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University of Southern California Dissertations and Theses
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Experimental and numerical investigations of charging interactions of a dusty surface in space plasma
(USC Thesis Other)
Experimental and numerical investigations of charging interactions of a dusty surface in space plasma
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Content
EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF CHARGING
INTERACTIONS OF A DUSTY SURFACE IN SPACE PLASMA
by
Ning Ding
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)
December 2012
Copyright 2012 Ning Ding
Dedication
...to my parents and beloved
ii
Acknowledgments
First, I would express my gratitude to my academic advisor Dr. Joseph Wang, who has
led me into a fantastic world of space plasma and electric propulsion at both Virginia Tech
and the University of Southern California. As an MIT Ph.D. graduate and former senior
staff member of NASA’s Jet Propulsion Laboratory, not only wisdom but also motivation in
aerospace engineering has Dr. Wang shown during the five-year period of my Ph.D. study,
making it very exciting to work and cooperate with him. Without his support emotionally
and financially, my research would not have been possible.
It is wonderful to have my Ph.D. dissertation committee. Thank you so much. Dr. Dan
Erwin, an expert in electronics, has been very willing to help me deal with instrumenta-
tion design for plasma diagnostics, charge measurement and dust manipulation. Dr. Mike
Gruntman is a talented and knowledgeable person and I really enjoy talking to him in all
aspects from rocket science and physics to culture and history of different nations. From
Dr. Joseph Kunc, I have realized some underling physics of space plasma flow which are
usually neglected by people in this area. Dr. Phil Muntz offered useful resources during
the initial stage of building our plasma lab at USC. Besides academics, he also has left
an awesome impression on me, as it is incredible that such a prestigious professor was a
fullback on a professional football team and also a jet pilot. I have learned a lot from Dr.
Keith Goodfellow’s advanced propulsion class and he has provided me with so much guid-
ance which eventually led to the successful development of the fully operational gridded
ion source utilized in the experiment.
iii
I would like to thank my lab partners John and Doug for working with me on every nut
and bolt at our Laboratory of Astronautical Plasma Dynamics, Department of Astronautical
Engineering. Also, many thanks to other members of Dr. Wang’s group, Ouliang and
Daoru, for computing and simulation support. It is unforgettable to have spent a great
amount of happy time with all of the research and teaching assistants. Every one deserves
credit for my research. I also sincerely appreciate the help from department staff, Dell,
Marrietta and Ana, during my program.
Special thanks to all current and past members of the Collaborative High Altitude Flow
Facility (CHAFF) in the high bay of the Rapp Research Building. CHAFF is an amazing
“warehouse” and almost everything except cash can be found at some corner of this magic
place. Thank you guys for letting me utilize so many pieces of equipment to build my
experimental facilities.
I thank all members of my big family, whose understanding, encouragement and sup-
port inspires and motivates me all the time. Dad, thank you for teaching me how to become
a real engineer with extraordinary hands-on ability. I still remember you bringing me to
the research institute you worked at and letting me play with so many fantastic and expen-
sive instruments. From my innermost, I appreciate your putting engineering ideas into my
blood and even now I still feel so proud that I was able to solder wires to a small DC motor
when I was in the kindergarten. Mom, thank you for letting me take everything apart at
home and break in a nasty 3.5 cc glow engine powered by methanol alcohol and caster oil
in my room a long time ago. I learned how to think independently and critically from you.
You always encourage me to explore the new frontier of science and technology to fulfill
my curiosity. Ying, it was very nice to first know you in high school and work together
on the best robot team in Shanghai. Without your keen insight and judgement we could
not have won the championship of the International Robot Olympiad. You always have so
much confidence in me and believe that I can do the best anywhere. I am of the greatest
honor to be your husband.
iv
This work is supported by funding from USC Viterbi School of Engineering and NASA
Lunar Advanced Science and Exploration Research Program under grant NNX11AHZ1G.
v
Table of Contents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Surface Charging in Plasma . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Dust Charging in Dust-in-Plasma and Dusty Plasma . . . . . . . . . 6
1.2.3 Electrostatic Levitation of Dust . . . . . . . . . . . . . . . . . . . . 7
1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 Charging of Lunar Surface . . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Electrostatic Levitation of Dust . . . . . . . . . . . . . . . . . . . . 12
1.3.3 Studies of Dust Charging in Dusty Space Plasma and Plasma Pro-
cessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.4 Experimental Studies of Dust Charging . . . . . . . . . . . . . . . 15
1.3.5 Electrodynamic Dust Manipulation . . . . . . . . . . . . . . . . . . 17
1.4 Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5 Dissertation Outline and Approach . . . . . . . . . . . . . . . . . . . . . . 20
Chapter 2: Capacitance Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Capacitance Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 A Multiple Dust System . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.2 Capacitance Matrix Method . . . . . . . . . . . . . . . . . . . . . 27
2.3 Approximate Calculation of Multiple Dust Particle Charging . . . . . . . . 31
vi
2.3.1 Effects of Mutual Elastance on Dust Charging . . . . . . . . . . . . 31
2.3.2 Analysis of the Approximate Solutions . . . . . . . . . . . . . . . . 35
2.4 Capacitance of Dusty Plasma . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5 Dust Particles on a Surface . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.6 Capacitance of a Dusty Surface in Plasma . . . . . . . . . . . . . . . . . . 42
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Chapter 3: Experimental Investigations of Multi-dust System Capacitances in Space
Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1.1 Parameter Normalization . . . . . . . . . . . . . . . . . . . . . . . 46
3.1.2 Methodology of Measurement . . . . . . . . . . . . . . . . . . . . 47
3.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2.1 High-sensitivity Electrometer Development . . . . . . . . . . . . . 49
3.2.2 Setups for Experiments . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2.3 Experimental Cases . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3 Capacitances of a Multi-dust System in Space . . . . . . . . . . . . . . . . 60
3.3.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.2 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Chapter 4: Experimental Investigations of Dusty Surface Charging in Plasma . . . 67
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.1 Surface Charge Calculation . . . . . . . . . . . . . . . . . . . . . . 69
4.2.2 Method of Surface Potential Measurement . . . . . . . . . . . . . . 70
4.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.3.1 Vacuum System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.3.2 JSC-1A Lunar Regolith Simulant . . . . . . . . . . . . . . . . . . . 73
