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Numerical and experimental investigations of ionic electrospray thruster plume
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Numerical and experimental investigations of ionic electrospray thruster plume
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Content
Numerical and Experimental Investigations of Ionic Electrospray Thruster Plume
by
Jeffrey Samuel Asher
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ASTRONAUTICAL ENGINEERING)
August 2022
Copyright 2022 Jeffrey Samuel Asher
I dedicate this thesis to Monica, my family, and loved ones.
Thank you for everything you do for me.
ii
Acknowledgements
I would like to thank my advisor Dr. Joseph Wang for his persistent support and guidance during
my time at USC. I am truly grateful for your teaching in space plasma physics, numerical methods,
and research in general. I owe a large portion of my own personal growth over these past 5 years
to the work that I was able to perform under your tutelage; thank you.
I would like to thank my committee members Dr. Daniel Erwin and Dr. Aichiro Nakano for
their productive insight and support for this thesis. Their time serving on my dissertation committee
and the advice they have offered has benefitted this work in ways I could not have predicted.
I would like to thank the entire Department of Astronautical Engineering faculty and staff. I
have enjoyed the stimulating and challenging curriculum as both a student and teaching assistant
over these years. I especially want to thank the excellent department staff: Dell, Marlyn, Linda, and
Luis. Your assistance has been of great help in the execution of this research, and your kindness
has made my time at USC all the more enjoyable.
I would like to thank all of my friends. To the members of Dr. Wang’s research group thank
you so much for your comraderie and support. To Dr. Rob Antypas, thank you for sharing so much
of your laboratory experience with me, and for putting in so much work getting USC’s electrospray
program off the ground. I’ll treasure all the time spent fixing vacuum pumps with you. To Chen
and Ziyu, thank you so much for your part in developing the multi-scale model presented in this
work. To my coworkers at the Johns Hopkins University Applied Physics Laboratory, especially,
Kelly, Doug, and Chris. Your guidance helped me through some of the most difficult parts of this
effort and I’m thankful for your friendship.
Finally, I would like to thank my family. To Monica, you are the love of my life and I am so
happy to have a partner in you. Over these past 5 years we have both grown so much, but more
iii
importantly we have grown so much closer together. The efforts in this work would not be possible
without you. Thank you to my mother, Susan, father, Steve, brother, Jon, step-father, Salvador, and
soon-to-be in-laws, Lisa and Chris. Your love drives me to do the things I do.
The author acknowledges the partial financial support of the Air Force Research Laboratory
Educational Partnership Agreement with USC. I would especially like to thank Dr. Dan Eckhardt
for his support for the research conducted in this work that was partially supported by the AFRL. I
would also like to acknowledge the tuition support provided by Johns Hopkins University Applied
Physics Laboratory’s Part-Time Study Program. Lastly, the simulations in this work were carried
out using resources made available by USC’s Center for Advanced Research Computing.
iv
TableofContents
Dedication ii
Acknowledgements iii
ListofTables vii
ListofFigures viii
Abstract xiii
Chapter1: Introduction 1
1.1 Electric Propulsion Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Gridded Ion Thrusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.2 Hall Effect Thrusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.3 Electrospray Thrusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.3.1 Ionic Liquid Propellant . . . . . . . . . . . . . . . . . . . . . . 10
1.1.3.2 Development History and Flight Experiments . . . . . . . . . . 10
1.1.4 Performance Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.1.5 Contamination and Plume-Spacecraft Interactions . . . . . . . . . . . . . . 17
1.1.5.1 Electrospray Thruster Contamination Concerns . . . . . . . . . 19
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.2.1 Experimental Characterization of Ionic Electrospray Thrusters . . . . . . . 21
1.2.2 Electric Propulsion Plume and Contamination Modeling . . . . . . . . . . 25
1.2.2.1 Electrospray Plume Modeling . . . . . . . . . . . . . . . . . . . 26
1.3 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.4 Thesis Outline and Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Chapter2: Methodology 32
2.1 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.1.1 Molecular Dynamics Method . . . . . . . . . . . . . . . . . . . . . . . . 32
2.1.2 Particle-Particle Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.1.3 Particle-In-Cell Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2 Laboratory Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.1 Pressure Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.2 Experimental Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.2.1 Probe Traversing System . . . . . . . . . . . . . . . . . . . . . 42
v
2.2.2.2 Faraday Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.2.2.3 Retarding Potential Analyzer . . . . . . . . . . . . . . . . . . . 44
2.2.2.4 Langmuir Probe . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.2.3 Commanding and Data Acquisition . . . . . . . . . . . . . . . . . . . . . 47
2.2.4 USC Testbed Thruster . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.4.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.2.4.2 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Chapter3: BaselineParticle-In-CellPlumeModel 53
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.1 Estimate on the Effect of Fragmented Ions . . . . . . . . . . . . . . . . . . 65
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Chapter4: Multi-ScalePlumeModel 74
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2 Simulation Model and Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2.1 Molecular Dynamics Model . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2.2 Immersed-Finite-Element Field Solver . . . . . . . . . . . . . . . . . . . . 76
4.2.3 Particle-Particle Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2.4 Particle-in-Cell Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.3.1 Single Emission Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.3.2 Effects of Multiple Emission Sites . . . . . . . . . . . . . . . . . . . . . . 87
4.3.3 Effects of Ion Fragmentation . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3.4 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Chapter5: ExperimentalValidation 96
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3 Numerical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.4.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.4.2 Numerical Chamber Model Results . . . . . . . . . . . . . . . . . . . . . 104
5.4.3 Comparison Between Experimental Estimates and Numerical Models . . . 105
5.5 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Chapter6: Conclusionandfuturework 115
References 118
vi
ListofTables
1.1 Reported ionic electrospray thruster parameters from ongoing characterization ex-
periments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1 UTT-3 characterized performance values . . . . . . . . . . . . . . . . . . . . . . 52
3.1 Thruster parameters informed by experimental design efforts. . . . . . . . . . . . . 54
3.2 Key simulation parameters in physical and normalized units for baseline PIC model
setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Empirical field free fragmentation rates for EMI-BF
4
as reported in [77] . . . . . . 68
3.4 Key simulation parameters in physical and normalized units . . . . . . . . . . . . 68
4.1 Physical input parameters for PP model setup . . . . . . . . . . . . . . . . . . . . 79
4.2 Key simulation parameters in physical and normalized units for PIC model setup . 80
5.1 Correlation data for collection of Langmuir probe measurements. . . . . . . . . . . 112
vii
ListofFigures
1.1 Diagram of electron bombardment gridded ion thruster . . . . . . . . . . . . . . . 6
1.2 Diagram of Hall effect thruster . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Different electrospray emitter tips . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Electrical schematics and primary components of colloid electrospray, ionic elec-
trospray, and FEEP thrusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Molecular structure of the EMI-BF
4
ionic liquid, with the EMI
+
cation and BF
− 4
anion [96] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.6 Previously flown ionic electrospray technology demonstration missions. Left: MIT
iEPS, Middle: MIT SiEPro, Right: Accion Tile . . . . . . . . . . . . . . . . . . . 12
1.7 Ionic electrospray thrusters in development. a) USC testbed thruster [6] b) North-
western Polytechnic University electrospray thruster [23] c) AFRL’s Air Force
Electrospray Thruster Series 2 (AFET 2) [82] d) Accion Tile [85] e) University of
Southampton’s PEEK-100 [68] f) MIT scalable ion electrospray propulsion system
(SiEPro) [45] g) Busek’s BET-100 h) Busek’s BET-300-P [37] . . . . . . . . . . . 12
1.8 Thrust versus efficiency for a collection of small satellite propulsion devices. Mod-
ified from [105] using data from [85] . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.9 Power requirements for a collection of small satellite propulsion devices. Modified
from [105] using data from [85] . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.10 Power efficiency versus thrust efficiency for a collection of small satellite propul-
sion devices. Modified from [105] using data from [85] . . . . . . . . . . . . . . . 15
1.11 Power efficiency versus thrust efficiency for a large collection of electric propul-
sion devices. Modified from [44] using data from [23, 37, 69, 82, 85] . . . . . . . . 16
1.12 Description of primary solvated ion fragmentation mechanisms: acceleration re-
gion fragmentation and field-free fragmentation . . . . . . . . . . . . . . . . . . . 20
1.13 Reported ionic electrospray plume composition . . . . . . . . . . . . . . . . . . . 22
1.14 Ionic liquid bridging damage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
viii
1.15 Ionic electrospray modeling regions . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1 MD simulation flow diagram of major subroutines . . . . . . . . . . . . . . . . . . 34
2.2 PP simulation flow diagram of major subroutines . . . . . . . . . . . . . . . . . . 36
2.3 PIC modeling flow diagram of major subroutines . . . . . . . . . . . . . . . . . . 37
2.4 Force weighting scheme for particle and neighboring grid points. . . . . . . . . . . 38
2.5 USC LEAP primary chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.6 Traversing probe suite for downstream plume sensing. The instruments from left to
right are: Phosphor screen, Retarding Potential Analyzer (RPA), Collection Plate
(at the back of chamber) (CP), MicroFaraday Probe (MFP), Langmuir Probe (LP),
Faraday Probe (FP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.7 Faraday probe construction and electrical schematic. . . . . . . . . . . . . . . . . 44
2.8 Retarding potential analyzer construction and electrical schematic. . . . . . . . . . 45
2.9 Example RPA scan data for thruster firing in negative mode. . . . . . . . . . . . . 45
2.10 Langmuir probe and electrical schematic. . . . . . . . . . . . . . . . . . . . . . . 46
2.11 Sample Langmuir probe sweep data used to estimate the plume potential at a given
sample position. a) LP scan b) Logarithmic scale with slope comparisons. . . . . . 48
2.12 LEAP LabVIEW user interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.13 LEAP command and control diagram . . . . . . . . . . . . . . . . . . . . . . . . 49
2.14 USC Testbed Thruster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.15 Exploded view of UTT with primary components . . . . . . . . . . . . . . . . . . 51
2.16 Emitted current and interception fraction for positive mode emission . . . . . . . . 52
3.1 Simulation domain setup with boundary conditions. The red cell denotes the area
of EMI
+
injection and the blue cells denotes the area of BF
− 4
injection . . . . . . . 58
3.2 Isometric view of logarithmic charge density contours. . . . . . . . . . . . . . . . 59
3.3 Plasma parameters in the XY plane, a) Normalized potential (with respect to Cube-
Sat) b) Normalized charge density c) Normalized electric field. . . . . . . . . . . . 60
3.4 Plasma parameters in the XY plane, a) Normalized potential (with respect to Cube-
Sat) b) Normalized charge density c) Normalized electric field.Top: Slice at BF
− 4
midline. Middle: Slice at domain midline. Bottom: Slice at EMI
+
midline. . . . . 62
ix
3.5 Plasma parameters in the YZ plane, a) Normalized potential (with respect to Cube-
Sat) b) Normalized charge density c) Normalized electric field. Top:
ˆ
X = 50, Mid-
dle:
ˆ
X = 125, Bottom:
ˆ
X = 200 . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.6 Phase space comparison of x-vx dimensions . . . . . . . . . . . . . . . . . . . . . 64
3.7 Phase space comparison of z-vz dimensions . . . . . . . . . . . . . . . . . . . . . 65
3.8 Potential at the plume midline for various slices along the X-axis displaying the
comparison between the cases: EMI
+
only, BF
− 4
only, bipolar. a) X = 60, b) X =
90, c) X=120 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.9 Top: XZ view of difference in BF
− 4
density between pair emission and single beam
emission in domain midline. Bottom: YZ view of difference in BF
− 4
density at
ˆ
X
= 120. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.10 Top: XZ view of difference in EMI
+
density between pair emission and single
beam emission in domain midline. Bottom: YZ view of change in EMI
+
density
at
ˆ
X = 120. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.11 Charge density of EMI(EMIBF
4
)
+
dimers. The decrease in dimers in the down-
stream region is caused by the constant fragmentation rate. . . . . . . . . . . . . . 69
3.12 Isometric view of charge density contours for, a) Monomer only baseline b) 50%
monomer, 50% dimer c) 50% monomer, 50% dimer with field-free fragmentation . 69
3.13 Normalized plasma parameters in the XZ plane, a) Charge density, b) Plasma
Potential, c) Electric field for Top: No Monomer only baseline, Middle: 50%
monomer, 50% dimer, Bottom: 50% monomer, 50% dimer with field-free frag-
mentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.14 Normalized plasma parameters in the XY midline plane, a) Charge density, b)
Plasma Potential, c) Electric field for Top: No Monomer only baseline, Middle:
50% monomer, 50% dimer, Bottom: 50% monomer, 50% dimer with field-free
fragmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.15 X-V
x
phase space comparison between, a) Monomer only baseline b) 50% monomer,
50% dimer c) 50% monomer, 50% dimer with field-free fragmentation . . . . . . . 72
3.16 Z-V
z
phase space comparison between, a) Monomer only baseline b) 50% monomer,
50% dimer c) 50% monomer, 50% dimer with field-free fragmentation . . . . . . . 72
4.1 MD emission of monomer and dimer species from an applied electric field. . . . . 75
4.2 The geometry of the emitter tip and extractor grid for calculating background field
properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3 Background a) electric potential and b) electric field strength in the acceleration
region for the positive emission case. . . . . . . . . . . . . . . . . . . . . . . . . . 78
x
4.4 Particle positions in the XZ plane (top) and YZ plane (bottom). . . . . . . . . . . . 83
4.5 Comparison of monomer velocity distribution functions (VDFs) at the input (Top)
and output (Bottom) of the PP model. Red denotes cation, blue denotes anion.
Left: Velocity distribution in the X direction. Middle: Velocity distribution in the
Y direction. Right: Velocity distribution in the Z direction. . . . . . . . . . . . . . 83
4.6 Comparison of dimer velocity distribution functions (VDFs) at the input (Top)‘
and output (Bottom) of the PP model. Red denotes cation, blue denotes anion.
Left: Velocity distribution in the X direction. Middle: Velocity distribution in the
Y direction. Right: Velocity distribution in the Z direction. . . . . . . . . . . . . . 84
4.7 Plasma potential contours for single emitter case. . . . . . . . . . . . . . . . . . . 86
4.8 Charge density contours for single emitter case. . . . . . . . . . . . . . . . . . . . 86
4.9 Electric field strength and vectors for single emitter case. . . . . . . . . . . . . . . 86
4.10 PP model particle positions in XZ plane for two emitter case. . . . . . . . . . . . . 87
4.11 Comparison of beam radial velocity distribution between single emitter and double
emitter case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.12 Plasma potential contours for triple emitter case. . . . . . . . . . . . . . . . . . . . 89
4.13 Charge density contours for triple emitter case. . . . . . . . . . . . . . . . . . . . 89
4.14 Electric field strength and vectors for single emitter case. . . . . . . . . . . . . . . 89
4.15 Comparison of radial position of monomer ions between simulations with and
without fragmentation a) EMI
+
ions b) BF
− 4
ions . . . . . . . . . . . . . . . . . . 90
4.16 Comparison of radial velocity distribution of entire beam for cases with and with-
out fragmentation included, a) cation beam b) anion beam . . . . . . . . . . . . . . 91
4.17 Plasma potential contours for fragmentation case. . . . . . . . . . . . . . . . . . . 92
4.18 Charge density contours for fragmentation case. . . . . . . . . . . . . . . . . . . . 92
4.19 Electric field strength and vectors for fragmentation case. . . . . . . . . . . . . . . 92
5.1 Representative electrospray thruster test profile for bipolar emission . . . . . . . . 97
5.2 LEAP chamber and experimental scan region dimensions. . . . . . . . . . . . . . 99
5.3 Comparison between LEAP chamber, experimental scan region, and numerical
simulation domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.4 Numerical simulation domain for UTT in LEAP chamber model. . . . . . . . . . . 101
5.5 Isometric view of Faraday probe current collected during 3D scan . . . . . . . . . 102
xi
5.6 Faraday probe current collected during 3D scan, displaying slices of interest along
XY plane for a) positive emission and b) negative emission at a downstream dis-
tance of approximately 3.875” . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.7 Faraday probe current collected during 3D scan, displaying slices of interest along
YZ plane for a) positive emission and b) negative emission at beam midline. . . . . 103
5.8 Faraday probe current collected during 3D scan, displaying slices of interest along
XZ plane for a) positive emission and b) negative emission at beam midline. . . . . 104
5.9 Isometric view of plume density isosurface for a) positive emission and b) negative
emission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.10 Isometric view of plume density isosurface for a) positive emission and b) negative
emission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.11 Plume number density comparisons between 1D Faraday probe scans and numeri-
cal models for positive (panels a - c) and negative emission (panels d - f). . . . . . 107
5.12 Plasma potential comparison between experimental measurements and numerical
predication at a downstream distance of 89mm. . . . . . . . . . . . . . . . . . . . 109
5.13 Plasma potential comparison between experimental measurements and numerical
predication at a downstream distance of 152mm. . . . . . . . . . . . . . . . . . . . 109
5.14 Plasma potential comparison between experimental measurements and numerical
predication at a downstream distance of 216mm. . . . . . . . . . . . . . . . . . . . 109
5.15 Diagram of principle mechanisms for sensor error . . . . . . . . . . . . . . . . . . 111
xii
Abstract
Ionic electrospray thrusters offer a promising novel high efficiency and low thrust propulsion ca-
pability for future space missions. Since the technology’s development in the early 2000’s, the
research community has been largely focused on maturing the technical design and standardizing
experimental characterization techniques. As this thruster technology has progressed, character-
izing and mitigating spacecraft integration hazards has become a pressing concern. Although
spacecraft integrations can be investigated in a laboratory setting, the development of an indepen-
dent numerical model of ionic electrospray emission is critical for a complete understanding of the
thruster and plume physics. This dissertation presents the most complete numerical modeling of
an ionic electrospray thruster plume to date in order to better assess thruster plume phyiscs and
potential hazards imposed on the spacecraft bus.
This work first presents a fully kinetic 3-dimensional particle-in-cell (PIC) simulation study
of the plume from a bipolar ionic electrospray thruster pair using 1-ethyl-3-methylimidazolium
tetrafluoroborate (EMI-BF
4
) ionic liquid propellant. The results show a unique beam neutraliza-
tion process, where there is little physical coupling between the positive cation and negative anion
beam. These dynamics are likely attributed to the similar mass ratio between the two beams and
the low current density of the beams at this scale. The small potential difference within the beam
suggests that low energy fragmented species will not be significantly scattered, ejected, or likely to
return as backflow. The weak electric field magnitude within the beam suggests that the fragmen-
tation of ion clusters within the plume may occur at a reduced rate than measured in laboratory
experiments.
To affirm the findings presented in the baseline PIC model, this work combines a molecular
dynamics model, a particle-particle model, and a particle-in-cell model to investigate the physics
xiii
of ionic electrospray propulsion over 9 orders of magnitude in length scale. The combined models
are applied to simulate beam emission for an ionic electrospray propulsion system with porous
emitter tips from the emission site to the downstream plume. The impact of multiple emission
sites from a single emitter tip is analyzed with regard to extractor grid interception and overall beam
neutralization for bipolar thruster pairs. In addition, ion fragmentation, the leading cause for low
energy ion generation within electrospray thrusters, is assessed for its impact on overall thruster
plume dynamics. Results show that beams consisting of species of different masses (i.e. monomer
and dimer species) are affected by particle-particle forces during acceleration and should not be
treated as a superposition of independently accelerated species in macro-scale plume models. The
activation of multiple emission sites also causes a noticeable increase in the beam’s spread, leading
to increased intercepted current but relatively little adverse effects in the downstream plume region.
The presence of energy loss mechanisms through ion fragmentation also increase the overall beam
spread as low energy monomers experience a higher overall divergence angle. This increased
divergence, while noticeable in the downstream region, is determined to show little overall impact
on the increase in grid impingement.
An experimental test campaign is conducted using the USC Testbed Thruster to investigate
plume plasma parameters, namely the beam density and potential. This test campaign is the first
to directly compare experimental plume measurements with high fidelity numerical estimates. The
results validate the findings of the numerical models presented. The experimental data reflects the
overall plume structure predicted by the numerical models, with the multi-scale model providing
the most accuracy. Differences between chamber and free space models indicate that plume density
measured in the laboratory environment in the near downstream region can have an error up to 50%
that is induced by the chamber environment.
This body of work implies that ionic electrospray thrusters offer a relatively small contamina-
tion risk to spacecraft when compared with other micro-electric propulsion devices. The electric
field in the downstream region is found to provide little resistance to beam expansion and is not
xiv
likely to induce backflow in low energy fragmented ions even during common off-nominal opera-
tions.
xv
Chapter1
Introduction
Throughout the history of spaceflight, advancements in propulsion technology have aided mankind
to reach out ever-further to the stars. Propulsion systems allow for navigation to and through space.
During the first two decades of the 21
st
century, the world has seen a drastic reduction in launch
costs, lowering the barrier to access and invest in space platforms. In addition, the development
and commercialization of small scale spacecraft bus technology has seen a marked increase in
organizations’ ability to field a fleet of affordable, low cost spacecraft. In conjunction with these
trends, the development and integration of small, low weight, and efficient means of spacecraft
propulsion are of particular interest to enable new missions and provide flexability and safety
while on-orbit.
Electric propulsion devices have enabled high mobility space platforms due to their inherently
high fuel efficiency. Electric propulsion devices convert electrical energy into thrust through the
generation, acceleration, and expulsion of molecular or atomic ions. Unlike most chemical rockets,
electric propulsion devices generate low amounts of thrust, and are thus designed to operate for
extended periods of time, from days to months, to perform the required maneuver. However,
due to these extended periods of operation, even minor deleterious effects of thruster operation can
compound to mission-threatening levels over the mission lifetime. Understanding the structure and
behavior of the plume environment is critical to accurately estimating these deleterious effects,
such as surface contamination, and, as a result, has been a significant effort for past missions
leveraging electric propulsion.
1
Due to the advancement and proliferation of small spacecraft technology, and the reduced cost
of space lift capability, several space agencies and organizations are beginning to leverage simpler,
less expensive, and smaller spacecraft in larger numbers to achieve mission objectives. These small
spacecraft can provide challenging volume constraints as well as power generation and dissipation
constraints. One popular small spacecraft standard is known as the CubeSat [42]. The standard
unit, or U, of a CubeSat is a 10cm× 10cm× 10cm cube, with spacecraft ranging from 1U to
3U, 6U, or even 27U. Scaling down spacecraft technology to the CubeSat standard has enabled
universities, and commercial startups to invest in spacecraft technology. To match this trend of
shrinking spacecraft bus sizes, propulsion providers have similarly begun investigating shrinking
existing propulsion designs, or developing novel, compact means of propulsion. These propulsion
devices are expected to be a key enabler for future small spacecraft to perform advanced missions
such as interplanetary missions or autonomous formation flight and swarming.
