A study of ignition effects on thruster performance of a multi-electrode capillary discharge using visible emission spectroscopy diagnostics

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Content A STUDY OF IGNITION EFFECTS ON THRUSTER PERFORMANCE OF A MULTI-ELECTRODE
CAPILLARY DISCHARGE USING VISIBLE EMISSION SPECTROSCOPY DIAGNOSTICS
by
Anthony P. Pancotti
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(AEROSPACE ENGINEERING)
December 2009
Copyright 2009 Anthony P. Pancotti
Epigraph
Your vision is not limited by what your eyes can see,
but by what your mind can imagine.
Many things that you take for granted were considered unrealistic dreams
by previous generations.
If you accept these past accomplishments as commonplace
then think of the new horizons that you can explore.
From your vantage point, your education and imagination
will carry you to places which we won’t believe possible.
Make your life count and the world will be a better place because you tried.
Ellsion S. Onizuka
ii
Dedication
to my parents
iii
Acknowledgments
AFRL, Marcus Young, E.P. Muntz, USC Faculty and Staff, Andrew Ketsdever, Andrew Smith, John
Duncan, Matt Gilpin, Jairo Ascencio, Tailor Lilly, Ryan Downey, Sergey & Natasha Gimelshein, Leonid
Pekker
iv
Table of Contents
Epigraph ii
Dedication iii
Acknowledgments iv
Abstract x
Preface xi
Chapter 1: Introduction 1
1.1 The Need for High Efficiency 2
1.2 Other Capillary Discharge Pulsed Plasma Thrusters 3
1.3 Other Capillary Discharge Applications 6
1.4 Capillary Discharge Description 6
1.4.1 Ablation Process 7
1.5 Capillary Physics and Assumptions 11
1.5.1 Pressure Ratio 12
1.5.2 Local Thermodynamic Equilibrium 13
1.5.3 The Non-Ideal Parameter 15
1.6 Evaluation of Thruster Performance 15
1.7 Ignition Methods 16
1.7.1 Wire Ignition 18
1.7.2 Paschen Ignition 20
1.7.3 Coaxial and 3-Electode Ignition 20
Chapter 2: Experimental Setup 23
2.1 Capillary 23
2.1.1 Capillary Design V1.0 for Wire Testing 23
2.1.2 Capillary Design V2.0 for Paschen Breakdown Testing 25
2.1.3 Capillary Design V3.0 with Coax Ignitor 28
2.1.4 Capillary Design V4.0 with 3-Electrode Ignitor 29
2.2 Circuit 31
2.2.1 Switches 32
2.3 Facilities 33
Chapter 3: Diagnostics 36
3.1 Current 36
3.2 V oltage 37
v
3.3 Mass Loss 37
3.4 Force Measurements 37
3.4.1 Piezoelectric Force Sensors 38
3.4.2 Thrust Stand 39
3.5 Optical Diagnostics 54
3.5.1 Temperature from Resistivity 56
3.5.2 Electron Number Density 60
3.5.3 Mach Disc diagnostics 65
Chapter 4: Modeling 68
4.1 Zero-Dimensional Model 68
4.2 One-Dimensional Model 69
Chapter 5: Results 71
5.1 Circuit 71
5.2 Wire Ignition 72
5.2.1 Test Procedures 73
5.2.2 Data 73
5.3 Paschen Breakdown Ignition 76
5.3.1 Test Procedures 76
5.3.2 Data 78
5.4 External Coaxial Ignition 81
5.4.1 Test Procedure 81
5.4.2 Data 81
5.5 Internal Three Electrode Ignition 83
5.5.1 Test Procedures 83
5.5.2 Data 84
5.6 Electron Number Density 85
Chapter 6: Discussion 93
6.1 Ignition Comparison 93
6.2 Electrode Erosion 97
6.3 Dual Mode Operation 99
6.4 Ablation Effects 101
6.5 Initial Discharge 103
6.6 Material factors 104
6.7 Background Pressure Effects 104
Chapter 7: Conclusions 108
Bibliography 110
vi
List of Tables
3.1 Coeffecients for 1st interation & optimized CD thrust stand 51
3.2 Ratio of conductivity in a Lorentz gas 58
3.3 Fractional Intensity Widths 64
5.1 Inductive Effects on Discharge Circuit Parameters 75
vii
List of Figures
1.1 Electrothermal and Ion Thruster Performance 3
1.2 Electrothermal PPT Performance History 4
1.3 Ablation Process within a Capillary Discharge 7
1.4 Ablation Mechanisms 9
1.5 PrismSpect Spectra of Various Capillary Materials 11
1.6 Radiative Energy of Materials 12
1.7 Photograph and X-radiograph of an Exploding Wire 18
1.8 Paschen Curve 21
2.1 Schematic of Capillary Discharge Design V1.0 24
2.2 Schematic of Capillary Discharge Design V1.1 25
2.3 Schematic of Capillary Discharge Design V2.0 26
2.4 Schematic of Capillary Discharge Design V2.1 27
2.5 Schematic of Capillary Discharge Design V2.2 28
2.6 Schematic of Capillary Discharge Design V3.0 29
2.7 Schematic of Capillary Discharge Design V4.0 30
2.8 Picture of Capillary Discharge Vacuum Chamber 34
3.1 Schematic of original Piezoelectric Force Sensor Setup 39
3.2 Data from Piezoelectric Force Sensors 40
3.3 Schematic of Capillary Discharge Thrust Stand 41
3.4 LVDT data showing Impulse Measurements 42
3.5 LVDT data showing Mass Loss Measurements 42
3.6 Picture of the Capillary Discharge Thrust Stand 43
3.7 LVDT Diagram 44
3.8 Michelson Interferometer Diagram 45
3.9 LVDT vs. Interferometer Data 46
3.10 Electrostatic Fin Validation Data 48
3.11 Hammer vs. ES Fin Data 49
3.12 Thrust Stand Deflection vs.K 50
3.13 Thrust stand Range vs.I 52
3.14 Thrust Stand Mass Loss Measurements 53
3.15 Diagram of Kinetics Mode Operation 55
viii
3.16 10m Optical System 57
3.17 Plasma Resistivity 59
3.18 High Speed Video Still Frames 66
3.19 Corresponding Current Data for High Speed Video 66
4.1 Energy Fluxes for a 5cm 2500V Capillary Discharge 70
5.1 Circuit Parameters 72
5.2 V oltage Dependence of Wire Ignition Current Data 74
5.3 Inductance Dependence Wire Ignition Current Data 74
5.4 Length Dependence of Wire Ignition Current Data 75
5.5 Paschen Ignition Current Data 78
5.6 Paschen Ignition Thruster Performance Data 80
5.7 Coaxial Ignitor Capillary Discharge Current Data 82
5.8 Coaxial Ignitor Capillary Discharge Thruster Preformance 83
5.9 3-Electrode Capillary Discharge Current Data 85
5.10 3-Electrode Capillary Discharge Thruster Performance Data 86
5.11 Lorentzian Fit of Experimental Data 87
5.12 Experimental and 1D Model Number Densities 88
5.13 Number Density for Various Capillary V oltages 90
5.14 Number Density for Various Capillary Lengths 90
5.15 High Self-absorbtion Spectral Profile 91
5.16 Comparison of FWHM and Shifts 92
6.1 Current Comparison 94
6.2 Thruster Performance Comparison 96
6.3 Photos of Anode Erosion 97
6.4 Diameter Change with Anode Erosion 98
6.5 Capillary and Electrode Mass Loss for Paschen Ignition 99
6.6 Capillary and Electrode Mass Loss for 3E Ignition 100
6.7 Photo of Capillary Failure do to External Ablation 102
6.8 Initial and Subsequent Current Traces 103
6.9 Current Traces for Various Capillary Materials 105
6.10 Current Traces for Various Background Pressures 106
6.11 Thrust Stand Deflection vs. Background Pressure 107
ix
Abstract
This work examined the effect of ignition on thruster performance characteristics of a capillary discharge
device. Early tests of the presented device, incorporating an exploding wire ignition, showed a strong
dependence on the initial plasma conditions. The literature supported these findings for more basic labo-
ratory capillaries, but the effect on a thruster device was unknown. An in-depth investigation of different
ignition systems were conducted for a capillary discharge based pulsed plasma thruster. In addition to
conventional wires, capillary discharges were ignited with low pressure gas and several different types
of spark igniters. These methods were compared with each other and with newly developed computer
models.
The viability of a capillary discharge based electrothermal pulsed plasma thruster as an in-space
propulsion system was examined. Thruster performance levels, and their ability to fill a desired niche,
which has historically shown rather poor efficiencies, have been explored. This work contains a back-
ground literature study, experimental setup and testing of a capillary design, and a comparison to perfor-
mance models created by others. New techniques have been coupled with proven plasma diagnostics to
investigate the internal plasma properties of the device. Visible-light spectroscopy techniques were devel-
oped to examine the time-resolved electron number densities at the exit. These measurements indicated
that there may be a slower rate for recombination than previous expected. Novel thrust stand techniques
were demonstrated, measuring thruster performance characteristics with a high degree of accuracy. It was
found the ignition method plays a very small role in discharge characteristics. Electrode erosions was
investigated and largely eliminated from the device. The research conducted here has not only increased
the understanding of ignition effects, but also the basic physics, of capillary devices.
x
Preface
This thesis focuses mainly on the investigation of different ignition techniques involved in capillary dis-
charges. In order to carry out this study a great deal of initial work was needed. Not only to design and
build a capillary discharge, but also to set up: the vacuum facility, the high powered circuits, the computer
control, and the data acquisition. When I began this project for my Ph.D research 5 years ago there was
only a stack of journal articles on my desk.
The bulk of this work, like most other research experiments, is based on the diagnostics. I was
introduced to several of the necessary tools early on in engineering, others took me years to perfect
during my graduate studies at USC. A large section of this thesis is related to experimental setup and
diagnostic techniques.
A.P. Pancotti
Los Angeles, California
December 2009
xi
Chapter 1
Introduction
In order to appreciate the potential of a capillary discharge based propulsion system, it is important to look
at existing technology. To justify and validate this research, there must be a need for it. The entire realm
of electric spacecraft propulsion was examined and an apparent need was noticed. There are currently
no flight qualified propulsion systems that have the capabilities of the proposed advanced electrotheramal
pulsed plasma thruster. These devices are not new and have been studied for many years, so an in-depth
literature search was done to gather and use previous knowledge in this work. There are several major
contributors, but none as influential as the work done by Burton. His work was guided by the same niche
observed today, it is discussed further in Section 1.1. In addition to the work done in propulsion with
coaxial electro thermal pulse plasma thrusters (PPTs), there are also a great number of other fields that
use capillary discharge technology, as is discussed in Section 1.3. While not linked to the engineering
challenge of a PPT concept, their respective works do provide useful insight into the physics of these
devices.
From the literature it is possible to compose a general idea of how these devices work. Their basic
design remains fairly consistent throughout the literature, and for different applicaitons. Capillaries are
sources of very high density plasma formed through an ablation process. By understanding the basic
physics described in this section, a capillary discharge thruster was designed for the tests conducted here.
Several different designs were tested before a suitable device could fire consistently and reliably. All
the design iterations are discussed in detail in Section 2.1. The capillary was powered by a high power
LRC circuit. A suite of diagnostics was developed to measure multiple discharge parameters ranging
from current and voltage, to temperature and density, to thrust and Isp. Using such a wide variety of
diagnostics, described in Section 3, yields a thorough, accurate understanding of the capillary discharge
physics.
Early exploratory experiments were conducted to determine how capillary discharges operated under
different voltages, inductances, and capillary lengths. From these initial tests, a strong dependence on
ignition became apparent. Limited information on ignition conditions of capillary discharges were found
in the literature, and no evidence of their effect on a thruster based system were found. Therefore, the
1
major effort of this work was the investigation of ignition characteristics and their effects on capillary
discharge operation, and more specifically, thruster performance. This works examines, in detail, previ-
ously used ignition methods, as well as alternative ignition methods and there effect on the discharge. The
Ignition methods tested are described in detail in section 1.7. The results of the tests are given in Sec-
tion 5, with further discussion in Section 6. Zero dimensional and one dimensional models, described in
Section 4, are compared to the experimental results. In addition to the ignition processes, other important
observations were noted and analyzed. These range from confinement issues to electrode erosion.
1.1 The Need for High Efficiency
The field of electric propulsion has existed for over a century[22]. During that time a wide range of
electric propulsion concepts have been investigated to satisfy spacecraft propulsion requirements, rang-
ing from stationkeeping[38][100][99][60] to orbit insertion[3]. There are also proposed applications of
drag compensation, formation flying[51], attitude control[66][20], and even planetary and deep space
exploration[23][6]. Electric propulsion systems have successfully demonstrated system mass savings
over traditional chemical propulsion systems for many non-time-critical applications. The optimal spe-
cific impulse for an individual mission can be approximately determined, by comparing the propellant
mass savings with the added power supply mass for a representative total mission V . Optimal specific
impulses are dependent on the specific mission, but they are almost always in the range of 1000s to 3000s
for Earth orbiting spacecraft[43]. Individual missions often have different optimal specific impulses dur-
ing the mission, depending on the time criticality of each individual maneuver. A thruster system capable
of operating with a specific impulse ranging from 1000s to 3000s at high thrust efficiencies,, would
be very advantageous for Earth orbiting missions. Electric propulsion systems are commonly categorized
into three classes: electrothermal, electrostatic, and electromagnetic according to their dominant accel-
eration mechanism[49]. The class of continuous electrothermal thrusters have, in general, demonstrated
high thrust efficiencies at specific impulses somewhat less than 1000s, but their thrust efficiency drops
precipitously at specific impulses approaching 1000s, this is due to material limitations and frozen flow
loss[13]. It is not possible to maintain a continuous electrothermal thruster at the required high pressures
and temperatures that would allow complete recovery of the input energy through full nozzle expansion.
In contrast, electrostatic and electromagnetic thrusters have demonstrated high thrust efficiencies at spe-
cific impulses somewhat greater than 1000s. Once again, however, as the specific impulse approaches
2
Figure 1.1: Electrothermal and Ion Thruster Performance[13]
1000s (this time from> 1000s) thrust efficiency continuously decreases due to the increasing relative
importance of the ionization cost. These trends are depicted in Figure 1.1. A thruster system that operated
at high thrust efficiency ( > 65%), only at a specific impulse of 1000s, would still be a useful technol-
ogy. It has been shown, as in Figure 1.2, that an electro-thermal pulse plasma thruster (PPT) can work
quite well in this area.
1.2 Other Capillary Discharge Pulsed Plasma Thrusters
A capillary discharge (CD) is a pulsed, ablative electro-themal PPT, capable of efficiently producing high
density plasma. These devices are characterized by their high aspect ratio. An arc is established in the
center of the capillary, which results in ablated wall material that constitutes the high density plasma. In
the case of PPT, one end is open, allowing the plasma to exit the capillary while at the same time creating
thrust. The capillary discharge PPT not only exhibits high efficiency, but also has an excellent balance
between highI
sp
and high thrust. Some of the most important contributions to CD PPT’s were made by
Burton in the 1980s[16, 13, 14, 12, 10, 11] and are discussed in the next section.
While the field of pulsed plasma thrusters has been extensively studied, the work done on the specific
high power (kJ) electrothermal PPTs of interest here is limited. One of the major contributors to this field
3
Figure 1.2: Electrothermal PPT Performance History
was Burton. Burton noticed a lack of high efficiency thrusters in the 750s to 3000sI
sp
range as shown in
Figure 1.1. His initial work, done at GT-Devices in 1982[16][13], investigated the predicted performance
of a pulsed electrothermal thruster (PET) concept that operated in the 1 10 kJ energy range. The
device dimensions were about 4 mm in diameter and a few centimeters long, with a pulse length of
10 20s and a current of 100kA. With this pulse mode Burton predicted a thruster efficiency as high
as 80% in the 1500 3000s range. The PET thruster had estimated plasma densities of 5:7 10
27
m
3
and temperatures of 4eV . One of the most important points that Burton highlighted in this early work
was the aforementioned efficiency. He looked at the 3-body ion combination rate[14] and calculated
the mean free path for recombination for his given plasma conditions. At the exit he showed a mean
free path of 2 10
11
m which is much smaller than the length of the nozzle. Therefore, the flow
should be in Saha equilibrium and the ionization cost should be nearly completely recovered. That is
the primary reason why pulsed electrothermal devices in general, and capillary discharges in particular,
boast such high potential efficiencies. Another reason for the PET Thruster’s high predicted efficiency is
the capillary’s high dimensional ratio (length=diameter), which indicates that the majority of emitted
radiation will strike the propellant walls. Assuming that the walls absorb all the radiation Burton[16]
4
goes on to show that of the 16eV of energy it takes to evaporate, dissociate, and ionize one molecule of
polyethylene (C
2
H
4
) all but 3:2eV can be recaptured into the directed flow by use of a nozzle. This leads
to a predicted efficiency of 87% for polyethylene.
In 1984 Burton published experimental results on his PET thruster design. He operated his device
in both an unsteady mode, with 15 s pulses, and quasi-steady mode, with 48 100 s pulses, and
recorded efficiencies of 56% to 37%, respectively. Of interest in Burton’s published work is the effect
of pulse length. He showed the highest efficiencies for unsteady 15 s, with a 23kA peak current. For
the quasi-steady tests (the 48s and 100s shots) both had the same peak current (15kA), however, the
efficiency was higher (42 % instead of 37%) for the longer pulse. It is possible that this improvement for
longer pulse lengths is due to the minimization of the late time ablation mentioned earlier in Section 1.2.
It is also important to note the trade-off inI
sp
vs. impulse for the two operational modes. The unsteady
test had a lowerI
sp
and higher impulse (1000s, 0:2Ns), while the quasi-steady test had a higherI
sp
and
lower impulse (1600s, 0:086Ns).
Burton continued his PET thruster development by focusing on developing a propellant feed mech-
anism instead of improving the thruster efficiency. Over the next 5 years (1984-1989) Burton tried
water[12], hydrazine[10], and hydrogen[11] propellant. After these early publications, Burton’s research
moved towards smaller, much less efficient pulsed plasma research[18]. It is the long term goal of this
project to continue with Burtons original PET thruster work, in an attempt to achieve thrust efficiencies
in excess of 65%, like he first predicted. It is conceivable that by increasing the pulse length even longer
than achieved in Burton’s capillaries, the late time ablation effect can be limited. In addition, lower cur-
rents would cause less electrode erosion and also lower pressures, while still operating in a regime where
ionization losses can be recovered. Hence the effects of capillary voltage, inductance, and geometry were
all investigated in this work.
The capillary discharge designed for this experiment was predicted to operate at densities one or
two orders of magnitude lower than Burton’s work. Therefore, it is important to check the three-body
recombination rate with predicted density to make sure that ionization energy can be recovered through
the nozzle expansion. The three-body recombination rate is[1]

e
=
3
n
2
= 8:75 10
27
T
4:5
n
2
= 3:9 10
10
[s
1
] (1.1)
5
WhereT is the electron temperature ineV , andn is the number density in cubic centimeters. Assuming
only the thermal velocity of the ion
u =
r
8kT
M
= 9:6 10
5
[cm=s] (1.2)
Where M is the average molecular weight, which for polyethylene is 5:33amu. It is then possible to
calculate the mean free path at exit.
=
u

e
= 2:5 10
5
[cm] (1.3)
While this value is orders of magnitude larger than Burton’s PET thruster it is still much smaller then the
characteristic length of the nozzle and therefore the propellant is able to adiabatically expand though the
nozzle.
1.3 Other Capillary Discharge Applications
Capillary discharges are efficient sources of high-density high-temperature pulsed plasmas which are
being developed for a wide range of applications. Capillaries have been investigated as wake field accel-
erators and optical guides for high power lasers[106] They have been used as x-ray sources[62] for low
pressure capillary discharges and electro-thermal-chemical guns[78, 108, 107, 35, 83] for high- pressure
capillary discharges. Capillary discharges have been used as pre-injectors for electromagnetic rail systems
that provide initial acceleration and the material needed for the plamsa armature.[88] A similar discharge
occurs in a devices called an ablation controlled arcs, which are essentially the same a capillary discharges
but with two open ends. These devices are often studied for gas-blast circuit breakers[79].
1.4 Capillary Discharge Description
Capillary discharges can produce high-density (5 10
25
5 10
26
m
3
), high-temperature (1 8eV )
pulsed plasmas. They typically consist of a long capillary of a nonconductive material, usually high-
density polyethylene (HDPE) or Teflon
R
with electrodes at both ends of the capillary as shown in Fig-
ure 1.3. The anode is typically inserted into one end of the capillary while the cathode is a hollow cylinder
6
15