4.3.3 Plasma Diagnostic Tools . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.4 3D Traversing System . . . . . . . . . . . . . . . . . . . . . . . . 78
4.3.5 Data Acquisition and Control System . . . . . . . . . . . . . . . . 81
4.3.6 Ion Source Development . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.7 Procedure of Surface Charge Density Measurement and Plasma
Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.4 Measurement of Dusty Surface Charging . . . . . . . . . . . . . . . . . . . 97
4.4.1 Experimental Case . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.4.2 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4.3 Dust Charging Results . . . . . . . . . . . . . . . . . . . . . . . . 103
4.4.4 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
vii
Chapter 5: Comparison of Dust Charging Models . . . . . . . . . . . . . . . . . . 107
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.3 Calculation of Dust Charging on the Lunar Surface . . . . . . . . . . . . . 112
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Chapter 6: Modeling the Interactions of a Charged Dust with Surface Traveling
Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.2 Dynamics of Dust Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.3 Concept of Dust Manipulation on a Dusty Surface . . . . . . . . . . . . . . 118
6.3.1 Sinusoidal Electrodynamic Wave . . . . . . . . . . . . . . . . . . . 118
6.3.2 Multi-phase Trapezoidal Electrodynamic Wave . . . . . . . . . . . 120
6.4 Dust Manipulation Simulation . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4.1 Case Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4.2 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4.3 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.4.4 Computational Domain . . . . . . . . . . . . . . . . . . . . . . . . 124
6.4.5 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4.6 Potential Calculation . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4.7 Electric Field Parameter Calculation . . . . . . . . . . . . . . . . . 127
6.4.8 Method of Wave Propagation for Simulation . . . . . . . . . . . . . 129
6.4.9 Model of Dust in Traveling Wave . . . . . . . . . . . . . . . . . . 130
6.5 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.5.1 Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.5.2 Dust Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.5.3 Cut-off Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.5.4 Dust Sorting Scheme . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Chapter 7: Design of An Electrodynamic Screen System for Dust Manipulation . . 141
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.2 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.3 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.3.1 Micro Computer . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.3.2 Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.3.3 High V oltage Driver . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.3.4 Electrode Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.3.5 High-voltage Power System . . . . . . . . . . . . . . . . . . . . . 148
7.4 System Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.5 Advanced Dust Manipulation Concept . . . . . . . . . . . . . . . . . . . . 149
7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
viii
Chapter 8: Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . 154
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.2.1 Dust Charging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.2.2 EDS Design and Fabrication . . . . . . . . . . . . . . . . . . . . . 156
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
ix
List of Figures
Figure 1.1: Dusty surface in space plasma . . . . . . . . . . . . . . . . . . . . . . 2
Figure 1.2: Single sphere charging in plasma . . . . . . . . . . . . . . . . . . . . . 4
Figure 1.3: Dust-in-plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Figure 1.4: Dusty plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Figure 1.5: Surface charging in plasma . . . . . . . . . . . . . . . . . . . . . . . . 8
Figure 1.6: Lunar surface potential as a function ofθ with 5 effective photoelectron
emissivities, prepared by Manka . . . . . . . . . . . . . . . . . . . . . 11
Figure 2.1: Packed dust on a dusty surface . . . . . . . . . . . . . . . . . . . . . . 22
Figure 2.2: Single dust charging . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Figure 2.3: Dust charging situation . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Figure 2.4: Two-dust capacitor system . . . . . . . . . . . . . . . . . . . . . . . . 25
Figure 2.5: Capacitances in a 4-dust system . . . . . . . . . . . . . . . . . . . . . 27
Figure 2.6: Potential field induced by a charge . . . . . . . . . . . . . . . . . . . . 28
Figure 2.7: Normalzed self-capacitance vs normalized distance between neighbor-
ing dust particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Figure 2.8: Normalzed self-capacitance vs normalized distance between neighbor-
ing dust particles on the log-log scale . . . . . . . . . . . . . . . . . . . 36
Figure 2.9: Normalized self-capacitance of a dust particle in a dusty plasma system
vs normalized separation . . . . . . . . . . . . . . . . . . . . . . . . . 39
Figure 2.10: Normalized self-capacitance of a dust particle in a dusty plasma system
vs normalized separation on the log-log scale . . . . . . . . . . . . . . 40
Figure 2.11: Dust grains on a flat surface . . . . . . . . . . . . . . . . . . . . . . . . 40
x
Figure 2.12: Packed dust surface in the plasma environment . . . . . . . . . . . . . 41
Figure 2.13: Normalized self-capacitance of a dust particle on a dusty surface in
space plasma vs normalized separation . . . . . . . . . . . . . . . . . . 43
Figure 2.14: Normalized self-capacitance of a dust particle on a dusty surface in
space plasma vs normalized separation on the log-log scale . . . . . . . 43
Figure 3.1: C
11
measuring circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Figure 3.2: C
12
measuring circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Figure 3.3: Discharge circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Figure 3.4: Integrator circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Figure 3.5: V oltage history of the integrator circuit for charge measurement . . . . . 53
Figure 3.6: Schematic of high-sensitivity electrometer . . . . . . . . . . . . . . . . 54
Figure 3.7: PCB design of high-sensitivity electrometer . . . . . . . . . . . . . . . 55
Figure 3.8: Completed PCB coated with tin and drilled holes . . . . . . . . . . . . 55
Figure 3.9: Back side of the PCB with all components soldered into position . . . . 56
Figure 3.10: The front side of the PCB with all connectors labeled . . . . . . . . . . 56
Figure 3.11: Setup for capacitance measurement test . . . . . . . . . . . . . . . . . 58
Figure 3.12: Charge with error bar vs biased voltage of a 200 pF testing capacitor . . 59
Figure 3.13: Single sphere case setup . . . . . . . . . . . . . . . . . . . . . . . . . 61
Figure 3.14: Two-sphere case setup . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Figure 3.15: Three-sphere case setup . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Figure 3.16: Four-sphere case setup . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Figure 3.17: Theoretical and measured
ˆ
C
11
and
ˆ
C
12
in the two-sphere case with dif-
ferent centroid distance
ˆ
d . . . . . . . . . . . . . . . . . . . . . . . . . 64
Figure 3.18: Theoretical and measured
ˆ
C
11
and
ˆ
C
12
in the three-sphere case with
different equal inter-sphere distance
ˆ
d . . . . . . . . . . . . . . . . . . 64
Figure 3.19: Theoretical and measured
