energy for ionization could each hit separate
molecules and cause these molecules to reach an excited state.
If the two impacted
molecules collide with each other before returning to their respective ground states,
ionization can occur. It is also important to note that ionization will not occur every time
an electron with kinetic energy greater than the ionization energy of the impacted
molecule strikes. Molecules are able to absorb energy in a variety of ways in addition to
electron excitation and ionization.
It is possible that some, or all, of the impacting
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28
electron’s energy could go to rotational, vibrational, or electronic energy in the impacted
molecule.
2.3
Propellant Heating
2.3.1
Electron Impact Energy Exchange
After a plasma has been initiated, free electrons continue to absorb energy from
the electric field and distribute some of that energy throughout the gas via collisions with
heavy particles. As propellant is injected into the plasma chamber after the initial near­
vacuum diffuse plasma is formed, the plasma coalesces into a rotating teardrop shaped
structure and the chamber pressure rises. For microwave frequency molecular plasma at
atmospheric pressure, the energy exchange is often assumed to be equilibrium in nature,
with Joule heating as the energy transfer mechanism.5 A review of the literature shows
that the electronic excitation temperature, usually found from a seed metal, and the
molecular rotational temperature are similar, but typically vary by 500 - 1,000 K.6'9 For
nitrogen plasmas, measurements of rotational temperature in referenced works vary from
4,500 - 5,5Q0K and excitation temperatures from 5,500 - 6,000 K.
Local thermodynamic equilibrium (LTE) is often assumed in these situations.
The transition from diffuse nonequilibrium to near LTE conditions in a contracting
plasma is known as a glow to arc transition.10 The plasma contraction in the MET is
indicative of a change from nonequilibrium towards LTE. However contraction of the
plasma is not in itself confirmation of LTE, as nonequilibrium can persist in resonant
cavity plasmas even with plasma contraction.11
While an assumption of thermal
equilibrium may be appropriate for devices designed for pollution monitoring or material
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29
processing, a relatively small change in chamber temperature can mean a significant
change in thermal rocket calculated performance. For example, a change in measured
nitrogen rotational temperature from 5,000 K to 6,000 K would mean a calculated
increase of 10% in Isp. Therefore, it is necessary to measure the heavy particle rotational
temperature directly, rather than the excitation temperature of a seed metal. This noted
deviation from thermal equilibrium is due to the electron impact excitation and
deactivation of molecular internal energy storage modes.
The fraction of the absorbed energy that is passed from the electrons to the heavy
particles and in what manner the energy is transferred is a function of both the heavy
particle characteristics and the particular distribution of energy that the electrons
have.12,13 In equilibrium, collisionless electrons have a velocity distribution function,
f(v), that can be described by a Maxwellian distribution. This can also be written in a
form that describes the energy distribution of the electrons, f(e), if the Maxwellian
distribution is divided by the term 2 £ v m /2 , as is done by convention in plasma physics.
(2.43)
|Vef(e)d£ = l
o
(2.44)
Figure 2.5 shows this energy distribution for three different free electron temperatures.
As the electron temperature increases, a larger fraction of the electrons exist in the high
energy tail of the distribution.
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30
l.E+01
1 .E+00
■
f++++++++^T¥7
^ C
O
O
O
O
O
O
C
^ ^ J J j ^
1 .E -0 1
+++++++°0ooo°oooooo
+++++.
>©
+ + + + . ++
1.E-02
1.E-03
1 .E-04
0.5
1.5
2
2.5
3.5
Electron E nergy, eV
■5,000 K + 12,000 K o 25,000 K
Figure 2.5: Maxwellian Electron Energy Distribution Function
For nonequilibrium collisional molecular plasmas, the Maxwellian energy
distribution no longer holds because the probability of energy transfer to heavy particles
is electron energy dependent. For this situation, the distribution f(v) is anisotropic in
velocity space. It is often approximated by a two term expansion. The first term, which
depends only on the electron kinetic energy, represents the isotropic part of the
distribution.
This term, f(s), is known as the electron energy distribution function
(EEDF). The second term, which can be expressed as a function of the first, describes
the anisotropic part of the distribution. The EEDF can be described by the Boltzmann
equation for molecular plasmas under the influence of an electric field.
df _
dt
dJF 3Je,
a
a
Be
Be
% a + In + S u p - ^ + I t a - £
Be
Be
N„
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(2.45)
31
If it is assumed that the electron energy change between collisions and the electron
energy change due to the electric field, elastic collisions, and collisions with rotational
energy change is small relative to the electron energy, Ae/e « 1 , then the first three
terms on the right hand side of Equation 2.45 can be written in differential form.
The first term on the right hand side of the Boltzmann equation describes the
effect of the electric field on the EEDF. The energy flux due to the electric field can be
expressed as a function of the diffusion of electrons due the electric field, Dp, which is a
function of the electric field strength, the collision frequency, and speed of the electrons
at a given energy. The frequency of momentum transfer collisions, vm, is the sum of the
frequency of elastic and all inelastic collisions.
JF = - D FV e | d£
(2.46)
(2.47)
(2.48)
In general, when an electric field is present in the plasma of interest, the EEDF is time
dependent and the unsteady Boltzmann equation must be solved. However, two limiting
cases can be explored. When the applied field is a DC or low frequency field, the EEDF
can be considered time-independent. When the plasma is dominated by a high frequency
electric field, the electron energy distribution cannot follow the field, and a steady state
solution may be found.
For harmonically varying electric fields of the form
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E = E0cos (cot), an effective electric field strength, Eeff, can be used for this steady state
solution.14
(2.49)
The second term on the r.h.s. of Equation 2.45 expresses the effect of elastic
collisions on the electron energy distribution function. The energy flux due to elastic
collisions is a function of the heavy particle translational temperature, the average
relative electron energy loss per collision, 5ei, the frequency of the elastic collisions, vei,
and the energy of the colliding electron.
Iel =-DelVe-—jielVef
^el —^el^eie^
(2.50)
(2.51)
(2.52)
(2.53)
v e, = N v J X a f
(2.54)
This term is typically the dominant form of energy exchange between electrons and
heavy particles in atomic plasmas, but in molecular plasmas inelastic collisions typically
cause greater change in the EEDF.
The third term on the r.h.s. of Equation 2.45 describes the effects of rotational
excitation and deactivation on the EEDF.
The energy flux due to electron impact
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rotational excitation and deactivation for molecules is a function of the energy of the
impacting electron, the frequency of this type of collisions, the average energy lost due to
these collisions, Aerot, and the rotational temperature of the colliding heavy particle. For
nearly all cases, the rotational temperature of the heavy particle is equal to the
translational temperature, and that is assumed to be the case here.
(2.55)
(2.56)
(2.57)
(2.58)
(2.59)
The fourth and fifth terms on the r.h.s. of Equation 4.25 describe the energy lost
and gained by free electrons due to excitation or deactivation respectively, from inelastic
vibrational and electronic energy exchange collisions. The process by which electrons
gain energy from vibrationally or electronically excited molecules is known as a
“superelastic” collision process.
The energy gained or lost during these inelastic
processes can be relatively large compared to the energy of the electron before the
collision. For neutral-neutral collisions, molecules typically change just one vibrational
quantum number. For electron impact excitation or deactivation, collision cross sections
for multi-quantum level change are non-negligible. The energy flux from, or to, the
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34
electrons from inelastic vibrational or electronic energy exchange collisions is a function
of the impacting electron energy and the characteristics of the heavy particle.
relationship is often written in terms of the threshold energies of the transitions,
This
or
*
^skn“
In = Z (vsnk(e + eZ We + e;nkf(e + C ) - v snk(e)Vef (e))
(2 .6 0 )
s, n, k
Sup= I
(vZ(e - e Z We -
f (e■
-e*to)■-
(e)Vrf(e))
(2.61)
s , n, k
v 5nk = N"vasnk
(2.62)
v L = Nfvo**,
(2.63)
The cross sections, a, for excitation and deactivation of vibrational or electronic states by
electron impact can be related to each other by the detailed balance formula.
<C(e) = — ■
^ !s-olt (£+e‘kn)
gk e
(2.64)
The sixth term on the r.h.s. of Equation 2.45 takes into account the effects of
electron-electron collisions on the electron energy distribution function. This process can
also be described by the effect the collisions have on the electron diffusion and mobility
in the plasma.
(2.65)
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35
However, these electron-electron collisions can be neglected in relatively lowtemperature, low ionization fraction, high-pressure plasmas such as those found in the
MET because of the very low frequency of electron-electron collisions.
The seventh term on the r.h.s. of Equation 2.45 describes how the electron impact
ionization process affects the EEDF. At the near equilibrium conditions with relatively
high pressures and temperatures found in the MET plasma chamber during steady state
operation, thermal ionization is the dominant form of free electron production. However,
electron impact ionization is still important.
3
lion=X Jvsi (s,,e)£f (si)dei- vsi(e)Vrf(s)
S’’ VE+Eli
(2 .66 )
y
v si(e)=N sva[(e)
(2.67)
v sii(£o e 2) = N sv(e1]a(£ ,,£ 2)
(2.68)
The integral in the Ijon equation represents the release of an electron with energy e from a
molecule in the “s” state by an impacting electron with energy £i. The second term
accounts for the energy loss of the impacting electron as for an ordinary inelastic
collision.
The total kinetic energy of the two electrons is £, - £*, where £* is the
ionization energy for the molecule in that state. By convention, after the collision the
electron with the higher energy is known as the scattered electron, and the electron with
the lower energy is known as the secondary electron. The differential ionization cross
section, <js;i, expresses the probability of an electron appearing with energy £2 after the
collision between a neutral molecule and a primary electron with energy £2. The electron
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36
could be either the scattered or secondary electron. The ionization cross section, a Si, can
be related mathematically to the differential ionization cross section.
6,-E,
(2.69)
2
The final term on the r.h.s. of Equation 2.45 is used to determine the electron
losses due to electron attachment and electron-ion recombination effects on the EEDF,
which are the major loss mechanisms in the plasma at the relatively high pressures used
in the MET. The quantity p is the rate at which electrons are removed from the plasma
by these processes. Assuming there is no external source of electrons, the ionization rate
must be equal to this loss rate for a stable plasma at steady-state operating conditions.
While the determination of the electron energy distribution function is important
in and of itself, the real value in knowing the EEDF is that it can be used to calculate bulk
plasma properties and kinetic rate coefficients. The plasma electron mobility, diffusion
coefficient, characteristic energy and average energy can be directly calculated once the
EEDF is known. Knowledge of the electron mobility allows for determination of the
electron drift velocity and current density as well.
3/
2 c
df ,
—
J
de
•pirt " ?
*-1
3me
o v ra de
(2.70)
f't
(2.71)
(2.72)
e = je^ fd e
o
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(2.73)
37
Formolecularplasmas, inelastic
transfer fromelectrons to
v d = |i eE
(2.74)
Je = E jiwNe
(2.75)
and superelastic collisions candominate
heavy particles in some cases. TheEEDF
the energy
can be used to
calculate the rate coefficients, k, for the inelastic excitation and deactivation of electronic
and vibrational states, as well as the rate coefficients for ionization.
i
2
k sn k = J —
K
(2.76)
k£fde
kskn
(2.77)
J
2.3.2
O2
and N 2
C ross
2 ~
— k ion£fd£
me o
(2.78)
Sections and R a te Coefficients
In order to accurately determine the plasma properties and kinetic rates outlined
above, it is necessary to know the collisional cross sections for the electron impact
processes occurring. Experimental and theoretical studies of these cross sections have
been completed for plasmas with different constituents and environments.15"19 Figure 2.6
shows the total momentum transfer cross sections for molecular oxygen and nitrogen as a
function of electron energy, as tabulated in Ref. 19.
Clearly, the electron impact
momentum transfer cross section is much larger for nitrogen over the entire energy
spectrum. The peaks in the cross section data are due to electron impact excitation of
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38
3.5E-15
E
o
c© 3E"15
vs
OT 2.5E-15
0
2E-15
1
® 1.5E-15
oX
IU
E
3
c
0)
E
o
1E-15
5E-16
S
0
1
2
3
4
5
6
7
8
9
10
Electron Energy, eV
Oxygen
- x - Nitrogen
Figure 2.6: Momentum Transfer Cross Sections vs. Electron Energy
vibrational states, which is particularly important for nitrogen. The data for this figure
and most investigations through the early 1980’s was determined by swarm and electron
beam studies in which free electrons interact with relatively cold heavy particles. In
these situations, nearly all molecules are in the vibrational ground state.