Figure 4: Capillary Discharge Ablation Process
3 Experimental setup
3.1 Capillary
The preliminary capillary discharge experiments employed a capillary that was 100mm in length
and 4mm in diameter. Polyethylene (~C
4
H
9
) was chosen as the capillary material because it has significant
heritage as a capillary discharge propellant. The preliminary capillary discharge experiments were ignited
using a thin (0.004” diameter) aluminum wire for the same reason.
3.1.1 Physical Setup
3.1.1.1 First Capillary Design
The first design used a machined polyethylene tube fitted into high pressure weld-neck flanges
that had been welded end-to-end. The anode was made from maraging steel and connected to the power
Anode
Propellant
Plasma Core
Transition Layer
Ablation
Radiation
Cathode
Plasma Core
Polyethylene
+
+
+
Figure 1.3: Ablation Process within a Capillary Discharge
on the opposite end of the capillary, although the reverse polarity also works. The capillary dimensions
are such that the ratio of length to diameter is large ( 20), giving it its name.
Capillary discharges are ignited by creating a predischarge plasma throughout the capillary using
some ignition source, typically an exploding wire ignition system. A capacitive electrical energy source
(either an LRC circuit or a more complicated pulse forming network) is connected across the electrodes.
Once a conductive path has been created between the electrodes, current will begin flowing between them
and the plasma will be heated by Joule heating. The heated plasma along the axis radiates, ablating
material in the wall. The ablated material becomes dissociated and ionized during its transit through a
thin (typically severalm) transition layer, adding mass to the capillary discharge as shown in Figure 1.3.
Mass is injected into the discharge from the entire capillary area while it is only lost from the discharge
through the relatively small exit orifice in the cathode, which allows high-densities (> 1 10
25
m
3
) to
be achieved.
1.4.1 Ablation Process
While ignition is the primary focus of this work, it is important to take a look at the overall operation of the
device. As stated earlier, it is the overall goal of this project to demonstrate a device with high propulsion
7
efficiency in the 750 3000sI
sp
range. After the ignition tests were under way, low efficiencies were
noted and will need to be addressed. The information in this section provides an in-depth view of capillary
processes and possible methods for improving efficiency beyond the ignition techniques described here.
The ablation process that occurs at the surface of the capillary wall is a complicated one. Different
ablation mechanisms have been isolated and studied, however, it is very difficult to understand how they
all interact with each other. In this section, the major ablation mechanisms are considered in more detail
to develop an understanding of the device, as well as to provide background information that may be
helpful in future capillary work.
There are two main transport mechanisms that can bring heat, or energy to the capillary wall. These
mechanism are convection and radiation. The process of convection is described by energy that is trans-
ported to the surface by collisions, where a particle within the plasma deposits energy to an atom on the
wall. The other main form of energy transport is radiation. Photons interact with the surface atoms either
by breaking molecular bonds directly, or are being absorbed into the vibrational modes of the molecules,
causing heating. Conduction, the third common heat transfer mechanism, only acts as a loss mechanism
in these discharges. Due to the relative long time scale in which conduction occurs, it does not effectively
aid in ablation during the short time of the discharge pulse. Any conduction that does occur would be
relatively small and regarded as a loss.
Ablation occurs in a number of different ways. The three main forms in which material can leave
the surface are photo-ablation, marcro-particles, and thermal pyrolysis, as illustrated in Figure 1.4. Photo
ablation occurs when a photon has enough energy to break a molecular bond of an atom directly, poten-
tially releasing it from the surface. In macroparticle ejection a localized hot spot within the bulk material
leads to a high pressure void which explodes outward ejecting macroparticles along with the originally
ablated gas. Often times these macro-particles are quickly dissociated and ionized in the plasma column,
but they do affect ablation rates and efficiencies. The third form, called thermal pyrolysis, simply refers
to an amount of material that leaves the surface due to the material’s elevated vapor pressure at a certain
elevated temperature.
Photo-ablation has been recognized as an important ablation mechanism[79] in ablation controlled
arcs. For different polymers the critical wavelength,
c
, lies between 250 and 350nm[81]. Photons with
wavelengths below
c
have enough energy to directly break chemical bonds and are typically absorbed
much closer to the surface. Photons with>
c
, in general do not, and penetrate deeper into the material
depositing their energy as thermal vibrational energy of the constituent atoms. This process heats both
the interior of the material along with its surface which leads to thermal pyrolysis because of greatly
8
increased vapor pressure. Short wavelength radiation can also cause damage at significant depths within
the material[68]. Any damage or heating that occurs within the material is a form of energy loss, for it
does not lead to ablation. It is also important to note that the description of the mechanisms given here are
strictly applicable only when each mechanism operates independently from the others. The true physical
picture with all mechanisms operating at comparable levels is significantly more complicated.
Figure 1.4 is an attempt to illustrate the various ablation mechanisms and the energy transport mech-
anisms that typically causes them. Only the most relevant energy paths are shown for simplicity. Lower
wavelength light is the only form that can cause photo-ablation as shown by the black line. Higher wave-
length photons can either pass directly through the material and leave the system as radiation as shown
by the green line. It can also be absorbed within the material where it is either lost through conduction or
causes ablation through macro-particles and thermal pyrolysis. Note that late time ablation causes large
efficiency loss in PPTs. Late time ablation is a result of the hot surface of the wall continuing to vaporize
material after the electrical arc has extinguished. This material is evaporated, but efficiently accelerated.
Obviously all of the mechanisms that cause ablation by thermal pyrolysis also cause late time ablation.
!"!#!$%&'()#*)+,-.#/&%&)0+#
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3
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9:(;(&$%&'()#
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3
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3#
•! !$A(,$#!#C#!
3
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Figure 1.4: Ablation Mechanisms
An ideal electrothermal PPT is one that operates by pure photo-ablation. This is not practical in a
capillary type dischage. However, research can be done to produce a discharge that contains more high
energy radiation and a material can be chosen or developed that is highly susceptible to photo-ablation.
Polymers, in general, have a strong sensitivity to UV light[61]. They have ablation thresholds lower
than metals[46], semiconductors[84], and metal oxide semiconductors[47]. They also have much higher
9
ablation rates[87], which make them attractive for PPT propellants. A wide range of polymers have been
tested, from white, grey, black[68], andCu doped PTFE[79] to more exotic materials like Celeon R
and
Tefzel R
[73]. White PTFE ablated less than black PTFE[79]. This is because the optical transparency of
white PTFE allows soft arc radiation to penetrate deeply into the material, causing only moderate heating.
It has also been reported that doping PTFE with a small amount ofCu (7%) increases the ablation
efficiency[79]. This is accredited to the optical penetration depth being reduced byCu molecules, and
by the fact that while theCu in the plasma do not significantly change the thermodynamic or electrical
properties of the arc, it does strongly increase the radiation emitted from the arc[89].
While understanding the absorption and ablation of materials is complicated, and not well understood,
it is clear that photo-ablation is important and UV (sub-critical) radiation causes it. So, in support of what
was found in literature, a spectrum simulation program called PrismSpect R
was used to model the plasma
that would be created by material once it has been ablated. PrismSpect R
does not model the ablation
process, or how well the material will ablate, but models the spectral profile of emitted radiation for a
given size plasma of known composition, temperature, and density. This spectral distribution helps in the
choice of a good material, at least from a radiator point of view. Several materials were simulated at a
density of 5 10
25
m
3
and a plasma temperature of 1:5 eV . These values are typical of a capillary
discharge. The PrismSpect spectra are shown in Figure 1.5. High Density Polyethylene, HDPE (C
4
H
9
),
7% atomic copper doped HDPE (C
4
H
9
Cu), and Teflon, PTFE (CF
2
), were all tested. In addition a black
body radiator at 1:5eV is shown as a base for comparison. Notice that for these given conditions, PTFE
produces the least amount of radiation and that by adding only as small about of copper to HDPE its
radiation is greatly increased. This supports the work reported by Ruchti[79]. Of even greater interest is
the distribution of energy that is in above and below the 300
n
m critical wavelength,
c
. Figure 1.6 shows
the integrated energy from 50 to 1000nm. This figure shows the total energy as well as the energy above
and below the critical wavelength which was chosen to be 300nm. Notice that while PTFE produced the
least amount of over-all radiation, it produced the largest percentage of radiation with wavelengths below
the critical cut-off. This would suggest that more energy is going directly into photo-ablating and less
into other less efficient processes.
Despite the results shown here, and the material testing reported in the field of ablation controlled arcs,
the tests conducted in this work where done with standard polyethylene. This material was used because
of its historic roll in capillary discharge and so that these results could be compared with Burton’s and
other electrothermal PPT research.
10
100 200 300 400 500 600 700 800 900 1000
0
0.5
1
1.5
2
2.5
x 10
11
Wavelegth (nm)
Intesity (Arb)

HDPE
Cu−HDPE
PTFE
Cu−PTFE
Blackbody
Figure 1.5: Spectrum produced by different plasma compositions at 1:5eV and 1:5 10
25
m
3
using
PrismSpect Software
1.5 Capillary Physics and Assumptions
There are three primary physical assumptions that are typically used to produce simplified capillary dis-
charge models. The first assumption (1) is that the capillary discharge is an electrothermal device so that
the effect of magnetic fields can be neglected. The validity of this assumption is quantified using the
plasma. This parameter is defined as the ratio of thermal pressure to magnetic pressure, must be signif-
icantly greater than one for the electrothermal assumption to be valid. The second assumption (2) is that
the plasma is in local thermodynamic equilibrium (LTE). Under LTE conditions charge particles are con-
sidered to be the same temperature, greatly simplifying the physical model. The third assumption (3) is
that the plasma is an ideal plasma. Ideal plasmas are those in which, for the majority of the time a plasma
particle is traveling, it is unaffected by other particles and only rarely experiences strong charge interac-
tions. The validity of the ideal plasma assumption is quantified by the non-ideal parameter, which is the
ratio of the mean potential felt by a particle to the mean particle kinetic energy. If the non-ideal parameter
is significantly less than one, it is reasonable to neglect charge coupling between ions and electrons and
model it as an ideal plasma. These simplifying assumptions are also used in this work. They must hold
11
HDPE Cu−HDPE PTFE Cu−PTFE Blackbody
0
2
4
6
8
10
12
14
16
x 10
4
Material
Radiation Energy(J)

<300nm
>300nm
17.39%
82.61%
22.80%
77.20%
18.77%
81.23%
24.48%
75.52%
22.56%
77.44%
Figure 1.6: Integrated energy from 50 to 1000nm for spectra from Figure 1.5
if meaningful comparisons between theory and experiment are to be made, and to allow interpretation of
the experimentally measured results. Each simplifying assumption is described in more detail below.
1.5.1 Pressure Ratio
The factor is the ratio of thermal pressure to magnetic pressure in the plasma. In order to model a
device as purely electrothermal, must be much less then one. As approaches unity, the magnetic
forces within the plasma are similar in magnitude to those due to thermal pressure and can not be ignored.
If is much larger then 1, the operating physics of the device are very different, and it operates as a z-
pinch device[101]; where the magnetic force causes the plasma column to collapse upon itself, generating
much greater pressures.
The parameter, as mentioned earlier, is defined as the ratio of thermal pressure to magnetic pressure
=
P
T
P
B
(1.4)
12
WhereP
T
is the thermal pressure defined by
P
T
=nkT (1.5)
AndP
B
is the pressure caused by the magnetic field.
P
B
=
B
2
2
o
(1.6)
The magnetic field in the capillary discharge is generated by the large current flowing though the plasma
column. The relationship between the plasma current and magnetic field can be assumed from Amperes
law
B =

o
I
2r
(1.7)
By substituting Equations 1.5 and 1.6 into Equation 1.4 an expression for is obtained,
=
8nkT

o

r
I

2
(1.8)
For a temperature (2eV ), density (1 10
25
m
3
), radius (0:002m) and nominal current (6kA) expected
in the experiments conducted here, the pressure ratio is about 22. Because 1 the device is
considered purely thermally driven. It is important to note that while is greater than 1, if the density is
an order of magnitude lower, while the other parameters are held constant, can get very close to 1 and
the previous assumptions may not be valid.
1.5.2 Local Thermodynamic Equilibrium
A system can be said to be in thermodynamic equilibrium if it is in thermal equilibrium (temperature),
mechanical equilibrium (pressure), and chemical equilibrium (chemical potential). The condition of local
thermodynamic equilibrium (LTE) exists when intensive properties (such as temperature) may change in
the system, but are doing so slowly so there is approximate equilibrium around a point. In LTE temper-
atures are well defined and the electron temperature is the same as the heavy particle (molecules, atoms,
and ions) temperature. To show that this is the case for typical capillary discharge plasmas produced in
this work, it is necessary to look at the energy heating the particles. The average energy exchanged in an
electron-ion collision is
"
e$i
=T

2m
e
m
i

(1.9)
13
Wherem
e
is the mass of the electron andm
i
is the mass of the ion. The average energy an electron gains
from a surrounding electric field between collisions is
"eE
e;drift

ei
(1.10)
Wheree is the unit charge,E is the electric field, and
e;drift
is the electron drift velocity which can be
defined by

e;drift

eE
ei
m
e
(1.11)
Here
ei
is the electron-ion collision frequency and can be expressed by
ei
=
1
ei
. Using this relation
and substituting Equation 1.5.2 into Equation 1.10 a new equation for the energy gained from the electric
field is obtained.
"
E
=
e
2
m
e
E

ei
(1.12)
The electron collision period, nu
ei
, can be described by the number of particles, their effective cross-
section, and the velocity in which they are moving.

ei
=nv (1.13)
where is the collision cross section area described by =r
2
o
in which the impact parameter is
r
o
=
e
2
4"
o
mv
2
(1.14)
Assuming a Maxwellian distribution the electron velocity can be estimated to an order of magnitude by
v
2
=
kT
me
. Substituting the values into equation 1.12 an equation is obtained for the average energy gained
by an electron between collisions, due to the electric field, as a function of the electric field, temperature
and number density.
"
E
=
256
2
"
2
o
k
3
e
6
T
3
E
2
n
2
(1.15)
The LTE parameter can now be defined[19] as a ratio of energy exchanged during electron-ion collision
to the energy gained by the electron from the electric field.
K =
"
e$i
"
E
(1.16)
14
Combining equations 1.9 and 1.15 into 1.16 a value for the LTE can be obtained.
K =
1
128
e
6

2
"
4
o
k
3
m
e
m
i

n
ET

2
(1.17)
Therefore at a given temperature of 4 eV , a number density of 1 25 m
3
and an electric field of
1 10
5
V=m the LTE parameter ofK 1 10
9
. This indicates that the plasma is strongly dominated
by collisions and can be considered in local thermodynamic equilibrium.
1.5.3 The Non-Ideal Parameter
The Non-Ideal plasma parameter, , is defined by
=
W
PE
W
KE
(1.18)
WhereW
PE
is the potential energy between two charged particles andW
KE
is the average kinetic energy
for a particle.
W
PE
=
e
2
4"
o
r
=
e
2
n
1=3
4"
o
(1.19)
Where the distance between the particles,r, can be express byn
1=3
. And the kinetic energy is
W
KE
=kT (1.20)
By combining these equations an expression for the non-ideal parameter is obtained.
=
e
2
KTn
1=3
4"
o
(1.21)
For a temperature of 2eV and a density of 1 10
25
m
3
, typical for the experiments conducted in this
work, the calculated is about 0:16. Because is less than 1 the plasma can be considered ideal and is
dominated by its kinetic or thermal energy.
1.6 Evaluation of Thruster Performance
Understanding the device physics is important, but the key metrics for consideration of pulsed electrother-
mal thrusters are the performance metric. A capillary discharge is being investigated as a spacecraft
15
thruster, and while measurements such as current and temperature are important in understanding the dis-
charge process, the overall concern is with developing a thruster that can be operated within the needed
niche discussed in Section 1.1.
Therefore one of the most importance diagnostic tools is the thrust stand that is mentioned in sec-
tion 3.4.2. This device permits a full evaluation ofe the thruster as a propulsion device. The thrust stand
can measure the impulse,I, directly and the average mass loss is calculated from scale data. From this an
average measurement ofI
sp
can be calculated by the folllowing relationship,
I
sp
=
I
mg
o
(1.22)
HereI is the total impulse inparted to the thrust stand by the thruster, m is the average mass loss per
shot, andg
o
is the gravittional constanst. The propuslion effeciencey,, can also be obtained from.
=
E
thrust
E
electrical
; (1.23)
where the thrust energy, E
thrust
can me described by
1
2
g
o
I
sp
I. TheE
electrical
is simply the electrical
energy used by the thruster,
R
Vjdt. HereV is the instantaneous voltage across the capillary, andj is
the instantaneous current that passed though the device. These 3 parameters, I, I
sp
, and , define the
performance of the capillary discharge as a thruster. There are many other parameters that are important
when considering a thruster for a spacecraft, but at this stage of basic research and development, these
parameters are sufficient to indicate whether the capillary discharge has potential as a future propulsion
system.
1.7 Ignition Methods
It has been shown that the ignition properties of a capillary discharge can greatly influence the plasma
conditions of the main discharge plasma[80]. Work in the field of soft x-rays producing capillary dis-
charges has shown[5]: low pre-pulse currents are insufficient for effective capillary pre-ionization and
high currents prevent effective pinching due to largely preheated plasma. In addition to what can be
found in the literature, initial capillary tests with wire ignition at the AFRL also showed a dependence on
the ignition condition, in the form of a dual mode of operation. These findings were part of initial work
associated with the study and are discussed further in Section 6.3.
16
It was felt that ignition was important to investigate. The presented study will examine how pre-
discharge condition influence the overall capillary operation. The research that was carried out chose to
explore: different ignition methods; how each method effected thruster performance; and to explain the
the dual mode operation observed in early wire ignition testing. Capillary discharges have been ignited
using many different techniques over the years. Some of these methods are used for their simplicity and
others for creating complex plasma profiles, as is done for plasma wave guides, mentioned in Section 1.3.
In this work wire, gas breakdown, and spark ignition techniques were examined and their effects on the
overall discharge and thruster performance investigated.
The preliminary capillary discharge experiments were ignited using a thin, 0:004 diameter, aluminum
wire, as described in Section 2.1.1. This method is certainly not appilicable in a spacecraft propulsion
system, but this method has frequently been reported in literature and thin wire is considered very reliable
and easy to implement. Through initial application of this method it is possible to understand and develop
the capillary circuit, become familiar with the techniques needed to contain high pressures, and to develop
and tune diagnostic equipment. It was also in these preliminary tests that the need to further explore the
effects of ignition conditions on device operation was established. It was noticed while using the wire
technique that the capillary would discharge in two distinct current modes. Further initial ignition tests
were not only an improvement in overall design for test purposes, but also provided a better understand
of multi-mode operation, which will be discussed further in subsequent chapters.
Following the initial ignition tests and proof of concept, a Paschen ignition scheme was adopted, as
is explained in Section 2.1.2. This permitted further progress towards a spacecraft thruster, and allowed
the device to be mounted on a thrust stand which enabled more accurate impulse and specific impulse
measurements . The discharge was also run in a reverse configuration by placing the anode at the exit of
the capillary. However it was quickly discovered that this method did not work with the current design.
Basically, as the discharge plume expanded into the chamber it created conductive paths between the
exposed anode and the grounded chamber walls, causing secondary arcs and stray discharges.
One of the most common and simplest ignition techniques use a spark plug, such as an integrated
semiconductor type spark plug[15], near the capillary exit. The 3rd design, which is described more
thoroughly in Section 2.1.3, uses a coaxial spark ignitor near the exit of the capillary discharge. This
technique allowed the testing of spark ignition techniques without committing to major redesign changes.
Initial tests showed that the method worked quite well, and the overall design was quickly changed to
incorporate this technique into a single housing, instead of continuing to investigate the external coax
spark ignitor.
17
Once the spark ignition technique was shown to be effective, an internal three-electrode system was
designed as described in Section 2.1.4. This design used the same technique at the coxial ignitor, but
placed the spark internally, between the anode and cathode, allowing a more reliable ignition.
1.7.1 Wire Ignition
Attempts to understand the electrically driven wire explosion process can be traced back as far as 1774
when Nairne was studying the conservation of current in series circuits.[21]. However, work on the
subject did not really progress until the late 1950s and early 1960s. This work continued through the
recent decades as more uses for exploding wire were discovered.
The wire ignition process, while very reliable in terms of its ability to ignite a capillary, is a chaotic
and nonuniform process. Capillary discharge operation not only depends on the mode of wire vaporiza-
tion, but the ablated mass and thrust energy will be strongly influenced by the initial plasma conditions
following the wire explosion. One of the most interesting works on wire explosion, as it applies to cap-
illary type devices, was reported by Taylor[91]. His work goes into great detail about the mechanism
and structure of an exploding wire. Figure 1.7 shows a wire explosion, as photographed by an intesified Formation of plasma around wire fragments
Figure9. Close inspection of the x-radiographs (exposure
time= 0.2242 ms (image 4 figure 8); wire diameter= 1 mm; detail
length∼ 40 mm).
Another important finding from images such as those
shown in figure 8, is that condensed material remains
essentially at the same location until it has all evaporated
away. This indicates that the Lorentz forces associated with the
buckled wire are insufficient to drive the condensed fragments
from their axial position, adding weight to the argument that
little current is being conducted through the fragments. (Lack
of Lorentz forces is also cited in [7] and x-radiographic images
clearly show it not to have any significant effect in reference
[8].) Further, the confinement of the wire in a capillary
(image 7, figure 8) appears to make little difference as far as
the physical mechanisms of the exploding wire are concerned.
Knowing the linear expansion coefficient for the
condensed phases of copper allows the temperature of the wire
to be determined from measurements of its length. The length
can be determined from the x-radiographs. (The magnification
of the wire images due to the non-planar nature of the x-rays
from theflash x-ray system has been taken into account.) Such
measurement of digitized x-radiograph images was performed
using image analysis software, and the temperature of these
wires determined. They confirm again that the bulk of the
wire is still a cool liquid for the majority of the resistance rise.
Measurements of the axial and radial expansion of the
wire confirm that no super-heating of the wire or rapid radial
expansion is occurring as some experimenters have found with
wire explosions under different conditions [2, 3].
Examination of the photographic and x-radiographic
images of the same event shows the relationship between
the plasma development and the fragmentation of the wire.
Figure 10 shows six photograph and x-radiograph ‘montages’
and a further two photographs highlighting intermediate
plasma development. The first image is a montage but not
simultaneous, with the x-radiographs being captured a few
microseconds prior to the photograph. The two images that
follow are enhanced digital images taken 1µs apart with
0.200 ms 0.211 ms 0.212 ms 0.231 ms 0.237 ms 0.249 ms 0.255 ms 0.273 ms
Figure10. Photograph and x-radiograph montages.
an exposure time of 100 ns. The following five images
are montages made from simultaneous x-radiographic and
photographic images.
The first image x-radiograph shows a developing kink at
the location of the subsequent plasma spot, together with the
spots at the electrodes. The second and third images show
the rapidity of the plasma development, and some interesting
but as yet unstudied ‘glow’ discharges along the length of the
wire. The fourth image shows the existence of apparently
continuous lengths of condensed material several centimetres
in length, within the plasma. The last four images show
the slow evaporation of the condensed material and the slow
development of the plasma sheath in the radial direction. Also,
some interesting plasma flares can be seen to break away
from the main discharge in the sixth image. These flares
developed in brightness over a period of around 30µs and
showed evidence of around 8 mm of motion seemingly towards
(more likely in front or behind) the wire throughout this time.
It is surmised that these flares were associated with complex
magnetic fields surrounding the plasma. Vlast´ os [19] reports
some quite interestingfindings on helical magnetic phenomena
during wire exploding studies.
4. Hypothesisforthediversionofcurrentaround
condensedwirefragments
It has been argued above that current is being diverted
around the condensed fragments of an electrically exploding
wire through the seemingly higher resistance plasma. This
phenomenon is also reported on work conducted for the
electric armour programme [7], for aircraft radome lightning
segmented divertor strips [5, 20] and segmented strip ETC
igniters [21]. Arguments are presented in [7, 21] that the effect
is essentially geometrical, limited to an aspect ratio of gaps
and fragments of about unity. In the work described here, the
fragment length is at least ten times that of the gap length.
A physical mechanism that explains current diversion is still
needed for these aspect ratios and the following argument
attempts to provide one.
It is stated in [5] that the electrical conductivity of the
metal vapour under exploding wire conditions was the most
difficult part of the process to model. Recently published
work by Desjarlais [22] has provided experimentally validated
[23] electrical conductivity data in the liquid vapour transition
705
Figure 1.7: Photograph and x-radiograph montages of an exploding wire[91]
fast frame digital cameara and a flash x-ray system, to obtain details of the wire structure hidden by the
expanding plasma. As can be seen the wire does not vaporize evenly. Breaks occur within the wire due
18
to hot spot formation in the material. These hot spots may occur due to a variety of inhomogeneous fac-
tors, most noticeably kinking during thermal expansion, but also; thermal stress waves, impurities, lattice
dislocation, and physical damage. As the breaks develop, the resistance increases, thus causing a voltage
drop across each break. A point is reached when the voltage attains the Paschen or similar threshold for
electric breakdown, and an arc discharge occurs. The discharge current, plasma temperature or resistivity,
and the spot dimensions will all effect the ohmic heating that occurs. The resistance of the entire sys-
tem rises as the length of the plasma section increase, and the amount of wire between the plasma spots
decrease. Once the wire is completely sheathed in a conductive plasma the energy distribution along the
length of the system is likely to become more uniform. This resistive equilibrium occurs 10
0
s, if not
100
0
s, of micro seconds into the explosion. At this point, within an ablative capillary, material from the
ablation capillary wall will govern that physical operation of the discharge. Therefore, it is likely that the
wire does not full explode to the late stages seen by Taylor. It is possible that initial fragmentation and
plasma hot spots formed in the early stages of wire explosion ignite the capillary discharge.
Another problem with wire ignition was its effect on spectroscopic diagnostics. Line spectrum from
the aluminum not only pollute the Stark broadened hydrogen Balmer lines, but would also change the
plasma density which was of interest. The amount of wire used to ignite the capillary was on order of
the amount of material ablated from the capillary walls. So it was possible that a large fraction of the
plasma composition could be aluminum. This is unlikely that the wire full decomposes. More probable
that a large number of macro particles are produced and expelled out the cathode. The degree or wire
explosion, the amount of ions formed, and therefore the exact plasma composition, could not be known.
The amount of aluminum material not only influenced the capillary discharge plasma composition, but
also made it impossible to measure accurately any thruster performance characteristics with confidence.
Wire material exiting the capillary would give sporadic impulse measurements, as well as making it
impossible to account properly for mass loss in order to calculate such metrics asI
sp
and. Because the
ultimate goal was to understand capillaries and their application as a spacecraft thruster, it was necessary
to develop a new ignition method and allow for proper thruster performance measurements.
In Summary, wire explosion is not valuable in a spacecraft propulsion system, it is also of limited
value for determining the effects of ignition conditions on overall performance because of its complexity
and nonrepeatability. The technique is, however, very widely used and it is included in this study for
comparison purposes.
19
1.7.2 Paschen Ignition
In order to successfully study and understand the capillary discharges and their ignition, it was strongly
felt that the wire needed to be removed and another method used. This not only progressed toward the
end spacecraft thruster design, but also allowed for more in-depth accurate studies. Removing the wire
removed that material from the plasma. This fact allowed more accurate analysis of the plasma, knowing
that it was not “polluted” with elements other then the carbon and hydrogen from the polyethylene (and
the small about of electrode material that is eroded). It also allowed for proper mass accounting and
confident Impulse andI
sp
measurements.
A Paschen breakdown ignition scheme seemed the most logical next step in the study of capillary
ignition phenomenon. The idea was to eliminate the wire from the experiment and lower the background
pressure to a range were the space between the anode and cathode would break down based on the prin-
ciples of Paschens Law. Paschen found that breakdown voltage could be described by the equation
V =
a (pd)
ln (pd) +b
(1.24)
WhereV is the breakdown voltage in volts,p is the pressure in atmospheres andd is the gap distance in
meters. The constantsa andb depend upon the composition of the gas. For air at standard atmospheric
pressure of 760Torr,a = 43:6 10
6
andb = 12:8[74]
By this accord it would take 49:5, 33:0, 24:7, and 19:8Torr to break down our 4, 6, 8, and 10cm
capillaries, respectively at 2500V . These values were based on pashcens law for parrelel plates and gave
a good idea, but not exact value to accuratley predict the breakdown for our geometry. What more, the
gas compasition can greatly effect the break down properties, as seen in Figure 1.8. Even a small change
in humidity can effect these curves.
1.7.3 Coaxial and 3-Electode Ignition
The coaxial igniter and 3-elctrode ignition system operate under the same general principle. They provide
an electric field disturbance as well as ionized material that allows the main discharge to occur. These
ignitions system use a voltage difference applied across two electrodes separated by an insulating material
to create a surface flash over. In the case of the coaxial ignitor this flash over is occurs radially as the core
is charged to high voltage and the shielding or outer cathode is held at ground, with a teflon insulator
separating the two. The 3-electrode igniter used the same concept but different geometry. A high voltage
20
ECE234/434 Handout 1/5 113/1/07
Electrical breakdown limits for MEMS
The argument usually presented to show how electrical breakdown
influences MEMS devices is based on Townsend (avalanche) breakdown in gases.
According to this well-known theory, an electric spark can occur only if free
electrons accelerated by an electric field gain enough energy between successive
collisions with neutral atoms (or molecules) to ionize the atoms. Ionization
releases an additional electron which also accelerates, collides with atoms, and
causes more ionizations. The resulting avalanche leads to a spark. This behavior
is represented by the familiar Paschen curve. The minimum in this curve occurs at
the condition where the electronic mean free path is just barely sufficient to allow
electrons to gain the ionization energy. Fig. 1 shows Paschen curves for air,
nitrogen, and hydrogen.
For an investigation of the influence of avalanche breakdown on MEMS
devices, it is reasonable to assume atmospheric conditions, that is, p = 1 Atmos. =
760 Torr: For large gaps, say one centimeter or larger gap between clean metal
Fig. 1. The Paschen curve for dry air, nitrogen, and hydrogen. Note the significant differences
between air and N
2
. (from J. D. Cobine, Gaseous Conductors, Dover, 1941).
Air
H
2
N
2
100
10
2
10
3
10
4
0.1 1.0 10. 100 1000
Voltage (V)
pd product (cm-Torr)
avalanche breakdown
V
min
= 327 Volts 327
Figure 1.8: The Paschen curve for dry air, nitrogen, and hydrogen.[24]
electrode is placed a small axial distance away from the capillary’s anode, separated by a polyethylene
insulator. Here the flashover occurs axially instead of radially.
There are two main schools of thought behind surface flashover. One predicts a sub-surface process
and the other an above-surface process; the second being the more widely accepted[67]. Above-surface
flash over of insulators in a vacuum can be described mostly as a 3 phase process[69]. Phase one is a
fast buildup of a saturated secondary electron avalanche. This phenomena takes place in about two nano
seconds and produces currents of 10 to 100mA. This avalanche occurs when electrons are released by
field emission from the cathode by means of mircofractions, impurities, and field increase[8]. The field
emitted electrons strike the insulator surface and release secondary electrons. If the yield is greater than
1, the struck position takes on a positive charge. This positively charged surface area re-attracts back the
secondary electron that was emitted, causing further electron surface strikes and secondary electrons. As
long as the secondary electron yield is greater the 1, an electron avalanche is formed. This avalanche
cascades towards the anode because of the electric field formed between anode and cathode. The second
phase occurs from electron induced gas desorption and current amplification via the Townsend process.
This leads to 10 to several 100 A in several hundred nanoseconds. The space between the electrodes
becomes more positively charged due to the slower drift velocity of ions in the desorbed gas layer. The
result is an enhanced internal electric field, and therefore more cathode field emission and total current.
The third phase is shorter, at several nanoseconds, and creates about 1A. It is based on the nonlinearity
between the field emission current and electric field, which leads to an impedance collapse.
21
The mechanisms involved in fully understanding surface flashover are complicated. For ignition of the
main capillary discharge, it is important that the neutral and charge particle leave the surface during the
second phase of the surface flash over. It is these particles that create a conductive path for the discharge
to occur. It is speculated that the mechanisms that start the surface flashover in the ignitor are the same
as those that starts the the main discharge. The processes can be thought of as a small capillary discharge
igniting a larger one.
22
Chapter 2
Experimental Setup
In this section the experimental setup involved in operating a capillary discharge will be examined.
Because this project was started from scratch there was significant required design work associated with
the capillary. Design iterations will be explained along with the logic behind each development and
change. It is often difficult to find good accounts of experimental setups in the literature. The information
in this section presents a detailed account of how the devices were built and tested, providing information
for future experimenters. This section also covers other hardware setups including; circuits, facilities, and
diagnostics.
2.1 Capillary
While the capillary configuration remained fairly constant throughout this test program, the housings
changed quite significantly. These changes were mostly motivated by; arc prevention, pressure seal-
ing, and the ignition method. Throughout the experiments standard, off-the-shelf, 4mm inner diameter,
6mm outer diameter, polyethylene tubing that is common to the medical and food industries, was used.
Polyethylene (CH
2
) was chosen as the capillary material because it has significant heritage as a capil-
lary discharge propellant[16, 13, 14]. All capillary designs allowed the testing of different lengths, from
40 100mm.
2.1.1 Capillary Design V1.0 for Wire Testing
The first design (V1.0) was machined polyethylene tube sized to fit into two high pressure weld-neck
flanges that had been welded end-to-end. The anode in this setup was made from maraging steel which
was connected to the power system by a copper rod screwed into the back of the anode. The anode
and transfer rod were insulated with several Teflon
R
pieces. A sketch of the internal workings of this
design is shown in Figure 2.1. Several problems arose with the design, the largest of which was electrical
23
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#((!MK@!O((!NK!&=)'6!!702$!&=)'!*$$'()8%!52&!32+'8%!23!&0'!K'$2;3!"!02;0!-.'$$=.'!58*3;'$!12&0!82&&8'!
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&.*3$5'.!.,/!
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*3,/'! -,8%'&0%8'3'!&=)'!
23$=8*&,.$!
2;32&2,3!12.'!
Figure 2.1: Schematic of Capillary Discharge Design V1.0
shorting that occurred around the anode. The insulation was composed of separate Teflon
R
pieces press-
fit together to form a seal, but the inevitable small cracks between the pieces would reveal a shorter path
to ground than the 100mm from anode to cathode. This would cause the device to short before ignition
took place. This initial problem was overcome by using more accurately machined parts that compressed
to form tight seals. However, after ignition, the high pressure gas or plasma would push between the
Teflon
R
pieces producing another short during the discharge. Because of the persistent electrical shorting,
the relative difficulty of loading the ignition wire, as well as the machining time to produce these parts, a
new simpler design was needed. Design V1.1 addressed these issue before any major testing could begin.
Capillary Design V1.1
Several different setups were considered to deal with the issue of blow-by gases. Factors such as wire
loading method, housing assembly, reload time, capillary mass loss measurements, and arc prevention all
had to be carefully considered. Different methods of sealing multiple tubes and sheathing were tested.
Ultimately, it was shown that a single long capillary that covered the entire anode with a single sheathing
would work best. This redesign phase used stock 4mm, ID, 6mm OD tubing fitted in a 6mm ID, 8mm
OD tube. This tube-within-a-tube assembly fit nicely in the Design V1.0’s high pressure flanges with
little modification. A resin casting compound was used in the thruster housing to fill the gaps for previous
design methodology. Several different anode material were tried to reduce electrode mass loss. Welding
electrode tungsten rod that was either 1:5% lanthinated or thoriated was used. Figure 2.2 shows a sketch
of Design V1.1 which was implemented the first round of wire ignition tests.
24
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*78,!5-38%!'&!4<<.'%$!4+!+,'&!<-')+!'+!8-7.$!847&%!+,%!&.'-7+!+,%!=48;!-5!+,%!+,37&+%30!A,'.%!&45%+/!<3%847+'-)&!6%3%!+4;%)B!+,%!'*<48+!-)!5-38%!*%4&73%*%)+!*4/!)-+!
=%!)%(.%8+4=.%0!C.&-B!6,'.%!=.-6!=48;!(4&!'&!)-+!8-*<.%+%!&+-<<%$!6'+,!+,'&!$%&'()B!'+!$'$!&+-37<+73%!4)$!84<'..43/!=.-6!-55!784+,-$%!3-$B!,-6%2%3!'+!$-%&!)-+!4<<%43!+,4+!(4&!*4;%&!'+!4..!+,%!64/!+-!+,%!-+,%3!%)$!-5!+,%!84<'..43/!H)%43!
+,3%4$%$!84=.%!4++48,*%)+!<-')+I0!!!
! J%&'()!E!<3-2%$!+-!=%!3%.'4=.%!4)$!&45%0!?,%!*4K-3'+/!-5!+,%!%L<%3'*%)+4.!3%&7.+&!<3%&%)+%$!')!+,'&!
<4<%3!6%3%!8-..%8+%$!7&')(!+,'&!$%&'()0!!C.+,-7(,!+,%3%!*4/!=%!$'55%3%)8%&!')!')&7.4+'-)!4)$!4)-$%!*4+%3'4.!
+,%!$%&'()!8-)8%<+!3%*4')%$!+,%!&4*%!+,3-7(,-7+!+%&+')(0!?,'&!$%&'()!4)$!'()'+'-)!+%8,)'M7%!64&!&'*<.%!
%)-7(,!+-!4..-6!<3%.'*')43/!')2%&+'(4+'-)!-5!+,%!84<'..43/!<,/&'84.0!A%!6%3%!4=.%!+-!+%&+!5-38%B!8733%)+B!4)$!
84+,-$%N,-7&')(!
4)-$%!
'))%3!+7=%! -7+%3!+7=%!
')&7.4+-3!
'()'+'-)!6'3%!
Figure 2.2: Schematic of Capillary Discharge Design V1.1
Several concerns arose from this design. Foremost, force sensors were attached to the high pressure
flange assembly, which could have difficulty acquiring accurate measurements. In this design the anode
is slip-fit into the inner most tube. The inner tube is then slip-fitted into the outer tube. These types of fits
could be problematic if the slip fits fails resulting in a shift of the tubes. Internal movement of comments
would causing inaccurate force measurements. While safety precautions were taken, the impact on force
measurement may be significant. The blow-back gas problem was not completely alleviated with this
design and it did cause capillary rupture and capillary separation at voltages above approximately 3250V .
Gas residue and charring occurred back up the Anode rod, however it did not appear that gas made it all
the way to the other end of the capillary (near the threaded cable attachment point).
Design V1.1 proved to be reliable and safe. The majority of the experimental results presented with
wire ignition were collected using this design. Although there may be differences in insulation and anode
material, the design concept remained the same throughout most of the wire tests. This design and ignition
technique was simple enough to allow preliminary investigation of the capillary physics. It was possible
to test current and voltage probes, as well as light collection from the capillary exit, in an effort to measure
temperature and pressure from emission spectroscopy that will be discussed in Section 3.5.
2.1.2 Capillary Design V2.0 for Paschen Breakdown Testing
For the next phase of testing a Paschen breakdown ignition system was implemented as mentioned in
Section 1.7. For this method there was no wire and the opportunity was taken to simplify the whole
setup and entirely redesign a new system. The large high pressure flanges were replaced with a standard
25
stainless steel pipe. This pipe was threaded and inserted into a simple stainless steel pipe union. The
other end of this union had an NPT to compression adapter fitting attached. A diagram of how these
parts are assembled is shown in Figure 2.3. The two main sealing issues were addressed in Design 2.
First was at the anode rod, which was again, slipped into the back of the tube and housing assembly.
The use of compression fitting allowed the tube to be squeezed around the anode rod forming a tight
seal. Throughout this phase of testing no blow-back gases were witnessed past the compression fitting.
This design implementation was carried throughout all future designs. The compression fitting did an
excellent job of holding the anode in place and no slipping occurred. Originally stainless steel ferrules
were used. There was a concern about arcing though the polyethylene due to the compression force
applied at this location, however, no incidences occurred. The other sealing attempt was made at the
cathode end. Charring was occasionally observed on the outside of the polyethylene tube. It was believed
to be from gas exiting at the cathode end. A small stainless steel insert was welded into the end of the
housing to form a seal with the tube end. This insert had two other important effects. It allowed for better
spectroscopic measurements by restricting the gas expansion until it reached a region were it could be
accessed by the optical system. This is discussed further in Section 3.5. The other added benefit was that
it resulted in easier Paschen breakdown since it brought the electrode material closer to the centerline of
the capillary. This resulted in increasing the view factor to the anode. In other words, creating a more
direct line-of-sight between the two electrodes.
Figure 2.3: Schematic of Capillary Discharge Design V2.0
Several problems did arise with this design as well; most of which were associated with the cathode.
First was the minor issue of the seal between the cathode and tube end. A significant about of soot
was witnessed between the inner housing wall and the outer capillary tube. The second and more major
problem was from cathode erosion. In almost all cases the amount of mass lost from the cathode was
significantly higher, on the order of several times, than that of the polyethylene tubing. These problems,
26
as well as the effect of erosion on thruster preformance are discussed in Section 6.2. It was clear that
the cathode needed to be redesigned. A Tungsten cathode would offer resistance to both conventional
electrode erosions and against the exiting high temperature gas.
Capillary Discharge V2.1
With the design concepts proven, the redesigned V2.1 housing was machined from one piece of stainless
steel, instead of using standard tubing and fittings. An insertable tungsten anode was adopted and held in
place by a standard AN nut. The housing now consisted of a 1=2in stainless steel tube with a compression
fitting machined on one end, and an AN fitting on the other, as shown in Figure 2.4. It was discovered
that this cathode insert design provided an excellent way to seal the tube at the cathode end. The tube was
loaded into the housing, allowing for a small amount of material to protrude past the edge of the housing.
This extended material could then be melted, or made malleable, using a heat gun and flattened into a
disc or lip. This lip was then compressed between the housing and the insert to form a tight seal. With