Recently developed ionic electrospray thrusters offer a promising step forward in the current
state of micro-electric propulsion technology. Ionic electrospray thrusters are a new type of electric
propulsion that offer low size, weight, and power (SWaP), simple design, and high thrust-to-power
efficiency; making them an attractive option for small, power limited and volume constrained
platforms like the CubeSat class spacecraft. Additionaly, its simple construction and scalability
offers future large-scale missions a new means of propulsion with potentially fewer integration
challenges. This technology is currently under development in academia, government labs, and
commercial startup companies for such applications [23, 37, 69, 82, 85]. As this technology has
matured, emphasis has begun to shift from technology readiness issues to mission integration is-
sues. Spacecraft contamination has been identified as a key mission integration issue for ionic
electrospray thrusters.
Several research activities are ongoing to mature thruster design and characterize performance.
However, no in-depth joint experimental and computational campaign has characterized the plume
structure, neutralization dynamics, or contamination environment introduced by operation of ionic
electrospray thrusters. In addition, multi-scale modeling has recently been recognized with the
2
2013 Nobel Prize in Chemistry for its ability to address complex physical problems. This disser-
tation introduces the predominant factors associated with ionic electrospray physics, and performs
a series of three-dimensional (3D) plume simulation activities, including a multi-scale analysis, to
advance our current understanding of electrospray thruster technology. These simulation results
are coupled with corresponding experimental measurements to validate the numerical methods. As
a result, this dissertation aims to provide an in-depth analysis of ionic electrospray thruster plume
environment and neutralization dynamics.
1.1 ElectricPropulsionBackground
Beginning in the early 20
th
century, scientists and engineers theorized of efficient means of manuev-
ering through the vacuum of space. Tsiolkovsky and Goddard, the same visionary leaders who
were instrumental in developing the first chemical rockets, also theorized the use of electricity to
eject particles from a rocket[25]. To fully understand the value of electric propulson devices, one
must first consider the underlying physics of rocket propulsion. The theory of rocket propulsion is
derived from Newton’s 2
nd
law of motion which states that the net force on an object is equal to its
change of momentum.
F =
d(mv)
dt
(1.1)
Rockets generate this force through the acceleration and expulsion of stored propellant mass. With
this constraint we can extend Newton’s second law to what is known as the rocket equation.
∆v= v
e
ln
m
0
m
f
= gI
sp
ln
m
0
m
f
(1.2)
Here,∆v represents the change in rocket or spacecraft velocity, v
e
is the exhaust velocity, m
0
is the
initial rocket mass, m
f
is the final rocket mass, g is the gravitational constant at the surface of the
Earth, and I
sp
is the specific impulse. From this simple relationship several key conclusions can
be made. First, maneuverability is logarithmically proportional to the the ratio between initial and
3
final mass. Second, maneuverability is linearly proportional to the exhaust velocity or specific im-
pulse of the engine. Propulsion systems that are capable of generating faster exhaust, are capable of
more maneuvers. Spacecraft leverage this principle by accelerating and expelling gases or particles
from the vehicle, resulting in a propulsive force. Chemical propulsion achieves this acceleration by
converting chemical energy stored in the bonds of the propellant into kinetic energy through com-
bustion or other reactions. Alternatively, electric propulsion converts electrical energy into kinetic
energy. Electric propulsion devices generate charged particles or plasmas and accelerate them to
high velocities. Since electric propulsion devices accelerate individual ions, it is able to achieve
much higher efficiency when compared with chemical propulsion systems. Due to this efficiency,
mission∆v requirements are able to be met with larger payload mass fractions, maintaining large
mass budgets for spacecraft systems. This relationship has allowed electric propulsion devices to
enable novel space missions with large amounts of in-space maneuvers.
Electric propulsion devices can be classified into electrothermal, electrostatic, or electromag-
netic devices. These classifications correspond to the principle forces that contribute to the ac-
celeration of the exhaust particles. Electrothermal propulsion devices operate very similarly to
chemical propulsion systems. For chemical propulsion systems, higher efficiency is able to be
achieved from a faster exhaust velocity, which is in turn achieved from a hotter combustion tem-
perature. Electrothermal propulsion devices leverage electrical energy to add heat to the chemical
combustion process, improving thruster efficiency. Resistojets and arcjets are common examples
of electrothermal thrusters. The efficiency of electrothermal thrusters are typically greater than that
capable of being produced by a similar unaided chemical propulsion system, with specific impulse
values of 500s to 1000s. Electromagnetic thrusters leverage both electric and magnetic forces to
generate thrust. Typical electromagnetic thrusters include pulsed plasma thrusters (PPT’s) and
magnetoplasmadynamic (MPD) thrusters. Electromagnetic thrusters offer higher efficiency on av-
erage than electrothermal thrusters, but are considerably more complex as they have to manage
eletrical and magnetic systems. Electrostatic thrusters are electric propulsion devices that accel-
erate ions through the use of electric forces. Gridded ion thrusters, Hall effect thrusters, field
4
emission electric propulsion (FEEP), and electrospray thrusters are all considered to be electro-
static thrusters. Electrostatic thrusters are capable of the highest efficiency when compared with
other common propulsion methods due to their ability to accelerate ions to very large velocities.
This section will expand further on the physics of operation and plume environment of gridded ion
thrusters and Hall effect thrusters. This insight is critical to enable comparisons between legacy
electrostatic thrusters and new findings for ionic electrospray thrusters. FEEPs and electrospray
thrusters will be discussed in detail in Sec. 1.1.3.
1.1.1 GriddedIonThrusters
Gridded ion thruster technology was first demonstrated in 1964 on the SERT-1 sub-orbital demon-
stration mission. This initial test spurred the continued development and maturation of the tech-
nology, leading to breakthrough propulsion devices such as the NSTAR engine, which enabled
ground-breaking interplanetary missions such as Deep Space 1 and Dawn in 1998 and 2007, re-
spectively. Since the development of the first ion engines for interplanetary space travel, commer-
cial interests have adapted the technology for efficient stationkeeping of Earth orbiting spacecraft,
typically in geostationary orbit. This development, alongside other current trends of shrinking
spacecraft buses, has developed a need for more compact and smaller ion thrusters. These thrusters
have been developed by commercial companies for use as primary propulsion and attitude control
or stationkeeping [104].
Ion thrusters inject gaseous propellant, typically Xenon or another noble gas, into an ionization
chamber where it is ionized through electron bombardment or radio frequency ionization methods.
The ionization chamber walls are protected by using permanent magnets to control the motion of
the resulting plasma environment. The propellant ions are then accelerated and extracted through
multiple biased grids. The result is a positive ion beam. An external hollow cathode neutralizer
expels electrons to neutralize the resulting beam and mitigate spacecraft charging. Figure 1.1
provides a diagram of a notional gridded ion thruster and its primary components.
5
Figure 1.1: Diagram of electron bombardment gridded ion thruster
1.1.2 HallEffectThrusters
Stationary plasma thrusters, or Hall effect thrusters, were originally developed in the Soviet Union
in the 1960’s, by Morozov’s group at the Fakel Experimnetal and Design Bureau [79]. The initial
stationary plasma thrusters were independently developed out of a pressing need for high power
(kW) electric thrusters to enable interplanetary missions. The first stationary plasma thruster was
flown on the Meteor-18 mission in 1971. Since the end of the Cold War, western space angencies
have further adopted the thruster for their own uses, notably being used on the European Space
Agency’s SMART-1 mission in 2003.
Hall effect thrusters leverage a gaseous propellent that is ionized due to electron bombardment.
Instead of using an ionization chamber, Hall thrusters ionize their propellant in an annular dis-
charge channel. The thruster employs multiple static magnetic coils to generate a radial magnetic
field within the discharge channel. The base of the discharge channel is a biased anode surface.
The combination of the axial electric field and radial magnetic field creates a J× B force which
causes the charged particles within the discharge channel to drift around the channel. This drift
enables efficient ionization as neutral propellant atoms are introduced to this high density electron
6
environment. After the propellant is ionized, the axial electric field accelerates the ions from the
discharge channel. Again, a separate electron source is used to neutralize the resulting positive ion
beam.
Figure 1.2: Diagram of Hall effect thruster
Trends of miniaturization have also impacted the design of Hall thrusters. Current research
areas have investigated the magnetic shielding of Hall thruster components, reducing unwanted
erosion [28]. Similar minaturized Hall thrusters have gained such popularity that they are currently
being fielded in the hundreds onboard today’s proliferated LEO constellations, namely Starlink
Block 1.
1.1.3 ElectrosprayThrusters
Electrospray thrusters are a class of electrostatic propulsion devices that extract ions directly from
a conductive liquid propellant. Electrospray devices, and the plume they produce are used in a
variety of applications including material etching [43], material deposition [49], and spacecraft
7
propulsion [66]. Electrospray devices have widespread use due to the large variability in design
features such as, various liquid ion sources, liquid delivery systems, and intended plume particle
mass and energy composition.
The underlying physics driving ion extraction from a conducting fluid was first theorized by Sir
Walter Rayleigh in 1882 [89], experimentally verified by Zeleny in 1914 [123], and mathematically
derived by Taylor in 1964 [101]. Electrospray devices used for space propulsion can be further
categorized into the following, colloidal electrospray thrusters, ionic electrospray thrusters, and
field emission electric propulsion thrusters (FEEP). This section provides a summary of these
propulsion technologies, their distinguishing features, and theory of operation.
Key distinguishing features between the classes of electrospray thruster are the type of pro-
pellant, emitter tip geometry, and propellant reservoir. Colloidal and ionic electrospray thrusters
use various types of conductive ionic liquid propellant, whereas FEEP thrusters use liquid metal
propellants, such as Indium or Gallium. The propellant is typically delivered to the emission site
actively, through pumps, or passively through capillary forces through a porous media via Laplace
pressure. The propellant is exposed to the electric field through a variety of emitter tip variants.
Tips include capillary structures, externally wetted tips, and porous tips. Thrusters contain several
emitter tips organized into linear [65], circular [56] or rectangular arrays[30].
Figure 1.3: Different electrospray emitter tips
Colloid electrosprays use active propellant transport and capillary emitter tips and generally
expel charged droplets via cone-jet emission. By contrast, ionic electrospray thrusters utilize a
porous propellant reservoir and emitter tip, relying on passive capillary forces to deliver the pro-
pellant to the emission site. This design allows for the propellant to be delivered to areas of large
8
electric field, leading to predominantly pure ionic emission, although emitted species can range in
size from monomers, to dimers, trimers, and even droplets. The use of an ionic liquid propellant
allows for the emission of both positive and negative species. This feature allows two ionic elec-
trospray thrusters to be operated in bipolar fashion to emit a net neutral beam, negating the need
for an external neutralizing cathode. Several different FEEP designs have leveraged both active
capillary tips [108] and passive porous tips [9]. One key operational constraint for FEEP thrusters
is the need to heat the propellant before firing to achieve a homogenous liquid supply. Addition-
ally, the liquid metal ion source is only capable of producing positively charged ions, necessitating
the use of an external neutralizing cathode. The key differences between these thruster types are
summarized below in Figure 1.4.
Figure 1.4: Electrical schematics and primary components of colloid electrospray, ionic electro-
spray, and FEEP thrusters
9
1.1.3.1 IonicLiquidPropellant
Ionic liquids are typically referred to as room temperature molten salts. As with traditional solid
salts, ionic liquids are comprised of a molecular anion and cation. The first notable room tempera-
ture salt was ethylammonium nitrate developed by Walden in 1914[110]. Since then, ionic liquids
have been adopted broadly by several industries as solvents. Ionic liquids can be composed of a
variety of anion and cation pairs, leading to a variety of designer features, affecting bulk properties
such as conductivity, viscousity, and toxicity. Key properties for ionic liquids used as electrospray
thruster propellant include: low vapor pressure to prevent boil-off when exposed to the space en-
vironment, nontoxicity for ease of handling, and moderate conductivity for emission stability. A
widely used ionic liquid propellant, and the primary propellant of interest in the works described
herein is 1-ethyl-3-methylimidazolium tetrafluoroborate (EMI-BF
4
). The molecular structure can
be seen in Figure 1.5.
Figure 1.5: Molecular structure of the EMI-BF
4
ionic liquid, with the EMI
+
cation and BF
− 4
anion
[96]
1.1.3.2 DevelopmentHistoryandFlightExperiments
Electrospray thruster development can be traced back to the 1960’s with early colloid thruster
development efforts led by the academic research community and US Air Force. However, interest
stalled due to design and implementation challenges that slashed utility margins. Required thruster
10
potentials rose to prohibitive values up to 10 kV , leading to massive amounts of insulation that
undercut the thrust efficiency gains [47]. Colloid thruster development was reinvigorated in the
2000’s with technology advances making electrospray technology feasible. Experimental thrusters
developed by Busek Inc. were flown on the LISA Pathfinder mission, and are planned to be used
in the upcoming LISA mission [3]. FEEP thrusters have seen the most recent surge of interest
with competing startup companies having recently acquired funding and flown several thrusters,
namely Enpulsion [56], and Morpheus Space [54].
Several authors contributed to the development of what would become ionic electrospray thruster
technology, with incremental steps, some of which include: the use of EMI-BF
4
as a propellant
[90], and the development of externally wetted emitter chips[109]. Propellant delivery instabilities
led to the investigation of porous substrates. The first experiments of ionic electrospray thrusters
with porous, passive-fed emitters, the predominant design feature, were conducted in 2009-2013
by Dan Courtney and Chase Coffman [26, 30]. Their work led to the development of MIT’s ionic
electrospray propulsion system (iEPS). The priority of this early work was focused on development
of a working, compact propulsion subsystem and the understanding of key operating principles.
This work led to experimental maturation of the iEPS system into a scalabe spacecraft subsys-
tem (SiEPro). The technology developed in this lab led to a spinoff company, Accion, that has
developed technology into a commercial product. As a result MIT has been involved in the first
flight ionic electrospray thruster flight experiments. Figure 1.6 displays the previously flown tech-
nology demonstration missions. All AeroCube mission data regarding thruster operation remains
unpublished. BeaverCube was recently launched in 2020 and has a mission objective to prove out
Accion’s Tile2 propulsion system.
Since their first development, multiple organizations from academia, government, and indus-
try have invested in developing experimental ionic electrospray technology. Notable developers
include: MIT, the Air Force Research Lab (AFRL), Accion Systems Inc., Busek Company Inc.,
the University of Southern California (USC), the University of Southampton, and Northwestern
11
Figure 1.6: Previously flown ionic electrospray technology demonstration missions. Left: MIT
iEPS, Middle: MIT SiEPro, Right: Accion Tile
Polytechnical University, Xi’an. Images of thrusters developed from these notable developments
are displayed in Figure 1.7.
Figure 1.7: Ionic electrospray thrusters in development. a) USC testbed thruster [6] b) Northwest-
ern Polytechnic University electrospray thruster [23] c) AFRL’s Air Force Electrospray Thruster
Series 2 (AFET 2) [82] d) Accion Tile [85] e) University of Southampton’s PEEK-100 [68] f) MIT
scalable ion electrospray propulsion system (SiEPro) [45] g) Busek’s BET-100 h) Busek’s BET-
300-P [37]
12
1.1.4 PerformanceComparison
When determining a propulsion solution for a mission, there are several trades that need to be
considered. There are often several mission constraints that prohibit classes of propulsion meth-
ods. Neglecting these types of mission -specific constraints, we can help to differentiate the value
from propulsion devices by the required mission functions they are able to provide. We can clas-
sify propulsion systems amongst two primary functions, primary propulsion and stationkeeping
or attitude control. Primary propulsion typically corresponds to needs expressed by deep space
missions that require high∆v while also reserving high payload mass ratios. Stationkeeping refers
to frequent and regular maneuvers meant to maintain spacecraft orbital parameters. Low thrust
autonomous formation keeping is a new area of research that is currently under investigation. Low
thrust formation keeping guidance algorithms are currently under development [60, 94, 95]. Of
the current guidance control laws put forward, the propulsion requirements are in line with that
for traditional stationkeeping requirements. It should be noted that the recent proliferation of small
satellite and picosatellite technology offer a new, less massive interplanetary bus class that provides
a venue for a low thrust electric propulsion device to satisfy primary propulsion requirements that
would otherwise be unattainable on a more massive traditional host. This section provides addi-
tional context to the proposed value of ionic electrospray propulsion by comparing performance
characteristics with other propulsion types and legacy thruster designs. A large majority of this
section will be compiling and reiterating the conclusions expressed in [44, 52, 78, 105] and the
references therein. The reprinted figures are modified to highlight or add points corresponding
to current best estimates of ionic electrospray thruster performance. This section uses the per-
formance estimates of the Accion TILE thruster described in [85] as it is the most thorough and
complete characterization of a commercial ionic electrospray thruster avaiable to date.
Figure 1.8 displays a collection of CubeSat propulsion technologies, categorized by type, and
their relationship between max thrust and specific impulse. Here, we can see that there are several
options for CubeSat propulsion in the mN range. Although chemical systems are able to contribute
13
at this scale, to achieve higher ∆v requirements, high I
sp
devices are required due to the limited
tank volume onboard CubeSats.
Figure 1.8: Thrust versus efficiency for a collection of small satellite propulsion devices. Modified
from [105] using data from [85]
In addition to volume constraints, CubeSat platforms offer power generation constraints as the
size of solar arrays are physically limited. Figure 1.9 displays the relationship between power
and specific impulse. One can see that electrospray and PPT’s provide a low power option for
power-limited spacecraft.
The value of ionic electrospray thrusters for the CubeSat propulsion market can be seen when
comparing the thrust-to-power ratio versus specific impulse, as displayed in Fig. 1.10. What can
be seen from this figure is that the low power electrospray thrusters provide similar thrust-to-power
ratios of higher power Hall and ion thrusters. As a result, ionic electrospray thrusters demonstrate
the capability to be a low power alternative to current Hall and ion thrusters, if scaled appropriately.
Figure 1.11 also displays the thrust-to-power ratio versus specific impulse for electric propulsion
devices across all bus classes. This figure displays shaded regions corresponding to performance
parameters that are beneficial for primary electric propulsion missions: north-south stationkeeping
14
Figure 1.9: Power requirements for a collection of small satellite propulsion devices. Modified
from [105] using data from [85]
Figure 1.10: Power efficiency versus thrust efficiency for a collection of small satellite propulsion
devices. Modified from [105] using data from [85]
15
(NSSK) of a Geostationary spacecraft, and primary propulsion for remote deep space missions. We
can see that with current performance estimates, ionic electrospray thruster technology provides a
high efficiency option for satisfying both critical mission functions [78]. These mission functions
were In addition, since the ion extraction and acceleration physics increases linearly with the num-
ber of emitter tips, ionic electrospray thrusters offer potentially attractive benefits for large scale
production.
Figure 1.11: Power efficiency versus thrust efficiency for a large collection of electric propulsion
devices. Modified from [44] using data from [23, 37, 69, 82, 85]
16
1.1.5 ContaminationandPlume-SpacecraftInteractions
The mission risk of hosting an electric propulsion device has been a concern for spacecraft engi-
neers since the technology’s inception [22]. In the 1980’s as ion thrusters were reaching matura-
tion, interest began to turn towards integration issues associated with hosting onboard scientific
spacecraft. This section introduces the general beneficial, neutral, or adverse effects of ion plume-
spacecraft interactions, and how these effects can be applied to ionic electrospray thrusters. This
section introduces interactions between the ion plume and spacecraft surfaces. The types of plume-
spacecraft interactions can be classified further into spacecraft charging, surface contamination,
force effects, electromagnetic effects, optical effects, and space environment modification.
Spacecraft charging is a natural phenomenon driven by current collection from the space envi-
ronment. The potential of the spacecraft surface floats to equalize the amount of incoming and out-
going current. Major sources of current include the ambient space plasma environment, photoion-
ization, secondary electron emission and backscattered electrons, and any active current emission.
The current expelled from electric propulsion devices tend to be at least two orders of magnitude
higher than the other principal current sources, and thus drive overall spacecraft potential when in
use. This relation provides a beneficial effect of neutralizing spacecraft charge when plume cur-
rent and accompanying neutralizer current are matched. Without proper neutralization of the ion
plume, the spacecraft can charge to the ion beam potential, typically in the kilovolts range. Large
potential differences between the spacecraft ground and insulated components can lead to arc dis-
charges that can damage components, degrade spacecraft optical surfaces, and even send phantom
commands within data and communication channels [58]. Additionally, fluctuations in spacecraft
ground can lead to adverse effects for onboard instrumentation. To remedy this, spacecraft design-
ers ensure common grounding, as well as institute spacecraft surface charging modeling campaigns
to understand spacecraft response to thruster firings or environmental fluctuations [70].
Surface contamination can occur due to material interaction with the ion plume. Surfaces under
direct impingement from the ion beam are likely to experience material sputtering, damaging the
surface and releasing low energy ions near the spacecraft, that can later be deposited on other
17
spacecraft surfaces. This method of surface contamination can be solved with appropriate keep-
out zones associated with the plume’s primary beam as it expands into vacuum. Several electric
propulsion devices, including Hall and gridded ion thrusters, are afflicted with mechanisms for
low energy ion generation independant from primary beam sputtering. Unlike high energy ions,
low energy ion trajectories are influenced by the nearby spacecraft electric fields, which can lead
plume species to deposit onto nearby sensitive spacecraft surfaces. The primary mechanism for
low energy ion generation within legacy electric propulsion devices is charge exchange collisions
(CEX). Charge exchange collisions occur between high energy beam ions and high-density neutral
propellant plumes immediately outside the thruster exit plane. The collision results in a low energy
ion and a high energy neutral. Although the absolute flux of particles is likely very small, electric
propulsion devices that are operating for a long period of time (days to months) can accumulate a
significant amount of contamination. Identifying and characterizing the effect of CEX ions on near-
field plume properties and the impact on spacecraft surface contamination has been a significant
effort in pathfinder electric propulsion missions of the early 21
st
century [97, 112]. Additionally,
as new propulsion mechanisms are developed and matured it is common to begin modeling and
testing their impact on host spacecraft contamination [99].
Force effects related to hosting an electric propulsion device relates to the unexpected torque
provided to the spacecraft due to returning beam particles. This effect is typically small due to the
low mass of returning ions but may become significant for an especially small spacecraft platform,
or if present over long periods of time.