For highly collisions! plasmas such as those found in the MET plasma chamber,
the electron energy distribution function and vibrational population distribution function,
VDF, are coupled.14' 17 As the electrons impact the heavy particles and excite non-ground
vibrational states, the VDF is changed, affecting the total inelastic cross section for
momentum transfer, which is the main factor in determining the EEDF. Figure 2.7 shows
the nitrogen momentum transfer cross section tabulated in Ref. 19 along with a
Maxwellian population distribution for free electrons versus free electron energy for
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several temperatures. Even at moderately low free electron temperatures, a significant
portion of the electrons will have energies that correspond to large nitrogen electron
impact cross sections.
0.8
■r o.s
® 0.4
0.2
0
1
2
3
4
5
6
7
8
9
10
Electron Energy, eV
—a— Nitrogen Collision Cross Section
5,500 K Electron Distribution
......... 24,000 K Electron Distribution
12,000 K Electron Distribution
Figure 2.7: N2 Electron Impact Cross Section and Electron Maxwellian Population
2.3.3
Thermochemical Effects
In addition to the fact that the electron impact heating effects are propellant
specific, the thermochemical differences between particular propellants also have an
effect on the heating process and potential thruster performance.
The temperature
dependant equilibrium thermal conductivity, dissociation fraction, and enthalpy of a
propellant all influence the final thermochemica! state of a propellant being heated by the
microwave energy. These properties can be compared using the CEA2 code developed
by researchers at NASA Glenn Research Center.20,21 While nonequilibrium effects can
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40
not be taken into account with this computer code, the equilibrium values of propellant
properties are of value because of the near equilibrium nature of the plasma. In addition,
the energy that is stored in free electrons and internal energy storage modes other than
rotational energy are unlikely to be recovered, and so the calculated equilibrium
performance values are likely to be realistic when compared to actual performance. The
equilibrium calculated properties of oxygen, nitrogen, and ammonia propellants and their
effects on the potential performance of the MET will be described in Chapter 5 of this
work.
2.4
References
1 Balanis, C., Advanced Engineering Electromagnetics, John Wiley and Sons, Inc.,
New York, 1989.
2
Tse Chow Ting V. Chan, and Howard C. Reader, Understanding Microwave Heating
Cavities, Artech House, Boston, 2000.
3
Raizer, Yuri P., Gas Discharge Physics, Springer-Verlag, Berlin, 1991.
4
Nasser, E., Fundamentals o f Gaseous Ionization and Plasma Electronics, Wiley and
Sons, New York, 1971
5
Fridman, A., and Kennedy, L., Plasma Physics and Engineering, Taylor and Francis,
New York, 2004.
6
Ogura, K., Yamada, H., Sato, Y., and Okamoto Y., "Excitation Temperature in HighPower Nitrogen Microwave-Induced Plasma at Atmospheric Pressure," Applied.
Spectroscopy, vol. 51, pp. 1496-1499, 1997.
R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w ith o u t perm ission.
41
7
Hadidi, K., Woskov, P., Flores, G., Green, K., and Thomas P., "Effect of Oxygen
Concentration on the Detection of Mercury in an Atmospheric Microwave
Discharge," Jpn. J. Appl. Phys., vol. 38, pp. 4595-4600, 1999.
8
Woskov, P., Hadidi, K., Berras, M., Thomas, P., Green, K., and Flores, G.,
"Spectroscopic diagnostics of an atmospheric microwave plasma for monitoring
metals pollution," Rev. Sci. Instruments, vol. 70, pp. 489-492, 1999.
9
Ohata, M ., and Furuta, N., "Spatial Characterization of Emission Intensities and
Temperatures of a High Power Nitrogen Microwave-induced Plasma," J. Analytical
Atomic Spectrometry, vol. 12, pp. 341-347, 1997.
10 Kunhardt, E., "Generation of Large-Volume, Atmospheric-Pressure, Nonequilibrium
Plasmas," IEEE Trans, on Plasma Set, vol. 28, pp. 189-200, 2000.
11 Passow, M., Brake, M., Lopez, P., McColl, W., and Repetti, T. "Microwave
Resonant-Cavity-Produced Air Discharges," IEEE Transactions on Plasma Science,
vol. 19, pp. 219-228, 1991.
12 Capitelli, M., Ferreira, C , Gordiets, B., and Osipov, A., Plasma Kinetics in
Atmospheric Gases, Springer, Berlin, 2000.
13 Biberman, L., Vorob’ev, V., and Yakubov, I , Kinetics o f Nonequilibrium LowTemperature Plasmas, Consultants Bureau, New York, 1987.
14 Capitelli, M., Celberto, R., Gorse, C., Winkler, R., and Wilhelm, J., “Electron Energy
Distribution
Functions
in
Radio-Frequency
Collision
Dominated
Nitrogen
Discharges,” Journal o f Physics D: Applied Physics, vol. 21, pp. 691-699, 1988.
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
42
15 Chrisophorou, L., ed., Electron-Molecule Interactions and Their Applications, vol. 1,
Academic Press, Orlando, 1984.
16 Itikawa, Y., Hayashi M., Ichimura, A., Onda, K., Sakomoto, A., Takayanagi, K.,
Nakamura, M., Nashimura, H., and Takayanagi, T., “Cross Sections for Collisions of
Electrons and Photons with Nitrogen Molecules,” Journal o f Physical and Chemical
Reference Data, vol. 15, p. 985, 1986.
17 Pitchford, L., and Phelps, A., “Comparative Calculations of Electron-Swarm
Properties in N 2 at Moderate E / N Values,” Phys. Rev. A, vol. 25, pp. 540-554, 1982.
18 Phelps, A., JILA Information Center Report, vol. 28, University of Colorado,
Boulder, CO, 1985.
19 Phelps, A., ftp://jila.colorado.edu/collision_data/ (unpublished), accessed September
7, 2004.
20 Gordon, S., and McBride, B., “Computer Program for Calculation of Complex
Chemical Equilibrium Compositions and Applications: I. Analysis,” NASA RP-1311,
1994.
21 Gordon, S., and McBride, B., “Computer Program for Calculation of Complex
Chemical Equilibrium Compositions and Applications: II. Users Manual and Program
Description,” NASA RP-1311, 1996.
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43
CHAPTER 3 - EXPERIMENTAL APPARATUS AND PROCEDURES
This chapter outlines the apparatus and processes used for experimental testing
during this investigation. The components used to create microwave resonant cavity
plasmas and conduct spectroscopic experiments are discussed first. Plasma formation
and spectroscopic testing procedures are then detailed.
3.1
Apparatus
3.1.1
Microwave Energy Input
Figure 3.1 shows a schematic of the microwave system used in this investigation.
Power is produced by a Gerling Laboratories model GL103 low ripple power supply
connected to a model GL131, 2.45 GHz magnetron. The microwave output of the system
can be tuned from 0-2.2 kW at a nearly constant operating frequency. Microwave energy
is sent from the magnetron via waveguide through a three-port circulator and dual
Coupler
Waveguide to
Coaxial
Transition
Forward Power
Reflected Power
Dummy Load
Power Meters
;.:M *1
Microwave
Power Supply
Control
Figure 3.1: Microwave System Schematic
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44
directional coupler to a coaxial input into the resonant cavity. A 0.8125 inch diameter
copper hemispherical probe antenna protrudes 0.9375 inches into the center of the base of
the cavity. The Gerling GL401A three-port circulator is used to direct power reflected
back from the plasma onto a water cooled dummy load to protect the magnetron. The
Gerling dual directional coupler is used to sample the forward and reflected power, and
Hewlett-Packard model 432A power meters are used to measure these powers. Chilled
water is forced around the magnetron and three-port circulator for cooling.
The 2.45 GHz frequency used can easily excite water molecules. Therefore, it is
imperative to ensure human exposure to radiation leakage is limited. The United States
Occupational Safety and Health Administration (OSHA) requires that workers be
exposed to an environment with no more than 10 mW/cm2 of microwave frequency
energy.1 A Holladay Industries model HI 1501 microwave survey meter is used to
periodically measure microwave energy leakage. Typically, leakage measurements on
the order of 1.0 mW/cm are found near cavity metallic junctures, with the radiation
rapidly decreasing to negligible amounts within inches of the cavity.
3.1.2
Resonant Cavity
Equation 2.32 governs the combinations of cavity length and radius that can be
used to create a resonance for the TMon mode. In order to minimize a toroidal region of
high electric energy density present near the mid-plane of the cavity, a cavity with a
relatively small radius is preferred. The cavity used was originally designed by F. J.
Souliez for his low power microwave arcjet testing, and has a radius of 2 inches and a
length of 6.2 inches.
The cavity is constructed of aluminum with a "non-sparking"
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45
copper specialty alloy #172 nozzle insert located at the center of one end. Some pitting
of the nozzle Insert occurred during testing at -high Sow rates and pressures. However,,
during nominal testing there was no obvious 'interaction between the diamber plasma and
nozzle insert. The exhaust gasses pass through a-conical converging nozzle with a sixty
degree cone angle, Nozzles with throat diameters o f 0.032 inches, 0.040 inches, 0.051
inches, and -0.075 -inches were -used. Figure 3.2 shows, a picture of the cavity nozzle plate
with a -copper alloy, nozzle insert.
Figure 3.2: Cavity Nozzle Plate with Insert
The cavity is divided into two chambers, a plasma chamber and an antenna
chamber, by a 0.25 inch thick quartz separation plate.
The circular plate is nearly
transparent to microwave frequency energy, but it can seal the antenna chamber from the
injected gas. This forces plasma formation to occur only in the plasma chamber, closest
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46
to the nozzle and where the pressure is lower, thus preventing antenna erosion. There are
three equally spaced 0.014 inch diameter tangential flow injectors located one inch below
the nozzle plate used for nearly all spectroscopic testing. Larger, 0.055 inch diameter
injectors were used for a set of high mass flow rate spectroscopic tests and 0.25 inch
diameter injectors were also used for phenomenological testing. These injectors help
ensure the plasma is located in a low-pressure region along the cavity axis by creating
vortical flow. There is a 2.0 inch diameter gridded viewing window in the side of the
plasma chamber that allows for optical confirmation of plasma formation and
spectroscopic investigations. The window is placed over a grid of 0.08 inch diameter
holes spaced 7/32 inch apart in the side of the chamber that prevents microwave leakage.
A pressure port is located along the chamber wall of the plasma chamber. Figure 3.3 and
Figure 3.4 show a schematic and picture of the resonant cavity system respectively.
Quartz Separation Plate
Tangential Flow Injectors
Probe Antenna
Plasma
Waveguide to Coaxial
Transition
N ozzle Plate
High Electric Energy Density Regions
Figure 3 3 : Resonant Cavity Schematic
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Figure 3.4; Picture of Resonant Cavity Thruster System
3,1,3
Gas Flow Regulation
The propellants used are stored in gas bottles, with pressure regulators used to
control the flow stagnation pressure, typically set between 70-80 psig. UNIT Instruments
mass flow controllers (mfc) model UFC-8100 and UFC 2050A are used to regulate the
volumetric flow o f gasses.
The UFC 2050A mfc is capable of controlling up to 5
standard liters per minute (SLM) of nitrogen flow.
The maximum amount of flow
allowed for other gasses is determined using conversion ratios provided by UNIT
Instruments and gas standard densities according to the following equation which relates
the mass flow rate, m, to the volumetric flow' rate, q, using the standard density of the
gas, po, and a conversion ratio, c.
m = cqp0
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(3.1)
Table 3.1 shows the full-scale mass flows for nitrogen and oxygen with the UFC 2050A 5
SLM controller. A 30 SLM UFC-8100 controller was also used for nitrogen and oxygen
flows and Equation 3.1 is applicable for that controller as well. A dedicated 750 standard
cubic centimeter per minute (seem) UFC-8100 was used for ammonia flow control.
Commands are sent to the mass flow controllers using UNIT Instruments URS-20 mass
flow meters. The flow meters show a display from 00.0 to 99.9 percent full-scale flow.
Flow can be controlled within 0.2 percent full-scale flow accuracy.
T a b le 3.1: 5 SLM UNIT Instruments UFC 2050A Full-scale Mass Flows
G as
C o n v e rs io n
R a tio
V o lu m e tric
F lo w R a te
(S L M )
S ta n d a rd
D e n sity
(k g /m 3)
M a ss F low
R a te
(m g/s)
N itro g e n
O xygen
1.000
0.977
5.00
4.89
1.2498
1.4276
104.15
116.25
In order to initiate plasmas, the pressure in the plasma chamber must be lowered
until a large enough electric field strength to pressure ratio is attained. This is done using
a Thomas Industries Welch vacuum pump. A tube is run from the pump to the nozzle
exit, and gas is pulled from the cavity and expelled through a hood vented to the
atmosphere. The pump is capable of lowering the pressure in the plasma chamber to
approximately 0.15 psia.