Figure 10: Pressure effects on mass loss (4x50mm, 2500V)

As can be seen in Figure 9 both the Thrust and the Isp based on the total mass loss decreased
with greater background pressure. In fact the thrust decreased by 33% by just increasing the background
pressure a mere 16 torr. These results seem startling at first. However, just as with the shot repetition
tests, it is unclear exactly the effect the cathode erosion and exit diameter change has on the discharge.
By looking at the mass loss of the components, it is obvious that the cathode is losing way more mass
and tube. It is also important to note that after the 4 torr and 10 torr test we conducted the cathode erode
enough of the weld that held it in place and was expelled from the thruster. Therefore, because of the
varying test condition the inability to reduce the test parameters to just background pressure these results
are highly inconclusive. They do however highlight the cathode erosion problem and the need to solve
it.
New Design (Tungsten Cathode)
It is strongly believed that the erosion of the electrode is do to either one of, or a combination of,
2 main factors. First is arc attachment. There is often erosion patterns seen on electrodes do to the
attachment of the arc to the surface. This erosion however is usually worst on the anode then the
cathode. The other major cause of this erosion is the hot gas or plasma passing over the cathode surface.
The plasma temperature within the capillary reach temperate of 1 to 2 eV

Figure 11: Tungsten insert housing design

A new design was created with a tungsten insert cathode instead the stainless steel housing that
acted as the cathode previously. Another advantage of this design was that once the tube was loading in
to the housing the tube could be slightly extended past the housing and heated so as to form a lip that
Polyethylene
Tube
Stainless Steel housing and
cap
Tungsten
Cathode
insert

Tungsten
Anode
Figure 2.4: Schematic of Capillary Discharge Design V2.1
this new design, cathode errosion was more reasonable, the overall assembly was lightened so it could
be mounted on the thrust stand, and new liner tubes could be easily loaded. This V2.1 design was used
throughout the Paschen breakdown experiments.
The one issue that the V2.1 design did not solve was, the charring between the liner tubing the the
stainless steel housing. While it was clear that the seals at both the anode and the cathode held, the soot
between the capillary tub and the housing increased. Capillaries began breaking, shorting in as little as 3
or 4 shots. The reasons for this are discussed in Section 6.4.
Capillary Discharge V2.2
One final revision was made to the second design. The original inspiration for the revisit of this design
was to fix problems associated with full tube collapse. In a tube collapse, the capillary brakes open near
27
the middle and the arc attached to the housing wall. This caused pitting and damage that made it more
difficult to load capillary tubes, or extract them, without damage. The design philosophy behind the new
housing was to use standard stainless steel tube for the housing. In the event of a collapse the main body
of the housing could be replaced without having to re-machine the entire housing. Also, the simplicity
and versatility of this design permitted a variety of materials to be tried for housings. The materials that
were tested and their effects on the discharge are discussed in Section 6.6.
!
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!
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53)0+%!3,'%+&!13&!4-&550-&!$'!13&!%$5(3,-.&!@&++6!Q!RN9:!R,-)+$1&!3)05$'.!@$++!,+5)!/&!1&51E!@3$(3!
53)0+%!/&!13&!51-)'.&51!)13&-!13&'!51&&+6!Q!(&-,8$(!?,+08$',A!@$++!,+5)!/&!1&516!Q'%!*$',++2!$*!,++!&+5&!*,$+!
,!S0,-1P!3)05$'.!@$++!/&!1-$&%6!!
!
4)+2&132+&'&!10/&!
3)05$'.!10/&!
,')%&!
(,13)%&!$'5&-1!
Figure 2.5: Schematic of Capillary Discharge Design V2.2
While the tungsten cathode inserts did reduce the erosion at the anode, they did not eliminate it
entirely. The cathode itself still exhibited the same erosion pattern as seen previously with the stainless
steel electrode, only taking much longer to develop.
2.1.3 Capillary Design V3.0 with Coax Ignitor
The initial proof of concept tests for the coaxial ignitor, discussed in Section 1.7, were conducted using
the Design V2.2 and a 1=8 in copper and Teflon coaxial rod. The ignition circuit, developed by RE
Beverly III and Associates for spark gaps, suited this application quite well. The circuit consisted of a
trigger transformer and power supply, controlled by a pulser or trigger generator via a fiber optic cable.
The pulser itself was triggered by a TTL signal from the control computer.
The coaxial rod assembly was positioned near the exit plane of the capillary, as shown in Figure 2.6.
Several different ordination angles and positions were tried before the capillary would ignite under full
vacuum. While the capillary was successfully ignited a few times, it was sporadic and unpredictable. It
was believed that this problem was due to worn electrodes from the previous Paschen testing. Ignition in
hard vacuum proved more difficult than the previous methods, and the electrode geometry played a larger
28
!!"#$%&'()*#")+(+#
!
!
!"#$%&'(()'**+'"#,"-&%'.&/"#,'
!
!"#$%&'(0)'**+'"#,"-&%'-&/-'12324556'
"#$%&'(!)$*+!
,#-.+)".-+'+!)$*+!
/'#0+!
1/&'!0&%2"/3(+!,#4+3!%$,,-.!
2#/5&/-!&('&)+3!
2/)"#0+!&'%+3)!
Figure 2.6: Schematic of Capillary Discharge Design V3.0
role. It is therefore not surprising that the short 4cm capillaries ignited more easily under this method
and the method in Section 2.1.4, than the 10cm capillaries. Because the relative difficulty of machining
tungsten, it was far easier to make completely new housings adapted to electrode geometry than to make
new electrodes. Therefore, it wasn’t until the set of electrodes for Design four were completed that the
coaxial ignitor could be tested.
The coaxial ignitor was only used for a small number of geometries and power levels, to prove that
the discharge could be started by either a spark or electric field disturbance. The ignition method of using
a spark igniter was designed into an internal section of the housing, known as our 3-electode ignition
system or 3EIS.
2.1.4 Capillary Design V4.0 with 3-Electrode Ignitor
The 3 electrode system contains a third high voltage spark electrode that creates a field disturbance to
start the capillary discharge, similar to the design used by Kaganovich[53]. The high voltage electrode is
placed behind the cathode (between the anode and cathode) separated by several mm of ignition material,
which is made out of the same material as the capillary itself. The ignition electrode was placed at that
location for several reasons. First it was anticipated that material (ions and electrons) emitted from the
ignition material surface would be caught between the anode and cathode, making ignition easier. The
second reason was that cathode erosion was still a problem, and a slight cone angle was machined onto the
cathode. While the cathode erosion was much less with tungsten, the same pattern was seen as with the
29
stainless steel cathode used in Design 2. As discussed in section 6.2, figure 6.4 indicated that the erosion
pattern tended to expand the exit of the cathode to a certain diameter. It was believed that by adding a
conical cathode, erosion would be reduced even further. 4 different cathodes were originally machined
with 0

, 5

, 10

, and 15

half angle, However only the 10

was used during these ignition tests.
Design V4.0 also employed many capillary discharge design lessons learned from all previous designs
(V1.0-V3.0). The anode end was sealed with a compression fitting as before. The housing was machined
from aluminum to add structural support to the polyethylene capillary, and to keep the device light so the
scale could resolve the mass loss. Material was also removed from the middle section of the housing for
the same reason. The old cathode end was replaced by a flange like system. This allowed for a larger
internal volume in which to place the ignition electrode with proper electrical insulation. The same lip
method was employed in this design. A set of 12 bolts supplied the compression needed to seal the
capillary, as shown in Figure 2.7.
Distribution A: Approved for Public release; distribution unlimited 22
Future work
Background Conclusions Results Diagnostics Introduction
Housing
Cathode
Ignition
Electrode
Ignition
Material
Tube
Anode
•! 3 Electrode ignition System
•! Energy deposition study
•! Propellant feed mechanism
Figure 2.7: Schematic of Capillary Discharge Design V4.0
The original ignitor housing was made from acrylic. This setup fired a couple of times, but the
materials dielectric strength was high enough and eventually arcing occurred through the material between
the ignition electrode and the bolts. Nylon bolts were used to secure the cathode and subsequent seals.
While this did stop the arcing problem it did not apply enough compression to seal the device, especially at
higher powers and pressures. The ignitor housing was redesigned with a large diameter hole pattern which
allowed for more material between the ignition electrode and the bolts. A different material with a higher
dielectric strength was also used, PolyChloroTriFluoroEthylene (PCTFE) called Kel-F
R
. PCTFE offered
30
a unique combination of physical and mechanical properties: nonflammability, chemical resistance, near
zero moisture absorption, and excellent electrical properties. It is also easy to machine and holds excellent
tolerances that are needed in the ignitor housing.
In this design the ignition electrode and the cathode were made out of 1:5% lanthinated tungsten,
which material has excellent electrical and thermal properties, but it is very brittle. The 1=16 in thick
ignition electrode would crack under compression, espeically if the lip that was used to seal the capillary
to the electrode was uneven. Several of the tungsten ignition electrodes were ruined during the first half
of the test matrix before the material was changed to stainless steel. While the mass loss of the tungsten
electrode was less, it proved too brittle. Stainless steel offered much better mechanical properties and
mass loss due to erosion was still only a few percent of the the total mass loss.
Tests began with 4cm capillaries and progressed to longer capillaries. For the final design the capil-
lary was operated reliably and repeatably at shorter capillary lengths. However, at longer capillary lengths
of 8cm and 10cm, ignition was not as reliable. The cause was most likely the same reason that caused
the external coaxial ignitor faults. It is a combination of; poor view factors between the anode and cath-
ode, which only gets worse as the cathode wears, and additionally the absence of conductive material that
occurs between the anode and cathode. As the capillary gets longer, it becomes ever more difficult to
generate a conductive path down the capillary, making ignition more difficult.
2.2 Circuit
Typical capillary discharge operate with both simple LRC circuits and more complicated pulse forming
networks (PFNs). For the present studies a simple LRC circuit was chosen, which allowed the circuit
parameters to be easily varied over a wide range, and resulted in simpler and more accurate compar-
isons with performance models. The capacitor bank assembled for this work consists of four 0:5 mF
capacitors
1
. Each capacitor has a maximum current rating of 100kA and a maximum voltage rating of
10 kV . The capacitors can be arranged in different configurations to achieve the required current and
voltage. Arranging all four capacitors in parallel provides a total capacitance of 2mF . The constant cur-
rent capacitor charging power supply was limited to 6000V , yielding a maximum useable pulse energy
of 36kJ and a maximum peak current of 400kA. Up to four 10H (nominal) inductors from Cortec
Enterprises were also added to control the responsiveness of the circuit.
1
General Atomic capacitors, model 32259
31
2.2.1 Switches
A circuit element that is effectively neglected in capillary discharge modeling, but has proven very impor-
tant in capillary discharge experiments, is the control switch. The switch can; input noise into the dis-
charge pulse, limit the maximum current for the discharge, limit the total lifetime of the system, and affect
the shape of the current pulse. Several different control switches were tested and the relative merits of
each are described below.
Insulated-Gate Bipolar Transistor (IGBT)
IGBTs are solid-state semiconductor switching devices that have been designed for industrial applications
such as air-conditioners and electric vehicles. They are noted for their high efficiency and can handle
relatively high currents and voltages, but are presently unable to handle the high peak current and voltage
(10
0
s of kA at up to 6 kV ) that can be encountered while testing capillary discharges. A Mitsubishi
2
IGBT was used during lower voltage capillary discharge experiments. IGBT peak current and voltage
specifications are steadily increasing, indicating that they may be able to fulfill the capillary discharge
switching role within the next decade. One of the benefits of IGBTs is the relative ease of operation.
IGBTs are voltage controlled latching devices that are turned on by simply applying the required voltage
to the gate. They stay latched open until the discharge itself is extinguished.
Spark Gap
The spark gap is a plasma switch that has been used in high-power applications for decades. While
simple in design and concept they have proven to be more difficult to set up and operate. A spark gap
switched circuit was tested for capillary discharges with capacitor voltages ranging from 2kV to 4kV .
The particular spark gap used during the tests was from Perkin-Elmer. The spark gap required a 20 +kV
spike to trigger the switch. They also have a minimum switching voltage which, for the specific switch
used in this study, was 2kV . Spark gaps can handle large instantaneous power loads, but are also greatly
limited in the total charge per pulse. The spark gap also introduced a large voltage spike in the main
capillary discharge which, caused several problems when trying to reach higher voltages.
2
Model number CM1200HC-66H
32
Silicon-controlled Rectifier (SCR or Thyristor)
A thyrister is a solid-state device similar to an IGBT. It has the added bonus of being unidirectional, much
like a diode, and capable of handling larger peak power levels. The thyristors currently installed in the
experimental setup are from West code
3
. It was possible to find commercially available driver boards for
thyristors that are designed to produce the fastest switching time. The thryristor currently installed in the
setup can switch the entire voltage range from 0 4500V in and has a maximum peak current of 30kA.
This allowed the full range of discharge tests to be conducted with a single switch. Also, unlike the spark
gap, there is no high-voltage trigger to cause voltage spikes at higher powers.
2.3 Facilities
Two separate facilities were used during capillary discharge testing. For the wire explosion tests, which
were conducted at atmospheric pressure, a cylindrical steel chamber was set up vertically to house the
discharge device. The device itself was mounted to the top flange and shot downward into the cylinder.
On the bottom flange a port was opened to an exhausted line that removed vapors from the chamber after
firing. There were 4 rectangular view ports on the side of the cylinder for optical access. The chamber
was not vacuum sealable, but did allow for a safe environment for testing. It also reduced the noise and
light produced by the discharge.
The second test facility used in the capillary discharge tests was a full vacuum chamber, shown in
Figure 2.8. This chamber had a vertical section similar to the atmospheric test facility. It also had a
horizontal section to house the thrust stand mentioned in Section 3.4.2. The chamber was constructed
out of a stainless steel ISO 400 4-way cross, and two ISO 400 Spools. An ISO 400 Tee section was later
added so that a 3500l=s diffusion pump could be added. The pump was never used because the 1000l=s
Varian 1000 turbomolecular pump provided adequate pumping. The Tee section did add more horizontal
length to the chamber, therefore allowing more space to manipulate the thrust stand and align it with
optical view ports.
The vacuum chamber’s turbo molecular and backing pump allowed it to reach pressures of mid
10
5
torr in several of hours. This pump down time was drastically increased as the inside of the
chamber became coated with carbon soot from the discharge. The carbon itself did not ultimately affect
3
Model number UK R3708FC45V
33












