Optical effects refer to the visible glow that can be observed from several legacy propulsion
devices such as Hall effect and gridded ion thrusters. This glow is generated by excited neutral
particles that have collide with energetic beam ions. Electrospray thrusters do not suffer from
optical effects like legacy devices due to their low density of emitted neutrals from the liquid
propellant. Glow discharge has been seen under very high voltages [23], however the leading
theory is that this glow discharge is caused by interactions induced by the chamber environment
[106].
18
Electromagnetic effects refer to signatures associated with the plume, or plume-space plasma
interactions throughout the electromagnetic spectrum. The charge particle beam, through emission
and return characteristics, can create current loops into or out of the spacecraft that have not been
designed for, causing interference on electrical equipment. Additionally, the emitted particle beam
has an impact on the local ambient plasma environment. The injection of this particle beam can
cause two stream instabilities, exciting plasma waves and other electromagnetic phenomena that
can interfere with spacecraft instruments or communications. This beam can also have larger scale
impact on the space plasma environment. Also, the presence of electrostatic discharges have been
observed to cause broad RF interference [61].
1.1.5.1 ElectrosprayThrusterContaminationConcerns
Ionic electrospray thrusters share several of the contamination concerns as past electric propulsion
devices, and thus require similar investigations. Primary concern for contamination is tied to the
expected constituents of the electrospray plume. Electrospray thrusters are designed to emit singly
charged anions and cations. These anions and cations are largely monomers and dimers, but are
known to also emit detectable numbers of trimers, tetramers, and small droplets. Furthermore,
nonpropellant effluent can be expected in the plume. This is to include sputtered extractor grid ma-
terial. Existing designs have leveraged stainless steel, molybdenum, and gold. Additional source
of nonpropellant effluent can be complex hydrocarbons generated through electrostatic breakdown
of the ionic liquid propellant during thruster shorting events.
However, the most important factor for understanding the potential contamination environment
and other spacecraft effects is due to low energy ion generation and backflow. Unlike traditional
electric propulsion devices, whose low energy ion species are generated due to charge exchange
collisions with unionized propellant at the thruster exit, electrospray thrusters generate low energy
ions from solvated ion fragmentation. Fragmentation refers to the process of a dimer, trimer, or
larger molecule splitting into a neutral molecule and a monomer. This process conserves kinetic
energy and results in the generation of lower energy monomers. Fragmentation can be classified
19
by its region of occurrence, acceleration region fragmentation, and field free region fragmentation.
The classifications of ion fragmentation are detailed in Figure 1.12 below.
Figure 1.12: Description of primary solvated ion fragmentation mechanisms: acceleration region
fragmentation and field-free fragmentation
Acceleration region fragmentation occurs when molecules break up at some point during ac-
celeration before the particle exits the extractor grid. This process generates monomers that can
vary in energy depending on the point at which the fragmentation occurred. Field-free region frag-
mentation occurs outside of the acceleration region and produces the lowest energy monomers.
Another intersting concern for elecrospray thruster contamination is the deposition of ionic
liquid molecules in thin films over spacecraft surfaces. Due to EMI-BF
4
’s low volatility, molec-
ular ionic liquid is likely to remain condensed on spacecraft surfaces once deposited. Coupled
with the conductive nature of the propellant, there is risk of electrical shorting as a result of thin
films of ionic liquid building up. There are currently efforts underway for investigating the be-
haviors of ionic liquids deposited as thin films. These efforts are largely motivated to develop
advanced material processing and manufacturing techniques [62]. However, insights gained re-
garding the advanced electrochemistry and physical interactions at ionic liquid-substrate interfaces
can be adapted and applied to the space environment. A complete review of work related to elec-
trospray thruster contamination is presented in Section 1.2.
20
1.2 LiteratureReview
Several authors are currently developing, characterizing, and demonstrating electrospray thruster
performance. This section provides a summary of recent work with regards to electrospray thruster
development and characterization. Items of particular interest for understanding the plume envi-
ronment will include previous works identifying typical plume mass, energy, and chemical com-
position. Past experimental works regarding ion fragmentation and return current will also be
discussed. The state of plume modeling efforts for legacy electric propulsion devices, FEEP, and
colloid electrospray is presented with an emphasis on low energy ion generation, contaminant
generation, transport, and deposition mechanisms.
1.2.1 ExperimentalCharacterizationofIonicElectrosprayThrusters
To develop an accurate model of the contamination environment induced by the hosting of ionic
electrospray thrusters, their plume composition, operating parameters, and contaminant generation
mechanisms must be well understood. This section provides a detailed account and analysis of
experimental characterization activites associated with ionic electrospray thrusters. Most previous
work has been focused on defining operating envelopes and quantifying thruster performance met-
rics, such as specific impulse, thrust, power, and overall efficiency. This work began in earnest
with Coffman and Courtney [26, 31] with experimental determination of emission characteris-
tics of planar emitter arrays from nickel and borosilicate substrates. This work first introduced a
majority of experimental practices such as combining time of flight and retarding potential ana-
lyzer measurements for determining plume composition, which is still preferred today. This work
led to the first modern ionic electrospray thruster in MIT’s ionic electrospray propulsion system
(iEPS) and its scalable version (S-iEPS) [55]. This system was first used in preliminary technology
demonstration CubeSat missions as an integretated experimental subsystem [45]. This subsystem
was capable of firing its 8 thrusters in a bipolar mode. Dedicated bipolar thruster operations ex-
periments have been conducted on a single pair of thrusters [29]. This effort focused primarily on
21
addressing key hardware design and implementation concerns regarding the thrusters and associ-
ated power processing unit.This work demonstrates that this operating mode is feasible. However,
further experiments of paired thruster operations have been limited due to developers focusing first
on validating single thruster performance over more complicated paired designs.
More recent thruster characterization activities have been conducted by academic, commercial,
and government entities [23, 68, 82, 85]. Figure 1.13 displays plume composition data for various
operating modes as presented by [23] and [82]. Commercial characterization of the Accion TILE
propulsion system does not directly report plume composition, but data provided for the positive
operating mode corresponds to a plume composition that is in family with these two reported.
Figure 1.13: Plume composition as reported from recent AFET-II testing [82] and from NWPU’s
linear emitter array thruster [23] for positive and negative firing modes.
The plume composition is fairly comparable with unfragmented species making up 50% - 79%
of the beam. The fragmented ion composition is also fairly comparable with a distribution of accel-
eration region fragmented ions and field free fragmented ions. The NWPU thruster suffered from
large amounts of high mass emission. This thruster was run at a much higher operating voltage
than the AFET-II thruster, and is thus likely a factor of the design parameters. It is important to
22
note that the plume composition and performance for a thruster firing in positive mode can be very
different than the same thruster firing in negative mode.
A summary of relevant characterized thruster parameters is presented in Table 1.1. Note that
values in parenthesis refer to the thruster operating in negative mode. If there are no parenthesis, it
is assumed that the reported values are applicable for both positive and negative emission modes.
Table 1.1: Reported ionic electrospray thruster parameters from ongoing characterization experi-
ments.
Name Specific Impulse [s] Current [ µA] Operating V oltage Plume Angle [
◦ ]
Nickel Chip [31] - +/− 400 800 - 1500 -
iEPS v2.1[26] 2000 +/− 600 800 - 1500 -
S-iEPS[55] 760 +/− 150 850 - 1200 60
8*S-iEPS[45] 760 +/− 1200 1000 -
PET-100[68] 7500 +3190/− 4750 1800 - 3000 20
UTT[6] 1650 - 2350 +/− 0.92 1200 - 1800 -
AFET-II[82] - +/− 700 800 - 1800 75
TILE[85] 2575 +/− 150 1050 45
NWPU[23] 3952 (3117) +/− 350 2000 - 3600 -
Early into the development of ionic electrospray thruster technology deleterious effects, such as
ionic liquid bridging and return current have been observed [45]. Ionic liquid bridging between the
emitter tip and extractor grid causes an electrical short, electrostatic arcing, and the vaporization of
the ionic liquid bridge. This can cause buildup of hydrocarbon contaminants on the extractor grid
and damage to the reservoir, emitter, and grid. A wide variety of thruster conditions can be seen
from Figure 1.14 as a result of lifetime testing. Ionic liquid bridging and electrostatic discharges
are fairly common occurrences during the first hours of thruster firing, but tend to subside during
stable operations. The presence of these marks shows one mechanism for contaminant creation.
The spacecraft charging effects of return current from ionic electrospray thrusters have been
discussed experimentally by Mier-Hicks [73]. This work created a simple charging model of space-
craft floating potential during thruster operation. This model used empirical thruster return current
from laboratory experiments, as opposed to a numerical kinetic model. It was observed that dif-
ferences in emitted current between thruster pairs cause a floating spacecraft surface to charge to
23
Figure 1.14: Image depicting damage to electrospray thruster grids after test campaign, largely due
to ionic liquid bridging [45].
potentials near the thruster voltage. Spacecraft charging concerns are partially mitigated for pos-
itive mode emission due to photoionization and other ambient plasma interactions. Additionally,
return current was cited as a key mechanism for charge neutralization for heavy mass ion thrusters
operating in bipolar pair. Although this current can be experimentally measured, insight into the
spatial distribution of return current is challenged. Anomalies in overall test unit charge were
attributed to chamber-induced background plasma, but requires further insight to confirm.
The primary source of return current is the backflow of low energy ion species. In ionic elec-
trospray thrusters, these low energy ion species are primarily generated by ion fragmentation in or
near the thruster. Fragmentation has been investigated as it relates to electrospray thrust efficiency
24
[27, 32]. Fragmented ions can be observed directly using retarding potential anylzers. These ions
are identified by their lower energy when compared to the overall ion beam. Acceleration region
fragmentation leverages molecular dynamics simulations. Field-free and acceleration region frag-
mentation rates for a variety of ionic liquid propellants has been investigated experimentally by
Miller [75, 77]. This work utilizes a single emitter tip setup as the alignment issues associated
with a multitide of emitter tips can provide a variety of beam energies that can be misconstrued for
fragmeneted ion species. Miller develops an experimental method for calculating fragmentation
rate for a variety of ionic liquid propellants. Rates were found to be dependent on propellant ion
temperature as well as electric field strength. The results displayed in Miller’s work shows that
EMI-BF
4
fragments at a higher rate than other ionic liquids, partly due to its use as higher cur-
rents, with a mean lifetime for dimers equal to approximately 1-2 µs. This method is sensitive to
errors associated with initial cluster energy distribution, and assumed compositions at the thruster
exit plane. The impact of propellant fragmentation rate on overall plume dynamics, neutralization,
and contamination risk has not been quantified.
1.2.2 ElectricPropulsionPlumeandContaminationModeling
As described earlier, the high fidelity modeling of electric propulsion thruster plumes has been a
critical area of research since EP devices have been integrated onboard operational scientific and
commercial spacecraft in the late 1980’s. Since then, these modeling activities have identified
several physical phenomena associated with EP plume expansion and neutralization processes.
This section highlights some of the key findings of past EP plume studies to provide context for
later comparisons with findings for ionic electrospray plumes.
Substantial PIC simulations studies have been carried out on the downstream plume dynamics
and related plume neutralization and contamination issues for ion thrusters [51, 93, 112, 111, 113,
115] and Hall thrusters [11, 15, 16, 17, 19, 74, 81, 107]. The primary mode of contamination
studies focused on characterizing the backflow environment induced by the low energy CEX ion
25
environment outside of the thruster exit plane. Investigations into neutralization dynamics high-
light significant electron coupling to the ion beam. Neutralizaing electrons are contained by the
potential well of the ion beam and, due to thermal motion, oscillate back and forth in this po-
tential well. Neutralization with bipolar thruster configuration has also been studied recently for
ion thrusters utilizing electronegative gases to produce either positive or negative ion beams, such
as the PEGASES (Propulsion with Electronegative GASES) concept [1, 53, 64]. This concept
identifies that neutralization is inhibited due to both thrusters operating near to the space charge
limit. Orienting the thrusters tilted inwards, such that the opposite polarity plume ameliorates the
space charge limit effects, is shown to have significant effects on the overall particle flow from the
consituent thrusters.
Electric propulsion contamination modeling has been primarily concerned with legacy electric
propulsion devices such as gridded ion thrusters and Hall effect thrusters, due to their integration
on several scientific and commercial spacecraft in the early 21
st
century. The primary contami-
nation concerns included sputtering from direct impingement of the primary beam on spacecraft
surfaces, and contaminant transport and deposition from CEX collisions and sputtering sources.
The primary contaminant for gridded ion thrusters was low energy molybdenum ions generated by
sputtering of the acceleration and extraction grid. Contamination modeling efforts have focused
on characterizing the deposition rate of contaminants over critical spacecraft surfaces to ensure
required performance during mission design life [20, 113].
1.2.2.1 ElectrosprayPlumeModeling
Electrospray propulsion is challenged by combining several disciplines from electrochemistry,
computer science, fluid mechanics, plasma science, and engineering. Modeling electrospray thruster
physics spans multiple length scales from nanometers, the molecular scale of Taylor cone forma-
tion, up to tens of meters, the spacecraft scale. Figure 1.15 highlights several regions of interest
in the accurate modeling of electrospray thrusters as first described by [120]. For clarity the dis-
cussion of electrospray plume modeling is broken up into distinct regions based on length scale.
26
The emission region refers to the nanometer region of interest at the tip of a Taylor cone. Emission
region modeling is dominated by molecular interactions with an external electric field and porous
emitter tip substrate. The acceleration region refers to the micrometer region within the thruster
body where emitted ions are accelerated. Acceleration region modeling focuses on the emitted ion
motion as the ejected species are affected by the accelerating field and space charge effects. Lastly,
the downstream plume region is the meter scale region ouside of the thruster body, surrounding the
host spacecraft. The downstream plume region focuses on particle motion after it is successfully
ejected from the thruster exit plane. This section will provide a review of the ongoing numeri-
cal modeling efforts associated with electrospray thrusters. This will include the current state of
modeling more mature FEEP and colloid-type thrusters.
Figure 1.15: Scale of electrospray regions and modeling approach.
The physics of Taylor cone emission has been extensively studied through the use of nonre-
active molecular dynamics (MD) simulations. MD simulations have been applied to character-
ize cone formation and emission properties for colloidal, mixed-mode, and pure ionic emission
[13, 14, 12, 27, 71, 72, 126]. The MD based modeling are typically limited to the immediate
region of emission. Recent studies have also attempted to link the effects of the emitted beam’s
electric field strength and space charge in the acceleration region to emission characteristics [126].
27
The extraction region is under investigation using molecular dynamics simulation. These sim-
ulations look into meniscus formation, and onset of jet emission by solving for the interatomic
and intermolecular forces directly, when exposed to an external electric field. This work provides
insight to the effect of acceleration region fields and charge density on emission characteristics and
resulting particle energy and velocity distributions [71, 72, 125].
Colloid FEEPs and colloid electrospray thrusters have seen more robust numercial modeling
efforts due to their relative technological maturity and heritage. Early capillary-fed FEEP thrusters
were modeled with similar concerns to the Hall thruster and ion thruster developments of the
time. The thrusters modeled by Tajmar [98, 99] and Roussel [92] were both dominated by CEX
collisions between propellant ions and neutral emitted propellant near the exit plane. Due to the
active propellant transport design and capillary tip, CEX is more likely for colloid thruster than
for a porous emitter system. This increased liklihood is due to higher propellant flux and larger
percentage of neutral emission. More recently, porous FEEP thruster interactions with the ambient
space environment have been modeled [63]. This model displayed the impact of a thruster plume
profile on the ambient plasma density contour around an assumed spacecraft surface. This work
did not attempt to make the connection between thruster operation and contamination concerns.
Detailed numerical modeling of the extraction region of colloid electrospray thrusters have been
able to generate insights into design considerations and lifetime limiting conditions [48, 103].
Ion acceleration physics has been studied extensively for both ionic and colloidal electrospray
thrusters to understand the interactions between charged droplets or ions as they are emitted from
the Taylor cone and accelerated out of the thruster exit plane[91, 103]. Particle-Particle (PP) mod-
els have been applied to characterized ion beam development within the acceleration region for
colloid thrusters[130]. Particle-in-Cell (PIC) models have also been applied to analyze the thruster
acceleration region for pure ion emission[36, 84].
Electrospray thrusters offer the additional ability to self neutralize through the use of bipolar
thruster pairs [33]. This self-neutralization entails one thruster emitting a positive cation beam
and a second thruster emitting a negative anion beam. Recently, a full-particle PIC model was
28
introduced to understand the unique neutralization process offered by operating a bipolar pair
of ionic electrospray thrusters [34]. These previous models, however, made several assumptions
regarding the properties of the emitted beams that are affected by small scale interactions.
A major lifetime-limiting component of electrospray thrusters is the windowed extractor grid.
Large amounts of direct impingement from the ion beam can result in erosion and contamination
of the the grid [103]. Contamination of ionic electrospray grids due to intercepted current has been
observed experimentally [45, 55, 73]. As a result, the characterization of electrospray emission
and acceleration physics is critical to further improve system reliability. Grid erosion mechanisms
and its adverse affects have been studied extensively for gridded ion thrusters [21, 35, 80, 88, 119].
Electrospray thrusters share some of these same concerns. A major concern is grid contamination
causing electrostatic discharge and electrical short circuits. The activation of secondary emission
sites on an individual emitter tip can drastically exacerbate this process. The primary intent when
designing electrospray thrusters is to form a single emission site per emitter tip that is centered and
parallel to the window normal. Operating thrusters at higher voltages provides a higher specific
impulse, but also potentially leads to the activation of secondary emission sites. Due to randomness
in the porous substrate, it is impossible to know exactly when or where a secondary emission site
will appear without rigorous laboratory characterization. Often, secondary emission sites are off
center from the peak of the emitter tip and, as a result, can experience electric fields that are
off-axis. The activation of secondary emission sites often coincides with a drastic increase in
intercepted current and off-axis emission [40].
To date, numerical modeling and simulation studies have mostly focused on characterizing
individual physical phenomena at their respective scales of interest. These individual phenom-
ena include pure ion emission from a Taylor cone, particle acceleration, and downstream plume
dynamics and neutralization.
29
1.3 ResearchObjectives
The advent of advanced micro-electric propulsion devices, including ionic electrospray thrusters,
provide incredible opportunities for the future of spaceflight and are currently enabling exciting,
new scientific investigations. Currently, basic thruster mechanics and designs have been demon-
strated, characterized, and matured to the point of more widespread adoption outside of research
laboratories. However, to further mature this technology and address critical mission integration
hazards, an in-depth understanding of the thruster plume physics and contamination environment
is required. To date, bulk plume-spacecraft interaction studies for ionic electrospray thrusters have
relied almost entirely on experimenal observations in a laboratory setting. In addition, these efforts
have not attempted to make characterizations on electrospray thruster neutralization and contam-
ination potential directly, opting to investigate underlying plume mechanics of fragmentation, or
other interactions such as spacecraft charging. A complimentary numerical model to inform en-
gineering research and design efforts are critical for understanding and characterizing the plume
environment of ionic electrospray thrusters.
As a result, the primary research objectives of this dissertation is as follows:
1. Develop a baseline numerical model that is complimentary to the extensive and ongoing
ionic electrospray thruster experimental characterization activities with the purpose of study-
ing bipolar thruster nuetralization and the impact on spacecraft contamination due to a vari-
ation of fragmentation rates and plume exhaust species. This model should include three-
dimensional characterization of the plume environment about a host spacecraft. This model
should also include investigation of the impact of fragmentation species on plume contami-
nation and backflow.
2. Develop a numerical model to include ionic electrospray thruster physics across 9 orders of
magnitude, accurately capturing the physical interactions from the emission region, accel-
eration region, and the downstream plume region. This model should provide further detail
to the baseline numerical model and provide insight into the effects of common thruster
30
operational phenomena such as secondary emitter tip emission and acceleration region frag-
mentation.
3. Perform experimental investigations on the plume environment of ionic electrospray thrusters,
to include direct measurement of plume anions and cations. This effort should provide exper-
imental validation for the numercial models and also enable the direct comparison between
numerical model and experimental measurement.
1.4 ThesisOutlineandOrganization
This thesis is organized into several sections. This chapter has provided an introduction to and
literature review of relevant topics within the scope of contributions provided by this work. Chapter
2 provides the approach and methodology for key contributions in this thesis. This will include an
overview of relevant numerical methods, as well as an overview of laboratory facilities and setup.
Chapter 3 presents the development and results of a baseline PIC model of the downstream region
of a bipolar ionic electrospray thruster pair. Chapter 4 presents an expansion of the baseline PIC
model by including an MD model to capture ion emission physics, and a PP model to capture ion
acceleration phyics. Chapter 5 presents experimental data of ionic electrospray thruster plume to
validate and compare to the presented models. Lastly, Chapter 6 highlights the primary conclusions
of this work and areas for further investigation.
31
Chapter2
Methodology
This section details the approach and methods used in the numerical and experimental investiga-
tions contributing to this thesis. Ionic electrospray beam formation and neutralization is an in-
herently complex process incorporating several physical phenomena across multiple length scales
of interest. All of these processes are also inherently a three-dimensional (3D) problems as there
are few areas where physical processes can be well-approximated by a 1D or 2D physical system.
This section provides an overview of the numerical methods pursued in this effort, namely molec-
ular dynamics (MD) simulation, the particle-particle (PP) method, and the particle-in-cell (PIC)
mehtod. Lastly, this section provides and overview of the laboratory facilities and instruments
used to set up experimental investigations.
2.1 NumericalMethods
2.1.1 MolecularDynamicsMethod
MD simulation is a first principle based modeling method that treats each molecule as a particle
and calculates inter-molecular forces based on the position of atoms and their associated force
field. MD simulation method grew out of the study of N-body systems in the late 1950’s. The
MD method first became popular in the study of materials science and is also very common in
biochemistry and biophysics applications. As a result, MD simulation is able to accurately capture
the motion of individual molecules within a continium of any phase of matter. MD simulation is
32
typically limited by the number of molecules that are able to be included in the simulation, thus
restricting the scale of interest to≃ 100nm. Here, we consider an MD model to investigate the
emission process of the ionic electrospray thruster, where molecules are extracted from an ionic
liquid continuum through the use of a large electric field.