3.1.4
Spectroscopic System
A major focus of this investigation concerns the spectroscopic analysis of
chamber plasmas for temperature determination. In order to complete this study, it is
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49
necessary to determine the intensity of light emitted over a range of wavelengths. The
optical setup used is shown schematically in Figure 3.5. The light given off by the
chamber plasma exits the viewing window and enters a 5 inch long tube with a 0.25 inch
Spectrometer
Collimating Lens
M
Traverse
System
Fiber Optic
Cable
eeQs
Focusing
Lens
Resonant Cavity
Spectrometer
Drive Unit
Am plifier/
Discriminator
Photometer
PC
Figure 3.5: Optical System Schematic
inner diameter. This probe attachment is placed on two mechanical traverses, one with
lateral control and one with vertical control. This allows for controlled spectroscopic
investigation of different spatial locations within the plasma chamber.
The probe is
connected to a fiber optic cable input. After passing through the fiber optic cable, the
light is collimated and then focused through the opening slit of a SPEX 1870
spectrometer and onto the diffraction grating.
The spectrometer has a 0.5 m, f/6.9
Czemey-Tumer system with a Bausch and Lomb 2,400 lines/mm ruled diffraction
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50
grating, blazed at 3,000 A.
The light is then passed through a second slit onto a
Hamamatsu model 1P28A photomultiplier tube (PMT). A Pacific Instruments model 126
photometer and AD-126 amplifier/discriminator convert the light to an electric analog
signal and amplify it.
The spectrometer and data acquisition systems are controlled by a Data
Translation 12-bit model DT2801 analog-to-digital input/output board that is driven by
BASIC programs from a personal computer. The programs were originally written by D.
J. Sullivan and modified for this investigation.3 The spectrometer system can scan from
3500 to 6650 A, in 0.01, 0.02, 0.04, or 0.10 A increments. The maximum scan range for
any particular scanning increment is 3,000 times the increment. The spectrometer input
and output slits can be opened up to 600 microns wide, in 1.0 micron increments. The
width of the lines in the detected spectrum is a function of the spectrometer slit widths.
For all tests, the input and output slits were set at the same opening width.
The
spectroscopic system creates a triangular lineshape for input light. Figure 3.6 shows the
variation of the full width of the spectral lines at half the maximum intensity of the lines
(FWHM) as a function of the spectrometer slit width. This variation was determined by
using a hydrogen arc lamp.
The system can be used in two different operational modes. For high intensity
light sources, such as lasers, a mode is selected where the current created by the light
hitting the PMT is directly measured. For relatively low intensity sources, such as the
MET chamber plasmas, the photons striking the PMT are individually counted. The
spectroscopic system is capable of counting a minimum of ten to a maximum of one
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51
0.9
0.7
S
0) °-6
5
0.5
u.
0.4
0.3 --
0.2
0.065
0.07
0.075
0.08
0.085
0.09
0.095
Slit Width, mm
Figure 3.6: Variation of Experimental FWHM with Slit Width
million photons at each wavelength, with nine intermediate ranges.
For this study,
counting ranges of three hundred thousand and one million were used.
3.2
Testing Procedures
3.2.1
Plasma Formation
In order to form plasmas in the MET plasma chamber, propellant gas is first
injected through the chamber for several minutes to ensure that only the desired gas is
present in the chamber and feed lines.
Then the Welch pump is used to lower the
chamber pressure to approximately 0.20 psia. The magnetron power is then turned on at
a relatively low setting of approximately 500 W and slowly increased.
After
approximately one second, diffuse plasma spreads throughout the plasma chamber. Mass
flow into the chamber is initiated through the tangential injectors at the desired flow rate
for the test. The valves between the Welch pump and vacuum lines are then closed. As
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52
gas accumulates in the chamber and the pressure rises, the plasma's appearance changes.
The plasma contracts into a rotating teardrop shape structure and becomes brighter.
Figure 3.7 through Figure 3.9 show the appearance of low pressure diffuse
plasmas and high pressure coalesced plasmas for oxygen, nitrogen, and ammonia,
respectively. The chamber pressures can be seen on the display in the figures, in psia
units. Once the pressure inside the chamber reaches atmospheric pressure, the vacuum
cap covering the exhaust nozzle is removed. The chamber pressure continues to rise for
approximately one minute. The final pressure value is dependent upon the mass flow
rate, absorbed power, nozzle throat diameter, and propellant in use.
Table 3.2 gives a
detailed list of the steps used to create a plasma in the microwave electrothermal thruster
for spectroscopic analysis.
Table 3.2: Detailed Procedure for MET Plasma Testing
Step
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Description
Turn on Magnetron Power Supply Circuit Breaker
Turn on Magnetron System Power
Turn on Pressure Transducer and Flow Controllers
Turn on Microwave Power Meters
Open Cooling Water Valves
Turn on Water Chiller
Turn on Water Pump
Open Propellant Gas Bottle
Set Propellant Flow Rate
Flow Propellant for Several Minutes to Remove Foreign Gasses From Chamber
Turn on Vacuum Pump and Attach Vacuum Cap to Nozzle Exit
Turn off Flow and Wait for Chamber Pressure to Reach 0.20 psia
Initiate Minimum Microwave Power and Raise to Desired Level
As Plasma Forms, Initiate Propellant Flow
Remove Nozzle Cap After Chamber Pressure Exceeds Atmospheric
Allow Chamber Pressure and Temperature to Stabilize (~ 2 minutes)
Conduct Spectroscopic Experiments
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Figure 3.7: (a) Low Pressure and (b) High Pressure Oxygen Plasma
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Figure 3 .8 : (a) Low Pressure and (is) High Pressure Nitrogen Plasma
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Figure 3 3t (a) Low Pressure and (b) High Pressure Ammonia Plasma
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56
3.2.2
Spectroscopic Analysis
The spectroscopic system used is very sensitive to the physical alignment of the
collection optics. Therefore, it is necessary to use a reference light source to ensure that
enough light passes through the spectrometer slits.
This alignment is done using a
Hughes 3225H-PC helium-neon laser. Each day before testing, a spectral scan of the
6329.8 A peak is completed. This scan is then compared to a baseline scan to determine
if more or less light is entering the spectrometer than under the baseline configuration. If
the light intensity is too dim, the alignment of the system optics is adjusted to correct this.
Figure 3.10 shows a typical laser calibration curve used during spectroscopic analysis.
For these scans, the spectrometer slits were set at 0.04 mm and the range was set at the
maximum, with the spectrometer and PMT operating in current measuring mode.
Once the incoming light intensity level is verified with the laser, the next step is to
gather light from the MET chamber plasma. The mechanical traverse system is adjusted
W a v e l e n g t h (Ang)
6326
6327
6328
6329
6330
6331
6332
6333
-0.4
>
-°-8
1_
£
CL
Figure 3. 10: He-Ne Laser Alignment Check Plot
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6334
57
so that the column of light is collected from the desired location,
initiated using the procedure stated above.
A plasma is then
After the chamber pressure stabilizes, a
spectroscopic emission scan is completed. The data collection lasts approximately three
minutes for each scan. Oxygen plasmas were scanned over the 3,500-3,750 A range, in
0.10 A increments and nitrogen plasmas were scanned over the 3,885-3,917 A range in
0.02 A increments.
3.3
References
1 OSHA Regulations (Standards - 29 CFR) Occupational Health and Environment
Control, Subpart G, Nonionizing Radiation 1910.97, March 7, 1996.
2
Souliez, F. J., "Low-power Microwave Arcjet Spectroscopic Diagnostics and
Performance Evaluation," M.S. Thesis, The Pennsylvania State University, 1999.
3
Sullivan, D. J., "Development and Performance Characterization of a Microwave
Electrothermal Thruster Prototype," Ph.D. Thesis, The Pennsylvania State University,
1995.
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58
CHAPTER 4 - SPECTRAL EMISSION MODELS
The history and theory of molecular emission models is presented first in this
work. The oxygen Schumann-Runge emission model developed for this investigation is
discussed next, as well as how this model is compared to experimental data. Third, the
commercially available LIFBASE N2+ emission model and data analysis scheme is
described.
4.1
Background
In 1900, Max Planck published his theory that the energy states of an oscillator
are discontinuous.1 Applied to molecules, this means that molecules can only be found in
distinct energy states. In order to change energy states, molecules must absorb or emit
electromagnetic energy in discrete amounts. Planck suggested the energy of the radiation
absorbed or emitted is related to the frequency by a simple formula.
AE = hf
(4.1)
There are several different types of molecular transitions that can occur.2 The differences
between these types of transitions are what define the electromagnetic spectrum and the
type of spectroscopy used to analyze the transitions.
Table 4.1 shows the different
regions of the electromagnetic spectrum, and the molecular energy change process that
defines each region.
frequency.
The regions are not rigidly defined by numerical values of
The regions overlap each other and different references use different
definitions to divide the electromagnetic spectrum.
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59
Table 4.1: Electromagnetic Frequency and Associated Energy Change Process
Electromagnetic Region
Frequency (Hz)
Radiofrequency
Microwave
Infrared
Visible and Ultraviolet
X-ray
Y-ray
3 x 106 3 x 1010 3 x 1012 3 x 10143 x 10163 x 1018-
3 x 1010
3 x 1012
3 x 1014
3 x 1016
3 x 1018
3 x 1020
M olecular Energy
Change Process
Nuclear or Electron Spin
Rotation Energy
Vibrational Energy
Valence Electron Level
Inner Electron Level
Nuclear Particle
When a molecule undergoes a transition from a higher energy state to a lower
energy state, the energy difference between the states must be dissipated in some way.
This energy can be transferred to other energy storage modes within the molecule, such
as vibrational or rotational modes. The energy can be transferred to other molecules via
collisional processes.
Finally, the energy can be released from the molecule by the
emission of a photon of electromagnetic energy. In order to model the emission spectrum
from a system of molecules undergoing energy state transitions, the transition energies,
intensities, and lineshapes must be known.3,4
Determining these factors requires
knowledge of statistical thermodynamics and a quantum mechanical analysis of the
molecules undergoing the transition.5,6 This investigation is concerned with the emission
of ultraviolet and visible light from plasmas. The type of energy transition of interest is
the change of valence electron energy levels.
4.2
Transition Frequencies
The frequencies at which photons are emitted from a vibrating and rotating
molecule undergoing an electronic transition depend on the difference in the initial and
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60
final state energies of the molecule. These transition frequencies are often given in
wavenumbers, with units of cm'1.
(4.2)
he
In this equation, Teiec represents the energy difference between the upper, n, and lower,
m, electronic state of the molecule. The subscripts Y, T and v", I" refer to the upper and
lower state vibrational and rotational quantum numbers respectively. The values of TeieC
have been calculated and experimentally verified for many molecular transitions of
interest, and are typically on the order of 25,000 cm '1, in the ultraviolet or visible region
of the electromagnetic spectrum.
In order to solve for the transition frequency, the
vibrational and rotational energy contributions to the total energy must be calculated for
both the upper and lower state.
To determine the rotational energy, Ej, for a molecule at a distinct rotational
energy state, Schrodinger's wave equation can be solved, assuming a rigid, non-vibrating
molecule. This means that there is no potential energy storage and a fixed intemuclear
distance.
Ej = hcBJ(l + l)
(4.3)
(4.4)
In these relationships, the rotational quantum number, J, can take integer values of 0, 1,
2.... B is a molecule dependent rotational constant, and I is the moment of inertia of the
molecule.
In reality, as the molecule rotates, the centrifugal force will increase the
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61
internuclear distance. This will cause a change in the molecular moment of inertia, which
will grow larger with increasing rotational energy. This change can be accounted for by
introducing a rotational correction term, D, which is typically much smaller than the
rotational constant.
E, = hc(B j(j + l ) - D J 2(j + l)2)
(4.5)
In order to determine the vibrational energy, Ev, of a molecule at a particular
vibrational state, it is necessary to model the vibrational motion of the molecule. A
molecule can be approximated as a harmonic oscillator with a vibration frequency v.
1
E = hv v + —
2/
v
(4-6)
The vibrational quantum number, v, can have integer values 0, 1, 2.... This molecular
vibrational energy can determined more accurately if the molecule is modeled as an
anharmonic vibrating oscillator.
(
1
he a>. v + ■ —®
w ex e
v
+ ®ey e V H
2
1Y
+.