ˆ
C
11
and
ˆ
C
12
in the four-sphere case with dif-
ferent equal inter-sphere distance
ˆ
d . . . . . . . . . . . . . . . . . . . . 65
xi
Figure 3.20: Ambient noise from the power grid collected by the sphere, frequency:
60 Hz, amplitude: 5.7 mV . . . . . . . . . . . . . . . . . . . . . . . . 65
Figure 4.1: Dust layer surface potential measurement . . . . . . . . . . . . . . . . 67
Figure 4.2: Illustration of non-contacting surface potential measurement . . . . . . 70
Figure 4.3: Experimental setup of packed dust layer charging . . . . . . . . . . . . 72
Figure 4.4: Different probes employed for surface potential measurement and plasma
diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Figure 4.5: Vacuum chamber for experiments . . . . . . . . . . . . . . . . . . . . 74
Figure 4.6: Initial top surface of JSC-1A simulant sample without pretreatment . . . 75
Figure 4.7: Top surface of JSC-1A simulant sample without pretreatment after pump-
ing down . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Figure 4.8: Langmuir probe measurement system . . . . . . . . . . . . . . . . . . 77
Figure 4.9: Nude Faraday probe measurement system . . . . . . . . . . . . . . . . 78
Figure 4.10: Emissive probe measurement system . . . . . . . . . . . . . . . . . . . 79
Figure 4.11: 3D traversing system . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Figure 4.12: Design of traversing system . . . . . . . . . . . . . . . . . . . . . . . . 81
Figure 4.13: Stepper motor control diagram . . . . . . . . . . . . . . . . . . . . . . 82
Figure 4.14: Stepper motor control unit . . . . . . . . . . . . . . . . . . . . . . . . 83
Figure 4.15: Data acquisition and system control flow . . . . . . . . . . . . . . . . . 84
Figure 4.16: Design pattern of the grid . . . . . . . . . . . . . . . . . . . . . . . . 85
Figure 4.17: Geometry of hexagonal grid . . . . . . . . . . . . . . . . . . . . . . . 86
Figure 4.18: Developed screen grid pattern . . . . . . . . . . . . . . . . . . . . . . 87
Figure 4.19: Developed acceleration grid pattern . . . . . . . . . . . . . . . . . . . 87
Figure 4.20: Screen grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Figure 4.21: Acceleration grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Figure 4.22: Assembled ion source in the enclosure . . . . . . . . . . . . . . . . . . 90
Figure 4.23: Ion source configuration . . . . . . . . . . . . . . . . . . . . . . . . . 91
xii
Figure 4.24: Ion source circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Figure 4.25: Vacuum chamber for testing . . . . . . . . . . . . . . . . . . . . . . . 93
Figure 4.26: Side view of extracted ion beam with neutralizer off . . . . . . . . . . . 94
Figure 4.27: View 2 of the extracted ion beam with neutralizer off . . . . . . . . . . 94
Figure 4.28: Ion current density contour of Case 1 with neutralizer on . . . . . . . . 95
Figure 4.29: Ion current density contour of Case 2 with neutralizer on . . . . . . . . 95
Figure 4.30: Potential contour of Case 1 with neutralizer on . . . . . . . . . . . . . . 96
Figure 4.31: Potential contour of Case 2 with neutralizer on . . . . . . . . . . . . . . 96
Figure 4.32: Top view of the experimental setup inside the chamber and relative
probe locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Figure 4.33: Plasma potential vs distance . . . . . . . . . . . . . . . . . . . . . . . 99
Figure 4.34: Electron temperature vs distance . . . . . . . . . . . . . . . . . . . . . 99
Figure 4.35: Electron density vs distance . . . . . . . . . . . . . . . . . . . . . . . . 100
Figure 4.36: Ion density vs distance . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Figure 4.37: Electron current density v.s. distance . . . . . . . . . . . . . . . . . . . 101
Figure 4.38: Ion current density above the testing surface . . . . . . . . . . . . . . . 101
Figure 4.39: Ion velocity vs distance . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Figure 4.40: Surface potential vs distance, error bar:±50 mV for all points . . . . . 102
Figure 4.41: Surface charge density vs distance . . . . . . . . . . . . . . . . . . . . 103
Figure 4.42: Charge deposited on dust particles vs the radius of dust at different
surface charge density states on the log-log scale . . . . . . . . . . . . 104
Figure 4.43: Charge to mass ratio of dust particles vs the radius of dust at different
surface charge density states on the log-log scale . . . . . . . . . . . . 104
Figure 5.1: Potential vs dust charge comparison between experimental results by
Sickafoose et al. and different models . . . . . . . . . . . . . . . . . . 108
xiii
Figure 5.2: Effective separation vs dust charge comparison of surface charging exper-
imental result (φ
d
= 10.60 V ,Q
d
= (1.26±0.13)×10
−17
C), experi-
mental result by Sickafoose et al. (φ
d
= 10.80 V ,Q
d
= (6.0±1.1)×
10
−15
C) and different dusty plasma models . . . . . . . . . . . . . . . 110
Figure 5.3: Effective separation vs dust charge comparison of surface charging exper-
imental result (φ
d
= 10.60 V ,Q
d
= (1.26±0.13)×10
−17
C), experi-
mental result by Sickafoose et al. (φ
d
= 10.80 V ,Q
d
= (6.0±1.1)×
10
−15
C) and different dusty plasma models on the log-log scale . . . . 110
Figure 5.4: Effective separation vs dust charge comparison of surface charging exper-
imental result (φ
d
= 10.60 V ,Q
d
= (1.26±0.13)×10
−17
C), experi-
mental result by Sickafoose et al. (φ
d
= 10.80 V ,Q
d
= (6.0±1.1)×
10
−15
C) and different dusty surface in plasma models . . . . . . . . . . 111
Figure 5.5: Effective separation vs dust charge comparison of surface charging exper-
imental result (φ
d
= 10.60 V ,Q
d
= (1.26±0.13)×10
−17
C), experi-
mental result by Sickafoose et al. (φ
d
= 10.80 V ,Q
d
= (6.0±1.1)×
10
−15
C) and different dusty surface in plasma models on the log-log
scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Figure 5.6: Charge on packed lunar surface dust vs dust size . . . . . . . . . . . . . 113
Figure 5.7: Charge to mass ratio of packed lunar surface dust vs dust size . . . . . . 113
Figure 6.1: Electrostatic traveling wave propagating in the x direction at two time
frames,t = t
1
andt = t
2
. . . . . . . . . . . . . . . . . . . . . . . . . 116
Figure 6.2: Three-phase EDS dust conveyor . . . . . . . . . . . . . . . . . . . . . 118
Figure 6.3: Propagation of potential wave on EDS . . . . . . . . . . . . . . . . . . 119
Figure 6.4: Propagation of a trapezoidal wave with amplitudeV
0
in thex direction
at two time frames,t = t
1
andt = t
2
. . . . . . . . . . . . . . . . . . . 121
Figure 6.5: Simulation case setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Figure 6.6: Biased potential shift sequence of four electrodes over one period from
t = 0 tot = T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Figure 6.7: Geographical locations of nodal points for the central difference method 125
Figure 6.8: Mesh for computational domain, locations of electrodes are marked . . 126
Figure 6.9: Initial boundary condition in thex direction atz = 0 . . . . . . . . . . 127
Figure 6.10: Sequence of shifting field parameters of the computational domain . . . 129
xiv
Figure 6.11: Storage of each field parameter as a 3D array in the computer memory . 130
Figure 6.12: Area weighed average parameter of a dust particle within a cell . . . . . 131
Figure 6.13: Potential distribution and electric field lines . . . . . . . . . . . . . . . 134
Figure 6.14: Distribution ofE
2
and its gradient lines . . . . . . . . . . . . . . . . . 134
Figure 6.15: Trajectory of moved dust,R
cm
= 1.0×10
−4
C/kg,dt = 1.0×10
−5
s,
N
shift
= 400,f = 62.5 Hz . . . . . . . . . . . . . . . . . . . . . . . . 135
Figure 6.16: Position and velocity history of moved dust, R
cm
= 1.0× 10
−4
C/kg,
dt = 1.0×10