By implementing an accurate force field between particles and integrating the Newtonian equa-
tions of motion, particle position and velocity can be determined. In this dissertation, GROningen
MAchine for Chemical Simulations (GROMACS) [2] was used to simulate the interactions be-
tween ionic liquid molecules. GROMACS was originally designed to capture the force fields of
complicated bonded interactions of biochemical molecules, and has been recently applied to the
MD studies of ionic liquids. The potential of each atom is shown in Eq.(2.1):
V =
∑
bonds
1
2
k
bonds
(r− r
0
)
2
+
∑
angles
1
2
k
angles
(θ− θ
0
)
2
+
∑
torsions
1
2
(V
1
(1+ cosϕ)+V
2
(1− cos2ϕ) +V
3
(1+ cos3ϕ)+V
4
(1− cos4ϕ))
+
i< j
∑
Coloumb
q
i
q
j
r
i j
+
i< j
∑
vdW
(
4ε
i j
"
σ
i j
r
i j
12
−
σ
i j
r
i j
6
#
(2.1)
where k
bonds
is the constant of bond potential, k
angles
is the force constant for potential induced
by angular differences, V
1
, V
2
, V
3
, and V
4
are Fourier coefficients for each dihedral, and ε
i j
is the
constant for the Lennard-Jones potential.
MD simulations can be extended to include chemical reactions. This effort neglects reactive
interactions between the chemicals, focusing on non-reactive methods of MD simulation. Figure
2.1 displays the typical simulation flow diagram discussed in this section.
33
Figure 2.1: MD simulation flow diagram of major subroutines
2.1.2 Particle-ParticleMethod
Once emitted, ionic electrospray propulsion plumes can be represented by collisionless plasma dy-
namics. In a collisionless plasma system, particle collisions are negligable. The kinetic description
is shown below by the collisionless Boltzmann equation.
δ f
i
δt
+v· δ f
i
δr
+
q
i
m
i
(E+v× B)· δ f
i
δv
= 0 (2.2)
where f
i
is the velocity distribution function, q
i
is the species charge, and m
i
is the species mass.
The electric field and magnetic field can be solved by Maxwell’s equations, displayed in (2.3) -
(2.6).
∇· E=
ρ
ε
0
(2.3)
∇· B= 0 (2.4)
∇× E=− ∂B
∂t
(2.5)
∇× B=µ
0
(J+ε
0
∂E
∂t
) (2.6)
34
where µ
0
refers to the permeabilty of vacuum and ε
0
refers to the permitivity of vacuum. ρ de-
notes the charge density and J is the current density. Due to the small current and length scales
associated with this analysis, it is assumed the effects of the magnetic field are negligable. With
this assumption, the Vlasov-Poisson system can be represented as follows:
∂ f
i
∂t
+v· ∂ f
i
∂r
+
q
i
m
i
E· ∂ f
i
∂v
= 0 (2.7)
E=− ∇Φ (2.8)
∇
2
Φ=
− ρ
ε
0
(2.9)
This system can be solved for with different simulation approaches. Most approaches fall under
two main branches, grid-based methods or particle-based methods. Particle-based methods offer
a great benefit over grid-based methods in computational efficiency for the scale of problems of
interest. Particle-based methods use simulation particles to statistically represent the distribution
function, f(r,v), and solve for the motion of the particles. Particle-based methods can be further
categorized by how the particle motion is solved. Predominant categories include particle-mesh,
particle-particle, and a hybrid particle-particle-particle-mesh.
One may consider the PP method as a reduced MD method focusing only on the Coulomb
interactions between charged particles in free space. The PP method does not store bulk properties
on a structured mesh, instead it calculates electrostatic forces on individual particles directly from
the Coulomb’s law between each possible particle pair. The total force on each particle in the
domain is described as the sum of the external background electric field and the summation of
all particle-particle forces. Therefore, the system of equations for particle motion is described in
Eq.(4.1)
m
d
2
r
dt
2
= m
dv
dt
=F=F
pp
+F
acc
= q(E
pp
+E
acc
) (2.10)
35
where q represents the particle charge,E
pp
refers to the electric field due to particle-particle forces
as described in Eq.(4.2), andE
acc
refers to any other background electric field.
E
(i)
pp
=
1
4πε
0
N
∑
j=1,i̸= j
q
j
|r
ij
|
3
r
ij
(2.11)
The PP method has been used previously to investigate the acceleration and interaction of
droplets within colloid electrospray thrusters [129]. In this effort, the PP method is applied to
the micrometer-scale acceleration region, where emitted ions are accelerated and ejected from the
thruster body. The PP method is typically not as computationally efficient as PIC because its
computation scales as O(N
2
), where N is the number of particles in the simulation. However, to
resolve the ion acceleration process over a region of O(1mm
3
) with a resolution of O(1µm), a PIC
model would spend most of its computing time on solving the elliptical Poisson’s equation due to
the domain mesh size. Since the PP approach does not use a mesh and thus eliminates field-solve
and particle-mesh interpolation, PP is computationally more efficient than PIC for this application
[129]. As a result, the ionic electrospray beam acceleration process is benefically suited to the PP
method due to the relatively modest particle flux, and required resolution and scale of simulation.
Figure 2.2 displays the simulation flow diagram described above.
Figure 2.2: PP simulation flow diagram of major subroutines
36
2.1.3 Particle-In-CellMethod
The PIC method is used extensively in space plasma physics and other plasma physics modeling.
The PIC process has been used in the past to simulate several problems associated with electric
propulsion and spacecraft interactions, including electric propulsion plume modeling [92, 99, 112]
and spacecraft interactions with the local plasma environment in low Earth orbit (LEO) [63],
geosynchronous Earth orbit (GEO) and other deep space orbits. The PIC method is documented
in Charles Birdsall’s and Bruce Langdon’s 1991 book “Plasma Physics via Computer Simulation”
[10]. Instead of computing the Coulomb interaction between each particle in the domain, the PIC
method relies upon a spatial mesh grid structure to store local plasma properties including plasma
potential, charge density, and electric field strength. By using the local grid points to drive particle
motion, high fidelity plasma simulation on relevant time and length scales is feasible with modern
computing technologies. Figure 2.3 details the PIC process’s flow and major subroutines: Force
Weighting, Particle Push, Particle Weighting, and Electric Field Solver. These subroutines will
be discussed further below. Additionally, proper numerical normalization schemes are critical to
efficient and accurate computations.
Figure 2.3: PIC modeling flow diagram of major subroutines
37
Force Weighting: Since the electic field is only solved for discrete grid points within the do-
main, weighting is required in order to determine accurate forces on each particle at their respective
position. A linear weighting scheme is a simple and accurate method for determining the electric
forces for each particle. The weighting scheme leverages only the electric field values at neighbor-
ing grid points when determining the weighted force. Figure 2.4 displays a graphical representation
of the linear force weighting scheme in two dimensions for a single particle.
Figure 2.4: Force weighting scheme for particle and neighboring grid points.
Here the black dot represents the particle position at(x
p
,y
p
). The four neighboring grid points
are uniquely colored and sized to display the weight of each point on particle motion. As can
be seen from the figure, the closest red grid point at (x
i
,y
j
) has the largest weight, while the
furthest green point at(x
i+1
,y
j+1
) has the smallest weight. The blue and yellow points are nearly
equidistant and thus have similar weightings. This relationship is captured for a 2D system in Eq.
(2.12).
w
x
=
x
p
− x
i, j
∆x
,w
y
=
y
p
− y
i, j
∆y
(2.12)
38
Here,∆x and∆y refer to the cell size in the x and y direction, respectively. From these individual
weightings, the overall force can be calculated from the following Eq. (2.13).
F= q[(1− w
x
)(1− w
y
)E
i,j
+ w
x
(1− w
y
)E
i+1,j
+(1− w
x
)w
y
E
i,j+1
+ w
x
w
y
E
i+1,j+1
] (2.13)
The linear weighting scheme is expanded to include a third dimension upon implementation.
Particle Push: The particle motion is solved in phase space by integrating the primary equa-
tions of motion. This equation of motion corresponds to the simplified form of the Lorentz force
equation with only electrostatic forces, as seen in Eq. (2.14). The particle position can then be
related to its velocity linearly.
d(mv)
dt
= qE (2.14)
dr
dt
=v (2.15)
The electric field in the domain is stored and weighted for neighboring grid points. This integration
is carried out using a leap-frog scheme. This scheme solves for the particle velocity and position
with a half timestep offset. This method is 2
nd
order accurate and is able to resolve oscillatory
particle motion as long as the timestep is sufficiently less than the expected oscillation frequency.
v
n+
1
2
=v
n− 1
2
+
q
m
E
n
∆t (2.16)
r
n+1
=r
n
+v
n+
1
2
∆t (2.17)
Here, n refers to discrete simulation steps, and∆t denotes the simulation timestep.
Particle Weighting: Particle weighting, also known as charge deposition, updates charge den-
sity within the domain at the grid points. The particle weighting scheme is identical to the inverse
of the force weighting scheme shown in Fig. 2.4. A linear scheme is used to assign particle charge
39
to neighboring grid points, again with the closer grid points receiving proportionally more charge.
This deposition can be represented by Eq. (2.18).
Q
i, j
= q(1− w
x
)(1− w
y
),Q
i+1, j
= qw
x
(1− w
y
),Q
i, j+1
= q(1− w
x
)w
y
,Q
i+1, j+1
= qw
x
w
y
(2.18)
Here, q represents the charge of the simulation particle and Q
i, j
is the charge deposited to the
neighboring grid point at (i, j). The total charge deposited is then converted to the local charge
densityρ as follows
ρ
i, j
=
Q
i, j
∆x∆y
(2.19)
Electric Field Solver: The electric field is directly related to charge density and plasma potential
via Poisson’s equation (Eq. (2.8), Eq. (2.9)). This section displays a sample solving method for
a two dimensional grid. The plasma potential at each point can be solved from the charge density
numerically using the finite difference scheme presented as follows.
Φ
i− 1, j
− 2Φ
i, j
+Φ
i+1, j
∆x
2
+
Φ
i, j− 1
− 2Φ
i, j
+Φ
i, j+1
∆y
2
=− ρ
i, j
ε
0
(2.20)
Here ∆x and ∆y represent the cell size in the x and y direction, respectively. Once the plasma
potential is determined, the electric field can be calculated numerically from a central difference
scheme shown below.
E
x
i, j
=− Φ
i+1, j
− Φ
i− 1, j
2∆x
,E
y
i, j
=− Φ
i, j+1
− Φ
i, j− 1
2∆y
(2.21)
Here E
x
i, j
and E
y
i, j
denote the x- and y-components of the electric field vector at grid point (i, j),
respectively. Note that the electric field subcomponents in each principal axis can be calculated
independently. These two differencing methods have 2
nd
order accuracy.
40
2.2 LaboratoryFacilities
Experimental investigations for this dissertation were completed in the Laboratory for Exploration
and Astronautical Physics (LEAP) experimental facilities. The LEAP experimental facility was
originally constructed to conduct investigations into solar wind dynamics, spacecraft charging, and
lunar dust charging and transport [24, 86, 122]. The facility consists of various vacuum chambers,
plasma sources, and plasma diagnostic equipment. In recent years, the LEAP facility has been
fashioned to support ongoing experiments regarding the design and operation of ionic electrospray
thrusters [4].
2.2.1 PressureSystems
The LEAP experimental facility is centered about a cylindrical 940-liter primary vacuum chamber.
This chamber is pictured below in Figure 2.5. The internal volume of the primary vacuum chamber
measures approximately 91.5 cm in diameter and 105 cm in length.
Figure 2.5: USC LEAP primary chamber
The primary chamber is fitted with three pumps enabling a floor pressure of 1 × 10
− 7
Torr. An
Alcatel roughing pump (also pictured in Fig. 2.5) can pump the chamber down to 20 mTorr. A
CVI TM-500 helium cryopump is attached to the rear of the primary chamber behind a pneumatic-
activated gate valve. Upon opening the gate valve to the cryopump, the chamber can reach its
41
floor pressure of 1 × 10
− 7
Torr. During thruster operation, the cryopump can maintain a pressure
of 2× 10
− 7
Torr for approximately 4 hours. Due to contamination of the cryopump’s cold plate,
the cryopump cannot operate for long periods of time in conjunction with thruster operation. The
primary chamber’s final pump, a T-1000 turbopump is used to enable long duration electrospray
thruster testing. The turbopump can maintain a chamber pressure of 1× 10
− 6
Torr for several
hours, augmenting the cryopump’s capabilities.
2.2.2 ExperimentalInstruments
The experimental instruments in the primary chamber are primarily current collecting sensors.
A suite of experimental instruments are grouped together on a 3D traversing system. This suite
includes a cylindrical Langmuir probe, a Faraday probe, a retarding potential analyzer, a micro-
Faraday probe, and a phosphor screen. In addition to the traversing suite, there is a large form
collector plate at the back of the chamber. These sensors are concurrently being used for advanced
electrospray thruster characterization experiments [6]. Figure 2.6 displays an image of the instru-
ment suite.
2.2.2.1 ProbeTraversingSystem
The interior of the primary chamber is outfitted with a 3-axis traversing system. This rig consists
of 3 DC motors with screw leads, and an arm fixture where the downstream probe suite is attached.
The position of the probe suit is controlled by an Arduino Mega and Ramps 1.4 stepper board.
The traversing system control interfaces directly to a LabVIEW interface which allows for users
to execute probe placement commands. This set up enables accurate probe placement and sub-
millimeter movement. The probe traversing system enables the spatial data collection of current
data throughout the interior of the primary chamber during thruster firing activities through a num-
ber of automated scans. The following sections will detail relevant instruments in the traversing
probe suite.
42
Figure 2.6: Traversing probe suite for downstream plume sensing. The instruments from left to
right are: Phosphor screen, Retarding Potential Analyzer (RPA), Collection Plate (at the back of
chamber) (CP), MicroFaraday Probe (MFP), Langmuir Probe (LP), Faraday Probe (FP)
2.2.2.2 FaradayProbe
The Faraday cup probe consists of two concentric stainless steel tubes, separated by Teflon insula-
tion, and joined by a detector plate. The probe has a diameter of 9.57mm and a length of 35mm.
This probe was designed for thruster diagnostic and characterization experiments. The Faraday
cup design offers higher signal fidelity when compared with a Faraday plate due to the increased
ability to re-collect secondary electrons and sputtered ions emitted by the high energy plume. This
increase in signal fidelity is attributed to the sensor’s narrow field of view, collection cavity, and
its ability to be biased, to reduce unintended particle emissions. The sensor field of view is ap-
proximately 15.6
◦ . The guard tube can also be biased to -40V to suppress electron collection when
firing in positive mode.
43
Figure 2.7: Faraday probe construction and electrical schematic.
2.2.2.3 RetardingPotentialAnalyzer
The probe suite’s retarding potential analyzer design is similar to the previously discussed Faraday
cup. The retarding potential analyzer consists of two concentric stainless steel tubes, separated
by Teflon insulation, and joined with a common graphite detector plate. This instrument was
designed following best practices as laid out by [38, 57, 127]. Three grids are framed in front of
this collection tube. Each grid has 78% transparency, allowing for an aggregate transparency no
less than 47.4%. The outermost grid floats, the second grid performs high voltage sweeps up to
2.5× the beam voltage, and the final grid suppresses electrons from entering the collector tube. The
collector tube measures 9.57mm in diameter. The high voltage grid is powered by a Bertan Model
315B power supply capable of providing both positive and negative voltage. The RPA is useful for
characterizing emitted thruster plume energy spectra. An example RPA scan is displayed in Fig.
2.9. This scan was taken during negative thruster operation and is, thus, normalized negatively.
The vertical lines depict energies for field-free trimer-to-monomer, dimer-to-monomer, and
trimer-to-dimer species, respectively. The presence of these species usually appear as distinct drops
in current collection. However, due to conventional machining of the UTT thruster from which
this data was collected, there is likely a variety of beam energies associated with the emission
characteristics for each of the 25 distinct emitter tips. This variation is one factor for the linear
44
Figure 2.8: Retarding potential analyzer construction and electrical schematic.
Figure 2.9: Example RPA scan data for thruster firing in negative mode.
spread depicted. Additionally, acceleration region fragmentation appears as a linear spread and
could also be contributing.
2.2.2.4 LangmuirProbe
A Langmuir probe is a versatile instrument capable of determining the plasma potential, electron
density, and electron temperature of a given plasma environment. The probe consists of one or
more electrodes immersed in the plasma under investigation. The potential of the electrode is
biased and the resulting current collected by the probe is analyzed to extract the relevant plasma
parameters. Biasing the electrode primarily reduces or increases the collection of ambient electrons
and the resulting current within the device. The LEAP probe suite features a cylindrical Langmuir
probe measuring 1mm in diameter and 5mm in length. The probe electrode is capable of being
45
biased between -50 to +65V . Figure 2.10 display the physical construction and electrical scehmatic
of the Langmuir probe.
Figure 2.10: Langmuir probe and electrical schematic.
The size and geometry of the electrode in relation to the expected plasma environment must
be appropriate and well understood to provide accurate readings. The plasma-surface interactions
related to Langmuir probes are well documented in plasma probe theory. The introduction of the
electrode surface naturally interferes with the surrounding plasma. This region of interference is
called the plasma sheath environment. Current collection through the plasma sheath can be largely
grouped into two limiting factors: space charge limited and orbital motion limited. Space charge
limited collection assumes that all particles that enter the sheath are collected by the probe surface.
This regime is valid when the probe’s characteristic length is much larger than the Debye length
of the plasma. In this regime, the only limitation on current collection is the phyiscal space charge
limit within the sheath thickness. Orbital motion limited theory applies when the probe’s length
scale is on the same order or less than the Debye length. In this regime, the amount of current
the probe is capable of collecting is limited by the attractive potential of the probe surface and
the velocity of the ambient particles. Similar to a meteoroid being caught by the Earth’s gravity
46
well, only a fraction of particles enterring the sheath region will be redirected enough to contact
the surface.
The Debye length of the plasma environment generated by the operation of an ionic electro-
spray thruster can be estimated given the current density and thermal energy of the expected ion
plume. The minimum expected Debye length, given at the thruster exit for a plume of either EMI
+
or BF
− 4
particles for a current density of 4.42× 10
− 2
A/m
2
, is approximately 10mm. Since this
Debye length is larger than the Langmuir probe’s length scale, orbital motion limited theory is
used to define the current collected by the probe’s surface.
The Langmuir probe is used primarily to estimate plasma potential within the chamber environ-
ment. Langmuir probe data experiences three current collection regimes: the ion saturation region,
the electron saturation region, and the transition region. The ion saturation region is defined by
a large negative bias on the probe such that only ion species are able to be collection and almost
all electrons are repelled from the probe surface. Alternatively, the electron saturation region is
defined by a large positive bias on the probe. Here, both ions and electrons are collected, with the
electorn current only limited by space charge effects. The plasma potential can be estimated by
the bias potential at which the probe current transitions between the electron saturation region and
the transition region. To estimate plasma potential, the Langmuir probe current data is analyzed
on a logarithmic scale. Figure 2.11 displays example Langmuir probe readings from the plume
plasma environment and how the plasma potential can be estimated. Previous studies have shown
that cylindrical Langmuir probes similar to that used in this effort have a general error of± 20%
[121].
2.2.3 CommandingandDataAcquisition
Commanding for all instruments is enabled by a direct LabVIEW and Arduino interface. The
LabVIEW interface allows for user input for traversing probe movement, instrument bias sweeps,
and thruster voltage control. Figure 2.12 displays the LabVIEW user interface.
47
(a) (b)
Figure 2.11: Sample Langmuir probe sweep data used to estimate the plume potential at a given
sample position. a) LP scan b) Logarithmic scale with slope comparisons.
Figure 2.12: LEAP LabVIEW user interface
There are three primary power supplies that the LabVIEW interface controls remotely: a Glass-
man High V oltage Series MK power supply which provides positive high voltage for the electro-
spray thruster, a Glassman High V oltage Series FJ power supply which supplies negative high
voltage for the thruster, and a Bertan Model 315B power supply which supplies bipolar high volt-
age for the retarding grid of the RPA as previously mentioned. The voltage commanding leverages
LabVIEW’s Arduino interface to control three separate digital to analog converters (DAC) which
regulate a control signal to the respective power supplies.
All instrument and thruster data is routed through an Agilent 24970A 20 Channel DAQ, and is
sampled at 1Hz. Command history for probe position and power supply voltage from LabVIEW
48
is also stored to later be correlated with instrument data. Figure 2.13 displays a block diagram of
the primary elements of the command and data acquisition systems involved.
Figure 2.13: LEAP command and control diagram
2.2.4 USCTestbedThruster
The USC Testbed Thruster (UTT) is a conventionally machined ionic electrospray thruster fash-
ioned after Dan Courtney’s original designs using a porous media [30] and the AFRL’s AFET-II
conventionally machined electrospray thruster [82]. The UTT was designed for ease of construc-
tion and operation, with the intention to serve as a platform for ongoing experiments to mature
electrospray thruster design, fabrication, and operation. A total of four UTT thrusters have been
constructed and operated within the LEAP facilities. Of the four, two currently remain in opera-
tions capable to be operated individually, or jointly in a bipolar thruster pair. The experimnental
measurements of backflow and return current will be made using these two thrusters, titled UTT-3
and UTT-4, respectively. Figure 2.14 displays a fully assembled UTT.
49
Figure 2.14: USC Testbed Thruster
2.2.4.1 Design
The UTT was design as a 1/2 scale version of the AFRL’s AFET-II conventionally machined
electrospray thruster. The UTT leverages a modular design allowing for the regular interchange
of different extractor grids, emitter tips, and propellant reservoirs. The major components of the
thruster are the thruster and reservoir housing, propellant reservoir and emitter tips, and the distal
and extractor electrodes. These components are pictured below in Fig. 2.15. The propellant
reservoir and emitter tips are made from a porous borosilicate glass substrate. This substrate was
chosen due to its electrochemical stability and insulating nature [26]. The propellant reservoir is
machined from 1cm diameter P4 borosilicate disk. The UTT has 25 distinct emitter tips machined
into a 1cm diameter P5 borosilicate disk. A porous interface layer is introduce in between the
propellant reservoir and emitter tips to ensure proper hydraulic connection between the disparate
surfaces. The UTT uses the ionic liquid 1-ethyl-3-methylimidazolium-tetrafluoroborate (EMI-
BF
4
) as a propellant, which is loaded and absorbed into the pores of the reservoir and emitter
tip assembly. The thruster biases the emitter tips and propellant reservoir with a stainless-steel
distal electrode. The reservoir assembly is pressed to the distal electrode with a small spring to
ensure stable electrical contact. The extractor grid is also manufactured out of stainless-steel. The
extractor grid has 25 holes that match and are aligned with the emitter tips with a tolerance of 25
µm. UTT-3 is outfitted with an extractor grid with 0.015” diameter windows. The distal electrode
50
and reservoir assembly are housed in a polyether ether ketone (PEEK) frame to provide electrical
insulation. This frame is then placed into the thruster housing. The thruster housing measures
0.5”× 0.5”× 0.25” in external dimensions and is machined from aluminum. The extractor grid is
fastened to the thruster housing with the use of four screws, and both are electrically grounded to
the facillity ground.