(4.7)
In general, molecules will simultaneously rotate and vibrate. The vibration will cause a
change in the rotational moment of inertia of the molecule and thus the energy storage
due to rotation. This can be accounted for by modifying the rotational constant and
rotational correction terms to account for this effect.
B v = B eq- a e v + —
+ Ye
V+ —
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(4.8)
62
(4.9)
The subscript v is used to note that the vibrational effects are included in the coefficients
and the subscript e is used to note the equilibrium coefficients. (Xg and fie are relatively
small vibration-rotation interaction constants. Therefore, the transition frequencies for
molecules undergoing simultaneous electronic, vibrational, and rotational transitions can
be determined by subtracting the molecular energy of the lower state from the upper
state, assuming a non-rigid rotating, anharmonically vibrating molecule.
(4.10)
+ b vj (j + i ) - d vj 2(j + i )2
(4.11)
V transition
4.3
Transition Probabilities
Molecules can exist with many different energy states and rapidly transition
between states. However, the probability of a molecule transitioning from a given initial
state to a given final state is not equal for all final states. In fact, many transitions do not
occur at all. The transition probability for a vibrating and rotating molecule undergoing
an electronic transition can be calculated.
In order for this solution to be possible, the
Bom-Oppenheimer approximation that molecular electronic and nuclear motions are
independent must be invoked.
Also, the assumption that vibrational and rotational
transition probabilities can be separated must be made. Based on these assumptions, the
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63
emission transition probability between any given electronic, vibrational, and rotational
states can be written.
J T i2
A
4.4
ranyv','r
3hc3e0g n
2J'+1
(4.12)
Transition Lineshapes
The Schrodinger equation allows for only discrete values of transition energy, and
thus emitted or absorbed photon energy for a molecule. However, the emission and
absorption spectrum of molecules does not consist of discrete energy peaks. Rather, each
transition peak has a lineshape.
There are three main mechanisms that cause this
broadening of transition lines in gaseous molecular systems: natural broadening, Doppler
broadening, and collisional broadening. Each process occurs independently of detection
equipment, and cannot be eliminated by increasing detection resolution.
Broadening
mechanisms are typically described with two factors, the full width of the line at the half
height of the line maximum (FWHM), and the shape of line, g(v). All lineshapes are
defined such that the integral over the entire frequency spectrum is equal to one for a
single transition.
Jg(v)iv = l
(4.13)
Natural line broadening is due to the fact that the energy and average lifetime, x,
of a particular energy state before it transitions to another state cannot be known exactly,
as postulated in Heisenberg’s uncertainty principle.
1
x= —
A 12
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(4.14)
64
A 12 is the transition probability between the upper and lower state. A Fourier transform
analysis of a molecule modeled as a radiating dipole can be used to find the FWHM, Av^,
and the Lorentzian lineshape around the center frequency, Vo-
(4.15)
(4.16)
Doppler broadening is caused by the random motion of emitting molecules
relative to the observer.
As an emitting molecule moves away from the observer, a
photon detected will appear to be of lower frequency. As an emitting molecule moves
towards the observer, there would be an apparent increase in frequency. The size of the
frequency shift is dependant upon the relative velocity between the emitting molecule and
the observer. If the system of molecules is in thermal equilibrium, the distribution of
molecular velocities is given by the Maxwell-Boltzmann distribution. The FWHM and
the lineshape, which is Gaussian, can be found by averaging the Doppler shift over the
distribution of velocities for a given temperature, T.
2v0 12kTln(2)
(4.17)
■41a(2).
(4.18)
Collisions between emitting molecules and other molecules in the system also
have an effect on the lineshape of the radiation. If the molecular radiation is modeled as
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65
coming from a dipole source with a wavetrain interrupted by collisions, a Fourier analysis
can be completed to show that the FWHM for collisional broadening is proportional to
pressure.
The pressure broadening proportionality coefficient, b, is a function of
temperature. The lineshape, gc(v), is Lorentzian and of the same form as Equation 4.16.
Avc = bp
(4.19)
In many situations, the thermodynamic state of the emitting gas and the required
spectroscopic resolution is such that more than one type of line broadening must be
considered. If the line broadening mechanisms create different lineshapes, the effects are
not simply additive. The Gaussian and Lorentzian profiles are commonly convoluted
into a single profile, known as a Voigt profile, gv(v). The FWHM for the natural and the
collisional broadening can be combined into a single FWHM, Avl, because the
mechanisms share a common Lorentzian profile.
Avd
(4.20)
(4.21)
(4.22)
(4.23)
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66
4.5
Population Distributions
For many radiation emitting molecular systems of interest, there are multiple
transitions occurring simultaneously with very similar energy differences. In order to
determine the relative intensity of the spectral emission lines from each of these
transitions, it is necessary to know the relative population of the initial upper states in
addition to knowing the transition probabilities for each transition.7 For a system in
equilibrium, the Boltzmann equation gives the proportion of molecules in the population
in each state explicitly.
kT
Nt
(4.24)
Q
Q = X g j ekT
(4.25)
Nj is the number density of particles with energy Ej, and gj is the degeneracy of the state.
N is the total number density of the system. The term Q, the partition function, describes
how molecules are distributed within the possible energy states. The relationships can be
used to describe how molecules are distributed in electronic, vibrational, and rotational
energy states independently, as the total energy of the system can be represented as the
sum of each energy class. For many spectroscopic systems of interest, only a single
electronic upper state is considered. In this case, only the distribution of vibrational and
rotational energy must be considered.
For a harmonically vibrating molecule with vibrational frequency v, the
vibrational energy is proportional to the vibrational quantum number, and the degeneracy
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67
is unity for all levels. The Boltzmann equation and partition function can be written in
terms of a characteristic temperature of vibration,
0 Vit>
(4.26)
1
(4.27)
0 ,vib
v=0
1 -e T
(4.28)
nt
Qvib
0 Vis typically on the order of several thousand Kelvin, and nearly all molecules are in
the lowest vibrational state unless heated to relatively high temperatures.
When determining the rotational state population distribution, the degeneracy
becomes a factor, as there are (2J + 1) energy states associated with every rotational
quantum number for diatomic molecules. The distribution is a function of the symmetry
factor, a, as well. The symmetry factor is important because homonuclear molecules can
not have as many unique spatial orientations as heteronuclear molecules can.
The
symmetry factor has a value of two for homonuclear molecules and a value of unity for
heteronuclear molecules.
There is also a characteristic temperature of rotation, 0 rot,
which is used in describing the population distribution.
(4.29)
1
-j(j+i)eru,
T
(4.30)
rot
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68
—j(j+i)er«
N, _g, ( 2J + l>
T
nt
(4.31)
The gi term is the nuclear spin degeneracy, which is dependent upon the rotational
quantum number and the molecule of interest. For example, molecular nitrogen has a
spin degeneracy of 6 for even rotational quantum numbers, and 3 for odd values of J.
Hydrogen has a spin degeneracy of 1 for even quantum numbers, and 3 for odd levels.
4,6
MET Plasma Chamber Emission Models
The preceding analysis can now be applied to microwave electrothermal thruster
propellants of interest to determine the transition frequencies, intensities, and lineshapes
of the plasma chamber emission spectrum as a function of temperature and pressure. For
this investigation, oxygen and nitrogen were used as propellants. Oxygen was chosen
because it is a constituent of water, which may be used in electrothermal devices in the
future, and because it has well known thermochemical and structural properties.
Nitrogen was chosen because it is present in many propellants and because it also has
well known characteristics. Previous researchers have categorized the types of transitions
possible within systems of gaseous diatomic molecules and their appearances.8 Table 4.2
shows the nomenclature and appearance for each type of transition.
The Schumann-Runge system in neutral oxygen (O2 SRS) and the first negative
system of singly ionized nitrogen (N 2 + FNS) have strong emission bands over the
wavelengths that can be probed by the experimental apparatus used. No accurate model
for the O2 SRS was available, and so a new model was developed for this investigation.
The commercially available LBPBASE software can accurately model the N 2 + FNS, and
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69
Table 4.2: Molecular Transition Appearance
Type of Transition
Appearance
'W e
'n - V E
2e -> 2e
Single P and R branches (single headed)
Single P, Q, and R branches (double headed)
Double P and R branches (double headed)
Double P and R branches with weak Q branch
(multiheaded bands)
Double P and R branches with weak Q branch
(multiheaded bands)
Double P, R, and Q branches (often double headed)
Double P, R, and Q branches (often double headed)
Triple P and R branches with weak Q branch
(triple headed)
2n - > 2n
W
2a
2n - > 2x
W 2n
3e - V e
so that program was used to compare the experimental data to analytical data.
A
description of the models follows.
4.6.1
Oxygen Schumann-Runge Emission Model
The Schumann-Runge system involves an electronic transition in molecular
oxygen between the B3Eu_ and the X3Eg_ states. The system is important in many
investigations, including the study of atmospheric absorption of radiation from the sun
and emission from air and oxygen plasmas. 9 ’10 A model has been developed to predict
the Schumann-Runge oxygen emission spectrum. For this model, the state energies were
d e te rm in ed
assuming an anharmonically vibrating, non-rigid rotating molecule.
Electronic, vibrational, and rotational initial and final state constants taken from reference
sources are compiled in Table 4.3 and Table 4.4 respectively, and applied in Equations
4.32 to 4.34.11'1'’ The values of Dv used are slightly different from published data for the
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initial, upper state. This modification was necessary to account for the variations in
spectroscopic constants given by the different sources used.
Table 4.3: Schumann-Runge X 3 E^ Ground State Constants
State Constant
To
ffle
COeXe
tOeYe
COeZe
CBtae
COebe
Be
Oe
Ye
8e
£e
Dv(all)
Value (cm'1)
0.0
1.58039e3
1.2112el
7.54e-2
-4.09e-3
1.30e-4
-2.21e-6
1.4451
1.523e-2
-8.25e-5
7.25e-6
-2.09e-7
4.79e-4
Table 4.4: Schumann-Runge B3! ^ Excited State Constants
S ta te C o n s ta n t
V a lu e (c m '1)
To
CDbae
4.935815e4
7.1283e2
1.3182el
5.502e-l
-7.39e-2
2.37e-3
COebe
-1.71e-5
Pe
8.2233e-l
1.6987e-2
l.lle -3
-1.59e-4
3.60e-6
4.44e-4
3.93e-4
4.37e-4
4.30e-4
3.56e-4
COgXe
COeYe
® eZ e
ae
Ye
8e
£e
Dv=o
Dv=i
Dv= 2
D v=3
Dy=4
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71
Dv values were changed so that the spectral peaks were located at the correct
wavelength, as determined by comparison with experimental data from previous
researchers (Ref. 10) and initial data from this investigation.
B v = 6 ^ - a e(v + -^) + ye(v + ^ ) 2 + 8 e(v + -^)3 + £e(v + ^ ) 4
^ = ®e(v + -L)- 03exe(v + U 2 + coeye(v + ^ ) 3
he
2
2
2
+ ®eze(v +
T =T
elec
0
—)4
(4.32)
(4.33)
+ ©eae(v + — ) 5 +©ebe(v + — ) 6
®e , ®eXe
2
4
®eYe
8
®e2e
16
32
®A
64
(4
3 4
)
Transitions between some initial states to some final states are not quantum mechanically
allowable within the electronic transition for the Schumann-Runge system.
All
vibrational transitions, Av = 0, ±1,±2,±3,..., can occur. However, rotational transitions
are limited to the P branch, AJ = -1, and the R branch, AJ = +1.
Also, rotational
transitions are only allowed from initial states with even rotational quantum numbers.
In order to determine the transition relative intensities, it was necessary to
calculate the transition probability for allowable transitions and the population
distribution of the initial upper state.
The electronic and vibrational transition
probabilities have been calculated for earlier studies, and are available in the literature.
For this investigation, the values have been taken from Ref. 9 for v' = 0,1,2,..., 12 and v"
= 0,1,2,..., 30.
For each allowable rotational transition there is a triplet system of
emission lines because of electron spin splitting . 14,15 However, these emission lines are
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72
very close spectrally, and are typically not resolved individually for thermometry
measurements. Each of these triplet lines has a different transition probability, Si, S 2 , and
S3 , and the probabilities differ for the P and R branch. For each branch, the rotational
transition probability for each transition is the sum of triplet transition probabilities. For
this model, 115 allowed rotational transitions were modeled for each vibrational band.
e
(J'-1)(2J'+1)
s- “
2 1 -1
(4 3 5 )
(4.36,
(J '+ lX 2 J '- l)
3P “
2J'+1
(437>
(2J'+ 3)J'
1R
2J'+1
(4.38)
_ J '(j’+2)
(4-39)
(J'+2)(2J'+1)
S" =
2J'+ 3
(4'40)
The vibrational and rotational population distributions in the excited state were
calculated as a function of temperature using Equations 4.28 and 4.32, assuming a
Boltzmann distribution for state populations and thermal equilibrium of the gas. Figure
4.1 through Figure 4.3 show the relative rotational population distribution at three
temperatures of interest, 300 K, 1,000 K, and 5,000 K. As the temperature increases,
more rotational states have non-negligible populations, with larger populations at higher
quantum numbers. As the temperature reaches 5,000 K, over seventy rotational states
from each vibrational band will contribute to the emission spectrum.