−5
s,N
shift
= 400,f = 62.5 Hz . . . . . . . . . . . . . . 135
Figure 6.17: Trajectory of trapped dust,R
cm
= 1.0×10
−4
C/kg,dt = 1.0×10
−5
s,
N
shift
= 5,f = 5000 Hz . . . . . . . . . . . . . . . . . . . . . . . . . 136
Figure 6.18: Position and velocity history of trapped dust,R
cm
= 1.0×10
−4
C/kg,
dt = 1.0×10
−5
s,N
shift
= 5,f = 5000 Hz . . . . . . . . . . . . . . . 136
Figure 6.19: Lower and higher cut-off frequencies of dust with different charge to
mass ratios in the traveling wave . . . . . . . . . . . . . . . . . . . . . 138
Figure 7.1: Architecture of a multi-phase EDS system . . . . . . . . . . . . . . . . 142
Figure 7.2: Arduino
R
MEGA micro computer by the Arduino Team . . . . . . . . 143
Figure 7.3: Photo MOSFET solid state relay system . . . . . . . . . . . . . . . . . 145
Figure 7.4: Schematic of the decoder system . . . . . . . . . . . . . . . . . . . . . 146
Figure 7.5: Schematic of the high voltage driver . . . . . . . . . . . . . . . . . . . 147
Figure 7.6: Multi-phase electrode screen board . . . . . . . . . . . . . . . . . . . . 148
Figure 7.7: Cross-sectional view of the multi-phase electrode screen board with
major dimensions in mm . . . . . . . . . . . . . . . . . . . . . . . . . 148
Figure 7.8: Electrode array board . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Figure 7.9: Gathering dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Figure 7.10: Dispensing dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Figure 7.11: Linear dust transportation . . . . . . . . . . . . . . . . . . . . . . . . . 152
Figure 7.12: Rotation of dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
xv
List of Tables
Table 1.1: Solar wind parameters at 1 AU . . . . . . . . . . . . . . . . . . . . . . . 5
Table 2.1: Sample dust capacitance on a dusty surface in plasma . . . . . . . . . . . 44
Table 3.1: Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Table 3.2: Component parameters and initial input voltage of the integrator circuit
for charge measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Table 3.3: Parameters of passive components used in the electrometer . . . . . . . . 54
Table 3.4: V oltage cursor measurement precision of Tektronix
R
TDS 640A digital
oscilloscope within different ranges . . . . . . . . . . . . . . . . . . . . . 57
Table 3.5: V oltage measurement precision of UNI-T
R
UT39A digital multimeter
within different ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Table 3.6: Measured self and mutual capacitances in multiple sphere cases . . . . . . 63
Table 4.1: Dimensions of grid holes . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Table 4.2: Operating conditions of the ion source . . . . . . . . . . . . . . . . . . . 92
Table 4.3: Operating conditions of the plasma source . . . . . . . . . . . . . . . . . 98
Table 4.4: Comparison of dust charge and charge to mass ratio . . . . . . . . . . . . 105
Table 5.1: Measurements and models for dust charging . . . . . . . . . . . . . . . . 107
Table 5.2: Comparison of dust charging models . . . . . . . . . . . . . . . . . . . . 112
Table 6.1: Simulation results of frequency response of dust with different charge to
mass ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Table 6.2: Errors of frequencies at different charge to mass ratios . . . . . . . . . . . 139
Table 7.1: Part list of EDS board . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
xvi
Nomenclature
Symbols
A Area, m
2
a Acceleration, m/s
2
B Magnetic field strength, T
C Capacitance, F
C
r
Coefficient of restitution
D Distance, m
d Separation or distance, m
d Hole diameter, m
E Electric field strength, V/m
E Energy, J
F Force, N
f(D) Distribution function with respect to distance, m
−1
f Frequency, Hz
g Gravitational acceleration, m/s
2
h Effective separation, m
I Constant current, A
i Time dependent current, A
J Current density, A/m
2
xvii
k Wavenumber
m Mass, kg
˙ m Flow rate, sccm
N Number of particles, matrix size, number of time steps
n Number per unit volume, m
−3
or number per unit area, m
−2
P General parameter
Q Charge, C
r Radius, m
R Resistance, Ω
R
cm
Charge to mass ratio, C/kg
s Elastance, F
−1
t Time, s
T Plasma temperature, eV
T Wave period, s
t
w
Web thickness, m
v Velocity, m/s
V V oltage, V
x x position, m
y y position, m
z z position, m
α Angle, rad
α Capacitance coefficient
β Capacitance coeffieient
Γ Flux, m
−2
s
−1
γ Yield
Δ Mesh cell size
δ Uncertainty
xviii
δ Yield
ε Permittivity, F/m
θ Angle, rad
λ Wavelength, m
λ
D
Debye length, m
ρ Charge density, C/m
−3
ρ
d
Mass density of dust, kg/m
−3
σ Surface charge density, C/m
−2
τ Time constant of a circuit, s
φ Potential, V
ω Angular frequency, rad/s
Subscripts
acc Acceleration
ad Adhesionn
ano Anode
beam Ion beam
bias Biased
c Chamber
Coulomb Coulomb
d Dust
diapole Dielectrophoresis
dif Differential
e Electron
f Feedback
fil Filament
xix
Fp Faraday probe
high Higher
i Ion
in Input
Lp Langmuir probe
low Lower
max Maximum
min Minimum
n Neighboring
out Output
p Plasma or phase
ph Photoelectron
pp Peak-peak
r Relative
s Surface
sh Sheath
sec Secondary
shift Phase shift
th Thermal
tot Total
w Wave
Constants
e Elementary charge, 1.602×10
−19
C
k Boltzmann constant, 1.381×10
−23
m
2
kg/(s
2
K)
xx
γ Euler’s constant, 0.577
ε
0
Permittivity of free space, 8.85×10
−12
F/m
Abbreviations
CAD Computer aided design
DSP Digital signal processor
EDS Electrodynamic screen
FEP Fluorinated ethylene propylene
JSC Johnson Space Center
MOSFET Metal oxide semiconductor field-effect transistor
NASA National Aeronautics and Space Administration
OML Orbital motion limited
RPA Retarding potential analyzer
UV Ultraviolet
xxi
Abstract
The objective of this dissertation is to study the charging interactions of a dusty surface in
space plasma through experimental, analytical, and numerical investigations. Specifically,
this dissertation investigates 1) dust charging on a dusty surface and 2) dust manipulation
on a dusty surface.
In the first area, an analytically approximate capacitance model for a dusty plasma
and dust layer using the capacitance matrix method and an averaged inter-dust distance
to account for dust interactions, has been developed. In the previous studies, the single
isolated dust charging model is commonly used for dusty surface charging with the OML
current collection model for potential calculation, and experiments conducted only mea-
sured the charge and charge to mass ratio for a single dust particle in plasma. Hence, the
capacitance model of a dust on a dusty surface in plasma was still not understood. In our
study, we first validated the capacitance model derived with experiment and then devel-
oped another experiment to measure the charging of JSC-1A dust layer in plasma inside
a vacuum chamber. It is found that the single dust charging model is no longer applica-
ble to packed dust charging on a dusty surface as it shows calculation results two orders
of magnitude higher than the measurement because the interactions between surrounding
dust particles were ignored. The dusty surface in plasma model developed assuming an
averaged inter-dust distance approximation provides an accuracy of 50% to 60% compared
with the measurement. This is found to be an accurate model to calculate the dust charging
on a dusty surface immersed in plasma.
xxii
In the second area, we investigated the underlying physics of dust behavior in the sur-
face electrostatic traveling wave on an electrodynamic screen (EDS) device using numerical
computer simulations. Previous studies only demonstrated the application of removing dust
particles accumulated on surfaces with three-phase or four-phase surface electrostatic trav-
eling waves without concluding the physics of the dust dynamics in such traveling waves.