Figure 2.15: Exploded view of UTT with primary components
2.2.4.2 Performance
The UTT thrusters have undergone extensive performance characterization test campaigns [4, 5, 6].
These test campaigns largely focused on determining average thruster performance parameters
such as: emitted current, intercepted current, plume mass composition, plume energy composi-
tion, nominal operating voltage, total thrust, and specific impulse. Plume energy composition was
measured using the traversing probe suite’s retarding potential analyzer. Plume mass composi-
tion was measured using time of flight data collected using multiple methods: a large aperture
Bradbury-Neilsen gate (BNG) and a standard current reflecting gate. Table 2.1 displays the sum-
mary of estimated UTT-3 performance parameters previously characterized by [4].
Figure 2.16 displays emitted and intercepted current behavior during an experiment. One can
see that the thruster current and interception fraction are nominally constant, but can undergo
51
Table 2.1: UTT-3 characterized performance values
Parameter Value Unit
Emitted Current 1 µA
Intercepted Current Percentage 8 - 11 %
Monomer Percentage 20 - 33 %
Dimer Percentage 67 - 80 %
Operating V oltage ± 1340 - 1910 V
Thrust 38 - 68 nN
Specific Impulse 3960 - 4960 s
Plume Half-Angle 14.5
◦ transient spikes. These transient events could correspond to sporadic shorting events or other
spurious discharge.
Figure 2.16: Emitted current and interception fraction for positive mode emission
52
Chapter3
BaselineParticle-In-CellPlumeModel
3.1 Introduction
To begin to analyze the downstream plume dynamics and neutralization behavior for ionic electro-
spray thrusters, first a simplified plume model needs to be considered. Effective self-neutralizing
of the electrospray beam can be achieved by either operating electrospray thrusters in a bipolar pair
[33, 45] or alternating the polarity of a single thruster at high frequency [128]. We note that the
bipolar operation method offers a simpler electrical switching architecture and has been preferred
by recent experimental efforts on ionic electrospray [33, 45]. The bipolar thruster configuration
was also studied recently for ion thrusters utilizing electronegative gases to produce either positive
or negative ion beams, such as the PEGASES (Propulsion with Electronegative GASES) concept
[1, 53, 64]. Hence, this chapter considers an ionic electrospray thruster plume under bipolar oper-
ation. This chapter investigates the downstream plume region for a self-neutralizing bipolar anion
and cation beam, presenting a full particle 3D PIC model as a baseline characterization of the
neutralization process for ionic electrospray thrusters. The length scale of the interaction region
considered is on the order of meters, allowing for the inclusion of an entire CubeSat structure. A
preliminary excursion is conducted to understand the impact of field free region fragmentation on
the overall neutralization process, where the results are directly compared.
The rest of the chapter is organized as follows: Section 3.2 introduces the derivation of key
simulation parameters and the PIC method; Section 5.4 presents the results of the simulation,
53
including plasma potential, electric field, and charge density, and discusses key findings; Section
3.3.1 presents variations on the plume results due to the impact of field free region fragmentation
and Section 3.4 provides a conclusion.
3.2 SimulationModel
Ionic electrospray thrusters emit molecular ions directly from the liquid propellant via Taylor cone
emission [101]. Ionic electrospray thrusters have been observed to emit a variety of primary beam
species, including monomers, dimers, trimers, tetramers, and droplets [23, 82] and low energy ions
generated through solvated ion fragmentation [32, 39, 75]. This model considers a beam composed
solely of monomer ions emitted close to the beam potential. As the primary goal is to understand
the beam dynamics exhibited by the simplest beam generated by an electrospray thruster pair, this
assumption forms the baseline for future investigations. The primary species are the monomer ions
from the ionic liquid propellant, EMI
+
and BF
− 4
.
A fully integrated electrospray beam model would incorporate inputs generated from lower
level modeling of emission sites and tip geometry. The scale of interest for this model allows
for extensions from previous analyses of individual emitter tips. This assumption is supported by
experimental findings of the uniformity of beam parameters near the thruster exit plane [40]. In this
paper, the input parameters for plume modeling, namely the thruster extraction potentialΦ
thruster
,
the expected current emitted from a single emitter tip I
emitter
, the area of a single extractor grid
window A
extractor
, and the total thrust area A
thrust
, are based on the measurements of the USC
Testbed Thruster (UTT) [6]. Table 3.1 summarizes these values.
Table 3.1: Thruster parameters informed by experimental design efforts.
Parameter Physical Value Units
Φ
thruster
1500 V
I
emitter
36 nA
A
extractor
0.811 mm
2
A
thrust
20.2 mm
2
54
In the simulation, the ionized particles emitted from the thruster exit plane are represented by
a drifting Maxwellian distribution
ˆ
f
m
(v)=
1
(v
th
√
π)
3
exp(− (v
x
− v
di
)
2
+ v
2
y
+ v
2
z
v
2
th
) (3.1)
where v
th,i
and v
d
i
denote the species thermal velocity and beam velocity for species i, respec-
tively.The beam velocity is determined by the thruster operating voltage
v
d
i
=
r
2q
i
Φ
thruster
m
i
(3.2)
where q
i
and m
i
are the species charge and mass, respectively. The emitter density of the species
”i”, n
0
i
is determined from experimental emitter current measurements
n
0
i
=
I
emitter
eA
extractor
v
d
i
(3.3)
We consider that positive and negative currents emitted by thruster pair are identical, J
EMI
+ =
J
BF
− 4
. Assuming that the current density provided by a single emitter tip is constant over the
thruster exit area, the current and current density emitted by the thruster in the simulation model
are 5.08 µA and 44.4 mA/m
2
, respectively. At the thruster exit, the ion densities are n
0
EMI
+
≃
5.45× 10
12
m
− 3
and n
0
BF
− 4
≃ 4.83× 10
12
m
− 3
. These parameters are consistent with measured ionic
electrospray performance. We further consider that the temperature of the positive and negative
ion beams are isotropic and equivalent, T
0
EMI
+
= T
0
BF
− 4
= 10 eV based on previous laboratory
investigations into linear [65] and arrayed [82] thrusters.
The diameter of the EMI
+
and BF
− 4
ions are on the order of 7.6
˚
A and 5.2
˚
A, respectively. For
the ion density considered here, the mean free path for inter-particle collisions is on the order of
hundreds of kilometers outside the thruster exit. As the collision mean free path is much larger
than the length scale of the interaction region considered here, inter-particle collisions are ignored
in this study.
55
The simulation model is extended from the immersed finite element particle-in-cell (IFEPIC)
code, the USC-IFEPIC [41, 114]. This code was previously applied in several ion thruster plume
simulation studies [51, 113, 114]. In the simulation, both the EMI
+
and BF
− 4
ions are represented
by macro-particles. The electric field, particle trajectories, and space charge density are solved
self-consistently from the Poisson’s equation and Newton’s second law subject to the required
boundary conditions:
−▽
ˆ
Φ=(n
EMI
+− n
BF
− 4
) (3.4)
d( ˆ mˆ v)
dt
= ˆ q
ˆ
E (3.5)
All simulation parameters are normalized by the BF
− 4
ion parameters, specifically
ˆ x=
x
λ
D
BF
− 4
, ˆ v=
v
v
th
BF
− 4
,
ˆ
t= tω
p
BF
− 4
, ˆ m=
m
i
m
BF
− 4
, ˆ q=
q
e
,
ˆ
Φ=
eΦ
k
b
T
BF
− 4
(3.6)
where λ
D
BF
− 4
=
r
ε
0
k
b
T
BF
4
n
0
BF
4
e
2
and ω
p
BF
− 4
=
r
n
0
BF
4
e
2
ε
0
m
BF
4
are the Debye length and ion plasma frequency
evaluated for BF
− 4
, respectively.
Figure 3.1 shows the simulation domain and boundary conditions. The simulation considers
a 1U size CubeSat with a thruster pair. As the charge density associated with the thruster beam
is orders of magnitude larger than that of the ambient plasma, the effect of ambient electron and
ion species are not included in this model. The simulation domain has 450× 75× 150 cells with a
cell resolution dx= dy= dz=λ
D
BF
− 4
. The simulation domain leverages midline symmetry and a
mirrored boundary along the -Y plane. The CubeSat is represented by a cubic box of 10λ
D
BF
− 4
× 10λ
D
BF
− 4
× 10λ
D
BF
− 4
, with the center located at(35,0,75). The thruster exit area is 1λ
D
BF
− 4
× 1λ
D
BF
− 4
At every time step, macro-particles representing the EMI
+
and BF
− 4
are injected into the simulation
domain along the X direction. The number of the macro-particles injected at every time step is 1693
for EMI
+
and 1913 for BF
− 4
. (One EMI
+
macro-particle represents 27,654 physical EMI
+
ions,
and one BF
− 4
macro-particle represents 32,051 physical BF
− 4
ions.)
56
To evaluate plume interaction effects on the spacecraft, it is important to obtain the plume po-
tential with respect to spacecraft. For spacecraft using EP, the spacecraft potential is tied to the
plasma plume potential because the thruster is a very effective plasma contactor [111]. As the
plume potential is determined by the charge imbalance in the plume and the plume expansion pro-
cess [116, 114], the potential of the spacecraft–plume system floats with respect to the ambient, and
is not known a priori. Hence, in the simulation, the CubeSat potential is taken to be the reference
potential and is set at zero, whereas the potential at the downstream boundary floats with respect to
CubeSat. Given the current-free emission from the thruster pair, the CubeSat potential is expected
to be very close to the unperturbed ambient plasma. The potential at the upstream boundary is also
taken to be zero as the upstream boundary is placed relatively close to spacecraft and there is no
beam perturbation in the upstream region. The potential at all other domain boundaries floats with
respect to spacecraft through the application of the Neumann boundary condition.
The simulation time is determined by beam propagation in the simulation domain. The simu-
lation is ended well before the beam ions reach the outer boundaries of the domain so to eliminate
any potential numerical effects from the domain boundary [116]. Test runs were carried out to
ensure that the domain used is sufficiently large and has no influence on the results. For the results
displayed in the next section, the simulations all run for 2700 time steps. At the end of the simula-
tion, the beam front is at about ˆ x∼ 400, and the total number of macro-particles in the simulation
domain is approximately 10 million. Table 4.2 shows key simulation parameters in both physical
and normalized units. In this table, dt is the simulation time step.
3.3 ResultsandDiscussions
Figure 3.2 displays an isometric view of the spacecraft surface and net charge contours at the end of
simulation to display the general 3D shape of the composite beam. Here, the red surface denotes
regions of positive net charge and the blue surface denotes regions of negative net charge. For
clarity, the remainder of the results will be displayed as a series of two dimensional slices along
planes of interest.
57
Figure 3.1: Simulation domain setup with boundary conditions. The red cell denotes the area of
EMI
+
injection and the blue cells denotes the area of BF
− 4
injection
Table 3.2: Key simulation parameters in physical and normalized units for baseline PIC model
setup.
Parameter Physical Units Normalized Units
n
0
EMI
+
5.45× 10
12
m
− 3
1.13
n
0
BF
− 4
4.83× 10
12
1/m
− 3
1.0
T
EMI
+ 10 eV 1.0
T
BF
− 4
10 eV 1.0
λ
D
BF
− 4
10.7 mm 1.0
v
d
EMI
+
50,900 m/s 10.8
v
d
BF
− 4
57,500 m/s 12.2
v
th
EMI
+
4,150 m/s 0.885
v
th
BF
− 4
4,690 m/s 1.0
m
EMI
+ 111.17 g/mol 1.28
m
BF
− 4
86.81 g/mol 1.0
dt 0.32µs 0.01
Figure 3.3 displays the results along the plane of symmetry. Figure 3.3a shows the potential
with respect to CubeSat with equipotential lines on a logarithmic scale, denoting values of +/-
0.1 and 0.01 normalized potential. Figure 3.3b shows the normalized net charge, rho. Red lines
denote contours of positive net charge and blue lines denote contours of negative net charge. The
contours are displayed on a logarithmic scale from 0.1 - 1× 10
− 4
. Figure 3.3c shows the electric
field strength and vectors in the region close to the spacecraft. The electric field magnitude is
displayed on a logarithmic scale. The electric field vectors denote the direction of the electric
58
field and are constant in length. (Any deviation in length is due to foreshortening by out of plane
components.)
Figure 3.2: Isometric view of logarithmic charge density contours.
As seen from Fig. 3.3, the beam exhibits a near-symmetric behavior in the near field region
in terms of potential and charge density. The ballooning of BF
− 4
towards the downstream region
is due to the negative ions being emitted with a faster exit velocity. As seen from Fig. 3.3b the
beam structures break down and appear well-mixed approximately 210λ
D
BF
− 4
from the exit plane.
This corresponds to a distance of approximately 2.25m. This behavior can be seen in more detail
in Fig. 3.5b. The charge density and potential countours also shows that the individual beams
expand into vacuum relatively unimpeded. The physical values of the potential are limited to small
values of +/− 3.8 V . This plane displays several characteristics critical to further understanding
thruster implications for return current. Just outside the thruster exit plane, the electric field is at
its maximumm and is directed opposing the beam flow. Additionally, note that the electric field
vectors create looping structures connecting the beam midlines and all spacecraft surfaces. The
presence of a retarding field upon exit provides a pathway for other low energy charged particles
and effluent separate from the primary beam to be deposited upon spacecraft surfaces.
Figure 3.4 shows the results across several slices along the XY plane. The potential contours
shown in Fig. 3.4a show that the potential contours of the EMI
+
beam exhibit convex shape, while
that of the BF
− 4
beam are concave. The net charge contours shown in Figure 3.4b further shows that
the positive charge wraps around a negative core. This appearance is likely due to differences in
59
(a)
(b)
(c)
Figure 3.3: Plasma parameters in the XY plane, a) Normalized potential (with respect to CubeSat)
b) Normalized charge density c) Normalized electric field.
60
beam divergence angles between the negative and positive beams. The electric field vectors shown
in Figure 3.4c again display a retarding electric field immediately downstream of the exit due to
the space charge in the beam. The electric field again shows a looped structure that connects back
to the spacecraft surface in the XY plane, providing another pathwayfor backflow of low energy
ions near the thruster exit. The electric field in the beam diminishes further downstream where the
beams intersect and the beam space charge is neutralized.
Figure 3.5 shows the results across several slices along the YZ plane in the beam normal direc-
tion. Here again it can be seen, through Fig. 3.5b, that the positive net charge appears to envelope
the outer edges of the negative beam. In the downstream region, the distinct areas of positive and
negative net charge are less well-defined and intermixed, marking neutralization. The electric field
shown in Fig. 3.5c displays a dipole-like pattern in the beam plane. This dipole structure is slightly
asymmetric, following a similar cant that is seen in Fig. 3.5b. As the beams expand, the paired
poles of this dipole structure can also be seen to weaken and separate in the downstream region. We
find the maximum potential in the plume with respect to CubeSat is +/− 3.8 V , and the maximum
electric field in the plume is 113 V/m.
The electric field in an EP thruster plume is determined by beam neutralization and expansion
processes [46, 111, 114, 116]. The neutralization of ion thruster and Hall thruster beams is by
electrons emitted from an external neutralizer. Such a neutralization process has been studied by
fully kinetic simulations [11, 18, 46, 114, 115, 116]. Full particle PIC simulations using realistic
ion to electron mass ratio [46, 114, 115, 116] showed that ion thruster beam neutralization is
achieved through an ion-electron “coupling” process, where thermal electrons ”bounce” within
the potential well established by the ion beam boundary. This coupling process leads to a new,
anisotropic velocity distribution for the electrons which affects subsequent beam expansion, and
thus, the beam potential with respect to the ambient [46, 115].
It is interesting to note that the neutralization in a bipolar electrospray beam is very different
from the ion thruster beam neutralization. The results show that there is little collective coupling
between the two beams, and the dynamics of the beams are almost independent of each other.
61
(a)
(b)
(c)
Figure 3.4: Plasma parameters in the XY plane, a) Normalized potential (with respect to CubeSat)
b) Normalized charge density c) Normalized electric field.Top: Slice at BF
− 4
midline. Middle:
Slice at domain midline. Bottom: Slice at EMI
+
midline.
62
(a) (b) (c)
Figure 3.5: Plasma parameters in the YZ plane, a) Normalized potential (with respect to CubeSat)
b) Normalized charge density c) Normalized electric field. Top:
ˆ
X= 50, Middle:
ˆ
X= 125, Bottom:
ˆ
X = 200
Thus, the resulting plume resembles a simple superposition of the two beam profiles. This can
be attributed to the near unity mass ratio between anion and cation, as well as the beam current
density being much below the space charge limit. The mass difference between EMI
+
and BF
− 4
is
13%. In comparison, the mass difference between a Xenon ion and a neutralizing electron is over
200,000%. Moreover, the ion beam density emitted by an ion thruster is at the space charge limit.
In a typical Xenon ion thruster, at an acceleration voltage of 1500V , the sheath penetration distance
from the acceleration grid into plasma is on the order of a few millimeter, d∼ O(1)mm. Thus, the
space charge limit is
J
SCL
=
4ε
0
9
r
2e
m
i
V
3/2
a
d
2
≃ 277A/m
2
For the electrospray thruster considered here, the beam density of 44.4 mA/m
2
is almost four orders
of magnitude below the space charge limit in a typical ion thruster beam.
We note that the bipolar electrospray plume is also different from that of the PEGASES ion
thruster concept. The PEGASES thruster also utilizes a similar bipolar thruster configuration to
emit positive and negative ion beams. However, the PEGASES thruster operates at the space
charge limit. Two-dimensional (2D) fully kinetic PIC simulations had been previously carried out
for the PEGASES ion thruster concept [64] and the results showed substantial beam ion backflow
63
due to potential barriers forming outside the thruster exit. We had previously also carried out a
2D fully kinetic PIC simulation of a bipolar ionic electrospray beam with similar beam emission
parameters [34]. Both the 2D results in Ref. [34] and the 3D results in this paper show little space
charge effects in the beam. Electrospray thrusters are currently limited by space charge effects
in their emission process as opposed to in the downstream region. As a result, the space charge
effects are negligible in the beam downstream of the thruster exit.
The lack of coupling between the individual beams is further displayed through structures
present in phase space. Figures 3.6 and 3.7 show that the EMI
+
and BF
− 4
beams lack significant
interactions as they expand. To confirm the notion that the bipolar beam resembles the superpo-
sition of the constituent beams, we further carry out simulations of single electrospray thruster
emission. In these simulations, we turned off one of the thrusters. All other simulation parameters
are the same as for bipolar operation. Figure 3.8 compares the beam potential at several different
downstream distances for bipolar emission, EMI
+
only emission, and BF
− 4
only emission.
Figure 3.6: Phase space comparison of x-vx dimensions
The superposition approximation near the thruster plane is fairly accurate with under 2% error
in the region of interest. This error can be attributed to differences in plume species densities
between bipolar and single thruster emission. Figure 3.9 shows the difference in BF
− 4
density
between the bipolar and single-thruster case. Similarly, Fig. 3.10 shows the difference in EMI
+
density betwen the bipolar and single-thruster case. These figures are cropped to focus on the near-
spacecraft region. Assuming a neutralized spacecraft, there are notable differences in the densities
64
Figure 3.7: Phase space comparison of z-vz dimensions
of the consituent species between the single thruster and bipolar cases. The operation of the both
thrusters in the bipolar condition influences the individual beam species towards the midline in
both the displayed XZ plane and YZ plane. This concentrating effect creates a slight asymmetry
in particle density. Comparing Fig. 3.9 and Fig. 3.10, this asymmetry is comparable and opposing
for the two species. Again, this equal mirroring is likely due to the similar masses between the
EMI
+
cation and BF
− 4
anion.
3.3.1 EstimateontheEffectofFragmentedIons
This section applies the 3D PIC plume model to assess the impact of field free region fragmentation
on the overall neutralization dynamics of the bipolar thruster pair. In this section we compare
beam parameters across three cases: Monomer only baseline, previously discussed in detail in
this chapter), 50% monomer and 50% dimer, and 50% monomer and 50% dimer with field free
fragmentation. The overall simulation setup is conserved for these cases. Although these new
cases introduce additional dimer species to the anion and cation beams, the current-free condition
is still enforced.
Ion fragmentation rates for EMI-BF
4
have been recently investigated experimentally by Miller
[76, 77]. It was observed that field free fragmentation occurred at a constant rate. Acceleration
region fragmentation rates are observed to be linear with respect to the extraction potential. This
65
(a)
(b)
(c)
Figure 3.8: Potential at the plume midline for various slices along the X-axis displaying the com-
parison between the cases: EMI
+
only, BF
− 4
only, bipolar. a) X = 60, b) X = 90, c) X=120
66
Figure 3.9: Top: XZ view of difference in BF
− 4
density between pair emission and single beam
emission in domain midline. Bottom: YZ view of difference in BF
− 4
density at
ˆ
X = 120.
Figure 3.10: Top: XZ view of difference in EMI
+
density between pair emission and single beam
emission in domain midline. Bottom: YZ view of change in EMI
+
density at
ˆ
X = 120.
effort neglects acceleration region fragmentation to focus solely on the lowest energy species pre-
sented by field free fragmentation. The constant field free fragmentation rate is described in Eq.
3.7
r(t)= 1− exp(
− t
τ
) (3.7)
where τ is the mean lifetime of dimer species in the field free region. This rate is discretized by
the simulation timestep to determine the percent of the dimer species to fragment at each timestep.
Table 3.3 displays empirical values for mean lifetime of EMI-BF
4
for a variety of operating
voltages and propellant temperatures. Given thruster operating conditions assumed in Table 3.1,
67
this effort will use the mean lifetime values listed for a voltage of +/- 940V . Table 4.2 shows key
simulation parameters in both physical and normalized units. In this table, dt is the simulation
time step.