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73
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46
Rotational Quantum Number
Figure 4.1: B3X _ State Relative Rotational Population Distribution at 300 K
£
c
1
Q
08
n,
0 .6
ffl
fl>
cc
h
i,
lllii.
ill
£
z °-4
0)
>
m
0.2
n
111
0
12
18
24
30
36
1
ii
IIIl l l i i i .. .__
42
48
54
60
66
72
78
84
Ro t a t i o n a l Qu a n t u m N u m b e r
Figure 4.2: B3£ _ Initial Relative Rotational Population Distribution at 1,000 K
I*
m
1
Q
° ’8
%
0.6
£
z QA
m
>
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14
28
42
56
70
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98
1 12
1 26
140
1 54
Rotational Quantum Nu mb e r
Figure 4.3: B3Eu_ Initial Relative Rotational Population Distribution at 5,000 K
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74
Table 4.5 shows the relative vibrational population distribution at the 300 K, 1,000 K,
and 5,000 K. At ambient temperature, over 96% of all oxygen molecules in the initial
upper state have a vibrational quantum number of zero. As the temperature increases,
more vibrational states are filled, with the lower states always more populated than the
higher states. At a temperature of 5,000 K over ten vibrational states have non-negligibie
populations.
T a b le 4.5: B3Eu. Initial State Relative Vibrational Population Distribution
V ib r a tio n a l
Q u a n tu m
N u m b e r (v)
% N v/N v=o
300 K
% N v/N v=o
1,000 K
% N v/N v=o
5 ,000 K
1
2
3
4
5
6
7
8
9
10
11
12
3.28
0.11
0.0035
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
35.86
12.86
4.61
1.65
0.59
0.21
0.08
0.03
0.01
0.0035
0.0012
0.0005
81.45
66.35
54.04
44.02
35.86
29.21
23.79
19.38
15.79
12.86
10.47
8.53
For this investigation, natural, Doppler, and collisional broadening were initially
considered in developing a lineshape model. For oxygen gas collision with only other
oxygen gas molecules, the self-broadening pressure coefficient has been determined
previously.
16
b=
P
0 3 / Hlo
Po V T
\ 0 -7
(4-41)
y
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75
Table 4.6 gives representative FWHM for each of the broadening mechanisms at several
temperatures of interest at 2 atm of pressure.
Table 4.6: Schumann-Runge Oxygen Natural, Doppler, and Collisional FWHM
Temperature (K)
300
1,000
5,000
(A)
FWHM
Natural
Doppler
9.31683 x 10'7 0.001559
9.31683 x lO'7 0.002847
9.31683 x 10’7 0.006367
Collisional
0.014389
0.006194
0.002008
For all temperatures, the natural broadening plays a relatively minor role in the spectral
lineshape. At relatively low temperatures, the collisional broadening has a larger effect
than the Doppler broadening, but as the temperature increases, the Doppler broadening
effect increases and becomes of the same order of magnitude as the collisional
broadening.
In practice, very high resolution spectroscopy must be conducted to determine the
actual shape of lines. More often, the broadening due to experimentally induced light
diffraction overshadows the thermodynamic broadening. The model was modified to
include this effect after initial experiments showed an instrumental broadening much
larger than the theoretical broadening. A triangular lineshape with a FWHM of 0.65 A,
corresponding to that of the experimental lineshape for oxygen plasma tests, was used.
With the spectral characteristics for the Schumann-Runge system modeled, it was
possible to construct full spectral emission profiles, using Equations 4.10, 4.11, 4.27,
4.28, 4.30-4.40 and tabulated data. The model calculates the transition wavelengths and
intensities using the calculated transition probabilities and lineshapes as well as the state
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76
population distributions.
Figures 4.4 through 4.6 show the modeled spectrum from
3,550-3,725 A at 300 K, 1,000 K, and 5,000 K.
0.8
£ 0.6
> 0.4
0.2
3500
3525
3550
3575
3600
3625
3650
3675
3700
3725
Wavelength (Ang)
Figure 4.4: Calculated Schumann-Runge Emission Spectrum at 300 K
0.8
0.6
> 0.4
0.2
3550
3575
3600
3625
3650
3675
3700
Wavelength (Ang)
Figure 4.5: Calculated Schumann-Runge Emission Spectrum at 1,000 K
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3725
77
0.8
0.6
> 0.4
0.2
3550
3575
3600
3625
3650
3675
3700
3725
Wavelength (Ang)
Figure 4.6: Calculated Schumann-Runge Emission Spectrum at 5,000 K
A Matlab code with a wavelength step size of 0.1 A was used for the calculations.
As the temperature increases, the emission spectrum clearly shows significant differences
in both the number of emission lines that have significant intensity and the relative
intensity of the lines. At 300 K, only emission lines from states with v' = 0 are evident,
and the vibrational bands do not overlap. At 1,000 K, the vibrational bands from the v' =
0 state begin to overlap, but still dominate the bands from higher initial vibrational
quantum number.
Finally, at 5,000 K, the bands resulting from emissions from
molecules at higher vibrational energy show intensities comparable to those from the
vibrational ground state.
This information can be used to analyze experimentally
observed oxygen emission to determine the gas temperature.
Initially, a least squares fit between the experimental data and the temperature
dependent model across the entire spectral range was considered.
However, testing
indicated the plasma may not be in vibrational equilibrium. This was suggested by the
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78
relatively large peaks present due to photon emissions from molecules with an initial
vibrational quantum number higher than the ground state. For this reason, it was desired
to find a way to determine the rotational temperature independently of the vibrational
temperature. In other words, it was presumed that molecular rotational temperature was
not equal to the vibrational temperature.
The Schumann-Runge spectral model code was run separately for initial
vibrational quantum numbers of 0, 1, 2, and 3 at 2,000 K. Figures 4.7 through 4.10 show
the output from these runs.
Spectral emission from molecules with higher initial
vibrational quantum numbers was negligible over this wavelength range. Four peaks
were identified as being relatively intense, but only having spectral components from
molecules initially in the vibrational ground state.
approximately 3551.8 A, 3594.3 A, 3629.5
A,
and 3722.5
These peaks are located at
A
and are noted in Figure 4.7
as peaks 1 through 4. Figure 4.11 shows the variation of the relative intensity of the
selected peaks with temperature.
Note that the intensities are normalized for each
individual peak, and not relative to each other. Figure 4.12 shows the variation of the
ratios of the peak intensities as a function of temperature.
0.8
§ 0.4
JS 0.2
3550
3600
3650
3700
Wavelength (Ang)
Figure 4.7: Schumann-Runge v' = 0 Modeled Spectral Output
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79
£
1
c °-8
£
°-6
I
°-4
0.2
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©
-A ...
3550
3600
3650
3700
Wavelength (Ang)
Figure 4.8: Schumann-Runge v' = 1 Modeled Spectral Output
&
1
c 08
©
JE 0,6
® 0.4
®
©
OC
0.2
o
3550
AJ
3600
3650
3700
Wavelength (Ang)
Figure 4.9: Schumann-Runge v' = 2 Modeled Spectral Output
£
1
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©
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°-6
§
0 .4
JS 0.2
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3550
.m tA A .J L A .Z L J >
3600
A
.A
A -
.A
A
A
3650
.M
M.
M
U
M .
3700
Wavelength (Ang)
Figure 4.10: Schumann-Runge v' = 3 Modeled Spectral Output
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80
£*
m
c
®
c
0 .7 5
0
>
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0
oc
0 .5
0 .2 5
1350
1550
1750
1950
2150
2350
Temperature (K)
—■ — 3551.8 Ang —X — 3594.3 Ang
3629.5 Ang
3722.5 Ang
Figure 4.11: Peak Intensity Variations with Temperature
4 .5
4
3 .5
C8
OC
i---- _ _ _ _ _ ----_____--_____----------______--------------------- --------¥
X
xv
3
2 .5
!
V
>
V
1
XxxxXXyx
2
1.5
^^WWWWWW
1
••••■ ••••••5 5 8 2 8 ^ ^
0 .5
0
1000
1200
1400
1600
1800
2000
2200
Temperature (K)
■ 1 /2
A 1 /3 O 1 /4 ♦ 2 /3 X 2 /4 • 3 /4
Figure 4.12: Peak Intensity Ratios vs. Temperature
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2400
81
To determine the temperature of the chamber plasmas, the experimentally
measured peak intensity ratios were compared to a database of modeled peak intensity
ratios from 1,000 K to 3,000 K in 25 K increments. This was done using a least-squareddifference summation scheme. When D(T) is minimized, that is considered the measured
oxygen plasma temperature for this method.
dn(T )=(E xpR n -M o d R n(T))2
(4.42)
(4.43)
n
Figure 4.13 shows a plot of D(T) for the operating conditions given in Table 4.7. The
analysis gives a temperature of 2,000 K for this test. The curve is smooth, has a single
minimum, and is a relatively strong function of temperature. This is a good indication
that this method can be used to determine the temperature with some confidence.
5
1500
2000
2500
Temperature (K)
Figure 4 .13: Least Squared Difference Summation vs. O 2 Temperature
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82
Table 4.7: P 2Example Experimenta
O2 Mass Flow Rate (mg/s)
Cham ber Pressure (psia)
Absorbed Power (W)
Nozzle T hroat Diam eter (in.)
Conditions
69.8
37.2
1,755
0.032
In order to ascertain the repeatability of the temperature measurements, ten tests
were run with the operating conditions given in Table 4.8. Figure 4.14 shows a normal
probability plot for the individual temperatures. The plot indicates that the distribution of
temperatures follows a normal distribution with a 95% confidence level, with a mean and
standard deviation of 2,033 K and 53.7 K respectively. Temperatures that are repeated
are automatically balanced above and below the line indicating the normal distribution.
Table 4.8: O2 Experimental Conditions for Repeatability Tests
69.8
O2 Mass Flow Rate (mg/s)
Chamber Pressure (psia)
37.0
Absorbed Power (W)
1,370
Nozzle Throat Diameter (in.) 0.032
99
95
90
80
70
60
50
40
30
20
10
5
1
1900
2000
2100
2200
Temperature, K
Figure 4.14: Normal Probability Plot of O 2 Temperatures for Repeatability Tests
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83
For all further MET oxygen propellant test conditions, a set of three tests was ran.
There are several possible sources of error in the temperature determination
analysis. First, although spectral peaks primarily caused by molecules in the vibrational
ground state were selected, there is some small contribution from peaks from other
vibrational initial states. Second, the experimental system was not calibrated with a light
source of known spectral output. The overall response of the system is very close to
constant over the spectral range studied.
However, even relatively small changes in
collection efficiency will have some effect on the intensity ratios. Third, random noise
from PMT dark current may cause each peak to appear slightly larger or smaller than the
true value.
The use of multiple ratios reduces the overall error introduced by small
measurement or modeling errors of individual peaks or ratios. In addition to this, the
summation of the least squared differences method also gives greater weight to ratios that
are stronger functions of temperature. These ratios are less sensitive to small changes in
intensity of individual peaks, because it takes a greater shift in relative intensity of a peak
to change the measured temperature. Testing multiple times at each test condition also
ensures that a true measure of temperature at each test condition is attained.
4.6.2
Ionized Nitrogen First Negative System Emission Model
For this investigation, the commercially available LIFBASE spectral simulation
software was used to model the N 2 + FNS emission spectrum.17 This is a transition from
the B2Eu+ excited state to the X 2 Xg+ ground electronic state of N 2 +, which is often evident
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84
in pure nitrogen plasmas. The LBFBASE program is capable of modeling different kinds
of spectra, including emission, absorption, and excitation laser induced fluorescence
(LDF) for several different molecules. The program can also be used to create a database
of spectral quantities of interest, such as emission coefficients, transition probabilities,
and transition line strengths. The particular transition band studied was the v' = v” = 0
transition. This was chosen because it is a relatively strong transition that has many
rotational transitions in the band that do not overlap with transitions from other
vibrational bands.