We found that there are two cut-off frequencies of the wave as a function of dust charge
to mass ratio; and a dust particle can only respond to a frequency between the higher and
lower cut-off frequencies and follow the surface traveling wave to be transported. With
the understanding of dust dynamics in the traveling waves, we also proposed a new design
of an EDS device using multi-phase surface traveling waves to precisely control the dust
motion. The capability of the new design includes dust mitigation, sorting and segregation
on the lunar, Martian and asteroid surfaces according to the dust charge to mass ratio.
xxiii
Chapter 1: Introduction
1.1 Overview
This dissertation is devoted to the study of charging interactions of a dust system and a
dusty surface immersed in space plasmas, a fundamental problem with many applications
in both planetary science and space engineering. As will be reviewed in Chapter 1.3, the
charging interactions of a dusty surface is revelant to the study of surface property and evo-
lution of the Moon and asteroids, the near-surface environments of the Moon and asteroids,
and the interactions of such environment with spacecrafts. Additionally, this problem is
also of interest to the development of new instruments to support lunar resources prospect-
ing and processing, and the characterization of near-surface environment for future lunar
surface and asteroid surface environment.
The research is applicable to two types of dusty surfaces: the first is the regolith surface
present on the Moon, the Mars and asteroids. The regolith is a layer of loose, heteroge-
neous material covering solid rock consisting of dust, soil, broken rock, and other related
materials. This regolith is formed over the last 4.6 billion years by the impact of large and
small meteoroids and the steady bombardment of micrometeoroids and solar and galactic
charged particles breaking down surface rocks [50]. In particular, nearly the entire lunar
surface is covered with regolith.
The second type is spacecraft surface contaminated by a dusty environment, such as
the elevated dust cloud and the lunar surface or dust storm on the Martian surface [76].
It is well understood that dust contamination on sensitive spacecraft surface may cause
surface property changes. For instance, dust surrounding spacecraft instruments may pre-
vent motion, clog sensors, and reduce the output of solar panels [92, 33]. Apollo astronauts
reported that dust could easily stuck to spacesuits [36] such that people are concerned about
1
dust sticking on the suit because the dust may damage the suit, obscure the vision and float
in living spaces due to reduced gravity in the lunar environment.
Figure 1.1: Dusty surface in space plasma
This dissertation focuses on a simplified dusty surface-plasma system, as shown in
Fig. 1.1. We consider a flat dusty surface immersed in a plasma. Dust particles on the
surface collect charges from plasma and build up potentials. We will discuss the current
collection model and investigate the capacitance model of a dust particle resting on a dusty
surface in order to estimate its charge. We will also conduct experiments to validate our
models and compare with other dust charging models. Based on the derived dust capac-
itance model and the frequency response of dust charge to mass ratio, we will propose a
2
design of an innovative electrodynamic screen (EDS) device for dust manipulation, sorting
and segregation.
1.2 Background
1.2.1 Surface Charging in Plasma
Surface charging is a fundamental process for objects immersed in a plasma. Surface charg-
ing has been been studied extensively with the context of spacecraft charging (Lai [58, 59],
Garrett et al. [10, 37, 39, 38]) as well as planetary and asteroid surface charging ( Whipple
et al. [95, 96], Stubbs et al. [83], Halekas et al. [47, 46, 45], Berg [8]).
A surface immersed in a plasma will collect current. The relation between the surface
charging and the current collection is given by Eq. 1.1, where, C is the capacitance of the
object,Q is surface charge,φ
s
is the surface floating potential. At steady state, the potential
is given by Eq. 1.2. In order to find the surface charge, one needs to understand the current
collection and the capacitance.
C
dφ
s
dt
=
dQ
dt
(1.1)
C
dφ
s
dt
=
dQ
dt
=
N
X
j=1
I
j
(φ
s
) = 0 (1.2)
Where, I
j
represents different current sources which may include currents from the
ambient plasma such as ion current, electron current as well as secondary electron current
and photoemission current [62].
In a stationary plasma at thermal equilibrium, the electron and ion current densities
going toward one direction are given by Eq. 1.3. These results can be easily extended to a
drifting plasma by changing the ion current density to Eq. 1.4.
3
J
e
= en
e0
r
kT
e
2πm
e
, J
i
= en
i0
r
kT
i
2πm
i
(1.3)
J
i
=
1
2
en
i0
erf
v
0
r
m
i
2kT
i
+1
(1.4)
However, the current flux that may be collected by a surface are influenced by the
plasma sheath, plasma flow and magnetic field on current collection. In particular, the
influence of the sheath on current collection is classified as either space charge limited or
orbital motion limited (OML). In the space charge limited situation, the size of an object is
much larger than the plasma sheath, therefore, all currents entering the sheath are collected
by the surface. While in the OML scenario, the plasma sheath is much larger than the
object, causing that only charged particles within the impact parameter can be collected by
the surface. Once the current collection is known, the floating potential of the object can
be calculated by
P
I(φ
s
) = 0.
Figure 1.2: Single sphere charging in plasma
4
Tab. 1.1 [67] shows a representative solar wind plasma condition. The Debye length
of solar wind plasma on the lunar surface is on the order of 10 m [41], much larger than
the characteristic size of a dust particle which is usually smaller than 100 μm. For an iso-
lated single dust in plasma shown in Fig. 1.3, the dust charging may be calculated from
I
i
(φ
s
)−I
e
(φ
s
) +I
ph
(φ
s
) = 0. Hence, currents I
i
(φ
s
), I
e
(φ
s
) and I
ph
(φ
s
) may be calcu-
lated using the OML model [2, 97, 5]. Since solar UV radiation comes from the infinity,
only a half of the surface is considered to emit photoelectrons. Eq. 1.6 and Eq. 1.7 are
the expression of calculating potential of a single dust, above or below plasma potential
respectively. When φ
d
> 0, ions are repelled; electrons and photo electrons leaving the
dust surface are attracted. Whileφ
d
< 0, ions are attracted; electrons and photo electrons
are repelled.
Table 1.1: Solar wind parameters at 1 AU
Parameter Value
Solar wind flux,v
0
n
0
3.8×10
12
m
−2
s
−1
Density,n
0
8.7×10
6
m
−3
Velocity,v
0
468 km/s
Ion temperature,T
i
10 eV
Electron temperature,T
e
12 eV
Magnetic field,B
0
6.2 nT
J
i
(φ
d
)A
d
−J
e
(φ
d
)A
d
+
1
2
J
ph
(φ
d
)A
d
= 0 (1.5)
n
i0
v
0
exp
−
2eφ
d
m
i
v
2
0
−n
e0
r
kT
e
2πm
e
1+
eφ
d
kT
e
+
1
2
n
ph
r
kT
ph
2πm
e
−
eφ
d
kT
ph
= 0 (φ
d
> 0)
(1.6)
5
n
i0
v
0
exp
1−
2eφ
d
m
i
v
2
0
−n
e0
r
kT
e
2πm
e
eφ
d
kT
e
+
1
2
n
ph
r
kT
ph
2πm
e
= 0 (φ
d
< 0) (1.7)
The classical electrostatic probe theory solves most of these problems as stated by
Chan [18], Hutchinson [53], Franz [34] etc. However, when the magnetic field and plasma
flow are involved, usually, charging problems in this category need to be solved numerically
due to the complexity of the plasma field.