Table 3.3: Empirical field free fragmentation rates for EMI-BF
4
as reported in [77]
V oltage [V] Current [nA] Temperature [
◦ C] Mean Lifetime [µs]
716 396 50 1.73
718 314 30 1.9
744 632 70 1.47
786 627 50 1.37
859 324 30 1.49
940 490 30 1.29
-697 -215 30 1.94
-698 -321 50 1.76
-715 -526 70 1.62
-770 -550 50 1.51
-859 -319 30 1.6
-939 -500 30 1.43
Table 3.4: Key simulation parameters in physical and normalized units
Species
Parameter EMI
+
BF
− 4
EMI(EMIBF
4
)
+
BF
4
(EMIBF
4
)
− Units
n
0
2.725x10
12
2.415x10
12
2.725x10
12
2.415x10
12
1/m
3
n
0
1.13 1.0 1.13 1.0 -
T 10 10 10 10 eV
T 1.0 1.0 1.0 1.0 -
v
d
50,900 57,500 30,507 31,776 m/s
v
d
10.8 12.2 3.55 3.28 -
v
th
4,150 m/s 4,690 2,491 2,594 m/s
v
th
0.885 1.0 0.53 0.55 -
m 111.17 86.81 309.15 284.79 g/mol
m 1.28 1.0 3.56 3.28 -
r - - 0.0245 0.0221 -
dt 0.32 µs
dt 0.01 -
λ
D
BF
− 4
10.7 mm
λ
D
BF
− 4
1.0 -
Figure 3.11 displays the impact of the constant fragmentation rate used in the simulation. The
figure displays the charge density of EMI dimers at the end of simulation time. Due to the constant
68
fragmentation, all dimers have fragmented within 10λ
D
of the thruster exit plane. This distance is
approximately 10cm.
Figure 3.11: Charge density of EMI(EMIBF
4
)
+
dimers. The decrease in dimers in the downstream
region is caused by the constant fragmentation rate.
The number of the macro-particles injected is 1693 for EMI
+
, 1913 for BF
− 4
, 1015 for EMI(EMIBF
4
)
+
,
and 1057 for BF
4
(EMIBF
4
)
− . For the results displayed in the next section, the simulations all run
for 2700 timesteps. At the end of the simulation, the total number of macro-particles in the simu-
lation domain is approximately 15 million.
Figure 3.12 displays an isometric view of the spacecraft surface and net charge contours at the
end of simulation to display the general 3D shape of the composite beam. Here, the red surface
denotes regions of positive net charge and the blue surface denotes regions of negative net charge.
For clarity, the remainder of the results compare results across a series of two dimensional slices
along planes of interest.
Figure 3.13 displays plasma parameters along the simulation plane of symmetry. Figure 3.13a
shows the normalized net charge with logarithmic contours ranging from 0.1 - 1× 10
− 4
. Red lines
(a) (b) (c)
Figure 3.12: Isometric view of charge density contours for, a) Monomer only baseline b) 50%
monomer, 50% dimer c) 50% monomer, 50% dimer with field-free fragmentation
69
(a) (b) (c)
Figure 3.13: Normalized plasma parameters in the XZ plane, a) Charge density, b) Plasma Poten-
tial, c) Electric field for Top: No Monomer only baseline, Middle: 50% monomer, 50% dimer,
Bottom: 50% monomer, 50% dimer with field-free fragmentation
denote contours of positive net charge and blue lines denote contours of negative net charge. Figure
3.13b shows the potential with equipotential lines on a logorithmic scale, denoting values of +/-
0.1 and 0.01 normalized potential. Figure 3.13c shows the electric field strength and vectors in the
region close to spacecraft.
As seen from Fig. 3.13, the structure of the beams are comparable but notably different from the
monomer only baseline. The beam spreads out wider due to the inclusion of slower beam species
and has a lower downstream density due to the proportionally fewer monomers. By introducing
monomer and dimer species, the beam has two wavefronts. The monomer species reach near to the
end of the domain, while dimer and fragmented species reach to about X=150 before the simulation
ends. As a result observations will be focused on the region where all beam species are present.
In this region the overall structure of the beam is comparable to the monomer only baseline. And,
if the simulation was able to run for a longer period of time it is likely that the new beam profile
would exhibit similar mixing and neutralization by about X=210. This corresponds to a distance
of approximately 2.25m. The physical values of the potential is limited to small values of± 3.8 V .
The electric field is largely comparable close to the spacecraft surface. Although the electric field
just outside the thruster exit plane is at its maximumm and is directed opposing the beam flow,
70
(a) (b) (c)
Figure 3.14: Normalized plasma parameters in the XY midline plane, a) Charge density, b) Plasma
Potential, c) Electric field for Top: No Monomer only baseline, Middle: 50% monomer, 50%
dimer, Bottom: 50% monomer, 50% dimer with field-free fragmentation
there is not any significant scattering caused by the inclusion of high mass and low energy beam
species.
Figure 3.14 shows the results across several slices along the XY plane. Comparing the potential
contours shown in Fig. 3.14b shows that the potential contours of the cation beam have expanded.
This is likely due to the decrease of large negative potential in the downstream region, again caused
by the reduction of monomer species. The out-of-plane net charge contours shown in Figure 3.14a
are comparable showing the positive charge contours wrap around a negative core, likely due to
differences in beam divergence angles between the negative and positive beams. The electric field
magnitudes and vectors are again comparable across all three cases.
We find the maximum potential in the plume with respect to CubeSat is +/− 3.8 V , and the
maximum electric field in the plume is 113 V/m.
The distinct lack of coupling observed in the monomer only baseline is preserved in cases
that include dimer species and field free region fragmentation estimates. As previously stated,
the mass difference between EMI
+
and BF
− 4
is much less that that between a Xenon ion and an
electron. Moreover, the mass ratio between the dimer beam species, is even closer to unity, with
a percent difference of only 8%. The lack of coupling between the individual beams is further
71
(a) (b) (c)
Figure 3.15: X-V
x
phase space comparison between, a) Monomer only baseline b) 50% monomer,
50% dimer c) 50% monomer, 50% dimer with field-free fragmentation
(a) (b) (c)
Figure 3.16: Z-V
z
phase space comparison between, a) Monomer only baseline b) 50% monomer,
50% dimer c) 50% monomer, 50% dimer with field-free fragmentation
displayed through structures present in phase space. Figures 3.15 and 3.16 show that the cation
and anion beams lack significant interactions as they expand. In addition, no features of turbulence
or instabilities are present. It is also clear to see the previously mentioned beam wavefronts.
3.4 Conclusion
This paper presents 3D plume simulations of an ionic electrospray thruster pair in bipolar opera-
tions. We find that the bipolar beam expands relatively unimpeded, with no significant coupling
between the positive cations and negative anions. The plasma potential and charge density of the
beam can be represented as a simple superposition of individual thruster beam profiles. The lack
of beam coupling is due to the relatively equal mass between the EMI
+
cation and the BF
− 4
anion,
and negligible space charge effect because of the small beam current density.
Ionic electrospray thrusters generate low energy ions through solvated ion cluster fragmenta-
tion. The lowest energy ions result from fragmentation outside of the thruster acceleration region,
72
also referred to field-free fragmentation, and have been reported to constitute 20-50% of the overall
beam [23, 82]. Studies on ion cluster fragmentation cite the internal ion energy and external elec-
tric fields as key drivers [27]. Present models for the field-free fragmentation rate are consistent
with empirical measurements indicating a constant rate of fragmentation [75, 77], thus implying
that all dimer species fragment. However, the results presented here suggests that only those ions at
the low energy tail end of the distribution will be scattered because of the very small electric field in
the bipolar ionic electrospray plume. Thus, in-space operation of ionic electrospray thrusters may
see significantly less field-free fragmentation than predicted from previous laboratory experiments.
Recent experiments also provide evidence that the electrostatic forces generated by ion gates used
for time of flight spectroscopy may lead to an over-production of fragmented ion species in the
plume [5], which could lead to over estimation of the fragmentation rate.
The results presented are for a pair of thrusters separated by a distance of four thruster diameters
emitting parallel ion beams below the space charge limit. As the beam dynamics are independent
of each other, changing the thruster placement and/or orientation will affect the plume profile but
not the beam neutralization process. On the other hand, as the emission current approaches the
space charge limit, beam neutralization can be influenced significantly by the spacing between
thrusters and the beam emitting direction as indicated by 2D simulations of the PEGASES ion
thruster [64]. Parametric simulations will need to be carried out to assess modifications to the
plume due to thruster placement and orientation as a function of the emission current.
The plume model presented here is intended as a baseline model for future contamination
studies for bipolar ionic electrospray thrusters, and assumes idealized plume energy and mass
composition. The following chapters will consider compare observations from this idealized setup
with a more sophisticated model that directly accounts for beam emission and acceleration physics.
73
Chapter4
Multi-ScalePlumeModel
4.1 Introduction
The physics of ionic electrospray emission is affected by interactions occurring in concert over 9
orders of magnitude in length scales: the spatial scale of the emission site is on the order of nano-
meters (nm), that of the acceleration region is micro-meter (∼ µm), and that of the plume region is
from centimeter (cm) to meter (m). To better understand the full spectrum of physical interactions
of an ionic electrospray thruster, a multi-scale simulation study is required. This chapter presents a
consistent simulation of pure ionic emission from a porous emitter tip by combining a MD model
for beam emission at O(nm), a PP model for ion interaction and acceleration at O(µm), and a PIC
model for plume neutralization at O(cm)-O(m).
In this chapter, the combined MD, PP, and PIC models are applied to simulate beam emission of
the USC Testbed Thruster (UTT) [6]. UTT is comparable in design to that of AFRL’s AFET-II [82].
Results from each sub-model are compared to highlight key physical interactions at each scale. The
resulting downstream plume and neutralization dynamics are also compared to previous results
from the baseline PIC model discussed in Chapter 3. This multi-scale model enables the analysis
of several off-nominal emission characteristics capable of being produced by ionic electrospray
thrusters. A case study is presented to better understand the impact of secondary emission site
activation on grid impingement and overall plume neutralization. Lastly, this model is used to
revisit the impact of ion fragmentation on beam formation and neutralization.
74
Figure 4.1: MD emission of monomer and dimer species from an applied electric field.
4.2 SimulationModelandApproach
The simulation model is composed of three sub-models: a MD model for ion emission, a PP
model for ion acceleration, and a PIC model for beam neutralization and plume structure. In
simulations, the MD model is first applied to determine the plume composition (i.e. percentage of
monomer, dimer, or trimer species), as well as a representative 3D velocity distribution function
in an extracting electric field. The PP model is then used to resolve the forces on the emitted
particles due to the background electric field and particle-particle forces. Lastly, the distributions
generated from both positive cation and negative anion emission are injected into the PIC model
to understand bipolar thruster pair neutralization. In the PP and PIC models, the immersed-finite-
element (IFE) field solver [41, 50] is used to solve the electric field generated by a complex shaped,
biased dielectric or conducting surface, such as the emitter tip and extractor electrode. This section
describes these models in detail, as well as their key assumptions and interfaces.
4.2.1 MolecularDynamicsModel
The MD model is applied to simulate the emission process at the emission sites on the porous
emitter surface, investigating the physics at a length scale of O(1-100nm).
The MD model is constructed using Large-scale Atomic/Molecular Massively Parallel Simula-
tor (LAMMPS) [102]. The model considers a column of EMI
+
and BF
− 4
molecules that is allowed
to relax to form EMI-BF
4
from the tip of the Taylor cone. An external electric field is applied to
the top 20 Angstrom, achieving emission. Figure 4.1 portrays the MD emission model emitting a
75
positive cation beam. The simulation domain is held at a constant volume of 6000× 400× 400 nm.
The total number of atoms used is 144,000, with 6,000 EMI-BF
4
molecules. These 6,000 EMI-
BF
4
molecules provide a large reservoir of neutral molecules to establish steady emission results
over the simulation time period. A fraction of these molecules are emitted in the simulation. These
emitted molecules correspond directly to every physical molecule emitted from an emission site.
Taylor cone emission starts once the electric field exceeds the emission threshold of about ± 1V/nm [13, 100, 124]. The electric field at an emission site is determined not only by its location
on the emitter tip, but also by the size and shape of the specific pore-propellant interface. This
interface cannot be known exactly due to the randomness of pore size/shape on the emitter surface
after tip manufacturing processes [26, 59, 82]. It has been observed that emission at electric fields
>± 2V/nm significantly reduces the dimer population entering the acceleration region [13, 100,
124]. As experimental characterization activities have detected the presence of a large proportion
(up to 50%) of the dimer species [23, 82, 85], the MD simulations considered positive cation and
negative anion emission across a variety of applied electric fields ranging from ± 1V/nm to ± 2V/nm.
The emitted particles are sampled to create representative particle velocity distribution func-
tions used in the PP model. The simulation time step is set to 1fs to ensure the inter-molecular
interactions are fully resolved. Each simulation case consists of 10
6
total steps and takes about 12
hrs of run time on USC’s high performance computer (HPC).
4.2.2 Immersed-Finite-ElementFieldSolver
The PP model considers emission from a single micro-machined porous emitter tip. The emitter
tip is modeled as a dielectric cone 300µm tall with a 75
◦ slope. The tip of the cone is rounded
with a radius of curvature of 14µm. The extractor grid is circular and assumed to be level with the
vertex of the cone, 49µm above the emitter tip. The extractor window is 508µm in diameter. This
geometry is consistent with previously published designs [82], and is displayed in Fig. 4.2. The
76
Figure 4.2: The geometry of the emitter tip and extractor grid for calculating background field
properties.
average pore size of the substrate is 1µm, consistent with P5 glass. It is the pores near the tip that
will be possible Taylor cone emission sites.
The background electric field generated by such a structure is solved using the IFE field solver.
This model is capable of solving the electric field and object charging self-consistently for complex
shaped objects, and had been previously applied to analyze a variety of electrostatic interaction
problems, such as that for charged composite materials [50] and lunar regolith surface [41]. Here,
we consider a dielectric glass tip with a permittivity equal to 30ε
0
. The -Z boundary is set to± 1500V with a Dirichlet boundary condition. All other external boundaries satisfy the Neumann
boundary condition. The extractor grid window is set to 0V and is assumed a perfect conductor.
We use a uniform mesh of cell size 5µm× 5µm× 1µm to resolve the geometric features of the
emitter tip and extractor grid in sufficient detail. The domain measures 201 × 201× 701 cells. The
background field is able to be solved with approximately 1.5 hours of runtime on the USC HPC.
Figures 4.3a and 4.3b display the background electric field in the acceleration region, subject
to the potential applied at the bottom plate of the emitter and the extractor grid, for the positive
beam emission case. The background electric field is solved up to the resolution of the IFE mesh
size, dx= dy= 5µm and dz= 1µm. The results show that the maximum electric field strength
77
(a) (b)
Figure 4.3: Background a) electric potential and b) electric field strength in the acceleration region
for the positive emission case.
is localized to the apex of the emitter tip and falls off drastically moving toward the base. While
computation limitation does not allow the IFE model to resolve the electric field at the nm scale,
we find the electric field strength around the apex of the tip is of the same order of magnitude of the
emission threshold, and correlates with the likelihood of Taylor cone emission sites being activated
at that location.
4.2.3 Particle-ParticleModel
The PP model is applied to simulate the ion acceleration region around an emitter, investigating the
physics at a length scale of O(1µm-1mm). The PP model is extended from a PP model previously
developed to investigate droplet acceleration in colloid electrospray thrusters [130] and ion thruster
beam neutralization [129]. The total force on each particle in the domain is described as the sum of
the external background electric field and the summation of all particle-particle forces. Therefore,
the system of equations for particle motion is described in Eq.(4.1)
m
d
2
r
dt
2
= m
dv
dt
=F=F
pp
+F
acc
= q(E
pp
+E
acc
) (4.1)
78
Table 4.1: Physical input parameters for PP model setup
Parameter Symbol Value Unit
Accelerating voltage φ
0
+/- 1500 V
Pore radius R
p
1 µm
Tip to extractor distance d 49 µm
Cation monomer mass m
EMI
+ 117 g/mol
Cation dimer mass m
EMI(EMI− BF
4
)
+ 309.15 g/mol
Anion monomer mass m
BF
− 4
86.81 g/mol
Anion dimer mass m
BF
4
(EMI− BF
4
)
− 284.79 g/mol
Particle charge q +/- 1.6× 10
− 19
C
Current I 16 nA
Particle emission rate
˙
N
d
10
11
s
− 1
where q represents the particle charge,E
pp
refers to the electric field due to particle-particle forces
as described in Eq.(4.2), andE
acc
refers to the background electric field. The background electric
field is solved by the IFE field solver. The result is interpolated to the particle locations in the PP
model using a linear force weighting scheme
E
(i)
pp
=
1
4πε
0
N
∑
j=1,i̸= j
q
j
|r
ij
|
3
r
ij
(4.2)
The PP model links to the MD model by generating injected particles using the composition
percentage, the velocity distribution function, and the emission rate produced by the MD emis-
sion model. Table 4.1 displays other relevant input parameters used to setup the PP model. The
simulation time step is set to 1ps. The PP simulation is ended when a statistically representative
number of particles have entered the downstream region, at approximately 1mm from the thruster
exit plane. The amount of time required to achieve this result varies with particle species and ve-
locities. A typical simulation case generates up to 60,000 particles, executes a total of 2,000 time
steps, and takes about 10 hrs of computation time on the USC HPC.
4.2.4 Particle-in-CellModel
The PIC model is applied to simulate beam neutralization and plume structure, investigating the
physics at a length scale of O(1cm-1m). The PIC simulation model is extended from the immersed
79
finite element particle-in-cell (IFEPIC) code discussed in Ref.[41, 114], the USC-IFEPIC. Here,
we reuse the same conditions put forward in Chapter 3. The simulation setup is identical, with one
cation beam and one anion beam being ejected from a notional CubeSat spacecraft surface. Again,
we assume that the injected current is equal, with J
EMI
++J
EMI(EMI− BF
4
)
+= J
BF
− 4
+J
BF
4
(EMI− BF
4
)
− .
The PIC model simulates the plume ejected by an entire thruster consisting of many emitter tips.
We assume that the values solved for a single emitter tip within the MD and PP models can be
generalized to represent the emission profile of the entire array of a single thruster (i.e. all emitter
tips in each thruster are identical.) The particles from the PP model are sampled by the PIC model
to determine the species composition and VDFs of particles entering the downstream region.
This simulation follows the same normalization scheme as derived previously in Chapter 3.
Although the emitted particle species are no longer represented by a Maxwellian distribution func-
tion, we still use the notional distributions to define our normalization scheme. The simulation
parameters are normalized to the BF
− 4
anion with an assumed isotropic temperature T
0
BF
− 4
= 10 eV
and initial density n
0
BF
− 4
= 4.83× 10
12
1/m
3
.
Table 4.2 shows key simulation parameters in both physical and normalized units. In this table,
dt is the simulation time step. The simulation domain and boundary conditions are comparable
Table 4.2: Key simulation parameters in physical and normalized units for PIC model setup
Parameter Physical Units Normalized Units
n
0
BF
− 4
4.83× 10
12
1/m
3
1.0
T
BF
− 4
10 eV 1.0
λ
D
BF
− 4
10.7 mm 1.0
v
th
BF
− 4
4,690 m/s 1.0
m
EMI
+ 111.17 g/mol 1.28
m
BF
− 4
86.81 g/mol 1.0
m
EMI(EMI− BF
4
)
+ 309.15 g/mol 3.56
m
BF
4
(EMI− BF
4
)
− 284.79 g/mol 3.28
dt 0.32µs 0.01
to that displayed in Chapter 3 as well. The effect of ambient electron and ion species are still
not included in this model. Given the current-free emission from the thruster pair, the spacecraft
80
potential is assumed to be the same as the unperturbed ambient plasma. In the simulation, the
upstream boundary represents the unperturbed ambient, thus the potential of both the spacecraft
and the upstream boundary is taken to be zero. The Neumann boundary condition is applied for the
potential at all other domain boundaries. The simulation domain leverages midline symmetry and
a mirrored boundary along the -Y plane. The simulation is ended before significant portions of the
injected beam ions reach the outer boundaries of the domain so to eliminate potential numerical
effects from the domain boundary. Test runs were carried out to ensure that the domain used is
sufficiently large and has no influence on the results. The simulation domain has 350 × 85× 170
cells with a cell resolution dx= dy= dz=λ
D
BF
− 4
. The CubeSat is represented by a cubic box of
10λ
D
BF
− 4
× 10λ
D
BF
− 4
× 10λ
D
BF
− 4
. The thruster exit area is 1λ
D
BF
− 4
× 1λ
D
BF
− 4
In the simulation, both the cations and anions are represented by macro-particles. The electric
field, particle trajectories, and space charge density are solved self-consistently from the Poisson’s
equation and Newton’s second law subject to the required boundary conditions:
−▽
ˆ
Φ= n
EMI
++ n
EMI(EMI− BF
4
)
+− n
BF
− 4
− n
BF
4
(EMI− BF
4
)
− (4.3)
At every time step, macro-particles representing the EMI and BF
4
monomers and dimers are
injected into the simulation domain. The number of the macro-particles injected is 1692 for EMI
+
,
1015 for EMI(EMI-BF
4
)
+
, 1914 for BF
− 4
, and 1057 for (EMI-BF
4
)BF
− 4
. This injection rate is nor-
malized, but can relate to a physical current of 5.08µA. Therefore, the PIC simulation represents a
thruster with an emitting area equal to approximately 318 distinct emitter tips. For the results dis-
played in the next section, the simulations all run for 2100 time steps. At the end of the simulation,
the total number of macro-particles in the simulation domain is approximately 13 million. Each
simulation takes approximately 3.5 days to run on the USC HPC.
81
4.3 ResultsandDiscussion
This section discusses results from multi-scale simulations to investigate i) the physics and inter-
actions at each scale of interest and ii) the impact of activation of multiple emission sites at all
scales. The results of the MD and PP sub-models are presented for both positive and negative
thruster polarity. The PIC model combines these results to investigate beam neutralization with a
bipolar thruster pair. Due to randomness imposed by unknown pore locations within the substrate,
and other unique micro-scale features and defects from emitter tip manufacturing, it is impossible
to predict exactly where and when primary and secondary emission site will appear. However,
this model allows for an example approach to make overall determinations into the effect of a sec-
ondary emission site if it is excited on a neighboring pore. Therefore, this simulation will present
a series of results for a case with a single emission site, as well as a case with a notional secondary
or tertiary emission site activated on the side of the emitter tip.
4.3.1 SingleEmissionSite
The single emitter case considers that the particle velocity distribution function injected at the PP
scale is consistent with that of the± 2 V/nm MD emission case.
Figure 4.4 displays a positive cation plume consisting of monomers and dimer species along
the XZ and YZ plane, respectively. Cartoon representations are included to roughly outline the
physical positions of the emitter tip and the extractor grid with respect to the plume. It is important
to note that the PP model does not include the extractor grid structure and, therefore, does not
remove particles that intercept the extractor grid. Here, we can see that the more mobile, lower
mass monomer species experience a larger spread than the higher mass dimer species in the cross-
beam, or Z direction. Additionally, it is noted that the overall scatter of the beam is slightly
asymmetric. This asymmetry is likely introduced by the particle initialization provided by the MD
model.
82
Figure 4.4: Particle positions in the XZ plane (top) and YZ plane (bottom).