This means that the spectrum studied will have relatively few
transitions over a given wavelength range, and only the rotational state populations,
transitions, and temperature will affect the spectrum.
The LIFBASE model uses a formula given by Schadee to calculate the emission
coefficients.18
am.wyr
_ g' 64 tcV
Sj r
g, 3h P w j r 2y+{
(4.44)
Transition probabilities are determined by integrating the rotational-vibrational
wavefunctions of the initial and final states with the electronic transition moment.
Solutions from Hamiltonian matrix expressions are used to determine the wavelengths of
transitions.19 Both Boltzmann and non-Boltzmann state population distributions can be
used, though only Boltzmann distributions were considered for this study. The software
can calculate either Lorentzian or Gaussian lineshapes for the transitions. Triangular
lineshapes were created by running the model at 0.01 A FWHM with a Gaussian
lineshape and then fitting the transitions to triangular lineshapes with the desired FWHM.
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85
A database of modeled spectra from 3,821 to 3,918 A was created in 0.02 A
increments with temperature intervals of 100 K from 3,000 K to 9,000 K. Figure 4.15
shows the normalized LIFBASE modeled N 2 1" FNS emission spectrum from 3,885-3,915
A for the v' = v" = 0 transition at several different temperatures with a 0.63 A FWHM.
The figure clearly shows the temperature dependence of the modeled emission spectra,
which can be compared with the measured spectra to determine the nitrogen translational
temperature in the MET plasma chamber.
0.8
£
m
c
®
c 06
0)
>
a
as
a
0.2
3885
3895
3890
3900
3905
3910
3911
W avelength, Ang
F
3,000 K
4,500 K
6,000 K
Figure 4.15t LIFBASE N 2 + FNS Emission Spectrum
The relative simplicity of the N 2 + FNS emission spectrum over the wavelength
range investigated allows for a complete comparison between the spectral model and
experimental data. The squared difference between every experimental data point and
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86
the corresponding LIFBASE modeled intensity is calculated as a function of temperature
from 3,000 K to 9,000 K in 100 K increments, except for the region between 3,896.3 and
3,898.0 A. In this region, there is absorption of the plasma emission by one of the optical
components used for testing. The chamber plasma temperature is determined when the
summation of the squared differences is minimized. The minimization scheme also takes
into account the different FWHM found due to variations in spectrometer slit widths used
for the nitrogen tests. Figure 4.16 shows a plot of D(T) vs. temperature for the operating
conditions given in Table 4.9. The analysis gives a temperature of 5,500 K for this test.
This curve is also smooth, has a single minimum, and is a relatively strong function of
temperature, suggesting that this least squared difference summation method can be used
to accurately determine the plasma chamber N 2 + rotational temperature.
4
------------------------------------------------------------
3 . 5 -------------------------------------------------------------------------------------------------------------------------------------------
to
0.5 -1----------------3000
1---------------------- 1-----------------------------1-
4000
5000
........................
6000
! ------------------------ - T - ........... .... .............
7000
8000
9000
Temperature, K
Figure 4.16; Least Squared Difference Summation vs. Na+ Temperature
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87
Table 4.9; N 2 Example Experimental Conditions
72.9
N2 Mass Flow Rate (mg/s)
16.5
Cham ber Pressure (psia)
Absorbed Power (W)
1,056
Nozzle T hroat Diameter (in.) 0.051
A repeatability check of the temperature measurement was conducted with nine
test runs, also at the operating conditions given in Table 4.9. Figure 4.17 shows a normal
probability plot for the individual temperatures. The plot indicates that the distribution of
N 2 + rotational temperatures measured also follows a normal distribution at a 95%
confidence level, with a mean and standard deviation of 5,500 K and 158 K respectively.
Temperatures that were measured multiple times are balanced above and below the
normal line in the center of the confidence interval.
For all further MET chamber
nitrogen test conditions, a set of five tests was completed. The N2+ FNS plasma emission
tests do not have the problem of interference between different vibrational bands because
99
95
90
80
70
60
50
40
30
20
10
5
1
5000
5500
6000
Temperature, K
Figure 4.17: Normal Probability Plot of N2+ Temperatures for Repeatability Tests
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88
only rotational transitions from one band, the v' = v" = 0 band, are considered. The
wavelength range investigated is also smaller than that of the oxygen plasma tests, and so
the effects of a possibly varying experimental spectral sensitivity are less important. The
effects of dark current on the determined temperature should also be minimal because of
the large number of data points sampled.
4.7
References
1 Planck, M., "Ueber das Gesetz der Energieverteilung im Normalspectrum," Ann. d.
Phys., Vol. 4, p. 553, 1901.
2 Banwell, Colin N., and McCash, Elaine M., Fundamentals o f Molecular
Spectroscopy, 4th edition, McGraw-Hill, London, 1994.
3 Bemath, Peter F., Spectra o f Atoms and Molecules, Oxford University Press, New
York, 1995.
4 Eckbreth, Alan C., Laser Diagnostics fo r Combustion, Temperature, and Species, 2nd
ed., Gordon and Breach Publishers, Amsterdam, 1996.
5 Fong, Peter, Elementary Quantum Mechanics, Addison-Wesley, Reading, MA, 1962.
6 Herzberg, G., Molecular Spectra and Molecular Structure I: Spectra o f Diatomic
Molecules, Van Nostrand Reinhold Co., Cincinnati, OH, 1950.
7 Vincenti, W., and C. Kruger, Introduction to Physical Gas Dynamics, Rrieger
Publishing Co., Malabar, FL, 1965.
8 Pearse, R., and A. G. Gaydon, The Identification o f Molecular Spectra, Wiley,
London, 1976.
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
89
9
Cann, M., R. Nicholls, et. al., "High Resolution Atmospheric Transmission
Calculations Down to 28.7 km in the 200-243 nm Spectral Range," Applied Optics,
Vol. 18, No. 7, April 1979.
10 Michelt, B., G. Lins, and R. Seebdek, "Measurement of the Rotational Temperature
of Oxygen in a High-power Inductively Coupled Plasma," J. Phys. D: Appl. Phys.,
Vol. 28, pp. 2600-2606, 1995.
11 Laher, R., and F. Gilmore, "Improved Fits for the Vibrational and Rotational
Constants of Many States of Nitrogen and Oxygen," Journal o f Physical and
Chemical R ef Data, Vol. 20, No. 4, 1991.
12 Laher, R., "O2 B-X (Schumann-Runge) Band System (Higher Precision)," Internet
site:
http://spider.ipac.caltech.edu/staff/laher/fluordir/02_B-X_mp.out,
Accessed
10/ 11/ 2002 .
13 Krupenie, P., "The Spectrum of Molecular Oxygen," Journal o f Physical and
Chemical Ref. Data, Vol. 1, No. 2, p. 423, 1972.
14 Kovacs, I., Rotational Structure in the Spectra o f Diatomic Molecules, Adam Hilger,
London, 1969.
15 Tatum, I., and J. Watson, "Rotational Line Strengths in the 3Z±-3S± Transitions with
Intermediate Coupling," Canadian Journal o f Physics, Vol. 49, pp. 2693-2703, 1971,
16 Lewis, B., L. Berzins, et. al., "Pressure-broadening in the Schumann-Runge Bands of
Molecular Oxygen," J. Quant. Spectrosc. Radiat. Transfer, Vol. 39, No. 4, pp 271282,1988.
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
90
17 Lique, J. and Crosley, D., “LIFBASE: Database and Spectral Simulation Program
(Version 1.5),” SRI International Report MP 99-009, 1999.
18 Schadee, A., “Unique Definitions for the Band Strength and the Electronic
Vibrational Dipole Moment of Diatomic Molecular Radiative Transitions,” J. Quant.
Spectrosc. Radiat. Transfer, Vol. 19, p. 451, 1978.
19 Brown, J., Colboum, E., Watson, J., and Wayne, F., “An Effective Hamiltonian for
Diatomic Molecules,” Journal o f Molecular Spectroscopy, Vol. 74, p. 294, 1979.
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
91
CHAPTER 5 - RESULTS AND CONCLUSIONS
In this chapter, the results and conclusions of this investigation are presented. In
the first section, the relationship between the fluid dynamic motion present in the cavity
and the plasmas is discussed. The relationship between the fraction of absorbed power
and the plasma operating conditions is shown as well. In the second section, the results
of the oxygen and nitrogen emission thermometry are presented. In the third section the
results of the thermochemical calculations are shown.
In the conclusion section, the
implications that these results have on the potential performance of the MET are
discussed.
5.1
P h e n o m e n o lo g ic a l R e s u lts
5.1.1
Plasma and Fluid Dynamics Interactions
In order for the microwave electrothermal thruster to be used on spacecraft, the
steady state operation of the thruster must be stable and repeatable. For tests conducted
with oxygen as the propellant, this was the case for all absorbed powers, mass flow rates,
and pressures measured. After a vacuum was created in the plasma chamber and the
microwave power was initiated, diffuse plasma would immediately form and fill the
entire chamber. Figure 5.1 shows a picture of the MET operating in this situation with an
absorbed power of 1.0 kW, an oxygen propellant mass flow rate of 13.6 mg/s, and a
chamber pressure of 2.3 psia, created with the 0.040 inch diameter nozzle used. The light
blue plasma absorbed 73% of the input power under these conditions. After the flow rate
was increased to 94.9 mg/s, the plasma coalesced to a white teardrop shaped structure,
R eproduced with perm ission o f the copyright owner. Further reproduction prohibited w ith o u t perm ission.
Figure 5.1: 13.6 mg/s Oxygen Plasma with 1.0 kW Absorbed Power
Figure 5.2: 94.9 mg/s Oxygen Plasma with 1.37 kW Absorbed Power
spherical except for a narrowing near the nozzle entrance. The pressure rose to 23.9 psia
and all the input power o f 1.37 kW was absorbed. Figure 5.2 shows the plasma in this
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
typical operating condition. The coalesced plasma spins about its centerline in a steady
manner and only slightly oscillates off the cavity axis as it does so. The plasma plume,
which is white in color, is visible about 0,75 laches above the nozzle exit and appears
very steady. In general, for a given set of operating conditions the visible plume will be
longer and brighter for larger mass flow rates and wider nozzle diameters.
For this
investigation, the MET was only operated with oxygen propellant using the smallest
0,014 inch diameter injectors,
MET nitrogen propellant plasmas showed steady and repeatable operation for
some, but not all operating conditions. For the operating conditions that were steady and
repeatable, the plasma characteristics were similar to those for the oxygen propellant
plasmas, At low pressures, diffuse plasma would fill the entire plasma chamber, as
shown in Figure 5 3 . This plasma was formed with 1.37 kW input power, of which 62%
Figure 5 3 : 15.6 mg/s Nitrogen Plasma with 0.85 kW Absorbed Power
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94
was absorbed,
The propellant mass flow rate used was 15.6 mg/s and the chamber
pressure was 1.6 psia. The 0.040 inch diameter nozzle was used for this test as w ell The
diffuse nitrogen plasmas are pink in color. As the propellant flow rate was increased, the
plasma coalesced into a .teardrop shaped structure, similar to the oxygen, plasmas
discussed earlier. The coalesced nitrogen, plasma, extends farther down into the plasma
chamber with a more oblong shape. Figure 5.4 shows a nitrogen MET plasma with 20.0
psia chamber pressure, 73,1 mg/s propellant flow rate, and 1,37 kW input power, of
which 75% was absorbed. The coalesced plasma is a bright white in color, surrounded
by a relatively dim purple glow. The visible plume is relatively small and dim, extending
only approximately 0.5 inch above the nozzle exit.
As the flow rate was increased further, to 93,7 mg/s, the plasma gradually
changed geometry to a more spherical shape, as shown in Figure 5.5. At this operating
Figure 5,4; 73.1 mg/s Nitrogen Plasma with 1.06 kW Absorbed Power
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95
Figure 5.5: 93.7 mgfs Nitrogen Plasma with 1.06 kW Absorbed Power
condition, the pressure was 24.4 psia, while the fraction of input power absorbed
remained the same. The color of the plasma did not change during this transition. At this
higher flow rate and chamber pressure the visible plume extended approximately 1.0 inch
above the nozzle exit. The plasma continued to rotate about the cavity axis in a steady,
stable manner, though more rapidly as the flow rate, and corresponding injection
velocity, was increased. With the smallest 0,014 inch diameter injectors used, nitrogen
propellant testing was steady for all operating conditions.