1.2.2 Dust Charging in Dust-in-Plasma and Dusty Plasma
Dust charging sensitivity depends on the relation between the inter-particle distanced and
the Debye length λ
D
. We can divide dust charging into two categories: dust-in-plasma
(d >> λ
D
) in Fig 1.3 and dusty plasma (d << λ
D
) in Fig. 1.4.
Figure 1.3: Dust-in-plasma
For dust-in-plasma, the dust charing calculation is straightforward. The capacitance
may be calculated by considering that between the dust and its sheath boundary as shown
6
Figure 1.4: Dusty plasma
in Eq. 1.8. Asr
d
/λ
D
<< 1,C
d
= 4πε
0
r
d
. The current collection may be calculated using
OML, then the charging can be calculated by Eq. 1.2.
C
d
= 4πε
0
/
1
r
d
−
1
λ
D
(1.8)
For a dusty plasma, one must consider the interactions of multiple dust within the
sheath. The dust charging is significantly more complicated because the capacitance will
be influenced by the neighboring dust.
1.2.3 Electrostatic Levitation of Dust
A direct consequence of charging dust is the electrostatic levitation and transportation of
charged dust. For instance the Surveyor spacecraft as lunar horizon glow following local
sunset, which was believed to be caused by scattering dust grains [75], and the Apollo
7
astronauts observed dust clouds suspending above the lunar surface [23, 69, 9, 8]. Cur-
rently, there is no generally accepted model to calculate dust charging in dusty plasma.
Almost all studies of dusty plasma still adopt the dust-in-plasma charging model.
The lunar surface is directly exposed to the ambient plasma environment and the solar
radiation. Hence, the surface floating potential is determined by the interactions between
the plasma, surface and emission of of photoelectrons and/or secondary electrons as shown
in Fig. 1.5.
Figure 1.5: Surface charging in plasma
For a charged dust on the lunar surface, when the electrostatic force becomes larger
than the gravity and adhesion force in Eq. 1.9, dust will be levitated [69, 92].
Q
d
E≥ m
d
g +F
ad
(1.9)
These levitated charged dust may be transported electrostatically and differentially
change the lunar surface. Hence, electrostatic levitation and transport of charged dust is
considered as an important process influencing the lunar surface evolution [74, 26]. Sim-
ilarly, the same electrostatic levitation and transportation process also occurs on asteroid
surfaces [61].
Electrostatic levitation is also of relevance to spacecraft contaminations. For instance,
it was reported that on the Magellan spacecraft, dust from the astroquartz blankets were
electrostatically levitated. These dust saturated the startracker by scattering light [43]. The
8
dust contamination is expected to be a major issue for future spacecraft operation in a dusty
environment, such as that near the surface of the Moon, the Mars and asteroids [25].
1.3 Literature Review
1.3.1 Charging of Lunar Surface
There are many studies of surface charging in plasma. As the objective of this research
is for applications of dust charging on lunar surface, only lunar surface charging work is
reviewed here.
The solar wind is a stream of charged particles including thermal electrons and fast
moving ions ejected from the upper atmosphere of the Sun. Solar wind causes surfaces
exposed to the solar wind plasma without the protection of an atmosphere and magnetic
field to be easily charged to some potential with respect to the plasma potential. Sun-
lit regions, dominated by photoelectron current, are positively charged while sun shade
regions, which lack ions, are charged negatively. Consequently, large potential differences
of hundreds of volts occur between the front side and the back side of an object immersed
within solar wind flow, which could transport dust particles or cause electric shock to astro-
nauts.
Grobman et al. [44] modeled current sources and their relation to the lunar potential
in the sunlit situation. The interplanetary magnetic field is weak and neglected since the
electron gyro radius is much larger than the Debye length. Expression of ion, electron and
photoelectron flux were given in this paper:
Γ
i
= n
0
v
d
cosθ (1.10)
Γ
e
= n
0
r
kT
e
2πm
e
(1.11)
9
Γ
p
= cosθ
Z
∞
eφ
dǫ
1−
p
eφ
Z
∞
0
dE g(E)γ(E)f
E
(ǫ ) (1.12)
whereθ is the angle between the solar wind flow direction and lunar surface normal,γ(E) is
the quantum yield of the surface material, f
E
(ǫ ) is the energy spectrum of photoelectrons
and g(E) is the solar photon flux distribution with energy. Lunar surface potential was
calculated by current balancing the three different species of charged particles. This paper
offered a fundamental and effective way to calculate surface potential; however in the paper,
the author did not state electron or photoelectron sheath thickness, which shows how far
the surface can shield incoming plasma flow.
Manka [62] applied probe theory to calculate the potential at the lunar surface for both
positively and negatively charged surface situations. Ion, electron, photoelectron and sec-
ondary electron current were included for potential calculation. In addition, sheath thick-
ness was taken in to consideration in the expression of electron current density. He used
simplified equations (from Eq. 1.13 to Eq. 1.16) to calculate photoelectron and secondary
electron current emitted from the surface:
Γ
ph
= Γ
ph0
cosθexp
−
eφ
s
kT
ph
φ
s
> 0 (1.13)
Γ
sec
= (Γ
e
δ
e
+Γ
i
δ
i
)exp
−
eφ
s
kT
sec
φ
s
> 0 (1.14)
Γ
ph
= Γ
ph0
cosθ φ
s
< 0 (1.15)
Γ
sec
= Γ
e
δ
e
+Γ
i
δ
i
φ
s
< 0 (1.16)
where Γ
ph0
is the photo electron flux density from the surface with normally incident sun-
light and δ
e
and δ
i
are the secondary production (yield) coefficients for primary electrons
10
and ions respectively. Fig. 1.6 shows the theoretical curve of lunar surface potential from
Manka’s calculation, with a potential of -38 V at the solar wind terminator. Equations
and their modifications of current density to local lunar surface conditions were listed in
detail to determine the surface potential with respect to the incoming plasma flow. Differ-
ent lunar plasma environments considered included the solar wind, high altitude tail and
plasma sheet. Based on the surface potential distribution, local electric field was approxi-
mated by E ≃ φs
λ
D
, even though the E field profile above the surface is more complicated
than a constantE field.
Figure 1.6: Lunar surface potential as a function ofθ with 5 effective photoelectron emis-
sivities, prepared by Manka
Freeman et al. [35] analyzed the lunar surface potential with experimental data from
the lunar surface suprathermal ion detector experiment (SIDE), deployed on the lunar sur-
face in the Apollo missions, with results of dayside surface potential: φ
s
: +10 to +18 V ,
terminator: φ
s
:≃ -10 to -100 and dayside electric field: E ≃ 10 V/m outward, terminator:
E≃ 1 to 10 V/m inward. The authors applied experimental data measured by SIDE devices
11
on the lunar surface, making the conclusion more convincing than only assumptions and
calculations.