Figure 4.5: Comparison of monomer velocity distribution functions (VDFs) at the input (Top)
and output (Bottom) of the PP model. Red denotes cation, blue denotes anion. Left: Velocity
distribution in the X direction. Middle: Velocity distribution in the Y direction. Right: Velocity
distribution in the Z direction.
83
Figure 4.6: Comparison of dimer velocity distribution functions (VDFs) at the input (Top)‘ and
output (Bottom) of the PP model. Red denotes cation, blue denotes anion. Left: Velocity dis-
tribution in the X direction. Middle: Velocity distribution in the Y direction. Right: Velocity
distribution in the Z direction.
Figures 4.5 and 4.6 display particle velocity distribution functions from the input and output of
the PP model. Both positive and negative emission modes are displayed for each figure. Focusing
on Fig. 4.5 (panel a), we find that the MD model produces a sizeable fraction of low velocity
monomers that have fragmented during the emission process. This is most easily seen by the
second peak in the V
x
distribution. Looking to the output of the PP model (panel d), we find that
traversing through the acceleration region helps to homogenize the resulting beam. Comparing
panels b to e and panels c to f, it is noted that the fraction of outliers in the V
y
and V
z
component
are reduced as well. Looking to Fig. 4.6, one can see in panels b, c, e, and f that the emitted
dimer species are emitted with less variation in their cross-beam velocity components, another
contributor to their occupancy of the beam’s core. We can also see the significant acceleration of
the dimer species along the X direction by comparing panels a and d. Comparing panel d for both
Fig. 4.5 and Fig. 4.6, the PP output of V
x
for both the monomers and dimers, it appears that the
positive beam achieves a more homogeneous exit velocity than the negative beam. The fact that
84
the positive monomers and dimers are proximate in exit velocity implies that we cannot assume
that species accelerate independently. This beam homogeneity is achieved sometime during or just
after the thruster exit plane.
The PP output can then be used to inject into the PIC model. Previous studies investigating the
downstream region [7, 8, 34] assumed that the particle beam was well represented by an isotropic
Maxwellian distribution drifting in the X-direction. Looking at Figures 4.5 and 4.6 (panels d, e,
and f), we can see that this previous assumption is inaccurate. The V
y
and V
z
component, while
comparable, provide a very steep decline for large velocities. The following figures display the
results of the 3D PIC model focused on the general structure of the downstream region. All figures
are presented as an isometric view of the data within the 3D domain.
Figures 4.7 - 4.9 displays results of the downstream plume PIC model. Figure 4.7 displays
the normalized plasma potential with logarithmic contours at± 0.1 and± 0.01. These contours
are semi-transparent to display the nested nature. Red contours denote areas of positive potential
and blue contours denote areas of negative potential. Figure 4.8 displays the normalized charge
density also with logarithmic contours at +/- 1× 10
− 4
. The red contours denote regions of positive
net charge density and the blue contours denote regions of negative net charge density. Figure
4.9 displays the normalized electric field. The figure includes arrows denoting the electric field
vectors throughout the domain. Note that the displayed arrows are of constant length and that any
variations in the perceived vector length is due to foreshortening by out-of-plane field components.
The magnitude of the electric field is captured by the color bar. A 2D slice displaying portions of
the XY plane and corresponding electric field vectors is provided to capture the 3D structure of the
electric field.
The overall features of the plume are very similar to those previously reported. In general, the
downstream plume behavior displays relatively little coupling between the positive and negative
beams. The plasma potential and electric field strength are slight, amounting to a maximum of
± 2.8V and 113 V/m, respectively. As a result, the beam expansion occurs relatively unimpeded.
Upon comparing Figs. 4.7 - 4.9 to previous results we can see the overall beam spread is larger
85
Figure 4.7: Plasma potential contours for single emitter case.
Figure 4.8: Charge density contours for single emitter case.
Figure 4.9: Electric field strength and vectors for single emitter case.
86
Figure 4.10: PP model particle positions in XZ plane for two emitter case.
along the Z-direction, but smaller in the Y-direction. There are also very small populations of the
beam that leave the thruster at large angles. Despite these differences, the overall neutralization
process of the beam appears to not be adversely affected.
4.3.2 EffectsofMultipleEmissionSites
The multiple emitter case introduces a secondary emission site at 5µm from the center-line. This
distance corresponds to an activation of the closest neighboring pore, assuming average porosity.
This case is analyzed in the MD and PP models, and results are displayed below. Due to the
symmetry in the PIC model, a triple emitter case was also tested which introduced two secondary
sites± 5µm from the center-line. We assume the primary emission site has an extraction field of 2
V/nm and that any additional emission sites experience a lesser electric field of 1.5 V/nm. Figure
4.10 displays particle positions for the XZ plane for the two emitter case.
Comparing between Figures 4.4 and 4.10, one can see the scattering induced by the activation
of a secondary emission site. Both the monomer and dimer portions of the beam experience an
increased spread along the beam-radial direction. Figure 4.11 compares the beam radial velocity
distribution for the single and double emitter cases. The average radial velocity of the particles
87
Figure 4.11: Comparison of beam radial velocity distribution between single emitter and double
emitter case.
is increased as well as the standard deviation, with the max radial velocity almost doubling. Ac-
tivation of the second emission site increases the number of particles capable of impacting the
extractor grid, leading to losses of thrust and grid contamination.
PIC model results are presented for a triple emitter case. Figures 4.12 - 4.14 display the relevant
plasma parameters as an isometric view once more. These plots are displayed in the same style
discussed previously in the single emitter case results. Here, we can see that despite the increase
in overall spreading, the primary downstream neutralization mechanisms are maintained. The max
electric field strength and potential are comparable to that of the single emitter case. The primary
difference between the two cases is the increased expansion angle of the beam. Otherwise, it
does not appear that the presence of multiple emission sites per tip adversely affects the beam
neutralization process.
4.3.3 EffectsofIonFragmentation
The ion fragmentation case incorporates a constant rate of fragmentation within the PP model
which encompasses the acceleration region and nearby field free region. The fragmentation rate
within the acceleration region is dependant upon several factors, namely the electric field strength
88
Figure 4.12: Plasma potential contours for triple emitter case.
Figure 4.13: Charge density contours for triple emitter case.
Figure 4.14: Electric field strength and vectors for single emitter case.
89
(a) (b)
Figure 4.15: Comparison of radial position of monomer ions between simulations with and without
fragmentation a) EMI
+
ions b) BF
− 4
ions
and internal energy of the emitted molecular ions [76, 77, 84]. Without a thorough understanding
of the internal energy distribution and fragmentation physics, we assume a constant fragmentation
rate. This simulation uses a constant fragmentation rate of 2× 10
− 4
ps
− 1
, comparable to that used
previously by [84] and informed by experimental measurements. This fragmentation rate was
assumed constant for the entirety of the PP model simulation, producing fragments within both
the acceleration region and field-free region. This constant assumption provides an overestimate
of fragmentation events as electric field strength decreases significantly as the beam expands and
enters the field free region. As a result, the figures presented offer a conservative estimate of
the impact of fragmentation on overall beam dynamics, as fragmentation is likely less frequent in
actual applications. The results compare beam parameters for two identical simulation setups, with
one simulation including a constant fragmentation rate, and the other containing no fragmentation.
Figure 4.15 displays the impact fragmentation on angular distribution of monomer ions for both
positive and negative beam cases. It should be noted that the fragmentation cases include a larger
number of monomers as a result of the fragmentation process. One can see that the presence of
fragmentation increases the number of monomer ions with lower angular spread from the emission
site. This is primarily due to the conservation of kinetic energy as a result of the fragmentation
process. These fragmented monomers originate in the core of the beam and have similar radial
velocities to dimer species. It should also be noted that the presence of these fragmented monomer
90
(a) (b)
Figure 4.16: Comparison of radial velocity distribution of entire beam for cases with and without
fragmentation included, a) cation beam b) anion beam
species at low divergence angles do not significantly reduce the maximum overall spread of the
emitted beam.
Figure 4.16 compares the probability distribution function of the radial velocity for the entire
emitted beam for both positive and negative plume cases. Here we include monomer, dimer, and
fragmented monomer species. For both subplots we see a bimodal distribution. Looking to the
cases without fragmentation, we can see that the distribution is shaped by the emission properties
of unfragmented monomers and dimers, with monomers responsible for the larger radial velocity
peak, and dimers responsible for the slower radial velocity peak. Comparing the cases with and
without fragmentation we can see that fragmentation scatters the fragmented ions from the beam
core. This scattering is seen as a reduction at the dimer peak and an increase in the distribution
function at normalized radial velocity values equal to 0.07. Despite this scattering effect, the
overall divergence of the beam is not increased as the fragmented monomers do not have radial
velocity components larger than the unfragmented monomer species.
PIC model results are presented for the fragmentation case below. The results were collected at
a timestep of 1600 steps. Figures 4.17 - 4.19 display the relevant plasma parameters as an isometric
view. These plots are displayed in the same style discussed previously in the single emitter case
results.
From Figure 4.18 we can see that the presence of low energy monomers creates a slower
external shell, contrinbuting to higher cross-beam spreading. Although Figures 4.15 and 4.16
91
Figure 4.17: Plasma potential contours for fragmentation case.
Figure 4.18: Charge density contours for fragmentation case.
Figure 4.19: Electric field strength and vectors for fragmentation case.
92
predict fragmented monomers do not contribute to beam spreading in the acceleration region, we
can see that the the fragmented monomer species make their way to the extremities of the beam in
the downstream region. Although it is likely that a large portion of the fragmented particles remain
in the core of the beam, any particles emitted with a high radial velocity has a higher liklihood of
divergence due to the particles’ slower downstream velocity. This relationship leads to a higher
overall divergence at a large enough length scale. Despite this spreading affect, the plasma plume
potential and electric field plots are largely similar to those presented previously, indicating that
fragmentation induces little adverse effects to the downstream neutralization process.
4.3.4 Discussions
The simulation results suggest that prior model assumptions that the beam species are accelerated
independently is inaccurate. The exact composition of the cation or anion beam will affect the
acceleration of each particle as they experience inter-particle forces in the acceleration region. In
addition, the distribution of the beam radial velocity components were shown to not strictly follow
a Maxwellian distribution. Furthermore, high mass species, such as dimers, trimers, tetramers,
or droplets, if emitted on-axis, experience less radial spreading and are more likely to be found
in the core of the beam. Results from the downstream region PIC model imply that inclusion
of MD and PP model physics do not adversely affect beam neutralization. The overall physical
interactions between the positive and negative beams are largely similar and comparable to the
simplified models previously examined. Adequate neutralization exists wherever the densities of
the individual thrusters are opposing and equal. Overall, this model further affirms the conclusions
presented previously by the simplified downstream model, while providing further insight into how
lower-level physics adjusts the primary mechanisms observed.
The impact of secondary site emission has been documented before experimentally [40], but
the underlying interactions between multiple beams within the acceleration region has not yet been
well understood. The introduction of a second or third emission site on a single emitter tip is likely
more dangerous for a thruster than it is beneficial. The presence of multiple emission sites causes a
93
marked increase in the overall expansion of the individual beamlets. This increases the likelihood
of contamination or destruction of the critical extractor electrode. Despite the adverse affects of
secondary site activation at the acceleration region scale, there are less noticeable adverse affects
inhibiting beam neutralization in the downstream region.
The effects of fragmentation on the acceleration region have been studied in other kinetic PIC
models [84], but this model provides more insight and flexibility to assess different regions of
interest at separate scales. The presence of fragmentation physics within the emitted electrospray
beam likely has low risk to spacecraft integration hazards or thruster longevity. Since fragmentated
ions are born from high mass dimer and trimer species, their radial velocity is more constrained
than unfragmented emitted monomers. As long as the beam emission direction is unperturbed by
other effects (i.e. secondary site activation), the presence of fragmented monomers does not impact
the development of the overall beam in a detrimental fashion.
4.4 Conclusion
Accurate understanding of ion emission, acceleration, and neutralization physics is critical in esti-
mating thruster performance, lifetime limiting effects, as well as larger scale impacts to spacecraft
surface contamination and ambient plasma interactions. This chapter presents, to our knowledge,
the first combined MD, PP, and PIC simulations of the ion emission, acceleration, and neutral-
ization processes for an ionic electrospray thruster with porous emitter tips using EMI-BF
4
ionic
liquid propellant. Results are presented on key characteristics of the interaction that take place
during the development of the ionic electrospray thruster plume from O(nm), O(µm), O(cm), to
O(m) length scales.
A major conclusion from this study pertain to the insight gained from investigating multiple
emission sites from a single emitter tip. In general, the activation of multiple emission sites on a
single emitter tip increases the likelihood for grid interception, and increases the overall beam half
angle. Specifically, we noted an increased spread of velocity distributions along the same axis that
contained the secondary emission site. This model is the first to be able to resolve the full three
94
dimensional particle dynamics to better understand how multiple beams can mix, interact, and
ultimately affect the current collection on the extractor electrode. To fully understand the impact
to a unique thruster, a dedicated joint numerical and experimental characterization effort is needed
to determine thresholds for nominal operation. Factors such as tip-to-extractor geometry, substrate
porosity, and manufacturing defects will likely contribute significantly to overall results.
Results show that the overall plume dynamics in the downstream region are similar to that
of previous PIC simulations using idealized beams presented in Chapter 3. We reaffirm that the
downstream region exhibits small electric fields and that the resulting patterns are driven largely by
superposition of the two expanding beams. Since, the electric field in the downstream region does
little to affect the overall particle trajectory, the resulting features reflect the injected distribution
functions output by the acceleration region. Therefore, interactions at the acceleration region scale
can cause subtle changes within the macroscopic plume.
Ion fragmentation has been included and assessed for its impact within the acceleration region
and in the downstream plume region. The implementation of a constant fragmentation rate in the
acceleration region produced a beam with a variable velocity. The chosen fragmentation rate pro-
duce a beam that was almost nearly composed of unfragmented or fragmented monomers with very
little dimers in the downstream plume region. The presence of fragmented monomers consistent
with empirical measurements shows no significant signs of disruption to the acceleration or neu-
tralization process. Fragmented monomers are scattered from the beam core, but have a resulting
radial velocity less than unfragmented monomer species.
This study represents a first attempt to develop a multi-scale model of ionic electrospray emis-
sion. Several important issues will still need to be addressed in future study. For instance, the
acceleration physics and momentum transfer between beam components in the acceleration region
needs to be investigated further. The extent to which monomers interact with higher mass particles
in the plume, and the effect of composition on performance is critical to furthering this model and
our understanding of ionic electrospray thruster physics.
95
Chapter5
ExperimentalValidation
5.1 Introduction
As described earlier in Chapter 1, a large body of work has been presented with regard to ionic
electrospray thruster experimental testing and characterization [23, 67, 82, 83, 85]. These charac-
terization activities have focused on estimating overall thruster performance, investigating plume
mass and energy distributions, as well as plume half-angle measurements. There have also been
limited investigations into the overall plume density and structure [82]. Although these previous
efforts have determined thruster performance parameters, physical insights into the beam expan-
sion process and the impact of test chamber environments are limited without a numerical analog
to compare to. To that end, the chamber environment has explicitly been cited as a source of
adverse effects for thruster operations and experimental readings such as backflow and glow dis-
charge [106]. This chapter presents the first joint numerical and experimental investigation into
ionic electrospray thruster plume with the goal of understanding expected thruster physics during
on-orbit operations, while delineating possible chamber-induced effects.
This chapter describes the experimental investigations into electrospray plume structure, pro-
viding an independent validation of the findings of the numerical models described in the previous
chapters. These investigations are primarily focused on the comparison of the spatial structure of
plume density and plume potential during thruster operation. This chapter will describe the ex-
perimental setup, present new simulation results consistent with the LEAP chamber dimensions,
96
present the experimental data, and most importantly compare the experimental results with numer-
ical models.
5.2 ExperimentalSetup
The experiments were conducted in the LEAP electrospray thruster test facility, described in Chap-
ter 2. All test data presented was produced by a single thruster, UTT thruster 3, to accomodate
direct comparisons. The thruster was operated in both positive and negative emission modes. Indi-
vidual test events involved steady thruster firing averaging approximately 3-4 hours each. During
the experiments, the thruster is mounted in the center of the chamber, and the traversing probe
instruments are positioned remotely to collect relevent data.
Figure 5.1 displays an example test profile for a given test event, displaying the thruster volt-
age and the raw Faraday probe data. The thruster was operated over a limited range of voltages
across a series of test events for both positive and negative emission. The data presented in this
chapter displays data collected from -1610 to -1750V for the negative plume scans and +1595V to
+1720V for the positive plume scans. The raw Faraday probe data displayed was taken during a
3-dimensional scan of the thruster plume. Therefore, the data appears as a series of spikes as the
probe traversed the thruster plume.
Figure 5.1: Representative electrospray thruster test profile for bipolar emission
97
This experimental investigation’s goal is the collection of spatial data corresponding to relavent
plume parameters. This test campaign was organized into two sets of activities, with one set of tests
focused on collecting plume density measurements and the other set focused on plume potential
measurements. The plume density measurements were made using the Faraday probe described in
Chapter 2. During positive mode operations, the Faraday probe is biased to -40V to reduce signal
error induced by loss of secondary electrons from the collecting surfaces. The Faraday probe is
unbiased during negative mode operations. A series of one-dimensional scans of the Faraday probe
are presented. These scans collected data along the principle axes along the thruster center lines.
In addition, a 3 dimensional spatial scan of Faraday probe data was conducted. The 3D probe
scan collects on a 3
′′
× 3
′′
× 2.25
′′
region roughly centerred on the thruster, approximately 3.5”
downstream. For the 3D scan, the probe suite dwells for 10 sec at each position. The collected
current is averaged over the probe dwell time. Figure 5.2 displays a scaled representation of the
experimental setup, highlighting the locations of the 3D scan region and targeted 1D scans. The
1D scan data presented here was measured using only turbopump operation with a background
pressure of 2× 10
− 5
Torr. The 3D scan data was collected during a separate test event which
operated both the turbopump and cryopump for the duration of the test, resulting in a chamber
pressure of 9× 10
− 7
Torr.
The Faraday probe provides current readings as raw data. Although raw measured current data
can be used to qualitatively compare the plume structure between the laboratory measurements
and numerical model, a more direct method is pursued. To directly compare the experimental
and numerical plume measurements, the collected current is translated to an estimated number
density. The estimated number density provides a composite measure, providing the aggragate
of the densities of all charged species in the plume. This estimate treats the thruster plume as a
1-dimensional cold drifting plasma with an average drift velocity. This conversion is displayed in
Eqn.5.1.
N
est
=
I
qv
d
A
pro j
(5.1)
98
Figure 5.2: LEAP chamber and experimental scan region dimensions.
Here, N
est
is the estimated number density of the probed region, I is the measured current, q is the
ion charge, v
d
is the assumed monomer drift velocity, and A
pro j
is the Faraday probe collecting
area corrected for clipping by area projection.
A
pro j
= Acos(φ)cos(θ) (5.2)
Here,φ andθ represent angles off of the thruster midline along the two principle X and Y axes.
The plume potential measurements are estimated from direct Langmuir probe measurements
with the thruster operating in positive emission mode. The plume potential was sampled at several
points in a series of one-dimensional scans extending from the beam midline to the extent of the
traversing system, approximately 10in. At each point, the Langmuir probe was swept from -50V
99
to +55V , and corresponding current data was collected. These scans were repeated at several
downstream distances (4.5in, 7in, 9.5in) to estimate the plume potential and chamber effects on
beam expansion.
The scan data can be analyzed directly to estimate plasma potential. The plasma potential is
determined as the inresection point between the electron saturation region current and the transition
region current. The electron saturation current is estimated by the current from 35V to 55V bias.
The transition region current is estimated by the current from the floating potential, from φ
f l
to
φ
f l
+ 10V .
5.3 NumericalModels
This chapter will compare results from previously presented and described numerical models.
Namely, the results from the Baseline PIC model and Multi-scale model presented in Chapter
3 and Chapter 4, respectively, will be compared directly with the experimental measurements.
For clarity, we will only consider the results of these models that do not include fragmentation.
It should be noted that the physical domain introduced by the LEAP chamber is much different
than the free-space simulations presented previously. Figure 5.3 compares the size of numerical
simulation domain used in Chapter 4 and the LEAP chamber.
Figure 5.3: Comparison between LEAP chamber, experimental scan region, and numerical simu-
lation domain
As a result, a third model needs to be developed to adequately represent the chamber environ-
ment and facillitate the direct comparison of plasma parameters. Figure 5.4 displays the domain
100
setup for this chamber-specific simulation. We consider a rectangular simulation domain of similar
dimensions to that of the LEAP chamber. For consistency with other models presented, the do-
main leverages symmetry about the y-axis midline. As a result, the -Y boundary features Neumann
boundary conditions. The remaining domain boundaries represent the chamber walls and exhibit
Dirichlet boundary conditions, with a potential set to 0V , representing facility ground. Within the
domain, the thruster body is represented by a 1λ
D
× 2λ
D
× 3λ
D
object that is grounded to the cham-
ber walls and also set to 0V . The thruster body has a 1λ
D
× 1λ
D
emitting area capable of emitting
either in positive or negative beams. The chamber model leverages the beam composition solved
for by the multi-scale model.
Figure 5.4: Numerical simulation domain for UTT in LEAP chamber model.
Lastly, it should be noted that the chamber environment introduces a background plasma envi-
ronment that is difficult to directly model. The primary plasma components within the chamber are
primary beam ions, backscattered or secondary electrons emitted by the chamber walls, instrument
surfaces, and other harness within the chamber, and sputtered ions. The sputtered ion and emitted
electron population will be referred to as the background plasma environment for the remainder
of this work. Upon comparing plasma parameters between the numerical and experimental mea-
surements, best attempts are made to identify whether measurements are made within the primary
beam region, or an area that may be under heavy influence by the background plasma environment.
The effects of the chamber effects on probe measurements will be discussed further in Section 5.5.
101
5.4 ResultsandDiscussion
5.4.1 ExperimentalResults
This section presents spatially correlated average Faraday probe current readings with no error
correction terms. Figure 5.5 displays an isometric view of multiple slices of collected plume
current from the FP over the 3D spatial scan for negative mode operation. From Fig. 5.5, we
can see the coherent beam structures. Figures 5.6 to 5.8 displays the same slices as a set of 2D
views for clarity. Contour lines are included at± 10nA,± 15nA,± 20nA to help highlight plume
structures.