With the larger 0,055 inch and 0.250 inch diameter injectors, MET operation was
not always steady or repeatable with nitrogen as the propellant. At the low pressures
found when the diffuse plasma is first initiated, the operation is independent of injector
size. However, once the propellant flow rate is increased to a relatively high level, this is
not the case. For example, with the 0.25 inch diameter injectors and 0.075 inch diameter
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96
nozzle, if there is no nitrogen flow when the plasma m initiated, and then the flow rate is
quickly raised to 150.0 mg/s, the chamber plasma would form a column-like structure, as
shown in Figure 5.6. If the propellant flow rate was slowly raised to 150,0 mg/s, a very
small, quickly rotating, ball-like structure was evident, as shown in Figure 5.7.
Figure 5,6; 150.0 mg/s Column-Like Nitrogen Plasma
For both of these tests, the absorbed power was 1.10 kW.
However, the chamber
pressure was not the same for the two eases. Rather, for the column-like structure it was
lower, 17.4 psia, compared to the 18.4 psia for the ball-like structure. For the case with
the column-like plasma structure, the visible plume was stable and approximately 1.25
inches in length. For the small ball-like plasma structure, the visible plume oscillates
rapidly in height and luminosity. The plume can be visible up to several inches above the
nozzle exit, as shown in. Figure 5.7, or visible less than one inch. Figure 5,8 shows the
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97
MET operating in the same mode and with the operating conditions as Figure 5,7, but
with a much smaller plume visible.
Figure 5,7; 150,0 mg/s Bali-Like Nitrogen Plasma with Large Plume
■1— 1
'
Figure 5.8; 150.0 mg/s Ball-Like Nitrogen Plasma with Small Plume
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98
This difference in final operating geometries is repeatable for all operating conditions
when using the 0.25 inch diameter injectors.
When using the 0.055 inch diameter
injectors, for relatively high flow rates the different final geometries can be achieved.
When using moderate flow rates (rii< 110 tag/'s) the large teardrop structure evident
during steady normal operation is evident.
MET operation with ammonia propellant was also successful for some operating
conditions.
Low pressure diffuse ammonia plasmas were formed using the same
procedure as for the diatomic propellants. Figure 5.9 shows a 0.7 psia diffuse ammonia
plasma with a propellant flow rate of 0,95 mg/s, with the 0.040 inch diameter nozzle and
0.014 inch diameter injectors used. The yellow plasma absorbed 75% of the 1.60 kW
input power.
Figure 5.9'. 0.95 mg/s Ammonia Plasma with. 1.2 kW Absorbed Power
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99
As the flow rate was Increased to 9,50 mg/s, the maximum possible with the apparatus
available, the plasma coalesced gradually to a light purple teardrop shaped structure, as
shown in, Figure 5,10, For this case, the 0,040 inch diameter nozzle and 0,014 inch
diameter injectors were used, and 87.5% of the input ! .60 kW of power was absorbed,
creating a 2,6 psia chamber pressure, Chamber pressures of 5,60 psia were achieved for
tests conducted with the 0.032 inch diameter nozzle.
However, at this pressure, the
plasma quickly grew dim and extinguished, regardless of the input power level used, For
all tests with ammonia as the propellant with chamber pressures less than 5.60 psia, the
plasma appeared stable and steady.
Figure 5.10s 9.50 mg/% Ammonia Plasma with 1.40 kW Absorbed Power
For ail MET tests with each of the propellants, nozzles, and injectors, there were
some common phenomena. For a given mass flow rate and chamber pressure, as the
input power was increased, the visible plasma would increase in volume and luminosity.
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100
If the MET was operating in the stable condition with the relatively large steady teardrop
shaped plasma, there was no associated rise in chamber pressure with the increased
plasma volume. If the plasma was in the column-like state or the very small ball-like
shape, the pressure would rise as the input power was increased. For a given mass flow
rate and input power, the plasma would appear more luminous at higher chamber
pressures. For a given absorbed power and chamber pressure, the plasma would appear
more luminous at higher propellant mass flow rates.
5.1.2
Power Absorption Measurements
Initial testing with oxygen propellant showed that not all input microwave power
was absorbed by the chamber plasmas for all operating conditions. The fraction of input
power absorbed by the plasmas was found to be a function of the propellant mass flow
rate and the input power level. Figure 5.11 shows the variation in the percentage of input
power absorbed as a function of propellant oxygen mass flow rate for three different
nozzle diameters. The input power level was held constant at 2.0 kW for all cases. The
fraction of power absorbed by the chamber plasma increases with increasing propellant
flow rate. Use of the different nozzles created a different chamber pressure at each flow
rate. However, it appears that this pressure difference had a negligible effect on the
fraction of input power absorbed. At an input power level of 1.37 kW, 100% of the input
power was absorbed for all oxygen propellant flow rates for each of these three nozzles.
As mentioned earlier, the oxygen plasma-fluid dynamics interaction appears to be the
same for all test conditions, with a relatively large and steady teardrop shape structure
present.
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101
1 100 "
|
60 -
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40- •—
20
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15 80- 8
——— ........- ----- r-------——i—
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□
A
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—r-
.....
100
120
Propellant Flow Rate (mg/s)
o 0.032 in. diameter nozzle □ 0.040 in. diameter nozzle A 0.051 in. diameter nozzle
Figure 5.11; Percent Power absorbed vs. Oxygen Propellant Flow Rate
For nitrogen propellant plasmas, the power reflected from the plasma could only
be eliminated for operating conditions with relatively small input powers (Pinp < 1.1 kW)
combined with relatively large propellant mass flow rates (m > 90 mg/s). In addition, a
decrease in reflected power was measured at high propellant flow rates when the nitrogen
plasma would contract into the tight ball-like structure.
Previous testing by other
researchers with nitrogen propellant has shown that the addition of an impedance
matching network to the MET power supply system results in full power absorption.
These network components have taken the form of three stub tuners and physically
adjustable antennas and shorting plates. Not all plasmas in this investigation absorb all
the input power because a fixed geometry was used, with no active tuning mechanisms.
The fraction of power absorbed changes for different operating conditions because the
impedance in the plasma chamber changes as the mass flow rate and pressure change and
the plasma changes size and shape.
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102
Emission Thermometry
5,2
5.2.1 Oxygen Schumann-Runge Emission
Figure 5,12 shows a comparison o f the modeled and measured oxygen SchumannRunge emission spectrum for MET operation with 69.8 mg/s oxygen propellant flow.
L40 kW absorbed power, and a chamber pressure of 37 psia, The wavelengths of the
emission lines match throughout the spectrum. The relatively large peaks that are the
result of emissions front molecules in the vibrational ground state match well in intensity.
The smaller peaks that are the result o f emissions from vibrationally excited molecules do
not match nearly as w ell The modeled spectrum underestimates the intensity of these
transitions. This may be because the vibrational temperature of the emitting gas is higher
than the rotational temperature. This is why peaks created by emissions from molecules
in the vibrational ground state were used for data analysis in determining the temperature.
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Figure 5.12; Comparison of Modeled and Measured Schumann-Runge System
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103
An initial set of tests was run for an oxygen propellant flow rate of 69.75 mg/s, a
chamber pressure of 37.2 psia, and absorbed power of 1,725 W with two different probe
locations. Fig. 5.13 shows the summation of the squared differences vs. temperature for
the two different spatial locations.
Location 1 is approximately 1.00 inch below the
nozzle entrance and 0.766 inch to the left of the chamber centerline, at the horizontal
edge of the plasma. Location 2 is 0.688 inch below the nozzle and is along the plasma
centerline. The temperatures were determined to be 2,000 K and 2,100 K for location 1
and location 2, respectively. Temperature does not have a strong spatial dependence for
this operating condition, nor did it for any of the other cases considered. The following
results discussed below are based upon data taken from location 2 for all cases.
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Figure 5.13: Squared Difference Sum for Two Locations
Fig. 5.14 shows the variation of temperature with pressure for a propellant mass flow rate
of 69.75 mg/s with an input power of approximately 1.4 kW, resulting in a specific
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104
absorbed power of 20.1 MJ/kg. The error bars represent one standard deviation (±53.7
K) in measured temperature. This figure suggests that the oxygen plasma temperature
measured in the chamber of approximately 2,000 K does not change with varying
pressure, within the testing resolution. This means that either the plasma is already in
thermal equilibrium, or that the collisional rate increase at higher pressures is ineffective
in bringing the system closer to thermal equilibrium over this pressure range.
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Figure 5.14: Temperature vs. Pressure for 20.1 MJ/kg Specific Absorbed Power
Fig. 5.15 shows the variation of temperature with specific absorbed power at a
nearly constant chamber pressure of approximately 17.0 psia and a flow rate of 23.3
mg/s, with the 0.031 inch diameter nozzle.
There appears to be a slight increase in
chamber temperature as the specific power increases, with a minimum temperature of
1,790 K at a specific absorbed power of 48.1 MJ/kg and a maximum measured
temperature of 1,933 K at a specific absorbed power of 69.5 MJ/kg. This is most likely
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105
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Specific Absorbed Power (MJ/kg)
Figure 5.15: Temperature vs. Specific Power at 17.0 psia
due to the increase in energy available per molecule. The temperature is not a strong
function of specific power though, as might be expected.
As mentioned earlier, the
portion of the chamber plasma that emits light in the visible spectrum appears to swell in
volume as the specific power is increased. Therefore, it is surmised that most of the
additional energy added goes to heating a larger volume of gas to a certain temperature,
rather than increasing the maximum temperature in the chamber.
The temperatures
measured at the operating conditions in Figure 5.15 are lower than those in Figure 5.14,
even though there was a larger specific absorbed power for the latter tests.
difference may be a result of the
power and mass
5.2.2
f lo w ra te ,
te m p e r a tu r e
being
a
This
function of the absolute absorbed
not just the specific absorbed power.
Ionized Nitrogen First Negative System Emission
Figure 5.16 shows a typical comparison of the
ionized nitrogen FNS emission
s p e c tr u m
m o d e le d
and measured 5,500 K
for MET operation with 73.0 mg/s propellant
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106
flow, 16,45 psia chamber pressure, and 1,056 W absorbed power. The wavelengths of
the peaks match throughout the spectral range. The intensities o f the peaks also match
well throughout, except for the small wavelength region where the emission is absorbed
by optica! components.
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3880
3895
3900
3905
3910
3915
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Wavelength, Angstrom
i — L iF BAS E
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K — Experim ental
Data j
Figure 5.16: Comparison of Modeled and Measured N2+ FNS System
Emission testing with nitrogen propellant also showed there was no spatial
variation in temperature for all operating conditions studied.
Figure 5.1? shows the
variation in N2+ rotational temperature with chamber pressure, for three different specific
absorbed powers. The error bars represent one standard deviation (±158 K) in measured
temperature. The measured temperature of approximately 5,500 K does not appear to
vary significantly with either pressure or specific absorbed power for these conditions.
All o f these tests were conducted with the 0.014 inch diameter injectors. The different
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107
8000 -i
7500 7000 -
S? 6500
-
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5500 -
m
Ol 5000 -j
F
4500 4000 3500 3000 10
15
20
25
30
35
40
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Pressure (psia)
[»11.84 MJ/kg ■ 14.40 MJ/kg
a 22.29
MJ/kg]
Figure 5.17: Variation in N 2 + Temperature vs. Chamber Pressure
pressures were caused by the use of the 0.032 inch, 0.040 inch, and 0.051 inch diameter
nozzles. For all cases, the plasma exhibited steady stable operation with a large teardrop
shaped plasma present in the chamber.
Additional nitrogen propellant emission spectroscopy was conducted at higher
propellant flow rates using the 0.075 inch diameter nozzle and the 0.055 inch diameter
injectors. The plasma was coalesced into a column-like structure for all of these tests.
Figure 5.18 shows the variation of N 2 + rotational temperature vs. specific absorbed power
for these high flow rate tests. The chamber pressure did not increase greatly during these
tests because of use of the large diameter nozzle. The plasma chamber pressure ranged
from 14.8 psia at the lowest propellant flow rate to 18.2 psia for the highest nitrogen flow
rate. The input power was 1.37 kW for all of the tests. The plasma absorbed 76.3% of
the input power for all but the highest propellant flow rate tests. For the tests with 181.2
mg/s of propellant flow, 80.3% of the input power was absorbed. Even at these relatively
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0
5
10
15
20
25
Specific Absorbed Power (MJ/kg)
Figure 5.18: Variation in N 2 + Temperature vs. Specific Absorbed Power
low specific absorbed powers, a chamber temperature of approximately 5,500 K was
measured.
5.3
Thermochemical Calculations
The NASA Glenn Research Center developed code CEA2 was used to calculate
equilibrium properties and performance for potential microwave electrothermal thruster
12
propellants. ’ In addition to oxygen and nitrogen, ammonia was analyzed because it is a
liquid storable propellant that has been demonstrated as a propellant for the MET.