Figure 2.8: Picture of Capillary Discharge Vacuum Chamber
34
the chamber pressure, but would adsorb water molecules readily and continuously desorb the water dur-
ing pumping. This carbon layer proved exceedingly difficult to clean, which would have to been done
on a regular based. To keep outgassing to a minimum, the chamber was always kept at a low pressure
to stop water molecules from adsorbing to the carbon. By only opening the chamber briefly to swap out
capillaries, pump down times were kept to a minimum.
The Chamber was equipped with three Baratron pressure transducers to measure the pressure from
atmospheric pressure down to 1mtorr. A hot cathode ion gauge was used to measure pressures below
1mtorr. In addition to these standard pressure gauges, the chamber also contained a residual gas analyzer
(RGA). This was useful for determining the partial pressures within the chamber, and whether or not
pumping problems were due to leaks, outgassing, or thruster exhaust.
35
Chapter 3
Diagnostics
A complete suite of high temporal resolution diagnostics has been assembled and validated to provide
a detailed understanding of the capillary discharge plasma, as well as time resolved comparisons with
capillary discharge model results. Both experimental control through synchronized triggering and data
acquisition functions are handled using a PXI based National Instruments data acquisition system (DAQ).
The PXI system was chosen primarily because of its high speed with parallel channels, allowing 2:5
Msamples/s on each of the 16 analog input channels. The PXI system is also equipped with an 8 channel
analog output card for control purposes. The fiber optic data transfer option was chosen so that the
control box is isolated from the experimental operator and also to reduce the signal noise during data
transfer. Since the PXI is a stand-alone system, it is able take advantage of a Labview Real-Time module
if feedback control is ever desired. The data collected though this system are current, voltage, and force
measurements.
3.1 Current
Commercial Rogowski coils
1
were used to measure current up to 12kA at various points in the capillary
discharge circuit. The coils are connected to an integrator box that outputs the instantaneous current
passing through the coil. The response time of the coils and integrator is shorter than that of the data
acquisition system. The output sensitivity is 0:5mV=A, it is calibrated to within0:2% and can typically
vary with conductor position by1:0%. These current probes are placed throughout the electrical circuit
and are noninvasive. The inductor loop simply needs to be placed around the wire in which the current
is to be read. Typically a coil was placed on the capacitor bus bar to measure the total current discharged
and a second was placed directly before the capillary. Probes were also used within the circuit to test
switch properties and the effects of parallel and series resistors.
1
Powertek model CWT60B
36
3.2 Voltage
A high-voltage probe
2
was used to measure the voltage relative to ground at various points in the circuit.
The probe could read a maximum of 12kV with an accuracy of 0:1% for DC applications. The standard
divider ratio of 1000 : 1 allowed the probe output to be directly connected to the National Instruments
DAQ. Currently two probes are employed, one reading the voltage on the capacitor bank at all times
and the other reading the voltage at the anode. Because of the large current, even with small resistances
in grounding lines, there can still be a measurable voltage drop between the cathode and earth ground.
Future experiments could also measure the cathode voltage relative to ground to obtain a more accurate
measurement of the voltage difference across the capillary discharge. These measurements were not
carried out in this work.
3.3 Mass Loss
The mass loss from the capillary wall is measured using a digital scale
3
with a readability of 0:1mg. The
individual masses of the tubes, anode, cathode, and ignition components (when present) are all weighed
separately and then weighed again after assembly. This technique, because of its redundant measure-
ments, also gives an indication of the measurement accuracy. After a set of 5 fires, all the components
are weighed again (both together and separately). By weighing the components together and separately
it is possible to determine the mass loss of the electrode as well as the material ablated form the capillary
wall. For calculating of specific impulse and efficiency the total mass loss of the device is used. Mass loss
measurements for the wire ignited capillaries, Design V1.0 and V1.1, is also take. No useful information
is determined from these measurements and they are not presented in this work
3.4 Force Measurements
Measuring the thruster performance characteristics of a capillary discharge presents many unique chal-
lenges. Because of its short pulse length, force is only output for several hundreds of microseconds. In
addition, during the discharge time there are high electric and magnetic fields that can affect and dis-
turb sensitive instrumentation, as will be shown in Section 3.4.1. PPTs use a solid propellant, making
2
North Star High V oltage model PVM-10
3
Sartorius CP224S
37
it impossible to use mass flow meters to measure propellant use and, therefore, obtain specific impulse.
Conventionally, PPT’s are weighed before and after testing to obtain mass loss. Usually PPT mass loss is
averaged over many discharges, 100’s or 1000’s of discharges. This method of weighing the solid propel-
lent before and after operation can also raises issues of handling, contamination, oxidation and absorption
which may complicate mass measurements. In this work two methods for obtaining impulse, and subse-
quent performance parameters, were attempted; a piezoelectric method, and at thrust stand method. The
problems and limitation of each method are discussed in the following sections.
3.4.1 Piezoelectric Force Sensors
Force measurements were originally planned to be made with 3 PCB Dynamic Force Sensors
4
connected
to a Sensor Signal Conditioner
5
. The backing plate of the thruster housing is attached to force transfer rods
as shown in Figure 3.1. These transfer rods allow the sensor to be preloaded with the required 100ftlb.
Plastic or rubber washers are used on both sides of the ring style sensor to protect them from the large
voltages and currents used in the experiment. Because the devices are piezoelectric devices, there was
some concern that the electromagnetic field that passed from the main power lead could affect the device,
especially since they are not strongly tied to ground. Tests were conducted with a straight copper feed
through and a high power resistor. This simulated the power for the discharge without creating any force
allowing noise levels and feed back to be observed in the sensor. These original test did not show any
problem with sensor interference. However, upon firing of the actual thruster, a large level of noise was
observed in the piezoelectric sensor data. Figure 3.2 shows a series of 10 different force measuremensts
using the setup shown in Figure 3.1. Throughout the 10 shots, the damping of the thruster assembly was
modified by using different insulating washers. The only change that made a significant difference was
the use of rubber washer adjacent to the force sensors. This was employed for the second half of the
firings (5-10) and it is clear that at the tail end of the Force graph the vibration is significantly less.
Despite the original optimistic outcome of these measurements the system proved to be problematic.
The noise during the wire explosion created a large negative force that has been cut off in Figure 3.2. In
addition the noise or vibrations after the discharge were much larger than the force from the discharge
itself. This was lessened by the rubber washers, but was still very significant. During testing, a number
4
Model 201B03 ICP R
5
Model 484B06 Line-Powered ICP R
38
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of sensors were damaged and stopped working. They were replaced and during that time the thruster
design was updated. When the system was put back together for testing again, it did not seem to read
properly. When the sensors were tested individually, and as a system, using a hammer they seemed to be
operating properly. However, the sensors did not seem to pick up any usable force data from the capillary.
Eventually, after much trouble shooting, the desired piezoelectric system to measure time resolved force
was abandoned for a simpler, more proven, diagnostic technique.
3.4.2 Thrust Stand
To avoid many of the issues associated with a piezoelectric force measurement system, a more conven-
tional thrust stand was adopted. A number of thrust stands for electric propulsion devices, and more
particularly PPTs, have been designed[105, 34, 25, 39]. In previous work done by Burton [13], a linear
thrust stand was used to measure his PET thruster performance. By measuring the recoil velocity and
knowing the recoil mass, he could calculate the impulse bit. The thruster was “freely suspended” by
using a linear bearing on a horizontal steel shaft, making sure the center of mass was on axis and directly
over the bearing to prevent off axis forces or binding. Current was feed through flexible strips of copper
mesh. The thruster was sealed to the vacuum environment using a flexible rubber diaphragm to separate
the electric connections and position sensors outside at atmospheric pressures. A coil spring was used to
counter balance the load from the pressure difference across the sealing diaphragm. The recoil velocity
was measured using a non-contatct inductive RF transducer. Calibration was carried out using a swinging
pendulum and laser system to measure striking and rebounding velocities. While Burton obtained results
39
2500 2550 2600 2650 2700 2750 2800 2850 2900 2950 3000
−20
0
20
40
60
80
100
120
140
Time (μ s)
Force (N)

Test 1
Test 2
Test 3
Test 4
Test 5
Test 6
Test 7
Test 8
Test 9
Figure 3.2: Data from Piezoelectric Force Sensors
from his stand, it was felt that improvements could be made. Burtons design had many contacts with the
surrounding environment, and was not “freely suspended”, which could influence impulse measurements.
Instead of using a linear stand, it was decided to use a torsion type system to measure the total impulse
of the discharge similar to the design described in [55], which is the result of a half-decade of development
at USC. While this system can not resolve time dependent thrust levels, as with a piezoelectric system, it
did offer many advantages. Because of the relatively high impulse levels, several new design challenges
were addressed, such as higher moments of inertia and stiffer spring constants.
The thrust stand used for measuring capillary discharge impulses is simply a damped torsional force
balance. The stand rotation motion can be described by an under-damped second order equation[55]
I

(t) +C
_
(t) +K (t) =M (t) (3.1)
40
whereI is the moment of inertia,C is the damping coefficient, andK is the spring constant.M(t) it it the
forcing moment acting upon the stand. Using a small angle approximation, sin = and the geometric
relation sin =
X
R
, it is possible to rewrite 3.1 as a linear question.
I

X (t)
R
s
+C
_
X (t)
R
s
+K
X (t)
R
s
=F
c
(t)R
c
(3.2)
whereX(t) is the linear displacement as a function of time,R
s
is the distance from the sensor to the pivot
point, F
c
(t) is the calibration force acting on a distanceR
c
from the pivot. These dimension are more
clearly illustrated in Figure 3.3, which shows the a simplified schematic of the thrust stand.
R
s
R
c
F
c
LVDT

pivot

!
c
x

Distribution A: Approved for Public release; distribution unlimited 9
Thrust Stand Concept
Background Conclusions Results Diagnostics Introduction
Figure 3.3: Schematic of Capillary Discharge Thrust Stand
Because the stand operated on the principles of low frequency oscillations the important infomation
of the stand occurs on a large time scale compared to that of the discharge. Any disturbance from the
discharge itself can most likely be disregarded. In addition, by mounting the thrust stand so that it defelects
in the horizontal plane, it is possible to simultaneously measure both total impulse and mass loss, as done
in Ref. [55]. This is done by examining both the dynamic and static characteristics of the stand. Impulse
measurements can be inferred from the range of the dynamic motion of the stand as shown in Figure 3.4.
The Range is the maximum distance the stand deflects in the thrust plane. By precisely measuring the
displacement caused by an impulse event, the total impulse can be determined based on the calibration
techniques discussed later in this section. It is worthwhile to note that the typically range is measured as
41
0 10 20 30 40 50 60 70 80 90 100
−10
−8
−6
−4
−2
0
2
4
6
8
10
Time (s)
Defelction (V)
Range
Figure 3.4: Simulated LVDT reading for expected impulse from an operational capillary discharge
0 20 40 60 80 100 120 140 160 180 200
−0.01
−0.008
−0.006
−0.004
−0.002
0
0.002
0.004
0.006
0.008
0.01
Time (s)
Defelction (V)
Offset
Figure 3.5: Simulated LVDT reading for expected mass loss from an operational capillary discharge
42
the distance between the maximum and minimum of the first oscillation. However, it is possible to use
subsequent peaks and values, if also done in the calibration. The static or steady state deflection stand
can reveal the mass loss of the device. Because the thrust stand is mounted in the horizontal plane, like a
balance scale, when mass is lost on one side, the stand should be offset to a different position. Figure 3.5
shows the same data as Figure 3.4, only zoomed in on a smaller Y-scale. The stand clearly has different
zero positions before and after the thruster fires. It is important to keep in mind that the mass loss is quick
and occurring at the same time as the impulse. However, the capillary discharge, as well as most thruster
systems with highI
sp
’s, the force due to mass loss is very small compared to the motion caused by the
thrust, therefore, the error caused to the impulse measurement should be very small (much less than 1%
in our case).
The thrust stand itself consists of 3 main components. The arm, whose mass created the majority of
the moment of inertia, I, the flexures which provide the restoring force or spring constant, K, and the
electromagnetic damping system, which uses eddy current effects to create a damping force, C. These
components are show in Figure 3.6. In addition to the main components of the stand itself, there are

American Institute of Aeronautics and Astronautics
Distribution A: Approved for public release; distribution unlimited.

4
to the stand and defines the useful range of the stand’s accuracy. The major components a thrust stand can be seen
in Figure 3.

Figure 3 Major thrust stand components.
Special consideration must be given to a choice in displacement sensors since the CD involves strong
electromagnetic fields during the discharge. Such fields will interfere with any locally mounted electronic force
sensors, such as piezo-based load cells. This interference is only a present during the thruster firing, for which the
thrust stand has an advantage. The pertinent measurement of the thrust stand’s motion required for an impulse
determination is made long after the thruster firing. Thus, for sensors which recover from the EMI sufficiently
quick, the effect from the interference is negligible. Linear variable differential transformers (LVDTs) have been
successfully implemented on a previous thrust stand [7]. These sensors have an advertised repeatability of ! 0.01%.
The useful range and accuracy of the detector, for a given thrust stand configuration, directly sets the maximum
impulse and minimum mass loss able to be resolved by the thrust stand.

Figure 4 Thrust stand deflection range versus imparted impulse from impact hammer (R
2
=0.9993)
Figure 3.6: Picture of the Capillary Discharge Thrust Stand
several other components that are required in order to make thrust measurements. The thruster itself,
43
which is described in section 2.1, is usually placed at the end of one of the arms. However, it can be
placed anywhere along the arm so long as it is oriented in the vertical direction, in order to oscillate the
stand. The other two components need to make thrust measurements and the displacement sensor and the
calibration system.
Displacement Measurements
Distance measurements for this kind of thrust stand are typically made with a linear variable differential
transformer, LVDT. A model of the device is shown in Figure 3.7. The primary coil (A) is the main
variabledifferentialtransformer,otherwiseknownasanLVDT.Amodelofthedeviceis
showninFigure3.4,wherethemiddlecoil(A)isthedrivingcoilandtheoutercoils(B)
are the sensing coils. During operation, the driving coil creates an alternating magnetic
field which is passed through the movable metallic core to the sensing coils. A current
isinducedinthesensingcoils,andthedifferentialvoltageproducedvarieslinearlywith
the position of the core. With the position accounted for, it then becomes necessary to
accurately know the spring constant of the test stand.

Figure 3.4: Cutaway view of a LVDT (courtesy of [2])
Measurement of the spring constant is necessarily accomplished by calibration, as
even slight changes in its value can have dramatic effects on the measured force. In
practice it has been found that the manufacturers stated spring constants are not nearly
accurate enough for scientific work, as even a 5% difference from specification creates
a5% error in the experimental data. The procedure for calibration is relatively straight-
forwardandrequiresonlythatseveralknownforcesbeappliedtothethruststandwhile
simultaneous measurements of the total deflection are made. In this set of experiments
a pair of electrostatic combs[51] were used to apply these forces very accurately. There
are several advantages to using electrostatic combs, the primary one being that force is
applied without contacting the thrust stand. This allows for in situ calibration without
34
Figure 3.7: Cut away drawing of an LVDT
driving coil and the secondary outer coils (B) are the sensing coils. A ferromagnetic core slides through
the coils along the center axes. The device operates by applying an alternating current through the primary
coil, usually between 1 to 10kHz. This causes a voltage to be induced in the secondary coils. As the
ferromagnetic core moves it changes the mutual inductance of the system and the induced voltage changes
in the secondary coil. This change in voltage can be correlated to the position.
Interferometers offer another good option for determining the displacement of the thrust stand. A
commercial off-the-shelf Michelson interferometer
6
was also tested with the thrust stand. This type of
interferometer, shown in Figure 3.8 uses the principle of superposition of light to determine distance. The
6
SIOS, SP-Series Plane-Mirror miniature interferomter, Model SP 120
44
Figure 3.8: Schematic of the light path through a Michelson interferometer
device operates by splitting a coherent light source into two separate paths. One path takes the light to
a stationary mirror and back to a collector. The other part of the light travels to a mirror that is moving.
when the light is recombined there is a phase difference between them. Waves that are in phase will
undergo constructive interference while waves that are out of phase will undergo destructive interference.
When one mirror is moving, the light moves through these patterns of interference, which creates a fringe
pattern of bright spots. The detector can be used to determine the change in this pattern and count the
fringes as they pass. Each fringe can account for a known distance of movement corresponding to the
wavelength of light, and a change in distance can be determined.
These devices are very accurate and their speed is only limited by the rate at which the detector can
read. Also, because the interferometer is an optical device, it is free from electro magnetic interference
that might be caused by a plasma environment.
A comparison of an LVDT and interferometer were conducted using the calibration technique dis-
cussed in Section 3.4.2. A comparison plot of the two measurement sensors are plotted in Figure 3.9
While there is a discrepancy between these two techniques it is small. The reason for the discrepancy
is still unknown. When both device where used to measure the displacement on a linear displacement
stage, they both measured identical values. It was only on the torsional thrust stand that this discrepancy
was seem. However, both devices are very linear and would work well with the thrust stand. The actual
displacement is irrelevant. The only requirement is that the relative displacement is linear and repeatable.
45
1.5 2 2.5 3 3.5
x 10
−3
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13
Range (mm)
Impulse (mN)

LVDT
Interferometer
Figure 3.9: LVDT and Interferometer data for as standard impulse calibration with electrostatic fins
This is because of the calibration technic discussed in Section 3.4.2. The LVDT was used with the cap-
illary discharge thrust stand because of its long history with this system. The interferometer does offer
many advantages it was not used until it could be better understood and fully characterized.
Calibration
Small thrust stands have used a wide variety of calibration schemes. Conventionally, calibration of similar
stands have used hanging weights from a string-pulley system[103, 59]. These system can be clumsy
and show errors in the milli-Newton range. A method developed by Jamison [50] used a gas dynamic
calibration method which used results from direct simulation Monty Carlo (DSMC) numerical models
and analytical solutions for free molecular orifice flow. This method, while reliable and accurate, involve
messy oil baths and sophisticated flow and pressure controls. The oil baths are not only used as viscus
dampeners on these stands, but also act as a seal for feeding the pressurized gas to the that calibration
device. Because the capillary discharges have a large impulse and need to be calibrated for larger impulses
there may have been problems with these kinds of oil bath seals.
46
The calibration system chosen for the capillary discharge thrust stand was an electrostatic calibration
system based on techniques from Gamero-Casta˜ na[31]. In this work an electrostatic calibration technique
is described that utilizes two parallel plate electrodes separated by a gap to create force. This force is
given by
F
ESP
=
1
2
"
o

V
L

2
A
p
(3.3)
where"
o
is the permittivity of free space of the gap medium,V is the voltage difference applied between
the electrodes,L is the gap distance between electrodes, andA
p
is the area of the electrode. Equation 3.3
shows that the force is a function of 1=L
2
. This is problematic for a torsional thrust stands where one
electrode would be attached to the stand, and therefore moving. Because the force is inversely propor-
tional to the square of the gap distances even a small change in distance can greatly affect the calibration
force. For this reason an electrostatic comb system was used based on work by Johnson and Warne[52].
This system is based on interlocking charged combs. When the gap distance is equal to the width of the
comb the applied force can be described by
F
ESC
= 2N"
o
V
2

1:0245
g
x
o

(3.4)
whereN is the number of comb pairs,g is half the gap distance andx
o
is the engagement of the combs.
Notice that as the engagement became larger then the gap distance the force asymptotes near 2N"
o
V
2
. A
more detailed account of these electrostatic comb calibration systems and their accuracies are discussed
by Selden[82].
Electrostatic combs can be used to produce very small forces. The system used by Selden[82] was
capable of only applying forces on the order of hundreds of micro-Newtons with reasonable voltages.
The capillary discharge can create large forces that only last for a brief period of time, hundreds of micro-
seconds. The total impulse has been estimated to be on the order of tens of milli-Newtons.
When creating large impulse electrostaticly there are limits in both voltage and pulse length. The
voltage limit can be determined by what can be applied in vacuum without arcing. This was safely
estimated to be about 3000V . The pulse time is limited to 1=10 the natural period of the stand[26]. Pulse
times greater than this effect the stand oscillation degrading the measurements. It has also been shown
that when measuring total impulse bits the force and pulse time do not matter so long as the 1=10 limit is
obeyed. In other words, we do not need to create a 100N force for 100s in order to create the 10mNs
47
need to calibrate in the range of our thruster. Instead it was possible to to create a 100 mN force for
100ms, provided the natural frequency of the stand was greater than 1s.
In order to achieve the impulses needed multiple sets of larger combs were designed and fabricated.
The number of comb pairs, N, was increased from 5 to 10 and the typical comb cross section of 1mm by
1mm was increased to 1mm by 20mm, which created more of a fin design. Finally, 3 sets were made
to attach on a single mount. By making these geometric changes it was possible to output a greater force
without violating the linear attraction force as discovered by Johnson and Warne[52]. Each individual
set of fins was precisely calibrated on a micro balance. The data for one set of scale data is shown in
Figure 3.10. It shows that the attractive force is very linear as a function of voltage squared. It is also
0 2 4 6 8 10 12
x 10
5
0
0.5
1
1.5
2
2.5
3
x 10
−3
Voltage Squared (V
2
)
Force (N)