(a) (b)
Figure 5.5: Isometric view of Faraday probe current collected during 3D scan
Figure 5.6 displays the Faraday probe collected current for both positive and negative emission
modes approximately 3.875” downstream from the thruster exit plane. At this beam cross-section
we can observe the core of the emitted beam, as well as spurious signals at the outskirts of the
scan region likely attributed to chamber-induced effects. From Fig. 5.7 and Fig. 5.8 we observe
slices of interest along the beam midplane. Here, we observe that collected current decreases at the
closest downstream distance (Z=16in). This is likely due to an increase in error caused by escape
of sputtered ions from the detector surface.
102
(a) (b)
Figure 5.6: Faraday probe current collected during 3D scan, displaying slices of interest along XY
plane for a) positive emission and b) negative emission at a downstream distance of approximately
3.875”
(a) (b)
Figure 5.7: Faraday probe current collected during 3D scan, displaying slices of interest along YZ
plane for a) positive emission and b) negative emission at beam midline.
103
(a) (b)
Figure 5.8: Faraday probe current collected during 3D scan, displaying slices of interest along XZ
plane for a) positive emission and b) negative emission at beam midline.
(a) (b)
Figure 5.9: Isometric view of plume density isosurface for a) positive emission and b) negative
emission.
5.4.2 NumericalChamberModelResults
This section presents the numerical results for positive and negative emission from the chamber
model. Figure 5.9 displays an iso surface of normalized charge density at ˆ ρ =+1× 10
− 4
and
ˆ ρ =− 1× 10
− 4
, respectively.
Figure 5.10 displays the normalized plasma potential for both positive and negative emission
cases. Contour lines are provided on a linear scale at values of
ˆ
φ =± 0.1,± 0.2,± 0.3We note that
the physical maximum potential due to the electrospray beam is +4.3V and -3.5V for the positive
and negative emission cases, respectively.
104
(a) (b)
Figure 5.10: Isometric view of plume density isosurface for a) positive emission and b) negative
emission.
5.4.3 ComparisonBetweenExperimentalEstimatesandNumericalModels
The Faraday probe current data can be converted to estimate the particle number density of the
given beam. First, it is important to highlight the differences between the experimental setup
and the numerical models and the steps taken to account for these differences. First, the numerical
efforts modeled a thruster with a higher current output than the UTT. Recall the UTT was 25 emitter
tips arrayed over an 0.1
′′
× 0.1
′′
area. For convenience, the numerical models assumed current
injection over one cell area of 1λ
D
BF
− 4
× 1λ
D
BF
− 4
= approximately 0.42
′′
× 0.42
′′
, or equivalent to a
thruster with approximately 318 emitter tips. As a result, the numerical model results for plume
density need to be scaled down to reduce this discrepancy. The scaling term can be directly tied to
the ratio of assumed emitter tips, which comes out to a factor of 12.32.
Thruster emitter area also affects the qualitative values presented by the numerical model. The
numerical model is limited in its resolution to 1 cell size. Although simulation results can be scaled
down to match the experimental thruster, the effects of a physically smaller thruster cannot be
directly corrected for with the given resolution. This error affects the behavior of the plume profile
in the cross-beam direction as the numerical results will display a resolution-limited clipping of
the overall structure.
Next, the numerical models presented in Ch. 3 and Ch. 4 assumed a notional thruster operating
at a potential of± 1500V . The experimental data was collected for an operating voltage ranging
105
from± 1595 to 1750V . The larger potential in the experimenal setup produces an ion beam that
is moving faster, so we would expect to see a smaller angular spread in the cross-beam directions
than predicted by the numerical model.
Lastly, the numerical models presented have an assumed plume composition. The Baseline
PIC model assumes a 100% monomer beam, the multiscale model uses approximately a 75%
monomer/25% dimer composition. The presence of slower species increases overall beam spread-
ing and can affect the comparison between the numerical and experimental estimates.
Figure 5.11 displays number density comparisons across the beam primary axes in one di-
mension. Displayed are the results for the baseline PIC model, the multi-scale model, the chamber
model and the experimental 1D scan measurements. Panels a-c display the comparison for positive
emission cases and Panels d-f display the comparison for negative emission cases. Note that the
discrimination between the Y and Z axes as presented in Fig. 5.11 is purely arbitrary. The Base-
line PIC model is symmetric along these axes, and although the Multiscale model has asymmetries,
they are arbitrarily oriented with respect to the UTT body axes.
We can see that the qualitative and quantitative behavior is reflected across all axes. Recall from
the previous chapters that the multi-scale model experienced more cross-beam spread as a result of
including the lower level emission and acceleration physics. Figure 5.11 shows that the chamber
model, leveraging the multiscale inputs provides a good approximation for the experimental data.
In addition, we can see that the Baseline PIC model estimates provide the poorest overall fit to
the experimental data. At times, the Baseline PIC model overestimates the plume density by up to
300%. This implies that the assumption of the emitted beam being represented by a Maxwellian
distribution is poor and that the larger spread induced by including the lower level emission and
acceleration physics better matches the plume physics.
The error in this measurement is assessed due to the Faraday probe’s design and construction.
We assess a 20% error in positive current collected caused by emitted electrons and up to 50%
error in negative collected current caused by sputtered ions. Note that these assessments invert the
106
Figure 5.11: Plume number density comparisons between 1D Faraday probe scans and numerical
models for positive (panels a - c) and negative emission (panels d - f).
107
error bars for positive vs. negative emission. The methodology for the derivation of these values is
presented in more detial in Sec. 5.5.
Figures 5.12 - 5.14 display a comparison between experimental and numerical plasma potential
measurements. The potential profiles for both the free space multi-scale model and the chamber
model are displayed. Here, we compare the spatial relationship of the plume potential at several
downstream distances. We can note that qualitatively, the experimental measurements roughly
follow the expected plasma potential. A +/- 1V error is assessed on the given measurements due
to inaccuracies in the curve fitting process. There exist multiple discrete measurements that ex-
hibit a large error from the predicted value. There are several factors that can contribute to this
error. First, potential measurements provided by a Langmuir probe are prone to error in flowing
plasma environments. Since the electron current follows and exponential curve within the transi-
tion region, small errors in probe bias can lead to large errors in collected current, thus leading to
misinterpretation of the probe data. Second, the plasma environment generated by the electrospray
thruster can be tenuous and dynamic with changes in emitted current from each individual emitter
tip. Lastly, the background plasma environment has also been previously reported as a source of
error in plume potential measurements [87].
Past studies have shown that the presence of background plasma can impact the plasma po-
tential measurements outside of the core region [114]. The effect of facility plasma is presents
as a plateau in the plasma potential. Comparing the numerical models for plasma potential for
the electrospray thruster, we can see that both models do not present with a potential plateau, and
the beam potential is able to adequately expand within the constraints of the experimental facility
size. These conditions are benefitted by the UTT’s small emitted current ( 1 µA) and small fraction
of expelled neutrals. Comparing the potential estimates for the free space and chamber models
we can see that the background facility plasma likely does not impede the expansion of the beam
within the test region.
Presented here we see that the experimental measurements are largely in agreement with the
predicted numerical estimates. The plume expansion reflects an overall structure that is matched
108
Figure 5.12: Plasma potential comparison between experimental measurements and numerical
predication at a downstream distance of 89mm.
Figure 5.13: Plasma potential comparison between experimental measurements and numerical
predication at a downstream distance of 152mm.
Figure 5.14: Plasma potential comparison between experimental measurements and numerical
predication at a downstream distance of 216mm.
109
by the plume simulations for number density. Moreover, the measured plume spread more closely
resembles the behavior predicted by the multi-scale model. This result further emphasizes the need
to include the lower level physics associated with the ion emission and acceleration regions.
Experimental plume potential measurements also agree with predictions from the numerical
chamber model. At the edges of the plume, either in the downstream region, or at high boresight
angles, it is likely that a tenuous background plasma of charged species exist that increase error on
instrument reading, but should not impact the overall expansion of the beam within the scanned
region. Future work aims to leverage an active current collecting probe, such as an emissive probe
to provide a better estimate of plume potential.
5.5 ErrorAnalysis
A simple error analysis was conducted to better understand the accuracy and fit of the measured ex-
perimental data. There are multiple sources of error associated with probe current measurements,
namely ion sputtering and secondary electron emission from the detector surface, and collection
of background plasma species. The laboratory chamber environment primarily consists of thruster
species (i.e. primary beam species, fragmented ions and neutrals, sputtered grid ions) and back-
ground plasma. The background plasma is likely very tenuous, primarily consisting of sputtered
ions and secondary electrons from the chamber walls. Moreover, the sensor’s detector emits ions
and electrons due to direct impingement by the high energy plume species that can lead to error
in the recorded measurements. This effort provides an assessment of the error of Faraday probe
current measurement data using a simplified 1-D approach. Figure 5.15 displays the approach for
this analysis, depicting the primary species under consideration.
We assume that the primary beam ions and neutrals enter the probe with an energy near the
thruster potential. We assume all ions enter the probe normal to the opening and impact the graphite
detector as opposed to the stainless steel inner walls. We assume that a fraction of the sputtered ions
are lost from the probe consistent with the probe’s field of view. In addition, secondary electrons
are emitted from the detector surface. For anion plume measurements, we assume a large portion
110
Figure 5.15: Diagram of principle mechanisms for sensor error
of electrons are returned to the probe detector surface as they are repelled by the negative space
charge within the probe. For cation plume measurements, the probe is biased negatively to equalize
the space charge within the probe, again significantly reducing the liklihood of electrons escaping
the probe. The overall equation defining this approach assuming an anion beam is given by Eqn.
5.3
I=− qA[Γ
m
+Γ
d
− γ
SEE
(Γ
m
+Γ
d
+Γ
n
) f
loss
e
+γ
sputter
(Γ
m
+Γ
d
+Γ
n
)θ
c
] (5.3)
Here ,I represents the recorded probe current, q is the elementary charge, A is the detector
area,Γ
m
,Γ
d
,Γ
n
denotes the particle flux for monomers, dimers, and neutrals, respectively, γ
SEE
is
the secondary electron yield, γ
sputter
is the angular sputter yield, θ
c
is the solid angle loss cone in
steradians, and f
loss
is the fraction of emitted particles that are lost from the probe cavity.
For similar instruments to the ones used in this study, it has been observed that secondary elec-
tron emission can make up to about 20% of the overall signal [117]. This 20% error in positive
signal is displayed directly on Fig. 5.11. For errors in negative current, we look to the likli-
hood of loss of sputtered ions. From [118] we can estimate an average sputtered ion loss of 0.06
ions/ion/steradian for 1500eV molecular ion impingement on graphite. Using the 15.4
◦ solid angle
from the detector surface provides an estimated 0.003 atoms/ion lost due to the graphite surface.
In addition to the graphite detector surface, ions can be lost from the stainless steel side walls of
the Faraday cup. We can assume a sputter yield for stainless steel of approximately 1 atom/ion
for normal incidence. Again, the average field of view of the side walls is used to determine the
111
total number of sputtered ions that escape. The field of view of the side walls of the detector to
the sensor orifice varies from a 45
◦ at the rim to 7.7
◦ at the base. This leads to an average field of
view of a 17.6
◦ and a estimated sputter yield of 0.195 atoms/ion. The total ion sputter yield of the
detector can be determined by the weighted average of the collecting surfaces and comes to 0.178
atoms/ion. Flowing this error into the current calculations yields an error of approximately 53%,
as displayed in Fig. 5.11.
Langmuir probe estimates of plasma potential are notoriously error-prone. To gain confidence
in the potential measured by the Langmuir probe a linear regression analysis was conducted on
the fit of the slopes within the electron saturation region and transition region. As the potential
measurement is estimated by the intersection of these two lines, their fit to the data is the most im-
portant factor for determining error. The electron saturation current linear regression was assessed
against the logorithm of the probe current when probe bias was greater than 20V . The transition
region current linear regression was also assessed against the logorithm of the probe current from
φ
f l
toφ
f l
+ 5V . Data regarding the correlation, or R
2
values for the electron saturation region and
transition region for the collection of Langmuir probe scans are displayed in Table 5.1
Table 5.1: Correlation data for collection of Langmuir probe measurements.
Parameter Transition Region Electron Saturation Region
Average R
2
0.877 0.847
Min R
2
0.739 0.642
Max R
2
0.961 0.931
Standard Deviation 0.0568 0.0831
On average, the linear fits used to assess the plasma potential can account for 80-85% of the
variation within the data sets. For a sample 5V measurement, this deviation can cause up to 1V
in error. This assessment cannot address variations within the plasma environment that can lead
to error. Future studies aim to use an emissive probe to provide more accurate plume potential
measurements.
112
5.6 Conclusion
In this chapter, experimental measurements of ionic electrospray thruster plume parameters, namely
beam density and potential, were presented and discussed. These experimental measurements
were compared directly to free-space models leveraging the previously described baseline PIC and
multi-scale models. In addition, a new chamber model was developed to provide a more com-
parable simulation for direct comparison. The experimental results largely agree with the overall
beam structure predicted by the baseline PIC and multi-scale models for both positive and negative
ion beams. The best fit to the density data was demonstrated with the newly developed chamber
model. The comparison between the free-space models and the chamber models indicate that mea-
surements taken within the chamber environment vs. those expected on orbit can vary up to 50%
in the beam core 50-150mm from the thruster exit. In addition, the fit of the experimental data to
the multi-scale model highlights the need to take into account the lower level physics when trying
to predict ionic electrospray plume parameters in the downstream region.
The plume potential was measured for postiive emission and compared to the chamber model.
We largely found good agreement between the laboratory measurements and the model predictions.
It is likely that a background plasma exists, but is tenuous enough not to inhibit the expansion of
the primary beam within the collection region.
A preliminary error analysis was conducted investigating potential sources of error in the probe
measurement current. We found that the current collected is within reasonable bounds even with
likely sources of error taken into account. Lastly, there are aspect to the physical thruster design
that could have large impacts on plume development that we have not considered. The UTT is
composed of 25 distinct emitter tips. Each tip has a unique shape, pore structure, and physical
orientation to its respective extractor window. Each of these variables likely have an effect on
the ion beam generated by that emitter tip, and thus an effect on the whole beam. This large
number of inter-related variables makes it difficult to individually assign causation through the
use of experimental observation. However, numerical models are more well attuned to be able to
assess the effects of varying these parameters. Future work in this area will look to understanding
113
the impact that manufacturing defects has on the overall beam development. Additionally, the use
of emissive current probes is warranted to provide higher fidelity potential estimates.
114
Chapter6
Conclusionandfuturework
This effort presented the first joint experimental and numerical investigation into ionic electrospray
thruster plume structure and bipolar neutralization dynamics. First, a baseline PIC model was pre-
sented to investigate the downstream plume dynamics associated with an idealized bipolar thruster
beam. Next, a higher fidelity multi-scale model, including an MD model for Taylor, a PP model
for ion acceleration, and a PIC model for downstream behavior. These numerical models assessed
several case studies adversely affecting electrospray beam development; ion fragmentation in the
acceleration and field-free region and secondary emission site activation. Lastly, an experimental
test campaign provided the first characterization of plume density and potential , as well as the first
comparison between experimental measurements and numerical estimates. The major findings of
this work is as follows:
• The neutralization process for ionic electrospray thrusters is very different than for that of
legacy electric propulsion devices like gridded ion thrusters or Hall effect thrusters. The
individual positive and negative beams expand relatively unimpeded, resulting in a plume
structure that can approximated by a simple superposition. This behavior is attributed to the
similar masses of the anion and cation beam species, and the fact that the beam is emitted
under the space charge limit.
• The multi-scale model largely affirms the physical neutralization dynamics presented in the
Baseline PIC model. However, the inclusion of ion emission and acceleration physics pro-
vides modifications to the plume distribution function.
115
• The activation of secondary or tertiary emission sites on a single emitter tip significantly
increases the beam half angle and standard deviation of the beam particles’ radial veloc-
ity. Although activating multiple emission sites provides more thrust, the amount of grid
interception and erosion is predicted to significantly increase as a result.
• Laboratory measurements of an ionic electrospray thruster plume were collected, compared
directly to numerical model predictions, and displayed good agreement. The experimen-
tal measurements more closely resembled the behavior displayed by the multi-scale mode,
reflecting the importance of lower level physics in overall plume development.
• The chamber environment likely induces errors in plume density measurements in the near
downstream region of the beam’s core by up to 50% of what could be expected during on-
orbit operations.
• Although ion fragmentation is a prevalent cause for energy loss amongst beam species, it
does not drastically impact the neutralization mechanisms associated with bipolar thruster
operation. In addition, the effect of fragmentation is not likely to lead to an increase in
adverse thruster effects like backflow, contamination, or grid impingement on its own. Frag-
mentation in the acceleration region produces low energy fragments that are scattered from
the beam core, but not more than the pre-existing monomer beam.
Ionic electrospray thrusters are a rich area for ongoing research as they experience several
different physical interactions that all inter-relate with one another. Although this effort provides
the highest fidelity model, to date, there are multiple other physical interactions that are not yet
well understood and this work would benefit from further research.
Firstly, the fragmentation model included in this effort was informed by empirical measure-
ments and used a constant rate of fragmentation. Although this model reflects experimental mea-
surement, a more complete understanding of the fragmentation physics of various common ionic
liquid propellants. This would ideally include relationships associated with molecular orientation
116
and electric field strength to better model exactly when and where fragmentation events occur
within thrusters, as well as diagnostic laboratory equipment.
Secondly, the multi-scale model presented in this work enables the investigation of the effects
of micro-scale defects or variations on overall plume development and impact on grid impinge-
ment. These defects could include chipped, clipped, or misaligned emitter tips, which are all very
common using today’s thruster manufacturing and assembly techniques.
The models presented only concerned themselves with impacts of steady state thruster oper-
ation. If these thrusters are to be used for applications such as formation maintenance or station
keeping maneuvers, then it is very likely that they will require frequent and regular activation. It is
commonly noted experimentally that thrusters require special operations during startup to enable
stable operations. It is unclear what, if any, transient events occur during startup that could be of
concern to spacecraft operators in terms of contamination and thruster health.
Lastly, the majority of this modeling effort focused on the physical interactions that occur at
the ionic liquid-vacuum interface and above. To better understand interactions such as Taylor cone
activation, secondary emission site threshold voltage, and associated impacts on emitter tip design,
modeling of the pore-liquid interface is required. Modeling at this level allows for an estimate
of thruster mass flow rate, which currently is not well understood for passive ionic electrospray
thrusters [83]. In addition, ion transport and replenishment from the bulk media can be further
studied in how it affects long term thruster operations.
117
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Abstract (if available)
Abstract
Ionic electrospray thrusters offer a promising novel high efficiency and low thrust propulsion capability for future space missions. Since the technology’s development in the early 2000’s, the research community has been largely focused on maturing the technical design and standardizing experimental characterization techniques. As this thruster technology has progressed, characterizing and mitigating spacecraft integration hazards has become a pressing concern. Although spacecraft integrations can be investigated in a laboratory setting, the development of an independent numerical model of ionic electrospray emission is critical for a complete understanding of the thruster and plume physics. This dissertation presents the most complete numerical modeling of an ionic electrospray thruster plume to date in order to better assess thruster plume physics and potential hazards imposed on the spacecraft bus.
This work first presents a fully kinetic 3-dimensional particle-in-cell (PIC) simulation study of the plume from a bipolar ionic electrospray thruster pair using 1-ethyl-3-methylimidazolium tetrafluoroborate (EMI-BF4) ionic liquid propellant. The results show a unique beam neutralization process, where there is little physical coupling between the positive cation and negative anion beam. These dynamics are likely attributed to the similar mass ratio between the two beams and the low current density of the beams at this scale. The small potential difference within the beam suggests that low energy fragmented species will not be significantly scattered, ejected, or likely to return as backflow. The weak electric field magnitude within the beam suggests that the fragmentation of ion clusters within the plume may occur at a reduced rate than measured in laboratory experiments.
To affirm the findings presented in the baseline PIC model, this work combines a molecular dynamics model, a particle-particle model, and a particle-in-cell model to investigate the physics of ionic electrospray propulsion over 9 orders of magnitude in length scale. The combined models are applied to simulate beam emission for an ionic electrospray propulsion system with porous emitter tips from the emission site to the downstream plume. The impact of multiple emission sites from a single emitter tip is analyzed with regard to extractor grid interception and overall beam neutralization for bipolar thruster pairs. In addition, ion fragmentation, the leading cause for low energy ion generation within electrospray thrusters, is assessed for its impact on overall thruster plume dynamics. Results show that beams consisting of species of different masses (i.e. monomer and dimer species) are affected by particle-particle forces during acceleration and should not be treated as a superposition of independently accelerated species in macro-scale plume models. The activation of multiple emission sites also causes a noticeable increase in the beam’s spread, leading to increased intercepted current but relatively little adverse effects in the downstream plume region. The presence of energy loss mechanisms through ion fragmentation also increase the overall beam spread as low energy monomers experience a higher overall divergence angle. This increased divergence, while noticeable in the downstream region, is determined to show little overall impact on the increase in grid impingement.
An experimental test campaign is conducted using the USC Testbed Thruster to investigate plume plasma parameters, namely the beam density and potential. This test campaign is the first to directly compare experimental plume measurements with high fidelity numerical estimates. The results validate the findings of the numerical models presented. The experimental data reflects the overall plume structure predicted by the numerical models, with the multi-scale model providing the most accuracy. Differences between chamber and free space models indicate that plume density measured in the laboratory environment in the near downstream region can have an error up to 50% that is induced by the chamber environment.
This body of work implies that ionic electrospray thrusters offer a relatively small contamination risk to spacecraft when compared with other micro-electric propulsion devices. The electric field in the downstream region is found to provide little resistance to beam expansion and is not likely to induce backflow in low energy fragmented ions even during common off-nominal operations.
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Asset Metadata
Creator
Asher, Jeffrey Samuel
(author)
Core Title
Numerical and experimental investigations of ionic electrospray thruster plume
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Astronautical Engineering
Degree Conferral Date
2022-08
Publication Date
07/07/2022
Defense Date
04/21/2022
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
computational plasma dynamics,electric propulsion,electrospray,numerical modeling,OAI-PMH Harvest,particle in cell,plume dynamics,propulsion
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Language
English
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Electronically uploaded by the author
(provenance)
Advisor
Wang, Joseph (
committee chair
), Erwin, Daniel (
committee member
), Nakano, Aiichiro (
committee member
)
Creator Email
jasher@usc.edu,jeffasher93@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-oUC111369229
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UC111369229
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etd-AsherJeffr-10813
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Asher, Jeffrey Samuel
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texts
Source
20220708-usctheses-batch-951
(batch),
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Repository Email
cisadmin@lib.usc.edu
Tags
computational plasma dynamics
electric propulsion
electrospray
numerical modeling
particle in cell
plume dynamics
propulsion