Ammonia dissociates into a relatively low molecular weight mixture at high
temperatures, which results in a relatively high Isp. Figure 5.19 shows the equilibrium
enthalpy addition needed to raise the propellants from the zero enthalpy condition at
standard temperature and pressure to a given temperature at 2 atm of pressure.
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109
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© 0 2 o N2
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NH3
Figure 5.19: Equilibrium Enthalpy Addition to Heat Propellants vs. Temperature
For all temperatures, the ammonia requires a larger equilibrium enthalpy addition, due to
the energy needed for dissociation of the propellant into molecular hydrogen and
nitrogen, which occurs at relatively low temperatures. The enthalpy needed increases
faster for ammonia than the other propellants because at the temperatures shown, much of
the enthalpy addition is used to dissociate the molecular hydrogen. For temperatures up
to 3,000 K, the equilibrium enthalpy addition needed for oxygen and nitrogen is very
similar. For higher temperatures, oxygen requires a significantly larger enthalpy increase
because of dissociation losses. For example, to heat the propellants to 5,000 K under
equilibrium conditions would require the enthalpy addition of 6.4 MJ/kg for nitrogen,
20.6 MJ/kg for oxygen, and 58.4 MJ/kg for ammonia respectively.
Figure 5.20 shows the percentage of molecules of hydrogen, oxygen, and nitrogen
dissociated under equilibrium conditions at 2 atm as a function of temperature.
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110
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o 0 2 □ N2
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Figure 5.20: Percent Dissociation of Propellants vs. Temperature
For temperatures above 3,000 K both oxygen and hydrogen are more than 5%
dissociated, and the fraction of molecules dissociated rapidly increases with temperature.
For temperatures below 4,500 K, nitrogen is less than 1% dissociated, and the fraction of
molecules dissociated increases less quickly with temperature than for oxygen or
hydrogen. Figure 5.21 shows the percent of enthalpy added to the propellant molecules
that is lost to dissociation as a function of temperature for equilibrium conditions at 2
atm. Ammonia loses a large fraction of input enthalpy to dissociation even at relatively
low temperatures because the polyatomic molecule easily dissociates into diatomic
hydrogen and nitrogen.
Because of nitrogen in the mixture, which is difficult to
dissociate, high temperature ammonia actually loses a smaller fraction of enthalpy to
dissociation than oxygen at high temperatures. Oxygen and nitrogen lose a significant
amount of enthalpy to dissociation above 2,500 K and 4,750 K, respectively.
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
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Figure 5.21: Percent Enthalpy Lost to Dissociation vs. Temperature
Figure 5.22 shows the variation of calculated specific impulse with temperature
for oxygen, nitrogen, and ammonia propellants with a chamber pressure of 2 atm,
equilibrium chemistry, and a nozzle expansion ratio of 250.
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Figure 5.22: ISP vs. Temperature for 0 2, N2 and NH3
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112
The propellant ammonia provides greater performance at low chamber temperatures
because of the relatively low molecular weight of the mixture.
The calculated
performance of ammonia increases relative to oxygen and nitrogen as temperature
increases because of the decrease in mixture molecular weight as the hydrogen
dissociates.
Once temperatures are reached where oxygen begins to dissociate, that
propellant has better performance than the nitrogen because of the relatively low
molecular weight.
Figure 5.23 shows a comparison of the calculated chamber propellant equilibrium
enthalpy vs. Isp for a 2 atm chamber pressure, with equilibrium chemistry and a nozzle
expansion ratio of 250. For enthalpy increases of less than 35 MJ/kg, nitrogen propellant
has a better Isp than oxygen.
Even though ammonia has a large enthalpy loss to
dissociation, it still can achieve a greater Isp than oxygen or nitrogen at any given
enthalpy because of the low molecular weight of the gas mixture resulting from
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Figure 5.23: Equilibrium Enthalpy vs. Isp for 0 2, N2 and NH3
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113
dissociation of the ammonia. For example, an enthalpy increase of 20 MJ/kg results in an
Isp of approximately 510 s for oxygen, 570 s for nitrogen, and 640 s for ammonia.
Figure 5.24 shows the temperature dependent equilibrium thermal conductivity of
oxygen, nitrogen, and ammonia at a pressure of 2 atm. For comparison, dry air at one
atmosphere of pressure has a thermal conductivity of 0.24 mW/cm-K and aluminum has a
thermal conductivity of 2,050 mW/cm-K. The propellant gas in the MET chamber can be
up to two orders of magnitude more thermally conductive than dry air. Gas thermal
conductivity is also a function of pressure, though the temperature dependence is more
pronounced. A relatively high thermal conductivity can assist the energy transfer from
the high temperature plasma to the surrounding gas. However, not all the energy that is
input into the MET plasma will be absorbed and used to increase the enthalpy of the flow
exiting the nozzle. Some of the energy will be lost by conduction through the plasma and
gas to the walls of the chamber.
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Figure 5.24: Equilibrium Thermal Conductivity for O 2 , N 2 and NH 3
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114
5.4
Conclusions
The heavy particle translational temperatures measured, 2,000 K and 5,500 K for
oxygen and nitrogen respectively, were nearly constant for all operating conditions. It
appears that as more specific absorbed power is input, a larger volume of gas is heated to
those temperatures, rather than a specific volume of gas being heated to higher
temperatures. One particularly significant result was that the N 2 + temperature measured
was still near 5,500 K even when the absorbed specific power fell to 6.07 MJ/kg. If the
equilibrium enthalpy added to nitrogen is less than 6.30 MJ/kg, the temperature should
not rise above 5,000 K. This means that the specific power lost through the nozzle as
thermal energy could not be as great as the power added to the plasma. In fact, it was
expected that the chamber plasma temperature would be less than that predicted by
equilibrium enthalpy calculations because of energy losses through radiation, conduction
losses to the walls, and other mechanisms. This effect can be explained by examining the
coupling between the plasma and fluid dynamics in the MET plasma chamber.
The location and geometry of the MET chamber plasmas are strongly dependent
upon the fluid dynamics created for the various operating conditions, as shown earlier. In
order for the microwave electrothermal thruster to be used on spacecraft, a relatively
large range of operating conditions must result in predictable and repeatable performance.
The temperatures measured in the plasma chamber correspond to theoretical specific
impulse values, which may not be achieved for practical operation of the device. For a
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115
thermal thruster, the average chamber temperature can be calculated by measuring the
f
T
pressure rise in the chamber due to the heating process because —^2L <*=
"^cold
v
Phot
V P co ld
It was seen during this investigation that two different plasma geometries can
result in different chamber pressures, even for the same input conditions. No effort was
made during this study to maximize the pressure rise due to plasma formation. This
pressure rise is a function of the nozzle geometry, and the large converging section of the
nozzle inserts allows for cold flow to easily pass around the plasma and through the
throat. This effect was clearly greater for the column-like nitrogen plasma than for the
ball-like plasma. If a larger fraction of the exhaust gas came directly from the plasma or
was effectively heated by the plasma, it is expected that greater chamber pressure rises
would result and the measured temperatures in the plasma would become closer to
equilibrium levels.
The results of the thermochemical calculations give a good measure of the
potential performance of the microwave electrothermal thruster operating with oxygen,
nitrogen, or ammonia as propellant.
Assuming the gas exhausted through the nozzle is
heated to the same temperature as the plasma in the chamber, a specific impulse of 205 s
could be achieved with oxygen as propellant and 395 s with nitrogen as propellant.
Clearly, the oxygen does not get hot enough for a thermal rocket propellant.
The
nitrogen performance is above typical bipropellant rocket performance, but not at the
level of conventional arcjet performance. However, these diatomic gasses are not likely
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116
to be used as device propellants because of the challenge of keeping them cryogenically
cooled in liquid form for extended durations.
Though they may not be used as propellants themselves, oxygen and nitrogen are
found as components of many other potential liquid-storable propellants. The results of
this investigation lead to the conclusion that having oxygen in a propellant gas mixture
will not lead to having high chamber temperatures, while the presence of nitrogen may do
so. For example, if the nitrogen present in thermally decomposed ammonia is heated to
5,000 K and heats the rest of the gas mixture to the same temperature, the potential
specific impulse is approximately 925 s, which is a desirable performance.
The
performance with other nitrogen containing mixtures also may be good. For example,
hydrazine exothermally decomposes into a mixture containing nitrogen, so there would
be no energy loss for the initial decomposition, with the additional energy used to heat
the mixture to even higher temperatures.
This investigation was the first to measure the propellant heavy particle
temperature in the chamber of the microwave electrothermal thruster. Knowledge of the
heavy particle temperature allows for calculation of potential performance parameters.
Oxygen temperatures of approximately 2,000 K are not sufficiently high for that gas to be
used as a propellant. Nitrogen propellant temperatures of approximately 5,500 K offer a
potential specific impulse of nearly 400 s, which compares favorably with combustion
devices. Nitrogen offers a more practical advantage as an energy absorbing molecule
present in the decomposition products of more complicated polyatomic liquid storable
propellants, such as ammonia and hydrazine. The results of this investigation suggest
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117
that research should continue on the MET, focusing now on measuring and optimizing
actual performance parameters, such as thrust and specific impulse, with practical
propellants.
5.5
References
1 Gordon, S., and McBride, B., "Computer Program for Calculation of Complex
Chemical Equilibrium Compositions and Applications: I. Analysis," NASA RP-1311,
1994.
2
Gordon, S., and McBride, B., "Computer Program for Calculation of Complex
Chemical Equilibrium Compositions and Applications: II. Users Manual and Program
Description," NASA RP-1311, 1996.
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
Vita
Silvio G. Chianese
Education:
The Pennsylvania State University
Ph.D. in Aerospace Engineering
M.S. in Aerospace Engineering
Graduate GPA: 3.83
May 2005
May 2001
B.S. with Honors and High Distinction in Aerospace Engineering
Undergraduate GPA: 3.83
May 1999
W ork Experience:
Research Assistant
PSU Aerospace Engineering D epartm ent
5/99 - 5/05
— D esigned and assembled microwave electrothermal thruster (M ET) com ponents
— Analyzed electron impact and thermochemical processes in the M ET plasm a chamber
— M odeled Schumann-Runge em ission spectrum o f molecular oxygen plasm a
— Conducted M ET chamber oxygen and nitrogen propellant em ission spectroscopy experiments
— Characterized MET operational stability at various power levels and propellant flow rates
— D esigned, constructed, and conducted m icrowave plasma enhanced com bustion experiments
Visiting Researcher
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NASA Marshall Space Flight Center
6/02 - 7/02 and 5/03 - 7/03
Designed, assembled, and tested Raman scattering laser diagnostics system
U tilized RAM SES Raman scattering m odeling code to predict spectral output
Assisted in design o f an optically accessible high pressure H2/ 0 2 com bustion chamber
Conducted diagnostics to determine pyrotechnic bolt speed for Shuttle C olum bia investigation
— A ssisted in the design and implementation o f high speed camera ignition delay measurements
— Analyzed ignition delay results for various kerosene-based fuel and H 2 O 2 oxidizer mixtures
Honors and Awards:
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2003 and 2 0 0 4 N A SA Graduate Student Researcher Program (G SR P) F ellow ship Recipient
Glenn E. Singley Memorial Fellowship Recipient
Paul Morrow Endowed Scholarship Recipient
2nd Place - 2000 A IA A Regional Student Conference Graduate Paper Competition
3rd Place - 1999 A IA A Regional Student Conference Undergraduate Paper Competition
— Sigm a Gamma Tau Aerospace Honor Society Member
Selected Publications:
Chianese, S. G., "Microwave Electrothermal Thruster Chamber Temperature Measurements and Energy
Exchange Calculations,” Doctoral Thesis, Department of Aerospace Engineering, The Pennsylvania State
University, University Park, PA, May 2005.
Chianese, S. G., and Micci, M. M., "Spectroscopic Emission Thermometry o f the Microwave Arcjet
Chamber Oxygen Plasma," AIAA Paper 2004-4125, July 2004.
Blevins, J. A., Gostowski, R., and Chianese, S. G., "An Experimental Investigation of Hypergolic Ignition
Delay of Hydrogen Peroxide with Fuel Mixtures," AIAA Paper 2004-1335, January 2004.
Chianese, S. G., "Spectroscopic Investigation of Microwave Air Plasmas Intended for Hydrocarbon
Combustion Enhancement," Masters Thesis, Department of Aerospace Engineering, The Pennsylvania State
University, May 2001.
R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w ith o u t perm ission.
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