0mm
0.5mm
1mm
1.5mm
2mm
2.5mm
3mm
3.5mm
4mm
Figure 3.10: Electrostatic Fin Validation Data
worth while to notice how the force changes with a function of engagement distance. As the engagement
becomes larger then the gap distance the engagement factor does not affect the force produced as pre-
dicted. All calibrations are done with 4mm engagement which allow for 2mm oscillations while still
reamaining in the constant force range.
48
A Piezo-electric hammer was also tested as a calibration system, but it was not implemented in our test
conducted in Chapters 5.2 - 5.5. The electrostatic fin system could create impulse up to about 10mNs.
While this is within the range of impulses created by the capillary discharge, it did not span the entire
range of operation. To fully calibrate the thrust stand the upper impulse range a piezo-electric hammer
could have been used
7
, which would allow calibraiton in the 10
4
to 10
1
Ns range. Figure 3.11 shows
a comparison of the 2 calibration techniques. In this comparison plot it can be seen that the piezoelectric
1 2 3 4 5 6 7
x 10
−3
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
Range (mm)
Impulse (mN)

Hammer
ES Fins
Figure 3.11: Hammer and ES Fin data collected utilizing the LVDT
hammer and electro-static fins are in close agreement. The hammer was able to impart impulse in both
in the same range and well above the range of the ES Fins. Even so, when the ES fin calibration line is
extended up to the higher ranges there is still good agreement.
The PE Hammer was not used for calibration in the test data presented here. While initial results
looked promising, the time to develop and implement a full calibration system to work in vacuum was
not trivial. The ES fin system did an excellent job calibrating in the low impulse ranges, and could be
extrapolated to higher impulses without introducing significant error.
7
PCB Peizotronics Impact Hammer, Model 086C01
49
Thrust Stand Optimization
The linear range and accuracy of the detector directly sets the maximum impulse and minimum mass loss
that can be resolved by the thrust stand[63]. The static or steady state condition that occurs both before
and after the capillary discharge is only a function of the mass lost during the discharge and the spring
constant,K, of the stand. The stiffer the flexures the less the stand will deflect. This deflection must be
enough to to be resolved by the LVDT and ancillary data acquisition system. The linear range determines
how far the stand can deflect and still remain within the usable range of the LVDT. The dynamic distance
the stand moves from the impulse applied by the discharge is a function of bothK and the moment of
inertia,I. It is a balance of these to constants that allows for the specific impulse to be made.
A simple Matlab code
8
was used to model the thrust stand motion. A first iteration of the thrust stand
was designed and built in order to validate this code. Once the code was verified the stand parameter could
be varied to see how the stand fundamental characteristic would change. Figure 3.12 shows how much
the stand would deflect for an expected mass loss of 12mg[75]. The plot shows that for better resolution
0 5 10 15 20 25 30 35 40 45 50
10
−3
10
−2
10
−1
10
0
K (Nm/rad)
Displacement (V)
Figure 3.12: Thrust Stand Deflection vs.K
8
Code written by T.C. Lilly
50
measurements, larger displacements can be obtained using smaller values of spring constant. With a 16-
bit DAQ, it is possible to measure less than amV on a5 to +5V scale as seen by the following analog
to digital conversion calculation.
10V
2
16
= 0:00015V (3.5)
Therefore it is possible to resolve the mass loss using any of these spring constant flexures shown in
Figure 3.12.
As mentioned earlier, the stand’s range is a function of a both theI andK. Figure 3.13 shows the
stand’s deflection as a function of moment of inertia for various K value flexures that are available from
the manufacturer
9
. The deflection shown here is based on the impulse predicted from Pekker[75]. The
range decreases with increasing spring constant and moment of inertia. Because the moment of inertia
scales logarithmically, it is desirable to use higher spring constants. This however could affect the limit
of mass loss measurements. This ultimately leads to choosing aK value that balances the steady state
sensitivity needed to resolve mass loss and the dynamic restoring force needed to limit the range from the
discharge’s impulse. In the end the stand was modified to handle the entire range of impulse and mass
loss. The stiffest flexures were used and the moment of inertia greatly increased to keep the stand from
deflecting out of range. This was done by attaching 5kg to the end of each arm. The damping plate was
also changed to a copper plate which provided a large eddy current dampening force needed to settle the
high inertial stand. The modifications made to the thrust stand are reflected in the coefficients shown in
Table 3.1. With this modifications the stand would oscillate about8V at maximum impulse, which is
Thrust Stand 1
st
Iteration Optimized
K [Nm=rad] 41:75 36:22
C [Nms=rad] 0:191 0:428
I [Nms
2
=rad] 0:245 1:988
Table 3.1: Coeffecients for 1st interation & optimized CD thrust stand
within the LVDT’s10V range. It would also cause the stand to have a steady state deflection of 2mV ,
which would be well resolved with the 16-bit DAQ.
9
Riverhawk Company’s Flexural Pivot Bearings
51
10
0
10
1
10
1
10
2
I (Nms
2
/rad)
Displacement (V)

K=0.6474
K=2.9002
K=5.1529
K=20.91
K=23.162
K=41.172
Figure 3.13: Thrust stand range vs.I for multipleK values
Thrust Stand Offset Problem
The thrust stand was set up in the horizontal position in order to take both impulse and mass loss mea-
surements. However, the thrust stand failed to take accurate mass measurements despite the prediction of
the model discuses in Section 3.4.2. While the deflection of the stand should have been readable by the
LVDT and DAQ, much larger and more sporadic mass loss measurements were observed. The deflection
the stand was experiencing would equate to 100’s ofmg, much higher than predicted, measured on the
scales, or is even reasonably possible. In fact the stand even showed a gain in mass indicating that the
problem was a measurement error. A trend was quickly noticed in this error that is shown in Figure 3.14.
This figure shows the mass loss of 10 consecutive capillary discharges, or rather 2 sets of 5. The first
set of firings was conducted in the afternoon, one right after the other, approximately 10 minutes apart.
The experimental setup was left intact and pumped down over night. In the morning, under the same
condition, on the same capillary, the second set was taken. The plot shows a trend towards the real mass
loss of about 10mg.
52
0 2 4 6 8 10 12
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Trace Number
Mass Loss (g)
Figure 3.14: Mass loss as measured by thrust stand displacement for 10 consecutive shots
There is speculation into what might be causing this effect; everything from thermal drift of the
sensor to loose flexures. The two most likely culprits are the high power wiring and an electronic jolt
to the LVDT. The cable that runs power to the stand carries a very large current for a very short period
of time. This high
di
dt
can cause magnetic fields that might affect the wire position or stiffness; just like
in the case of an inductor constrict around the center. It is possible that the wire at sharp corners might
create fields and forces that could move the wire location. A number of different wires, both stranded
and unstranded, were tested, as well as the wire location. Different mounting brackets were used to either
hold the wire more tightly or looser, as it weaved its way form the voltage feedthrough to thruster. While
these did seem to affect the measurement, it was not conclusive, and didn’t eliminate the problem.
The other possible cause for this phenomenon is with the LVDT Sensor itself. There has always been
an unexplained drift with this sensor. The effect is small, fairly linear, and can be calibrated out for long
displacement traces. It was thought that the plume from the discharge might be effecting the sensor,
causing some type of instantaneous drift. Tests were run using the sensor grounded and ungrounded,
and even with a Faraday type cage surrounding it to eliminate any effects from charged particles or
electromagnetic fields. Non of these modification effected the signal or zero offset problem. It was also
53
thought that the large power spike might effect the devices electronics. This can sometimes be seen in
the current traces when the rogowski coils will read zero current before the discharge switch is opened
and then after the current pulse, when the probe should be reading zero current, it is offset by a couple
of amps. The effect is very small and introduces very little error into measuring the large currents. But a
similar effect on the LVDT that attempts to resolvemV , this may be a problem.
The stand was never able to read in-situ mass loss and the measurement was taken using a scale before
and after fired to obtain an average mass loss for the firings. There is an ongoing effort to make individual
in-situI
sp
measurement per shot. A modified thrust stand adapted for supplying power directly though
the flexures eliminating the need for wires is being constructed. There has also been work to use an
interferometric displacement sensor instead of the LVDT. Since is an optical measurement technique it
should be free from electrical noise created by the discharge. This results will hopefully be shown in
future publication.
3.5 Optical Diagnostics
The plasma densities and temperatures routinely encountered in capillary discharges make them difficult
to investigate experimentally. Commonly used plasma probes such as Langmuir probes are not suited
to make plasma measurements for typical capillary discharge temperatures, pressures, and time scales.
Instead it was chosen to use Optical Emission Spectroscopy (OES), in which the light that is emitted
from the plasma is observed through a spectrometer and analyzed. The captured spectrum can either be
analyzed by spectral intensity or spectral shape. Accurate intensity measurements have been used on
these types of discharges[?], however this method involves very elaborate calibration schemes. For this
experimental work spectral line shape were examined to reveal information about plasma.
The capillary discharge is a pulsed device necessitating time resolved measurements. Within the
lifetime of the plasma there is an ignition process, a rapid heating process, a near quasi-steady state
discharge and finally an extinguishing period. It is necessary to take spectral measurements with sufficient
temporal resolution to resolve the critical features of the discharge. A minimum temporal resolution
of roughly 10 20s would be required to take more than ten spectral measurements in a nominally
200 400s discharge pulse. There is also a wide range of radiant intensities encountered during the
different phases of the discharge pulse. In order to achieve the required temporal resolution a Princeton
Instruments Pixis CCD camera (400B) was used to collect the separated light from a half meter Acton
spectrometer (SP500i). The CCD camera has the capability to run in kinetics mode. Kinetics mode is
54
method of binning and shifting the pixels of the CCD to allow rapid consecutive exposures. To do this the
collected light was transported in a 10m fiber optic cable illuminated only the uppermost portion of the
chip, while the rest of the chip sits in darkness. The illuminated section of the chip collects charge for a
specified amount of time before the charge is then shifted down into the dark part of the chip where it is
stored. When the chip is full, it is read off all at once. The chosen CCD chip has 400 vertical pixels. The
original setup was capable of illuminating a minimum of 10 pixels with a 100m fiber. This allowed a
maximum of 40 spectral measurements (39 usable, because the last could be over exposed) to be stored
on the CCD before it must be read. The time resolution is primarily a function of the shift speed or charge
transfer rate from pixel to pixel. If it takes 3s to transfer one pixel and each spectral measurement
consists of 10 pixels from light to dark, then the time resolution is 30s. The overall data collection
time for 40 spectra is 1:2ms. Figure 3.15 showns how kinetics works. The boxes represent super pixels,
27

The capillary discharge is a pulsed device necessitating time resolved measurements. Within the
lifetime of the plasma there is an ignition process, a rapid heating process, a near quasi-steady state
discharge and finally an extinguishing period. It is necessary to take spectral measurements with sufficient
temporal resolution to resolve the critical features of the discharge. A minimum temporal resolution of
roughly 10-20µs would be required to take more than ten spectral measurements in a nominally 200-400µs
discharge pulse. There is also a wide range of radiant intensities encountered during the different phases of
the discharge pulse. In order to achieve the required temporal resolution a Princeton Instruments Pixis
CCD camera (400B) was used to collect the separated light from a half meter Acton spectrometer (SP500i).
The CCD camera has the capability to run in kinetics mode. Kinetics mode is method of binning and
shifting the pixels of the CCD to allow for rapid consecutive exposures. To do this a 10µm fiber optic
cable illuminated only the uppermost portion of the chip, while the rest of the chip sits in darkness. The
illuminated section of the chip collects charge for a specified amount of time before the charge is then
shifted down into the dark part of the chip where it is stored. When the chip if full, it is read off all at once.
The chosen CCD chip has 400 vertical pixels. The original setup was capable of illuminating a minimum
of 10 pixels with a 100micron fiber. This allowed a maximum of 40 spectral measurements (39 usable,
because the last could be over exposed) to be stored on the CCD before it must be read. The time resolution
is primarily a function of the shift speed or charge transfer rate from pixel to pixel. If it takes 3 !s to
transfer one pixel and each spectral measurement consists of 10 pixels from light to dark, then the time
resolution is 30 !s. The overall data collection time for 40 spectra is 1.2ms.

Figure 11: Kinetics
Spectra 1

Spectra 2

Spectra 3

Spectra 4

Spectra 1

Spectra 2

Spectra 3

Spectra 1

Spectra 2

Spectra 3

Spectra 4

Spectra 5

Figure 3.15: Diagram of Kinetics Mode Operation
which in our case would be 10 pixels in height and 1 pixel in width (wavelength). The yellow area is
the region exposed to light. Charge builds up over the exposure time and is then shifted down the chip,
quickly filling it up.
The maximum shift speed of the Pixis CCD camera was advertised to be 3:2s. However, at that
speed the charge exchange efficiency (CEE) is very low and the data is completely lost and unreadable off
the chip. At 6:2s the data gets slightly corrupted as it is transferred down the chip. Charge bleeds over to
surrounding pixels and spectral peaks are broadened and distorted. The magnitude of the distortion can be
determined by taking spectral measurements of a light emitting diode (LED). Early spectra undergo much
more distortion than later ones because they travel farther on the chip, undergoing more charge exchanges.
The fastest transfer speed with acceptable distortion for the factory calibrated setup is 9:2s. By keeping
the charge per pixel low by using heavy filtering of incoming light, the kinetics mode can be run with
little degradation in signal. Collaborative work with Princeton Instruments carried out to optimize the
55
camera operational voltages that would allow quicker charge transfer with better CEE without sacrificing
well depth (the total amount of charge each pixel can hold). After several modification 3:2 s were
successfully achieved
It is also important to make the illuminated spot as small as possible on the CCD chip. A custom
fiber optic system was setup in order to accomplish this. A custom system was created by Oz Optics.
Light is captured through a collimator assembly which is designed to collect a 100m spot 25cm away.
This allows good spectral resolution from outside the chamber. The collimator focuses the light into a
10m silicon fiber that carries the light throughout our optical system. The light travels though a filter
housing assembly in which various 0:5in neutral density filters can be used to reduce the light intensity.
Light is then carried to a 3-way beam splitter that divides the light up equally into 3rds. One of those 3
leads takes the light into our spectrometer and CCD. The other 2 leads are available for future diagnostic
equipment. Another nice feature of the optical setup is an additional beam splitter after the collimator.
The splitter has a ratio 95% and 5% so that most of the light travels to the spectrometer. The other lead
from the splitter is connected to a visible LED laser also supplied by Oz Optics. This feature allows for
easy alignment and focusing of the optical system. However, all these fiber optic components added a
significant about of noise to the spectral data. In the final setup only a short fiber was used between the
lens and the spectrometer.
With a 100m fiber the spot size was 20 pixels. The 10m fiber does not allow a spot size of 2 pixels
due to optical properties of the mirrors and gratings of the spectrometer. A spot size of only 5 pixels was
achieved. By positioning the spot half off the edge of the chip so that it illuminates only 5 pixels and
achieving the 3:2s shift speeds, a time resolution of 16s was achieved.
3.5.1 Temperature from Resistivity
Because the magnetic field is relatively small it is possible to calculate temperature based on the Spitzer
resistivity[4, 85] which is defined as the ratio of the rate at which electrons in the unit volume gain
momentum by impact with positive ions, to the current density.
=
P
ei
j
(3.6)
The momentum gained by an electron in a collision ism
e
(v
i
v
e
), wherev
i
andv
e
are the electron and
ion velocities, respectively. The number of collisions per unit time can be expressed simple byn
e
, where
56
29

With a 100 micron fiber the spot size was 20 pixels. The 10 micron fiber does not allow a spot size
of 2 pixels due to stigma and optical properties of the mirrors and gratings of the spectrometer. A spot size
of only 10 pixels was achieved. By positioning the spot half off the edge of the chip so that it illuminates
only 5 pixels and achieving the 3.2 !s shift speeds (still in process) a time resolution of 16 !s will be
achieved.

Figure 12: 10µm Optical System
3.3.5.1 Temperature
A common and proven method for determining plasma temperature from emission spectroscopy is
a Boltzmann Plot. This method uses the following equation to relate temperature and intensities.
(3.1)
10mm ferrule to
attach to
spectrometer
Any size ferrule
to attach to
monochromatic
Any size ferrule
to attach to
monochromatic
Spot size "100!m

Collimator and/or
focuser to
achieve desired
spot size at
desired distance

~25cm

Interchangeable
filter housing
Electrode
Quartz viewport
Vacuum Chamber

Open Air

SMA connector
10!m UV fiber
Electrode
Diode Laser for
alignment
Beam combiner Beam splitter
Figure 3.16: 10m Optical System
is the collision frequency. The current density can be expressedn
e
e(v
i
v
e
)=c. Using these simplified
definitions Equation 3.6 becomes,
=
m
e
c
2

n
e
e
2
(3.7)
This however is an order of magnitude approximation and it has been shown that for a fully ionized gas
there is large uncertainty in collision frequency. A more rigorous calculation can be made to achieve a
more precise value. A Lorentz gas assumption was used, which states that the electrons are not interacting
with each other and the ions are not moving. With these assumptions the resistivity can be written as

L
=

3=2
Zm
2
e
c
2
ln
2(2kT )
3=2
(3.8)
In order to make this expression more accurate election-electron interactions must be taken into account.
This is done by adding a ratio of conductivities for a Lorentz gas
=

L

E
(3.9)
57
The values for
E
have been determined by Spitzer and H arm[86] and are shown in the Table 3.2.
Ionic Charge Z 1 2 4 16 1

E
0:582 0:683 0.785 0.923 1.000
Table 3.2: Ratio of conductivity in a Lorentz gas
The Spitzer resitivity is valid for a fully ionized plasma. For a partially ionized plasma it is important
to consider both collision frequencies of the ion and the neutrals. Classically the conductivity of a plasma,
which is simply the inverse of the resitivity, and can be expressed as
=
n
e
e
2
m
e
(
ei
+
en
)
(3.10)
Wheren
e
is the electron number density,e is the electron charge,m
e
is the mass of the electron,
ei
is the
collision frequencies of electrons with ions and
en
is the collision frequencies of electrons with neutrals.
The electron-neutral frequency can be written as

en
=V
e
(n
C0

eC0
+n
H0
+
eH0
) (3.11)
Where, n
C0
is the neutral carbon atom concentration in the plasma, n
H0
is the neutral hydrogen atom
concentration in the plasma,
eC0
is the electron transport cross-section with neutral carbon atoms, and

eH0
is the electron transport cross-section with neutral hydrogen atoms, and V
e
is the mean electron
velocity that is defined as
V
e
=

8kT
m
e

1=2
(3.12)
The ion-neutral cross-sections are assumed to be constant and were obtained from Powel and Zielinski[76,
77].

eC0
= 30a
2
0
(3.13)

eH0
= 17a
2
0
(3.14)
The expression forv
ei
is more complete, and can be expressed as,

ei
=
38Zn
e
e
2
log

1 + 1:4
2
0
4"
0

1=2

e
m
e
T
3=2
(3.15)
58
Where,n
e
is the electron concentration,Z is the average ion charge, and
e
is a function ofZ as expressed
in Table 3.2. The
m
term is an expression derived by Zollweg and Liebermann[109] and is given by

m
=
12"
0
kT
Ze
2

"
0
kT
n
e
e
2
+

3
4n
i

2=3
!
1=2
(3.16)
The equation above can be rewritten so as to show a clear distinction between and kinetic energy and the
coulomb potential energy. For an ideal plasma, where the high temperatures cause the kinetic energies to
be much greater than the potential energy, as determined in Section 1.5.3, it is possible to simplify this
equation into the usual Spitzer result for conductivity. However, for the calculations done here, the full
set of equations is used and the resistivity can be calculated for given temperature and pressure. These
resitivities for the plasma’s conditions are plotted as shown in Figure 3.17. By using this plot it is possible
to estimate the temperature.
0 0.5 1 1.5 2 2.5 3
10
−5
10
−4
10
−3
10
−2
10
−1
Temperature (eV)
Resistivity (Ωm)

n
e
=1e22 m
−3
n
e
=1e23 m
−3
n
e
=1e24 m
−3
n
e
=1e25 m
−3
Figure 3.17: Polyethylene plasma resistivity as a function of temperature for various number densities
59
3.5.2 Electron Number Density
There are numerous ways to measure the electron number density, n
e
, of a plasma. Two of the most
common methods, for high density plasmas, are based on the phenomena of Thomson scattering and
Stark broadening. Thomson scattering, or the scattering of light by free electrons, is an active technique
of measuring both n
e
and the electron temperature, T
e
. This method uses a laser beam that is passed
through the plasma and measured by a spectrometer on the other side. TheT
e
can be determined from
the FWHM of the broadened laser light from the relation
Thomson
= 7:1 10
7

o
(T
e
=m
e
)
1=2
. The
n
e
can be determined from the integration of the intensity of the full spectral profile, after proper calibra-
tion. The Thomson scattering technique can be difficult, expensive, and impose numerous experimental
difficulties[92]. The other option is Stark broadening which is a passive method that is based on the
broadening of spectral lines spontaneously emitted from the plasma itself to determinen
e
, providedT
e
is
known. Also, techniques have been developed to acquire bothn
e
andT
e
simultaneously using multiple
Balmer lines[94]. Stark broadening is well characterized, especially for hydrogen lines, it is considerably
faster, easier, and less expensive.
Hydrogen Line Broadening
There are several mechanisms that contribute to the broadening of a spectral line. These mechanisms
can cause shifting as well, which can complicate the analysis even further. Because of all the different
broadening mechanism, it is important to understand which is the dominant one and which ones can be
neglected.
Natural Broadening is caused by the uncertainty in energy states of an excited particle as dictated by
the uncertainty principle. Typically this broadening effect is valued to be

N
1=2
1 10
4

˚
A

(3.17)
It is typically neglected and will be neglected here as well.
Doppler broadening is an effect of the motion of the radiating particles themselves. This is similar
to the Doppler effect observed with sound waves. A siren traveling towards an observer will exhibit a
higher pitch to the observer than the same siren moving away from the observer. Similarly, a photon
emitted from a particle moving towards the observer will under go a shortening or red-shift, and a photon
emitted from a particle moving away from the observer will under go a lengthening or blue-shift. This
60
broadening effect has a Guassian distribution. The full width half max, FWHM, for this guassian-type
Doppler distribution is

D
1=2
= 7:16 10
7

o
r
T
M

˚
A

(3.18)
Where
o
is the natural wavelength in Angstroms, T is the plasma temperature in K, and M is the
emitter mass in atomic mass units. In the plasma considered here, which has relatively low temperatures,
the Doppler effect onH

andH

is less then 1
˚
A. It is also possible to neglect this effect as well for the
capillary discharge conditions. If the plasma was hotter the effect would be increased and if the plasma
was less dense the pressure broadening would be much smaller and the effect could not be ignored.
Resonance broadening or self broadening is broadening caused by the neutral perturbation of the
atom itself. This effect takes place when atoms of the same species transition from a higher energy state
to ground state of the same type. The full width half maximum can be expressed by

R
1=2
= 8:6 10
30
r
g
i
g
k

2
o

r
f
r
N
i

˚
A

(3.19)
Here,g
i
is the statistical weight of the upper energy level,g
k
in the statistical weight of the lower energy
level,
o
is the natural wavelength in angstroms,
r
is the wavelength of the resonant line in angstroms,f
r
is the oscillator strength of the resonant line, andN
i
is the ground state number density incm
3
. Because
this broadening effect is due to neutral-nuetral collisions, it can usually be neglected if the ionization
fraction is greater then a few percent. In the presented work a fairly hot plasma that is highly ionized is
being studied, as a result the neutral-neutral broadening can be neglected.
Van der Waals broadening is similar to that of resonant broadening. It is caused by dipole transitions
of excited atoms with atoms in ground state of different types. An estimation of the effect can be written