Wang et al. [89] developed a full-particle particle-in-cell charging method to study
the charging at the lunar terminator region. The simulation model considers the effect of
mesothermal plasma flow on current collection by the lunar surface. Results show that the
lunar surface potential is a function of the sun elevation angle α . At mean flux density,
the lunar surface is charged to -29.3 V when α = 0
◦
and increased monotonically to -2.1
V asα increases to 10
◦
. At 5% flux density condition, the lunar surface is floating at -28.5
V at α = 0
◦
, turning to positive potential when α = 8
◦
, and eventually reaches 1.1 V at
α = 10
◦
.
1.3.2 Electrostatic Levitation of Dust
When an isolated horizontal planar surface is surrounded by plasma, it will float at a differ-
ent potential to maintain zero net current flux. In such a case, the approximate electric field
inside the sheath is on the order ofE ≃ φs
λ
d
[62], exerting an electrostatic field forceQ
d
E,
pointing upwards, on dust particles. Once the field force is large enough to overcome the
gravity, cohesive and adhesive forces, a dust grain can leave the surface and levitate in the
plasma sheath.
To accurately describe the motion of dust particles in the plasma sheath, Nitter et al. [69]
analyzed the three possible potential profiles inside the photoelectron sheath and corre-
sponding electric fields, assuming no disturbance from charged dust particles in the sheath.
Analysis of dust dynamics was based on Newton’s Second Law in Eq. 1.17, and electric
force and constant gravity were taken into consideration, where x is the height of a dust
above the surface. Collisional force and any rotation were neglected. However, when the
illumination angle is very small (α ≃ 0 and θ ≃ π
2
), the photoelectron sheath vanishes,
and drifting ions flowing parallel to the surface deflect by90
◦
and enter the electron plasma
12
sheath perpendicularly at an ion acoustic velocityC
s
[88], which would change the expres-
sion of ion current density and lead to a finite negative floating potential in this case.
m
d
d
2
x
dt
2
=−Q
d
dφ
dx
−m
d
g (1.17)
Sickafoose et al. [79] conducted dust grain levitation experiments in a collisionless
argon plasma environment with three kinds of particles: polystyrene divinylbenzene micro-
spheres, glass microballoons and JSC-1 lunar simulants. In the experiments, potential
profiles and heights of levitated dusts were measured with different surface bias poten-
tial. Measurements of heights matched results calculated by the OML theory. Also, a UV
source was utilized to trigger photo emission and results suggested UV radiation could only
affect the levitation height by 10% if the surface was biased to the same potential. In the
solar wind circumstance, plasma is mesothermal; ions move at about 400 km/s. Performing
the same measurements in a drifting plasma would strengthen the conclusion.
Colwell et al. [26] studied motion of charged dust in the photoelectron sheath by both
numerical simulation and experiments. A time dependent charging model for dust parti-
cles was used to calculateQ
d
in the simulation. Simulation results showed particles tend to
accumulate in shadowed regions such as craters and large boulders on Asteroid Eros, there-
fore horizontal motion was deduced and particles smaller than 1μm were shown to levitate
at tens to hundreds of meters. In the experiment, dust particles spread parallel to the hori-
zontal supporting surface during the initial exposure to plasma due to the change of surface
potential during the initial charge, which confirmed the simulation results. Horizontal dust
motion could be caused by nonuniform surface potential distribution on irregular surfaces,
which pulls charged dust particles along the electric field lines to lower potential areas.
Stubbs et al. [84] proposed a dust fountain model to explain the levitated dust at about
100 km above the lunar surface. This is an electrostatic model to describe high-altitude dust
particle motions. In the dust fountain on lunar surface, charged dust particles due to local
13
plasma environment and the photoemission of electrons from solar UV and X-rays fol-
low ballistic trajectories, subsequent to being accelerated upward through a narrow sheath
region by the surface electric field. These levitated particles could affect the optical qual-
ity of the lunar environment for astronomical observations and interfere with exploration
activities.
Farrell et al. [32] studied complex electric fields of the lunar terminator region. Results
demonstrate that sudden surface potential change across the sunlit region to sun shade
region such as a crater leads to strong electric fields. Surrounding charged dust particles
can be accelerated to high velocities due such nonuniform potential distributions. The
author also suggested that this process may account for the high-energy dust detected by
Apollo 17s LEAM instrument [9].
Most of studies used the single dust charging model to study dust charging on surfaces
for dust-surface interactions. Wang et al. [89] used two different assumptions for dust
charging. The first one applied the dust-in-plasma OML model to calculate the floating
potential. The second one assumed that a dust on the surface had the same potential as the
surface. Results show that under the first assumption, the levitated dust trajectory is only
dependent upon the electric field profile and is independent of dust grain size; under the
second assumption, only a dust with r
d
smaller than the thresholdr
d,max
is able to collect
enough charge to overcome its gravity and levitate above the lunar surface.
1.3.3 Studies of Dust Charging in Dusty Space Plasma and Plasma
Processing
The study of dust charging is also an important aspect in the study of dusty space plasma
and processing.
Goertz [40] studied dust charging schemes in dusty plasma of the solar system with
isolated dust charging model based on the OML current collection.
14
Winske [98] reviewed different dusty plasma effects in the solar system, including the
ring of Saturn and cometary dust tail as well as two less known plasmas: the dust streams at
Jupiter and noctilucent clouds in the mesosphere. In the model, current balance was based
on the OML model and the capacitance of a dust grain was calculated as a single isolated
sphere.
Mendis et al. [68] presented a critical review of dust-plasma interactions in the cosmic
environment. Dust charing was modeled as isolated sphere with OML current collection.
Both single-particle and collective effects were discussed with the necessities of further
research pointed out. The authors indicated that the collective charged dust cloud acted as
a heavy plasma species and interacted with plasma waves. The authors also provided the
needs for laboratory studies, emphasizing the necessary means for the theoretical studies
and to test the predictions of these theories.
Scales et al. [77] developed a electrostatic two-dimensional model to study dusty
plasma. A hybrid particle-in-cell simulation code was used to calculate the dust surface
potential and the capacitance of a dust was also based on the single isolated sphere capaci-
tance.
Almost all work done previously modeled charge on dust by using single isolated dust
with OML current collection. Inter-dust interactions were not taken into consideration
for dust charging. To strengthen the dust charging mechanism in a dusty plasma, effects
between dust in the system should be considered.
1.3.4 Experimental Studies of Dust Charging
Many experiments have been carried out to determine the dust charge to mass ratio in a
laboratory setting. A typical way to conduct dust charging experiment is to first charge the
dust particles with a plasma source, then dust is dropped into a Faraday cup by a mechanical
agitator.
15
Horanyi et al. [52] experimentally studied the electrostatic charging properties of lunar
dust, returned by the Apollo 17 mission in 1972 and compared the results to two lunar dust
simulants, Minnesota Lunar Simulant (MLS-1) and Johnson Space Center (JSC-1). In the
experiment, an emissive tungsten filament was biased negatively in the vacuum chamber
to charge dust dropping from the top of the chamber with thermal electrons by ionizing
background argon gas. Simultaneously, a Faraday cup on the bottom was employed to
measure the charge of dust grains. Secondary yield of the three different materials was
tested with different electron beam energy. From the yield-energy curves of Apollo 17
samples in the paper, secondary yieldδ grew exponentially and became larger than 1 when
beam energy was higher than 30 eV , reaching a peak of 4.9 with beam energy on the order
of hundreds of eV . Results showed the charging properties of Apollo 17 sample to me
intermediate between MLC-1 and JSC-1.