W
1=2

= 3 10
30

2
o
C
2=5
6

T

3=10
N

˚
A

(3.20)
Where
o
is the natural wavelength in angstroms,C
6
is the interaction constant,T is the plasma temper-
ature inK, is the atom-perturber reduced mass, andN is the perturber density incm
3
. Again, and for
the same reason as resonance broadening, Van der Waals broadening can be neglected as well.
Another type of broadening worth mentioning is the broadening effect from the instruments and opti-
cal equipment. This broadening effect can vary for different equipment and setups. It can also vary as a
function of position on the CCD chip. Luckily this broadening effect is constant and can be calibrated out
using a simple mercury pen lamp. The spectrometer used in this experiment show mercury line on the
61
order of an couple of angstrom. Considering the line broadened of interest here is on the order of 10’s of
nm this spectrometer broadening could be ignored.
Stark broadening is the final type of line broadening. Stark broadening is due to the interaction
between charged particles. This interaction between emitted electromagnetic radiation and the sounding
electric field was first described by Johannes Stark in 1913. The first statical approach to explain the phe-
nomenon was developed by Holtsmark[44]. His model was based on aquasi-staic theory that took into
account static ions which played a much larger roll than electrons. Later models included the influence of
both ions and electron collisions, such as models done by Hill[40, 41].
While line broadening can be fit with relatively simple Lorentzian profiles, their actual shape is much
more complicated. Original theoretical profiles[96, 54] based on thequasi-static approximations show
much more structure around the centerline line the experimentally observed[102, 42]. Unified theory or
VCS[96] usually over predicts these structures. InH

the centerline is greatly extended, displaying much
hight peak intensities. UnlikeH

andH

, H

has no central unshifted stark component and therefore
exhibits a dip or central miniumn[102].H

has less structure around the centerline but shows exagerared
shoulders or wings to its profile.
Although highly exaggerated by early models these structures are very physically sound. Structure,
like the central dip inH

, increases with the electron density. And for a givenn
e
the dip becomes less
pronounced whenT
e
is increases[94]. This observation stressing the importance of ion dynamics on the
line shape. These structures are also effected by the mass of a perturbing ion. A reduced mass,, is often
used which can range from 0:5 for protons to nearly unity of heavier ions likeAr
+
[72]. In the case of
H

, heavier ions create deeper dips[2]. By increasing to inf it was found that the profile become more
like Unified theory[102]. By including the effects of ion dynamic and reduced mass model has lessened
these large structural exaggerations and have come much closer to matching experimental data.
Microfield model methods (MMM) take into account ion (and electron) dynamics and reduced mass.
The charge particles move during the interaction time, changing the electric field as it interacts with the
emitted light. Further developments were made to use computer simulation (CS) theory which include
more full and relevant process. TheGig-Card[33, 32] theory has been used extensively to studyH

,H

,
andH

. TheGig-Card is computation numeric simulation that based on all the all the particle in the
plasma. The plasma is considered neutral, homogeneous, and an isotopic system in thermal equilibrium.
Atoms, ions, and electrons are moving quasi-randomly on the plasma. Gigososetal model consitutes
one of the most accurate approximations at the moment[94].
62
H

Line Structure
In the plasma studied here, H

was examined because of was the only line in the Balmer series that
was not disperse completely into the background spectra. One of the major problems with high density
plasma is the approach of near-thershold[27] conditions were spectral lines overlap and merge to give an
apparent shift of the continuum spectrum[48]. As a plasma becomes higher in opacity, these effects add
to the photorecombination continuum, causing large and uneven background radiation[98].
At the temperature and pressure witnessed in the AFRL capillary discharge, lines from the Paschen
series were also visible. This lines have also been studies[104], but were not choose because they are in
the infra red region and little data is available.
Of the Balmer series line, H

is the most intense. However, it has not been popular for diagnostic
purposes. In many cases this spectral zone in known to have with a great number of line the can blur the
spectrum[33]. However this is clearly not the case with the polyethylene capillary discharge where the
only 2 constituent of the plasma are hydrogen and carbon. It has also been claimed thatH

is without
good theoretical description of it’s stark broadening and the theoretical predicted line shape does not
often agree with experimental results[37, 95]. This poor agreement however has been addressed by Oks’
theory[70] and others who have incorporated more and more effects perturbing electric fields and ion
dynamics. These effect are show to be more pronounced in cooler plasma as they approach a non-ideal
state[30]. These models, and their progression, are discusses further in Section 3.5.2. H

can also be
problematic because of known self absorption issues[92]. A central dip was seen in theH

line of the
capillary discharge at higher currents, which would mean highern
e
. The structure of hydrogen lines can
often show dips within their central region as purely a function of the broadening mechanism. However
this is not a phenomenon observes in lines as discussed in Section 3.5.2.
To calculate strak broadening ofH

exactly would be very difficult. Fortunately the pattern is well
approximated by a Lorentzian fit with a full width half max as described by

S;H
1=2

= 2:5 10
9

1=2
N
2=3
e

˚
A

(3.21)
Where
1=2
is the fractional intensity width in angstroms andN is the electron density incm
3
. The
fractional intensity widths are referenced from Huddlestone[45] and tabulated in Table 3.3.
While hydrogen broadening has been heavily studied there are few devices that can create a hydrogen
plasma withn
e
10
24
. This is one of the reason it is hard to find data and models suited for CD plasmas.
63
T (K) T (eV ) N (#=m
3
)
1=2
5000 0:431 1 10
21
9:69 10
3
5000 0:431 1 10
22
14:9 10
3
5000 0:431 1 10
23
18:9 10
3
5000 0:431 1 10
24
N=A
5000 0:431 1 10
25
N=A
10000 0:862 1 10
21
7:77 10
3
10000 0:862 1 10
22
13:4 10
3
10000 0:862 1 10
23
18:6 10
3
10000 0:862 1 10
24
21:5 10
3
10000 0:862 1 10
25
N=A
20000 1:723 1 10
21
6:01 10
3
20000 1:723 1 10
22
11:4 10
3
20000 1:723 1 10
23
17:5 10
3
20000 1:723 1 10
24
22:6 10
3
20000 1:723 1 10
25
23:5 10
3
30000 2:585 1 10
21
4:98 10
3
30000 2:585 1 10
22
10:0 10
3
30000 2:585 1 10
23
16:6 10
3
30000 2:585 1 10
24
22:5 10
3
30000 2:585 1 10
25
25:7 10
3
40000 3:447 1 10
21
4:50 10
3
40000 3:447 1 10
22
9:22 10
3
40000 3:447 1 10
23
15:8 10
3
40000 3:447 1 10
24
22:3 10
3
40000 3:447 1 10
25
26:9 10
3
Table 3.3: Fractional Intensity Widths[45]
Three devices often used to validate theory at high densities are gas-liner pinches[7, 17], laser-produced
underwater plasmas[29, 28], and flash tubes[97]. A gas-liner pinch by B¨ oddeker produces the highest
n
e
( 10
25
m
3
) but at much higherT
e
( 6 10eV ). Models have been fit to this work[71] with some
degree of success. The capillary discharge may be uniques in being able to produce cooler higher density
plasmas.
Stark broadening of has been used to measure electron number densities in ablative discharges. Car-
bon has been used to measure lower densities, n
e
= 3 10
22
m
3
, in PPTs[64]. In teflon (CF
2
)
plasmas, where fluorine is present, number densities can be determine using Stark Broadening up until
n
e
= 3 10
23
m
3
, where strong broadening and raising background spectrum wash out the line[58].
Hydrogen has been in much higher density plasma.
One of the more relevant works on Hydrogen broadening in capillary discharges was done by Ashke-
nazyetal[4]. In their work they examinedn
e
of a capillary discharge in the range of 10
22
10
25
m
3
using both H

and H

line broadening. Both lines showed good agreement with each other up to
64
3 10
23
m
3
, as was predicted by literature[36].H

was used to measure densities up to 1 10
25
m
3
,
however results shown as shift and discrepancy above 510
24
m
3
. This was attributed to self-absorbtion
of the line causing the FWHM to be larger do to poor Lorentzian fits. One on the major problem with
Ashkenzyetal work was that the optical emission spectroscopy (OES) measurements were made by time
integrated over the whole discharge. Others[90] have taken a similar measurements using an OMA with
a fast gate to take one quick spectra in the during their discharge. However, with current technology and
state of the art CCD cameras it is possible to make full time resolved measurements of the a capillary
discharge, which was done here.
The reasons behind asymmetry are not well studied. To date most MMM, whether based on theory or
computer simulation, have only taken into account terms of first order in the perturbing electric field, and
therefore can only produce symmetric profiles[93]. In order to model these shifts and asymmetric higher
order terms must be included. Some of the mechanisms that might be responsible for these effects are:
the quadrupolar effect, electron impacts, the quadratic Stark effect, and fine structure of ions. However
all this effects are not of the same importance and their relative importance can vary depending on theT
e
andn
e
of the plasma.
While the exact reasons for the shifts and asymmetries are still debated, there has been reasonable
success in modeling and predicting them, specially in regards to line shift. Flih[30] shows an excellent
fits toH

’sFWHM and a near linear trend is shown forn
e
in the 1 5 10
24
m
3
at 1eV . It
is probable that this trend would hold for our higher densities. However, as we have see experimentally,
H

gets harder to profile with simple lorentians at higher densities because of self-absorption. While this
greatly effect Lorentzian fit and theirFWHM values it might not effect the shift of the center line of
these fits. Flih’s work also show a very linear trend of this shift withn
e
. One problem is that theFWHM
can range from 6 15nm while the shift is only 0:6 1:8nm. It may be hard to resolve such small
shifts over such a largely broadened and distorted profile.
3.5.3 Mach Disc diagnostics
It may be worthwhile to note that based on work done by Kohel[56], it may be possible to use the geometry
of the under expanded plasma jet to determine plasma properties. Based on preliminary high speed video
it is possible to see a clear shock structure in the capillary plume, as shown in Figure 3.18. The most
65
Capillary Plume
(a)!2µs (b) 35.6µs (c) 69.2µs
(d) 102.8µs (e) 147.6µs (f) 214.6µs
(g) 237.2µs (h) 259.6µs (i) 282.0µs
Figure 3.18: Still frames from high speed video of a capilary discharge
Capillary Plume
(a)!2µs (b) 35.6µs (c) 69.2µs
(d) 102.8µs (e) 147.6µs (f) 214.6µs
(g) 237.2µs (h) 259.6µs (i) 282.0µs
Figure 3.19: Current trace showing when images from Figure 3.18 occur
66
noticeable feature is the Mach disk that is pushed out of the capillary opening some distance from the exit
plane. This type of diagnostic was not attempted but may be of interest in future work.
67
Chapter 4
Modeling
A parallel effort was conducted in developing a computational model for the capillary discharge. This
work was conducted by others, but there was close collaboration between the experimental and compu-
tational work. The zero-dimesional model was used in designing the capillary discharge device and in
interrupting the experimental data so the work will be described here. Certain short coming that are inher-
ent of a zero-dimensional model were observed and a one-dimensional model was created in an effort to
better match experimental results.
4.1 Zero-Dimensional Model
Work done by Leonid Pekker[75] has followed the progression of capillary modeling starting with the
work done by Loeb and Kaplan[65], which used a many assumptions to simplify a capillary discharge
model. Later work done by Powell and Zielinski[76] added the Saha equation to more actually calculate
plasma composition and enthalpy. From these previous works Pekker developed a model based on the
conservation laws for mass and energy. Mass is conserved though the balance of mass addition do to
ablation of the walls and mass loss due to flow out the exit, per unit volume.
d
dt
=
d
a
dt
+
d
e
dt
(4.1)
The conservation of energy can be expressed by
d
dt
" =j
2
+
d
e
dt
h
e

2
R
q
r
j
Rc
+
d
a
dt
h
a
(4.2)
Where the total energy and enthalpy includes kinetic and internal energies. The enthalpy contribution due
to the mass addition is accounted for in the second term and the contribution due to mass loss though
the exit is accounted for in the fourth term of the right hand side of Equation 4.2. The first term on the
right hand side of the Equation 4.2 is the Ohmic heating and is determined by the plasma conditions,,
the plasma resitivity andj, and current density. The third term is the radiation flux to the capillary wall.
68
Modeling the radiation flux is one of the more challenging parts of capillary discharge modeling. Before
any experiments were done two different radiation models were used in the model. These two different
types of radiation models helped us bound the capillary discharge operational regime. This is discussed
further in the next section. Because experimentally the capillary operates in between the 2 extremes a
radiation software package called PrismSPECT R
was used to calculate the total radiation flux. This
software can accurately model the radiating spectrum for a given composition, temperature, and density.
A database was formulated from these 3 input parameter and was used in Pekkers capillary discharge
code when comparing to experimental data shown in Chapters 5.2 - 5.5
4.2 One-Dimensional Model
A one-dimensioal model was created by Sergey & Natasha Gimelshein in order to incorporate some of
the flow field physics that were missing from the zero dimensional model. This axial 1D model was
based on the work down by Edamitsu and Tahara[?]. Their computational and experimental work was
on a smaller, lower energy, electrothermal PPT with energies of 5 to 15J. While considerably different
from the capillary discharge presented in this work, the same basic concepts and physics applied. Their
unsteady numerical model simulated the electrical circuit, plasma flow, heat transfer to the wall, heat
conduction inside the wall, and ablation. The results of which matched their experiment very well[?].
The assumptions used in the 1D model are similar to the 0D. The plasma flow was considered in
ionization equilibrium, single ionized, one-fluid plasma flow, and in LTE. The Effects of the magnetic
field are not concidered and the total pressure and electron number density were assumed to be radial
constant. The conservation of mass, momentum and energy are conserved axial and expressed by:
@(A)
@t
+
@(Au)
@x
=L
cir
(4.3)
@(Au)
@t
+
@
@x

A(u
2
+p)

=p
@A
@x
fL
cir
(4.4)
@(Ae)
@t
+
@
@x
[Au(e +p)] =A(Q
j
Q
rad
Q
conv
+Q
ab
) (4.5)
whereA is the cross-sectional area, is mass density, is ablation mass flux,u is the average velocity in
the cross-section,p is the pressure,f is the frictional stress on the surface, is the energy dissipation due
to viscosity, ande in the total energy.
69
In the energy equation 4.5, for typical experimental voltage and capillary length the convection energy
loss term term,Q
conv
, and viscous energy losses, , are more than two orders of magnitude less than the
joule heating,Q
j
, and radiation energy loss,Q
rad
. The energy fluxes as a function of time are shown in
Figure 4.1. The curves forQ
ab
and are omitted as they are indistinguishable from zero. The convection
0 1 2 3 4
x 10
−4
−4
−2
0
2
4
6
8
10
12
14
x 10
12
Time (s)
Energy (J/m
2
)

Joule Heating
Ablation Energy
Radiation Energy
Total Energy
Figure 4.1: Energy Fluxes for a 5cm 2500V Capillary Discharge
flux and viscous losses did not affect the results of the 1D model as they were much smaller than other
energy fluxes, and where omitted in increase computational time. It was also observed that the results very
weakly depended on the polyethylene saturated vapor pressure as a function of temperature so that the
surface temperature adjusted itself in such a way that the mass flux of polyethylene remained the same.
Therefore, there was no need to solve the heat transfer equations for the capillary wall. The polyethylene
flux from surface was determined by the energy flux coming to the surface divided by polyethylene
”unzipping” energy. This simplification produced similar results obtained by the full simulation with
heat transfer equation for capillary wall, but ran much quicker.
70
Chapter 5
Results
In this chapter the data collected from the capillary discharge experiments will be summarized. The data
follows the progression of the capillary discharge similar to the design progression in section 2.1. The first
section will cover the basic circuit setup and subsequent sections will examining the ignition data. Just as
the experiment became more elaborate in design so did the diagnostics. While the data for wire ignition
was interesting and yielded a gave good understanding of capillary physics and modeling, it wasn’t until
the Paschen and 3-electorde ignition experiments that interesting thruster performance data was produced.
5.1 Circuit
The basic circuit is a simple one, as described in Section 2.2. In order to fully understand the discharge it
is important to understand the circuit controlling it. The LRC circuit was assembled as it was to be used
in the experiment. All the same components, bus bars, cabling and connectors were used. Originally,
tests used an extended anode that would run completely through the thruster housing, grounding to the
cathode. This setup was compared a simpler setup in which the power cable was connected directly to
ground. There was no noticeable effect on the circuit parameters between these 2 setup, and that later was
used. The only other difference between the experimental setup and the test circuit was a 0:5
resistor
1
that approximated the resistance that would normally be due to the discharge plasma. This resistor had a
known resistance to within5% and therefore the circuit parameters could be known to5%.
The circuit was discharged and the current profiles recorded. This data was then fed into a least
squares fit model
2
that could vary theL,R, andC parameters until the profiles matched. This was done
for a variety of different inductances that would be tested in Section 5.2. The results of this analysis are
shown in Figure 5.1. Plot (a) shows that the inductance of the circuit increases linearly as four inductors
are added in series. It also shows that the circuit itself has an inductance of 7 0:4H and that each
1
Gerneral Atomics, High Energy Resistor, Model 93849
2
Model written my Dr Marcus Young, AFRL
71
0 1 2 3 4
0
2
4
6
x 10
−5
(a)
Number of Inductors
Inductance (H)
0 1 2 3 4
0
0.2
0.4
0.6
0.8
1
(b)
Number of Inductors
Resistance (Ω)
0 1 2 3 4
0
0.2
0.4
0.6
0.8
1
x 10
−3
(c)
Number of Inductors
Capacitance (F)
0 2 4 6
x 10
−5
2
3
4
x 10
−4
FWHM Pulse time (s)
Inductance (H)
(d)
0 2 4 6
x 10
−5
600
800
1000
Peak Current (A)
0 2 4 6
x 10
−5
600
800
1000
Figure 5.1: (a) Inductance, (b) resistance, and (c) capacitance as a function of number 10H inductors.
(d) Pulse length and peak current as a function of Inductance
inductor had an average inductance of 13 0:7H, not the 10 advertised by the vender. Plot (b) shows
that each inductor adds slightly more resistance. By subtracting 0:5
from these resistance values it is
possible to estimate the parasitic resistance of the circuit, ranging from 24 1
to 91 5
. Plot
(c) indicated the the capacitance is not affected and is within the specification of the manufacturer. Plot
(d) shows how that inductance affects the pulse shape. As the the inductance increases the pulse time
increases and the peak current decreases, as is expected from LRC circuit theory. The circuit parameters
obtained in this analysis are also used in both computer models.
5.2 Wire Ignition
Wire ignition was carried out first because of its historical importance in capillary discharge research.
While this method can not be seriously considered for any space applications, it has been proven in many
laboratory capillary discharges. The techniques of exploding wire ignition are discussed in Section 1.7
and the associated test apparatus is described in great detail in Section 2.1.1.
72
5.2.1 Test Procedures
As mentioned in Section 2.1.1 the original design went through many iteration before properly operating
and sealing. The system used in these ignition tests consisted of a tube within a tube configuration. The
outer tube was reused, but a new inner tube was replaced between each firing. The inner tubes were held
rigid using a 4mm metal rod while the outer tube was pressed on. The two tubes fit very tightly within
each other. Subsequent to assembly the support rod was removed and the aluminum wire was feed down
the length of the tube assembly. The wire was usually cut long to make it easier to feed in the tubes and
trimmed later. The anode was then slid into the back end of the tubes, holding the wire in place. The
insertion depth was varied in order to create the correct length capillary for the desired test. This whole
assembly was then introduced into the housing through the exit orifice until the outer tube butted against
the internal insulator, which can be seen in Figure 2.2. The fit of the tubes inside the house was such that
it could be introduced without requiring much force, yet would hold in position. Once in place, the power
cable could be connected to the anode and the wire attached to the cathode flange. The wire was attached
by looping it out with plenty of slack, or pulled tight to the attachment point, it did not seem to affect the
discharge.
5.2.2 Data
Once the discharge was operating reliably and repeatably a number of parameters were varied in order
to observe the corresponding effects on the discharge. The first and easiest of these parameters was
the voltage potential of the capacitor bank. By changing the capacitor to different voltages, the voltage
driving the capillary discharge was varied. Figure 5.2 shows the discharge current as affected by these
voltage changes. As the driving voltage or potential across the discharge increases so does the current
and total power input into the device. While the current increases the pulse width does not. Discharges
typically last 250 to 300s. The discharges can also vary more significantly at lower voltages, about 8%
variation, compared to at higher voltages, where there is a variation of 2%. The initial current pulse seen
in Figure 5.3 around 100s are due to wire explosion. This clearly demonstrates the chaotic nature of
this ignition system as discussed in Section 1.7.1.
To change the pulse length one needs to modify the circuit parameters. By increasing the inductance
the current pulse flattens out with lower peak currents and longer pulse lengths, as exhibited in Figure 5.3.
Four separate 10H inductor coils were used to change the overall inductance of the circuit. The parasitic
73
0 50 100 150 200 250 300 350 400 450 500
−1000
0
1000
2000
3000
4000
5000
6000
7000
Time (μs)
Current (A)

2500V
2750V
3000V
3250V
3500V
Figure 5.2: 10cm, 10H capillary discharge currents for varying capacitor voltage
0 100 200 300 400 500 600
−1000
0
1000
2000
3000
4000
5000
Time (μs)
Current (A)

10 μH
20 μH
30 μH
40 μH
Figure 5.3: 10cm, 3000V capillary discharge currents for varying inductances
74
inductance of the wiring, capacitors, and circuit components was not small compared to the coils, as
shown in Section 5.1. From the Table 5.1 notice that while the change in current peak and pulse length
were not proportional, they are in fact such and the total power input into the system changes very little,
with a percent deviation of less the 2%.
Num. Inductors Inductance change int
discharge
change inJ
max
1 10H 0% 0% 1149J
2 20H 37% -20% 1159J
3 30H 53% -35% 1188J
4 40H 89% -42% 1182J
Table 5.1: Inductive Effects on Discharge Circuit Parameters
The other major parameter changed in these initial tests was length. By sliding the anode deeper
into the capillary ,the capillary length was shortened. The effect of this geometry change is shown in
Figure 5.4. Plot (a) indicated that by shortening the capillary, the peak discharge current increases. This
0 100 200 300 400 500
−1000
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Time (μs)
Current (A)
(a)

0 100 200 300 400 500
−1000
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
(b)
Time (μs)
Current (A)
4 cm
5 cm
6 cm
8 cm
10cm
Figure 5.4: (a)Low Current and (b)high current modes of a 2500V capillary discharge currents for varying
lengths
75
makes sense in that the capillary plasma column has a resistivity or resistance per length. So if the column
is shortened, the overall resistance will decrease, causing larger currents. Another way to think of this is,
if the capillary length is shortened for a given V between the anode and cathode, the voltage gradient
increases, which leads to larger currents.
One of the most interesting effects seen in the capillary discharge experiments preformed in this study
are the random occurrences shown in the Plot (b) of Figure 5.4. These current plots were taken at test
conditions identical to the data shown in Plot (a). This high current (HC) mode of operation, shown
in Plot (b), produced significantly higher current pulses and slightly smaller pulse widths. Despite the
difference between these 2 modes, the power of the high current mode is only about 12% less that of the
lower current or normal mode. The two modes occur at random, but the discharge always operates at one
of the two forms and never in-between . The HC mode also occurred more frequently as the length of the
capillary was decreased. Most of the previous tests were at 10cm and no HC mode was ever observed.
It wasn’t until testing started for an 8cm capillary that the phenomenon was observed. Of the five 8cm
shots fired in Figure 5.4, the HC mode discharge occurred only once. It occurred 2/5 times at 5 and 6cm,
and 3/5 times for the 4cm test. Section 6.3 contains discusses of this phenomenon.
5.3 Paschen Breakdown Ignition
Paschen breakdown proved the next logical step in the ignition tests. The reasons and techniques for
which are discussed in Section 1.7.2. Details of the apparatus are described in Section 2.1.2
5.3.1 Test Procedures
For these ignition tests dry nitrogen was used to create the required background pressure. The capillary
was mounted on the thrust stand, as described in Section 3.4.2 within the vacuum chamber. The chamber
was pumped down to its lowest limit using just the backing pump; usually around 20 mTorr. The
chamber was then refilled back up to the operating pressure necessary for breakdown, usually around
20Torr, depending on the length and voltage being tested. This was done in order to keep a more stable
and repeatable ignition environment for testing.
The exact breakdown pressure was determined experimentally for each new capillary setup. This was
done quickly by over filling the chamber with nitrogen, around 50Torr. The capacitors were charged
to the voltage desired and the control switch was left open. The valve to the pump was opened slightly
and the chamber pressure would start to decrease. Eventually the pressure become enough for a Paschen
76
breakdown to occur. The breakdown pressure was noted for future tests with that particular length capil-
lary and voltage.
Tests were set up and run for a variety of lengths and voltages. For each length and voltage com-
bination a capillary tube, cathode, and anode were all weighed. The entire thruster assembly was put
together compressing both the anode and cathode seals, as described in Section 2.1.2. The device was
then mounted to the thrust stand. The thrust stand LVDT core was aligned and tested to make sure that
there was no contact or rubbing that could disturb the measurement. The combs were also checked to
make sure that they were aligned and engaged as prescribed in Section 3.4.2 Once the chamber was
sealed and pumped down to the appropriate pressure for ignition, the capillary was fired five times. After
five consecutive shots the chamber was pumped down further so that calibration could be completed at
lower pressures, where the 3000V placed on the combs would not arc. After the calibration was suc-
cessfully completed, the chamber was vented and the the device disassembled. The capillary, housing
assembly, anode, and cathode were all weighed separately. The mass before and after were compared and
an average mass loss per the five shots was calculated.
One of the important characteristics to note when working in this regime is the occurrence of sec-
ondary discharges or restrikes. This originally happened because the SCR switch was opened with a
trigger pulse that was 1s long. This presented no problem at atmospheric pressures because the condi-
tions required for restrikes never occured. However at lower pressures, after the first discharge occurred,
a secondary restrike would occur somes later, sometimes as much as ams later. This was caused by
the remaining voltage on the capacitors. This left over charge resulted in potentials which were usually in
the range of 700 to 1500V depending on the original charging voltage and the capillary geometry. As the
pressure dropped within the capillary after the current shut off and the main discharge was over, a pressure
was reached that allowed this secondary restrike to occur. While it was an interesting phenomenon, it did
affect impulse and mass loss measurements. The restrike problem was eliminated by only allowing the
SCR switch to open for a short period of time, no longer than the discharge itself. Even though a GTO
(gate shut off) switch was not used, the current dropped to zero before the restrike, which allowed the
switch to latch shut preventing any further discharges from occurring. It may be worth while keeping this
phenomena in mind for future multi-shot operations.
77
5.3.2 Data
As with the wire ignition tests, several parameters were varied to observe their influence on the thruster.
A compete data matrix was taken for this ignition method, so that five separate voltages were tested for
each of the four lengths. As with the case with previous tests, five consecutive shots were taken to build
a statical average for total impulse and to increase total mass loss. Figure 5.5 shows the two parameter
changes and their effect on the discharge current. Plot (a) exhibits, for a 6 cm capillary, the change
100 200 300 400 500 600 700
0
1000
2000
3000
4000
5000
6000
(b)
Time (us)
Current (A)

100 200 300 400 500 600 700
0
1000
2000
3000
4000
5000
6000
(a)
Time (us)
Current (A)

4 cm
6 cm
8 cm
10cm
2000 V
2250 V
2500 V
2750 V
3000 V
Figure 5.5: (a) 6cm discharge currents at various capacitor voltage and (b) 2500V discharge currents for
varying lengths capillaries using Paschen ignition
in current with various driving potentials. These results showed the same trend as the wire ignition,
increasing peak current with increasing voltage. Plot (b) shows the current for a 2500V discharge for
different length capillaries, The results here were as expected and the current, pulse width, and total
power all increase for shorter capillaries. The results are compared more thoroughly in Section 6. It is
also apparent from Figure 5.5 that there are different tails or extinctions for the discharge. This anomalous
extinction led to current tails that could last 100’s ofs to 1ms. These tails, and possible mechanisms
for them, are discussed in Section 6.6.
78
As mentioned in Section 1.7.2 the use of Paschen breakdown ignition allowed the determination of
thruster performance characteristics, described in Section 1.6, such asI,I
sp
and. These 3 parameters
allow, for the first time, a view of how the device was operating as a space craft propulsion device. They
are plotted as a function of the energy in Figure 5.6. This energy is total energy input into the device and
is caluculated by
E =
Z
j(t)V (t)dt (5.1)
where the currentj is measured by Rogowski coils, andV is measured by a voltage probe.Plot (a) shows
an increase in total impulse with increasing input energy. This input energy is determined from the
voltage on the capacitor used to drive the discharge. For a given capacitor potential, shorter capillaries
are driven to higher total input energies. At a potential of 2500 V , a 4 cm discharge consumes about
1400J,whilea10cm consumes only 650J. Impulses ranged from 20 to 100mNs for various lengths
and voltages. It is also worthwhile to note that the impulse is relatively independent of capillary length,
and that within the length variation available, different length capillaries can create approximately the
same impulse; provided that proper energy levels can be reached.
Plot (b) shows measurements ofI
sp
. This data exhibits a significant amount of scatter. With in the
range of conditions, 4cm capillaries show some of the best performance, and also the worst. TheI
sp
for
4cm capillaries range from 350s to 650s, and have a stand deviation of about 105s. 10cm on the other
handle are fairly constant at about 600s, and a standard deviation of 33s. This scatter is mostly accredit
to erroneous mass loss. The mass loss used in theI
sp
calculations are based on total mass loss of the entire
system, including the anode and cathode which were still experiencing large mass losses, in some cases
about 50% of the total. The sporadic nature of theI
sp
measurements can be traced directly to the sporadic
mass loss due to electrode erosion as will be discussed in Section 6.2. The efficiency measurements are
also corrupted by electrode mass loss as shown in plot (c). Because of this, the efficiency ranges from
about 8% to 18%.
While much of this Paschen Ignition data was not as clean and concise as desired, it did provide a good
first look at how the discharge was operating. The capillary discharge as a thruster could linearly create
impulses of 28 to 100mNs, independent of capillary length. And, over the complete range of lengths
and voltages, the capillary discharge exhibited an averageI
sp
of about 550s and an average efficiency of
about 12%.
79
400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
0
0.02
0.04
0.06
0.08
0.1
(a)
Energy (J)
I (mNs)

4 cm
6 cm
8 cm
10 cm
4 cm Trendline
6 cm Trendline
8 cm Trendline
10 cm Trendline
200 400 600 800 1000 1200 1400 1600 1800 2000 2200
300
400
500
600
700
800
Energy (J)
I
sp
(s)
(b)
200 400 600 800 1000 1200 1400 1600 1800 2000 2200
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Energy (J)
η
(c)
Figure 5.6: (a)Impulse, (b)Specific Impulse, and (c)Propulsion Efficiencyas a function of input energy for
4, 6, 8cm Capillaries using Paschen ignition
80
5.4 External Coaxial Ignition
A coaxial igniter describe in Section 2.1.3 allowed the gap between the Paschen ignition and a full internal
three electrode ignition system to be bridged. By using this method the ignition principles outlined in
Section 1.7.3 could be tested without committing to a major design change.
5.4.1 Test Procedure
For these tests it was conceived that a coaxial cable would be held near the exit plane of the capillary. The
housing that was used could be the same at the previous Paschen breakdown tests. The only difference
was that the SCR switch that normally triggered the discharge was opened earlier and a high voltage
ignition spark was used to initiate the discharge. This required some basic circuit, control wiring, and
data acquisition modifications.
The first attempts to ignite a capillary discharge with the coaxial ignitor did not work. This ignitor
itself appeared to be working fine and emitted a spark or glowing discharge. However it failed to ignite
the capillary. Many different angles and orientations were tried before the capillary discharge was suc-
cessfully ignited. The only way to cause ignition was by placing the ignitor directly at the edge of the exit
orifice. By doing so it caused ignition, but in turn was heavily eroded by the exit plume. It was believed
that easy ignition would not occur because of a worn electrode geometry that interfered with the formation
of proper electric fields for the formation a conductive path. A new set of tungsten electrodes were being
machined for a three electrode design, and it wasn’t until they were finished that coaxial ignition could be
tested. The assembly for these test was therefore the same housing as the three electrode setup minus the
ignition electrode and ignition material shown in Figure 2.7.
As already expressed, the coaxial ignitor was only tested for a short number of cases before an internal
three electrode system was implemented. Only a 6cm tube was tested for a variety of voltages. A voltage
up to 3500V was tested, in order to check and qualify the sealing configuration of the design. This was
a higher voltage than previously used and the seal held quite well.
5.4.2 Data
The current plot for the coaxial ignition looks very similar to previous current plots as shown in Figure 5.7.
The current increases with increasing voltage. The current traces were clean from start to finish, not
plagued by the noise of the wire ignition or the random tails from the material used in the Paschen
81
0 100 200 300 400 500 600
−1000
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Time (us)
Current (A)

2000 V
2500 V
3000 V
3500 V
Figure 5.7: Current as a function of time for various capacitor voltages using Coax Ignitor
ignition. These current traces show very similar intial profiles, however their extinction profile change
significantly with voltage. This form has been seen in previous igntion tests, but is not as pronounced as
shown in this case. As the driving voltage increased the
di
dt
became larger and the pulses become more
symmetiric.
The thruster performance plots for the coaxial ignition exhibited much cleaner results. As presented
in Figure 5.8 plot (a), the impulse has a linear relationship with the electrical energy used in the discharge
with very little deviation. The I
sp
and in plots (b) and (c), respectively, show downward trends as a
function of energy, as was expected for a 6cm case. The data for these tests still showed significant mass
loss of the electrode, however this mass loss was more consistent than with the Paschen ignition test. This
can me seen in theI
sp
and plots, results show a much reduced scatter compared to Figure 5.6. The issue
of electrode mass loss is discussed further in Section 6.2
82
0 1000 2000 3000 4000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Energy (J)
Impulse (mNs)
(a)
0 1000 2000 3000 4000
300
400
500
600
700
Energy (J)
I
sp
(S)
(b)
0 1000 2000 3000 4000
0.08
0.1
0.12
0.14
0.16
0.18
Energy (J)
η
(c)
Figure 5.8: (a)Impulse, (b)Specific Impulse, and (c)Propulsion Efficiency as a function of input energy
for a 6cm Capillaries using Coaxial Ignitor
5.5 Internal Three Electrode Ignition
After the coaxial ignitor test proved effective, the spark ignition concept was incorporated into the thruster
housing as described in Section 2.1.4. This was the final ignition method and incorporated all the design
improvements that had been progressively introduced in the previous tests.
5.5.1 Test Procedures
To test the system the same preliminary data was taken as for the coaxial case. A 6 cm capillary was
tested at 2000V , 2500V , 3000V and 3500V . These results can be compared to show that indeed these
two methods preform in very much that same way.
After the preliminary testing of the three electrode ignition system(3-EIS) a full set of data was taking
for several lengths and voltages, similar to that of the Paschen and wire ignition methods. 6cm capillaries
were tested first, followed by 4 cm and 8 cm. 10 cm data was attempted last and was unsuccessful.
The capillary discharge had trouble igniting at these lengths. While ignition was possible it was erratic,
83
occurring off time, or igniting once out of every ten tries. This made it very difficult to acquire a full data
set of more than few attempts. The reason for the failure of the 10cm case is most likely due to the same
reason as the initial coaxial tests. By this stage of testing the electrodes were worn and geometry did not
lend itself towards good electric fields and conductive paths. At longer capillary lengths it become harder
to ignite simply because it is harder to form conductive path along a greater length. This, in combination
with a shrinking view factor between anode and cathode, made it very difficult to ignite the 10cm cases.
All testing in this section was done using pre-discharged capillaries. It has been observed that the
first firing of a new tube can be quite different from the following discharges, as explained in Section 6.5.
Because of this, the capillary was preconditioned by pumping down and firing several times through the
capillary. It is then removed from vacuum and disassembled so mass measurements can be taken before
the actual tests. There was only a small observed change in diameter from this preconditioning, no effect
due to this change was seen in the discharge itself.
One of the major difficulties with this design was sealing the cathode and ignition electrodes. Quite
a large force had to be applied in order to do so. This however would cause the ignition electrode to
crack. The ignition electrode was a wire EDM (Electric Discharged Machined) 1=16 in thin tungsten
disc. It was made thin so as to fit within the ignitor housing and not create a large surface area for the
discharge to ablate. Tungsten is a hard but brittle metal and at this thickness it can be broken by hand.
Several ignition electrodes were broken, before the material had to be changed. Stainless steel held up
much better structurally and was used for the second half of the testing. Little effect from this electrode
switch was seen in the data.
5.5.2 Data
The effects of length and voltage on the current profile are shown in Figure 5.9. From these plots it is
easy to see the, by now, classic response of increasing current for both increasing voltage and decreasing
length. It is worthwhile noting the low deviation in the current profiles. The 3-EIS discharges were highly
repeatable and consistent.
The performance measurements also show much less scatter. The trends have become much more
apparent. If one looks at the performance plots in section 5.3, these same trends are also present, but much
less believable, due to the data’s sporadic nature (caused by random electrode mass loss).The impulse
measurements in Figure 5.10 plot (a) shown that the total impulse is very consistent for all lengths, with
84
100 200 300 400 500 600 700
0
1000
2000
3000
4000
5000
6000
7000
(b)
Time (us)
Current (A)

100 200 300 400 500 600 700
0
1000
2000
3000
4000
5000
6000
7000
(a)
Time (us)
Current (A)

4 cm
6 cm
8 cm
2000 V
2250 V
2500 V
2750 V
3000 V
Figure 5.9: (a)6cm discharge currents at various capacitor voltage and (b)2500V discharge currents for
varying lengths capillaries using 3EIS
slightly higher values for longer capillaries. The specific impulses shown in Plot (b) clearly exhibit a
negative trend for all lengths as a function of voltage, with 8cm having the highestI
sp
in the 600’s and
4 cm having the lowest, ranging from 550 s down to 350 s. It is interesting to note that the negative
slope of these approximately linear lines decreases as the length increases. It is even possible that a
10 cm capillary would have positive returns for increasing discharge energy. This same trend appears
in the efficiency as well. A 4 cm capillary decreases in efficiency with more power however an 8 cm
capillary increases. It seems that both of the trends are most likely due to electrode erosion. And while
less sporadic, electrode erosion is still a major issue and discussed in detail in Section 6.2.
5.6 Electron Number Density
Hydrogen Balmer alpha lines were used to determinen
e
as discussed in Section 3.5.2. The optical setup
used to capture these spectral lines is described in Section 3.5. The experimental data of emission intensity
versus wavelength was compared to a least squares fit of a Lorentzian, as shown in Figure 5.11.
85
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0.02
0.04
0.06
0.08
0.1
0.12
0.14
(a)
Energy (J)
I (mNs)

4 cm2
6 cm
8 cm
4 cm Trendline
6 cm Trendline
8 cm Trendline
600 800 1000 1200 1400 1600 1800 2000 2200 2400
300
350
400
450
500
550
600
650
Energy (J)
I
sp
(s)
(b)
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0.08
0.1
0.12
0.14
0.16
0.18
Energy (J)
η
(c)
Figure 5.10: (a)Impulse, (b)Specific Impulse, and (c)Propulsion Efficiency as a function of input energy
for 4, 6, 8cm Capillaries using Coax Ignitor
86
6.3 6.4 6.5 6.6 6.7 6.8 6.9
x 10
−7
0
0.5
1
1.5
2
2.5
3
3.5
4
x 10
4
Wavelength (m)
Intensity (Arb)

Expimental Data
Lorentzian Fit
Figure 5.11: Lorentzian fit of experimental data using least squares fitting
The fit shows the spectrum from a 6cm capillary operated at 2500V . Both the experimental results
and the fitted profile are in very close agreement except at the line center. Here, a central dip is observed
experimentally. While there are many causes of central dips in spectral lines, this one was most likely due
to self-absorption. The rest of the profile agrees very well, it can be assumed that the fitted Lorentzian is
representative of the spectral shape with no self-absorption. Based on this Lorentzian profile, the FWHM
can be found and correlated ton
e
, as discussed in section 3.5.2.
The number density is highly independent of temperature for the range of temperatures typical of a
capillary discharge. It is only slightly affected by the coefficient
1=2
shown in equation 3.21. Figure 5.12
plots the number density as a function of spectral number. Each spectrum is only 16s apart using the
kinetics mode operation. The plot showsn
e
for a number of different temperature ranging from 1 to 2eV .
Over this range then
e
has a percent deviation of less than 1%.
Figure 5.12 also compares the experimental results with the 1D computational model. The model
outputs the electron number density at several locations along the capillary. The Capillary middle is half
way between the anode and cathode. The Capillary end is the end of the capillary material, where it
87
35 40 45 50 55
0
1
2
3
4
5
6
7
8
9
x 10
24
Spectrum Number
Electron Number Density (m
−3
)

1.0 eV
1.2 eV
1.4 eV
1.6 eV
1.8 eV
2.0 eV
Cap Mid
Cap End
Cathode End
Figure 5.12: Comparison ofN
e
between expirmetnal results and 1D model
meets the cathode. The cathode end is the exit plane of the device and the location where the optical
measurements are taken. The Cathode, as discussed in section 2.1.4, is 1=4in long and has a half angle
of 10

. It is because of this geometry that the model predicts an expansion of the exit plume and a cooling
of the plasma. A slightly cooler plasma has significantly lower electron number densities as represented
by the black line. In the 6cm case shown in the figure, these values are 2 orders of magnitude lower at
the end of the capillary.
Even though the electron number densities are measured at the end of the cathode, they match the
number density predicted at the end of the capillary by the 1D code, within 15%. A likely explanation for
this is that at the plume is not expanding uniformly as predicted by the code. The code is based on a 1D
model and does not take into account the axial profile of the discharge. Therefore, the number densities
are an average across the cross section. It is very possible that the core of the discharge is significantly
hotter and the edges much cooler. To complicate matters farther, when the the plasma is expanded through
the cathode, the edges may cool rapidly, while the core remain generally unaffected. Because the core
remains hot it still radiate brightly while the surrounding cooler plasma radiates little. CFD calculation
for a hot gas at the temperatures and pressure predicted in the capillary show that this expansions should
88
be fairly uniform. However the discharge is a plasma and has many other processes occurring. The most
relevant of which is the de-excitation and recombination. Though 3-body collision the ionization causes,
can be recovered. While the thermal energy is 1 to 2eV the ionization energy is 12eV . If this energy
is recovered it would be converted into thermal energy and could greatly effect the temperature of the
expanding plasma.
The electron number density was also be examined over a range of voltages and length. V oltage tests
were conducted with a 6cm capillary. As shown in Figure 5.13 the electron number density increases
as a voltage increase. This corresponds well with the thrust data measured in Section 5.5. The length
tests were conducted by varying the capillary length for a 2500V discharge. The electron number density
decreases with longer capillaries as shown in Figure 5.14. This occurred because of two reasons. As seen
with the thruster performance data, for a given voltage potential, longer capillaries have larger resistances
and less power is dissipated into the discharge. So even though the voltage is constant, less energy is
used, therefore the temperature is lower and the ionization is less. It is generally understood that longer
capillaries have higher densities, but lower temperature.
In Figure 1.20 discharges at 2750 and 3000 V showed significantly higher number densities than
would be expected. This large jump is also seem for the 4 cm capillaries shown in Figure 1.20. This
measurements correspond ton
e
values larger than 5 10
24
m
3
. This discrepancy was also observed by
Ashkenazyetal[4] in there studies of capillary discharges at densities above 5 10
24
m
3
. The reason
for this can be see in figure 5.15 which shown the Lorentzian fit for a 6cm 2750V test. Here the central
dip do to self absorption is much larger and starts to affect the fit. While this dip can be seen in main of
the spectrum, if it is small, it introduced little error into the fit and the FWHM can be determined with
confidence. Here however it is easy to image a fit that has a higher peak. A high peak with a similar base
would be less broadening curve with a smaller FWHM and therefore a lower electron number density.
Several attempts were made to modify the least squares fitting routine to fit the curve better. Trying to
fit a Lortenzian using just the wings required high fidelity data. A secondary absorption loretnzian was
superimposed to account for the central dip. This however did not yield a single solution.
A final attempt was made to resolve n
e
measurements above 5 10
24
m
3
using the shift of the
hydrogen Balmer line. As mentioned in Section 1.20, Flihetal[30] looked at the correlation between
H

broadening and shifts. He showed there exists a fairly large, and linear, shift in hydrogen broadened
line. His work predicted that for a number density of 5 10
24
m
3
there is a FWHM on the order of 10
to 15nm and a shift of 2 to 3nm. The FWHM data collided for this capillary discharge agrees very well
89
36 38 40 42 44 46 48 50
0
0.5
1
1.5
2
2.5
x 10
25
Spectrum Number
Electron Number Density (m
−3
)

2000 V
2250 V
2500 V
2750 V
3000 V
Figure 5.13:N
e
for a 6cm capillary at 2000, 2250, 2500, 2750, and 3000V
36 38 40 42 44 46 48 50 52 54
0
2
4
6
8
10
12
14
16
18
x 10
24
Spectrum Number
Electron Number Density (m
−3
)

4 cm
6 cm
8 cm
10 cm
Figure 5.14:N
e
for a 2500V capillary at 4, 6, 8, and 10cm lengths
90
6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9
x 10
−7
1
1.5
2
2.5
3
3.5
x 10
4
Wavelength (m)
Intensity (Arb)

Expimental Data
Lorentzian Fit
Figure 5.15:H

line with high self-absorbtion
as shown in Figure 5.16 However the results for the shifting of the centerline did not agree. Figure 5.16
(b) shows a plot of the centerline as found from the least squares fit Lortentzian profile. Shifts of 0:4 to
0:6nm were observed. In addition it was seen the shorter capillaries had a blue shift while longer ones
shifted red. The mechanism that caused this could not be identified and a shift method could not be used
to measure the number density greater than 5 10
24
m
3
.
91
35 40 45 50 55
0
2
4
6
8
10
12
14
16
18
20
(a)
Spectrum Number
FWHM (nm)
35 40 45 50 55
657.2
657.4
657.6
657.8
658
658.2
658.4
658.6
(b)
Spectrum Number
Centerline Wavelength (nm)

4 cm
6 cm
8 cm
10 cm
Figure 5.16: (a)FWHM and (b)centerline shifts as a function of time
92
Chapter 6
Discussion
Wire, Paschen, and three electrode ignition tests for the capillary discharge have all been conducted.
Throughout this process diagnostics have been refined, and the capillary device improved. In this section
these ignition methods will be compared. The work presented here discusses much more than just the
ignition, it provides a greater understanding of capillary discharges and hopefully will provide valuable
information for future researchers in this field. Electrode erosion, material effects, external ablation, and
background pressure effects will be discussed.
6.1 Ignition Comparison
When comparing the different ignition techniques, the first parameter evaluated was the current profiles
shown in Figure 6.1. In most cases the profiles looked very similar, except for some minor details.
Surprisingly the wire ignition was not that much different than the other methods, despite the wire material
added to the plasma. Capillaries ignited by wire explosions have slightly higher currents at all lengths and
it was initially supposed that this was due to the additional material from the exploding wire. At 10cm
the wire ignition exhibited a much slower start and had a much more symmetric profile. This slower start
is a trend for both the wire and Paschen breakdown ignition as a function of length, though much more
pronounced with the wire. This has been proposed to be an effect of the background pressure, rather than
the ignition method itself. Further discussion is presented in Section 6.7.
The 3 electrode ignition system had higher peak currents than Paschen ignited capillaries, but lower
than the wire ignition. It is reasonable to assume that this has something to due with the density of the
igniting plasma. With the Paschen breakdown the column of low pressure gas within the capillary breaks
down, ionizing the internal capillary volume. It is possible that this creates a plasma that is initially higher
in density and lower in temperature, and therefore would have a higher resistance. In the case of the 3EIS
there is not much material and the plasma starts at a very low density, allowing it to get hotter and less
resistive. The fact that the wire ignition had the highest peak current could suggest that the exploding
93
0 100 200 300 400
0
1000
2000
3000
4000
5000
6000
7000
8000
4cm
Time (μs)
Current (A)
0 100 200 300 400
0
1000
2000
3000
4000
5000
6000
7000
8000
6cm
Time (μs)
Current (A)
0 100 200 300 400
0
1000
2000
3000
4000
5000
6000
7000
8000
8cm
Time (μs)
Current (A)
0 100 200 300 400
0
1000
2000
3000
4000
5000
6000
7000
8000
Time (μs)
Current (A)
10cm

1D
0D
Exp−3E
Exp−Paschen
Exp−Wire
Figure 6.1: Camparison of discharge currents for 0D, 1D, and 3 ignition methodes for 4,6,8, and 10cm
capillaries at 2500V
94
wire created a hot but not necessarily dense plasma. This also supports the fact that all discharges had
the same basic profile as stated earlier. If the wire was adding its own mass, equal to that of the capillary
ablation mass, then it would be expected that the discharge would be be very different. In section 1.7.1,
wire explosion was discussed in greater detail and the chaotic nature of this process was examined. It is
very possible that when the wire explodes it creates only small pocket of hot plasma and the majority of
the material is ejected from the capillary without fully melting, vaporizing, or dissociating. This could
also support why a dual mode of operation was never seen in other ignition tests. If the high current mode
has a very high temperature, low resistance plasma as an initially conductive path, this could only happen
for wire explosion and, more likely, for shorter capillary lengths.
Both models compared very well to experiments for shorter capillary lengths. The 0D model exhibited
a long tail extinction. The reason for the tail was never determined and could not be eliminated from the
results. The 1D model describes the experiment a little more accurately. It showed very good agreement
with shorter capillaries. Experimentally current pulse width decreased as the capillary got longer, going
from about 300s for 4cm to 200s for 10cm. The model however predicted the opposite trend, with
discharge times going from 300 to 340s for 4 and 10cm, respectively.
The model was then compared with thruster performance. The plots from the model shown in Fig-
ure 6.2 only take into account the mass loss of the capillary and not take into account any mass loss of
the electodes. The difference between including and not including the mass loss of the electrodes can
give very different results in I
sp
and effeciency. While ignoring electrode mass loss does not provide
an accurate presentation of the performance of the device, it does allow for more consistent comparison
with the model. From figure 5.6 and 5.10 we can see howI
sp
and decrease with energy. However if
one neglects the mass loss from the electrode, these parameters trend upwards very similar to the model
prediction.
The large discrepancy between the model and experiment for I
sp
and is most likely attributed to
late time ablation which is not accounted for in the model. It has been shown that late time ablation can
account for a large percentage of the total mass loss, on the order of 1/3 of the total mass loss[14]. This
seems particularly true based on the information discussed in Section 1.4.1 about the ablation process. If
a large amount of the energy is not going to photo-ablation, it goes into heating the surface. Because heat
conduction is so poor within the polyethylene capillary, the surface remains hot well after the discharge
has stopped, causing mass to be evaporated off the capillary surface.
95
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0.02
0.04
0.06
0.08
0.1
0.12
0.14
(a)
Energy (J)
I (mNs)

600 800 1000 1200 1400 1600 1800 2000 2200 2400
400
600
800
1000
1200
1400
Energy (J)
I
sp
(s)
(b)
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0.1
0.2
0.3
0.4
0.5
Energy (J)
η
(c)
Exp −4 cm
Exp −6 cm
Exp −8 cm
Model −4 cm
Model −6 cm
Model −8 cm
Figure 6.2: Comparison of (a) Impulse, (b)I
sp
, and (c) efficiency for experimental and 1D model results
96
6.2 Electrode Erosion
Electrode erosion has been a large factor in this work. While the major goal was to investigate ignition,
this could not be done without first looking at erosion patterns and trying to mitigate them. Major erosion
problems were first noticed the minute mass measurements were taken to calcuateI
sp
’s and effeciencies.
As mentioned in section 5.3, early tests showed that mass loss due to electrode errosion was significant;
on order of, or significantly higher than, the mass loss from the tube itself.
To study these patterns early on, testing was done with stainless steel electrodes. While these were
poor electrodes because they eroded so quickly, they did allow the observation of patterns in a relatively
small amount of shots. It was noticed that the mass loss from electrodes became decreased as the device
was fired more. It was also noticed that the exit orifice was expanding to such an extent that the weld used
to secure that exit orifice was eventually compromised, causing the insert to come loose. A new housing
and insert were created and tested. This time the erosion pattern and rates were more closely monitored.
Figure 6.3 shows the life of that cathode over a series of tests at 6cm of length at a capacitor voltage of
2500V . From these photos it can be seen how quickly the stainless steel erodes. This is consistent with
Figure 6.3: Photos of Anode Erosion
what was seen in the mass loss test, in that the more consecutive firings that were preformed, the less mass
loss occurred during each shot. Within 15 shots the exit diameter increased by 23%. Electrode erosion is
common when dealing with high powered arcs. Usually, however, it is the anode that erodes more than
the cathode, which was not observed in our case. Through setting up and testing the stainless steel anode
again, it was possible to study this pattern with fewer shots because of the high erosion rate. Normally
arc attachment, localized heating(anode or cathode spots), and sputtering cause the majorty of erosion to
electrodes, however, in this capillary setup there are other factors involved. Looking at the inner edge
of the cathode at the exit plan, a curled jagged edge was observed, similar to a crested wave traveling
outward from the center. It was also observed that the diameter at the exit plane was larger than that
97
0 5 10 15
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
Number of Shots
Diameter (mm)
Figure 6.4: Plot of the anode erosion over 15 Firings
at the base of the insert, forming a conic shape. From these two observations it was concluded that high
cathode erosion was due to the high temperature, high pressure gas exiting the device. This gas melted the
stainless steel at the surface and forced it outward. If one looks at the plot of diameter as a function time,
as in Figure 6.4, the expansion rate decreases with time. Given the aforemetioned conclusion, this makes
sense in that the erosion pattern naturally develops into a nozzle, causing the gas to expand, accelerate,
and cool in passing through it. From Figure 6.4 it can be estimated that diameter change could asymptote
somewhere around 5mm. This could be were the flow is cooled enough by expansion so as to not to erode
the cathode tip.
As described in Section 2.1.2, after this initial expansion pattern was recognized, tungsten electrodes
were used in subsequent tests. This material held up better and did not erode as quickly, but the same
pattern was still observed. As can be seen from the Paschen ignition data, not only was the mass loss high
but it was also sporadic. Figure 6.5 exhibits the percent mass loss of both the electrodes and the capillary
tube, for all of the Paschen ignition tests. As seen in plot (a), the shorter capillaries seem to suffer much
greater electrode erosion than the longer capillaries at a given energy. This was expected because of a
higher ratio of capillary surface area to electrode surface area for longer capillaries. While this must be
98
a factor it is likely not the dominant cause of such high erosion rates in shorter capillaries. By plotting
mass loss as a function of peak current, as shown in Plot (b), it is possible to see a dependence free of
capillary length. It becomes clear that electrode erosion is heavily dependent on peak current. Therefore,
the major reason 10cm capillaries show less electrode mass loss is because they experience much lower
currents. It turns out that the mass loss of the capillary stays fairly independent of length, as shown in
0 500 1000 1500 2000 2500
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Energy (J)
Percent Mass Loss
(a)
2000 4000 6000 8000 10000
0
0.2
0.4
0.6
0.8
1
1.2
Peak Current (A)
Percent Mass Loss
(b)

Tube (4 cm)
Tube (6 cm)
Tube (8 cm)
Tube (10 cm)
Electrodes (4 cm)
Electrodes (6 cm)
Electrodes (8 cm)
Electrodes (10 cm)
Figure 6.5: Plots of the percent mass loss for Paschen tests as a function of (a) energy and (b) current
Figure 6.6, plot (a). This plot also shows how significantly the electrodes erode compared to the ablation
of the capillaries for the three electrode ignitions system. Further investigating of the mass loss indicated
that while both anode and cathode increase in erosion as a function of energy, it is the anode erosion that
increases at a much faster rate, as shown in plot (b) of Figure 6.6.
6.3 Dual Mode Operation
The results shown in Figure 5.4 in Section 5.2 exhibit a clear dual mode of operation, the root cause of
which was never discovered. The high current operation mode was only seen under the test conditions
99
500 1000 1500 2000 2500
0
0.005
0.01
0.015
0.02
0.025
0.03
Energy (J)
Mass Loss (g)
(a)

Tube (4 cm)
Tube (6 cm)
Tube (8 cm)
Electrode (4 cm)
Electrode (6 cm)
Electrode (8 cm)
500 1000 1500 2000 2500
0
0.005
0.01
0.015
0.02
0.025
Energy (J)
Mass Loss (g)
(a)

Anode (4 cm)
Ande (6 cm)
Anode (8 cm)
Cathode (4 cm)
Cathode (6 cm)
Cathode (8 cm)
Figure 6.6: (a)Precent mass losses and (b) mass loss in
described for atmospheric wire ignition. During all of the Paschen, PPT, and 3-electode ignition runs, no
second current mode was ever witnessed.
One of the theories as to why this occurs is based on the initial plasma conditions. It is proposed that
due to the chaotic nature of an exploding wire, it is possible that the initial condition of the capillaries
are different. As shown in Figure 1.7, the wire does not instantly form a plasma inside the capillary.
The wire heats and breaks apart in segments before fully vaporizing. If the wire was to break at one end
first, as opposed to the other, it may cause the capillary to start differently. Or perhaps, In the case of the
high current mode the wire did break down much more evenly, filling the capillary with an already highly
ionized medium to initiate conduction. This would allow for a higher
di
dt
because a strong conduction path
in the capillary has already been established. This is opposed to the instance where the wire breaks down
in one location first, and the discharge therefore needs to build a strong conductive path using ablated
material from the wall. This argument could also explain the frequency at which the high current mode
occurs. For a long capillary it would be hard to create this instant conductive plasma column uniformly
over such a large distance. However in a short capillary it becomes more likely as the segment of wire
that needs to evenly explode becomes shorter.
100
6.4 Ablation Effects
As mentioned in section 1.4.1 the ablation process is very complicated. Radiation can be absorbed at the
surface for penetrate into the depth of the capillary wall. These processes become even more complicated
when electrode erosion in considered. Cathode and anode spots are caused by the glow-to-arc transition
that occurs there[9]. The electric field near the anode and cathode can be 100 to 1000 times higher than
the rest of the plasma column, causing small defects in the electrode surface to explode, with metallic
particle leaving the surface at very high velocities. These hot fast moving particles travel axially and
imbed themselves into the capillary wall. This effect has been well documented by Kukhlevsky et al[57].
In their capillary discharge experiment, similar to the one presented in this work, they showed that this
particle could penetrate up to 2:4 mm into the walls. The penetration path would close and the hot
particle would vaporize the surrounding material causing a bubble to form. These bubbles were estimated
to reach a few tens of atmosphere before bursting. Kukhlevsky et al measures about 40 bubbles/mm
3
and
showed that they added significant mass to the plasma column. This phenomenon was also seen in the
tests conducted here. Simple examination of the white polyethylene tubes showed spots in the capillary
wall. Some of these spots were dark, some were light, and others were metallic in appearance. These
spots were much higher in concentration near the anode. While it is not clear whether these spots formed
bubbles that exploded into the capillary, it seems clear that the electrode erosion can affect the ablation
process.
While collecting data sets using the tungsten cathode design, tubes would be critically damaged after
only a few of firings. This seemed odd, as the amount of material ablated from each shot is not sufficient
to wear though the tube in 5 or 10 shots. However, tube failures have occurred in just 4 shots. When the
tube fails, it seems to collapse inward. Because the smoothness of the bending of the tube wall, it was
originally believed that this was caused by heating of the cathode and housing, causing the plastic material
to melt or become soft and be deformed. There was also a considerable amount of soot on the outside of
the tubes as has been seen throughout the history of our capillary testing. It was always assumed that this
soot was gas that slipped between the cathode and the housing upon exiting the capillary. Because the
new design incorporated a “lip” type seal at the cathode and a swage seal at the anode, it became evident
that the soot from the outside of the tube was not merely blow by gas from the main discharge. Instead
this soot came from ablation on outside of the tube. This outside ablation causes a pressure build-up
between the housing and the tube. The new sealed design would eventually cause the tube to fail inward,
collapsing in upon itself.
101
In Figure 6.7 are pictures of highly outside ablated tubes. Both of these tubes were fired at 2500V , 5
times. The lip seal as been cut off as shown by the rough surface on the right side. This unfortunately is
necessary to extract the tube from the housing after the swage seal as been placed on the anode (left) end.
In the case of the first picture the tube failed under a full collapse. The lip seal at the cathode ripped and
caused more damage, and mass loss, to the cathode. In addition a hole was made close to the anode. This
caused the arc to attach to the inner housing instead or the cathode. The second picture shows a tube that
collapses but did not fail completely by spitting open.
Figure 6.7: Photo of Capillary Failure do to External Ablation
Evidence of a large amount of energy leaving the capillary is also corroborated by the heating of
the stainless steel housing. On a average test firing the stainless steel housing increased in temperature
an average of 10

C. The temperature change is measured by placing a smallT=C on the cathode cap.
The temperature spikes high during (immediately following) the discharge, but fell just as rapidly back
to near the original temperature. It is unclear weather this is due to electrical noise or an actual thermal
phenomena. However, after the original temperature spike, the temperature would slowly increase to a
maximum value, and then decrease very slowly. This was primarily the housing coming to a uniform
temperature as the thermal load diffused through the housing. For Stainless steel the heat capacity is
0:5J=g=

C, therefore it would take 400J to raise the 80g housing 10

C. Considering that the discharges
used 400 to 1600J of energy, a large fraction of the total energy that is deposited into the thruster was
not being used to ablate of heat the plasmas but instead is being wasted.
102
6.5 Initial Discharge
One phenomenon that was observed during the Paschen ignition tests, when more than one firing was
taken on a tube, was that the first discharge was always different than subsequent ones. A good example
of this is shown in Figure 6.8, in which the current profile is plotted for a set of Paschen breakdown
tests. Here 5 shots were taken on the same tube. The first discharge had noticeably higher currents
0 50 100 150 200 250 300 350 400
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Time (μ s)
Current (A)

1st Discharge
2nd Discharge
3rd Discharge
4th Discharge
5th Discharge
Figure 6.8: Five consecutive fires on a 6cm capillary at 2500V
and longer discharge times. Such an effect it most likely due to the optical properties changing after
the discharge. After the first discharge occurs the material surface is significantly different. It is not as
smooth, roughened from the boiling and evaporation that occurs during the ablation precess. There is
also soot that coats the surface from previous discharges. While this effect was also seen using black
capillaries, it was not nearly as pronounced. This initial discharge effect can help explain some of the
sporadic data from the Paschen tests; especially in the cases when one data point is slightly off from the
103
rest of the group. This problem was remedied in the 3EIS tests by not only using black polyethylene, but
by preconditioning the capillaries as discussed in Section 5.5
6.6 Material factors
Material factors played a larger roll than originally thought in capillary discharges. Not only in the
capillary material but also the material of the housing that surrounding it. As discussed in Section 6.4
external capillary ablation became a large problem. The capillary design was changed in order to deal
with this problem. The original inspiration to change the design to standard tubing was simply to allow
for the ease of replacement. A full collapse and arcing to the housing wall causes pitting and damage
that makes it exceedingly more difficult to load and extract capillary tubes without damaging them. The
idea for the new housing was to use standard stainless steel pipe that could be replaced without having to
re-machine the housing. When it was realized that the outside of the capillary was abating as well, this
design allowed the use of different housing material in order to try to minimize or eliminate the secondary
ablation.
A series of tests were conducted using either clear or black polyethylene tubes in, stainless steel,
clear polycarbonate, or alumina housings. The effect of these materials on the current profile are shown
in figure 6.9. Notice that a clear polyethylene in stainless steel had a long tail, while the same tube in
alumina had the shortest tail. The black tubing showed small tails and were also affected slightly by
the housing material. This suggests that radiation not only penetrates deep into the capillary wall, but
also passes through the capillary material to interact with the housing wall. The energy that reaches that
far is; either absorbed at the surface causing the exterior ablation, absorbed within the housing causing
the temperature raise discussed in section 6.4, or as suggest here, reflects back into the plasma effect the
discharge itself. It is interesting to note that neither material of the tube nor the housing influenced current
rise or peak power, but mostly effected the extinction of the device. There was an except in the case of
the polycarbonate and clear polyethylene tests which resulted in slightly higher peak currents.
6.7 Background Pressure Effects
As seen in Firgure 6.1 and mentioned in Section 6.1 wire ignition tests showed a much different initial
current profile than the other ignition methods. This was particularly true for longer capillaries. It is
104
0 50 100 150 200 250 300 350 400
0
500
1000
1500
2000
2500
3000
3500
Time (μ s)
Current (A)

Clear SS
Black SS
Clear Lexan
Clear Alumima
Black Alumima
Figure 6.9: Current Traces for Various Capillary Materials
believed that part of this effect was due to the background pressure of the capillary. A small series of tests
were conducted using the wire igntion method at a variety of different background pressures. The same
housing and setup that was used in the Paschen ignition was also used for these tests. The thin igntion
wire was simply attached between the cathode and anode. A 6cm capillary at 2500V was fired over 5
orders of magnitude of pressure. The pressure showed a clear effect on the discharge current as shown in
Figure 6.10. The current profiles in this graph have all been normalized to the same peak value to more
clearly illustrate the shifting profiles. The peak current was not affected outside the normal deviations
seen between shots. The extinction, or second half of the current profile, was also unaffected. What was
influenced is the
di
dt
after the wire explosion. For the atmospheric test, there is a clear change in curvature
and the presence of an initial current pulse from the exploding wire. This transitions away with lower
pressures until , at 0:4mtorr, the initial hump is no longer present and there is a consistent
di
dt
throughout
the entire ignition process. It is difficult to determine weather the effects are purely consequence of the
pressure within or outside of the capillary. It is very possible that within a certain pressure regime the
105
0 50 100 150 200 250 300 350 400
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Time (μ s)
Current (A)

690 torr
69 torr
6.9 torr
0.069 torr
Figure 6.10: Current Traces for Various Background Pressures
wire acts like the dominant mechanism for that regime. For example, it is possible at very low pressure
that the wire breaks, creating a spark similar to the 3EIS and causing it to ignite by those mechanisms.
Because of the small but noticeable effect of pressure on the current profile, it would have been nice
to investigate the effect of the pressure on thruster performance. However none of the other ignition
techniques can be used over a wide range of pressures. The Paschen ignition only worked for a very
specific pressure, around 10torr, and the 3EIS needs higher vacuum for ignition.
The wire ignited capillary was put on the thrust stand to investigate the impulse. NoI
sp
of could be
measured because of the inability to accurately account for the mass. The results of the stand deflection
as a function of background pressure are shown in Figure 6.11 The results from this test show a surprising
trend, however the reasons are inconclusive. It is believed that the performance differences is based on a
combination of plume expansion and amount of wire that is vaporized. At atmospheric pressures, where
there is a slower current rise, it is possible that the wire material breaks down more completely and adds
to the plasma composition. In the low temperature range, near the Paschen regime, the first little break
106
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
10
1
10
2
10
3
3.5
4
4.5
5
5.5
6
6.5
Pressure (Torr)
Deflection (V)
Figure 6.11: Thrust Stand Deflection vs. Background Pressure
in the wire could cause a Paschen breakdown, large sections of wire might be blown out the the capillary
without fully vaporizing. Consequently little material would be added to the discharge and would be
unavailable for heating, thus creating little added thrust. This does not however explain way the impulse
increases again at full vacuum conditions. If it became the case that the wire now more fully explodes,
because the capillary became harder to ignite again, it is reasonable to would assume that this would show
up in the current profile.
107
Chapter 7
Conclusions
Capillary discharge ignition methods were studied in depth. Effects on discharge properties and thruster
performance were observed. The wire ignition method proved to be the most reliable over all lengths of
capillaries. However, this method produced a dual mode of operation. The dual mode was caused by the
chaotic nature of the wire exposion within the capillary, which caused the initial conditions to vary. Dual
mode operation was not seen using other ignition methods.
Despite initial believes, the type of ignition method did not play a large roll in the discharge process.
The methods tested here did not largely effect the over all discharge. While the wire method did produce
slightly higher currents, it is easily accredited to the additional mass introduced by the wire and not a
fundamental difference of operation. Even the larger fracdidt seen in longer capillaries ignited with
wire are explained by the difference in background pressure. Once the main capillary discharge is started
the arc is quickly controlled by the ablated material process, and the method that was used to achieve
those conditions had little effect.
The Paschen ignition method also worked well over a full range of capillary lengths. Paschen ignition
allowed for the first look at AFRL capillary thruster performance. The Paschen setup also made it possible
for a number of capillary issues to be addressed; from electrode erosion, to pressure sealing, to diagnostic
development. In the end Paschen ignition did not lead to a spacecraft system, but it did have valuable
merits. One of the more interesting phenomenon seen with Paschen testing were capillary re-strikes.
The restrike occurred after the capillary extinguished itself. As the remaining gas exhausted out of the
capillary, the pressure would drop to a range where the capillary could discharge again, based on the
remaining charge of the capacitors. These were eliminated by only allowing the SCR switch to open for a
short period of time. This was not advantageous for thrust measurements conducted here, but may be used
in the future for repeat operation using a pulse forming network. It could be conceived that the capillary
would only need to be ignited once for a series of consecutive discharges.
Of the three ignition methods tested, the three-electrode ignition system worked the most reliably
and is the most suitable for space applications. This method showed no major performance differences
over the other methods, but is did allow for ignition in full vacuum and for thruster measurements to be
108
made. The 3EI system did have trouble igniting the longer capillary lengths. However, it is believed that
with less wear on the cathode, and more accurate machining of ignition electrodes and material, longer
capillaries can be ignited.
The AFRL capillary used in this ignition study has not been fully optimized and is therefore not
operating near it’s full potential. As mentioned earlier in this work, similar capillary discharges have
show experimental efficiencies as high as 56% and a theoretical efficiency as high as 80%. The two major
factors needed to increase the efficiency of the ARFL CD are a nozzle and better ablative materials. In
order to study ignition a nozzle was not necessary. However, to convert the high thermal energy of the
capillary plasma into directed kinetic energy a nozzle is needed. It is also important to consider the length
of the nozzle. The nozzle needs to allow time for the plasma to de-ionized. This allows for a large amount
of the energy used to ionize to be -re-introduced into the flow as thermal energy, which is than expanded
by the nozzle into directed energy, ultimately producing higher thrust and efficiency.
Another important contributor to the efficiency is the material. As was learned throughout these
ignition tests the material plays a large role in the extension of the discharge. It was also observed that a
significant amount of the radiation energy does not ablate material, but passes into or through the capillary
material. This was evident by both the outside ablation and the heating of the housing. However, even
when black polyethylene was used, and outside ablation was eliminated, thrust efficiency did not improve.
This suggests that radiation is still being absorbed through the capillary. While the radiation energy does
not pass through the capillary it is not being absorbed near the surface. The energy is dissipated though the
capillary volume which does not lead to efficient ablation. There is a large resource of material ablation
literature that could aid in the selection and testing of different material. Paper on PPTs and ablation
controlled arc have already looked at different materials in the ablation process. While the devices are
slightly different, there is useful knowledge that can be obtained.
Electrode erosion was also identified as a key contributor to performance differences between ignition
method. Because of the design differences between the various housings, and the improvements made
to electrode material and shape, the elctrodes were changed frequently during testing, thus the electrodes
wear changed throughout testing. While in an ideal experimental setup only one variable is changed, it
was difficult to achieve this condition for these tests. For future work it would be important to recall the
improvements made to electrodes in this study, and interesting to test other materials like a carbon anode
and a longer cathode with more surface area.
109
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Abstract (if available)

Abstract This work examined the effect of ignition on thruster performance characteristics of a capillary discharge device. Early tests of the presented device, incorporating an exploding wire ignition, showed a strong dependence on the initial plasma conditions. The literature supported these findings for more basic laboratory capillaries, but the effect on a thruster device was unknown. An in-depth investigation of different ignition systems were conducted for a capillary discharge based pulsed plasma thruster. In addition to conventional wires, capillary discharges were ignited with low pressure gas and several different types of spark igniters. These methods were compared with each other and with newly developed computer models.

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University of Southern California Dissertations and Theses

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Creator Pancotti, Anthony P. (author)

Core Title A study of ignition effects on thruster performance of a multi-electrode capillary discharge using visible emission spectroscopy diagnostics

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Aerospace Engineering (Astronautics)

Publication Date 11/09/2009

Defense Date 09/03/2009

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag ablation,ablation controlled arc,anode,capillary discharge,cathode,efficiency,electron number density,Erosion,impulse,multi-electrode,OAI-PMH Harvest,OES,optical emission spectroscopy,Paschen breakdown,polyethylene,specific impulse,temperature,three-electrode,thruster performance,wire ignition

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Muntz, E. Phil (committee chair), Erwin, Daniel A. (committee member), Ronney, Paul D. (committee member), Wang, Hai (committee member), Wang, Joseph (committee member)

Creator Email anthony.pancotti.ctr@edwards.af.mil,appancotti@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2719

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Repository Location Los Angeles, California

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