Wang et al. [92] experimentally investigated charging properties of both conducting
and insulating dust on conducting and insulating surfaces beneath collissionless plasma.
Conducting surfaces used in their experiments were biased by an external DC power supply
to different potentials to test the amount of charge grains can carry in plasma, as measured
by a Faraday probe. Both insulating and conducting dust grains on the conducting surface
with an oxide layer were charged more positively (higher Q) on the surface which was
biased more negatively because ion current dominated. The charging of conducting and
insulating dust sitting on insulating glass surfaces was independent on the biased voltage
of the metal plate which was placed to support the glass plate. It proved that the polarity
of the charge a single particle carried in the plasma was controlled by the dominant current
collected. However, in nature, a surface and its surface dust must carry the same sign of
charge because the surface in the plasma does not have an artificial current drain and can
only have a steady state at floating potential. This study has provided an idea of how dust
will be charged on different materials in plasma. A spacecraft exposed to plasma is in such
an situation, as it usually has surfaces of different materials, resulting in inhomogeneous
16
surface potential distribution. Dust grains on the spacecraft are charged to states depending
on the local surface potential.
Abbas et al. [1] presented the first laboratory measurements of photoelectric efficiencies
and yields of individual dust particles from Apollo 17 and Luna-24 samples, compared with
JSC-1 lunar simulant. In the experimental setup, a deuterium lamp UV source illuminated
the particle and an electrodynamic balance was employed to measure the charge-to-mass
ratio. Results showed that photoelectric yields were dependent on incoming photon energy,
as every 20 nm difference of photon wavelength led to one order of magnitude difference in
yield. Yields of particles with size parameter
2πr
λ
smaller than 100 had strong dependency
on size, increasing with size exponentially, wherer andλ are the radius of the particle and
the wavelengnth of UV radiation respectively. Yields became almost constant if the size
parameter was larger than 300, leading to an estimate of the photoelectric yield of dust
layers which contain particles with relatively large size parameters.
In summary, the charge to mass ratio is well characterized for a single dust. However,
no experiment studies have been carried out to determine the charge to mass ratio either for
a dusty plasma or for dust on surfaces.
1.3.5 Electrodynamic Dust Manipulation
This dissertation will also study dust mitigation and manipulation technology. Such tech-
nology may be applied to dust mitigation, segregation and sorting in future space missions.
Masuda et al. [65] introduced the concept of traveling electric fields to move particles
by applying multi-phase AC voltage to parallel electrodes embedded on a dielectric plate.
Later, Masuda et al. [66] proposed a method of moving blood cells in liquid by traveling
waves, which lent support to moving dust particles with a similar approach. In recent years,
the idea of traveling waves was applied to control dust, primarily by Kawamoto’s group at
17
Waseda University, Japan, and Calle’s group, NASA Electrostatics and Surface Physics
Laboratory.
Kawamoto et al. [55] developed a dust conveyor to move dust by an non-mechanical
means. Such a device contained parallel copper electrodes, 0.5 mm in width and 1 mm of
offset. A four-phase square wave with amplitude of±800 V was applied to transport dusts
parallel to the line electrodes. There were three situations of dust transportation, dependent
upon wave frequency, according to the results presented by the authors. Dust could be
transported in the direction of wave propagation at low frequency (30-50 Hz), opposite to
the wave propagation with low speed at relatively high frequency (80-250 Hz) or vibrated
at high frequency (above 250 Hz). A relatively simple and effective method was proposed
to transport dust but application is limited to dust removal.
Kawamoto [56] modeled and simulated the dust transportation on the EDS conveyor to
predict the performance on the lunar surface. It was assumed that dust particles were either
charged or polarized in the traveling wave to study the dust dynamics. Also, different
electrode patterns were introduced and more complicated dust trajectories were achieved
such as curved, spiral, gathered and linear motion in a closed tube. Although dust particles
were manipulated in a desired path, an appropriate electrode pattern must be designed to
meet the requirement.
Calle et al. [14] demonstrated a parallel electrode dust control device in simulated mar-
tian and lunar environments with JSC-1 martian and Minnesota lunar simulants, respec-
tively. In the Martian environment case, the dust control device was driven by sinusoid
waveform with an amplitude of 400 V in a vacuum chamber at a 7 Torr CO
2
condition. In
the simulated lunar environment, 10
−6
kPa, the breakdown voltage was higher due to high
vacuum. For both cases, clearing factor reached as high as 90%.
Bock et al. [11] described the power system for EDS to clean solar panels in space.
The dust control device was fabricated with transparent indium tin oxide (ITO) electrodes
on a glass substrate. In the system, power for the EDS (parallel electrodes) was regulated
18
by a switch bank, which contained 6 metal-oxide-semiconductor field-effect transistors
(MOSFET), to generate square waves on the electrodes. A digital signal processor (DSP)
controlled the switch bank. A DC-DC converter generated 1 kV output voltage powered
by a 12 VDC source. The authors provided an effective way to manage power required by
a dust removal device for in space missions.
Calle et al. [13] developed an EDS device to remove dust accumulated on thermal radi-
ators for lunar exploration and tested that device in a simulated lunar surface environment.
Two structures of EDS were fabricated by the authors: thermal paint and coated Fluoro
Ethylene Polypropylene (FEP). For the thermal case, a polyimide (Kapton) sheet covered
the spacecraft, and electrodes were aligned on the Kapton base and painted with thermal
paint. Test results showed that electrode spacing less than 0.1” performed well and higher
applied voltage (above 3000 V) had better clearing effect. Compared with solar panel EDS,
much higher voltage can be used to clean the thermal radiator since thermal radiators are
not as vulnerable to high voltage and arcing as solar cells.
In order to design effective EDS devices, it needs to understand dust charging since the
dust dynamic behavior in any electrodynamic traveling wave generated by an EDS device
is sensitively determined by the charge to mass ratio of a dust particle.
1.4 Motivation and Objectives
The goal of this dissertation is to advance the understanding of charging interactions for a
dusty layer in space. Specially, this dissertation considers two inter-related subjects. The
first one is the charging of dusty layer. As discussed in Chapter 1.3, almost all previous
studies of dusty plasma or dusty surface charging have adopted the single dust charging
model. No generally accepted charging model currently exists to calculate the charging of
a dusty surface. Hence, the first objective is to determine the dusty layer charging through
analytical and experimental studies.
19
The second is to manipulate dust on a dusty surface for potential applications in dust
effect mitigation, dust sorting and segregation. The recently developed EDS technology
shows a possibility to manipulate dust on a dusty surface electrostatic force and charge
on dust. Hence, the second objective is to understand the physics of electrostatic dust
manipulation through simulation and to develop concept design for a EDS system.
1.5 Dissertation Outline and Approach
The following outline states the remaining contents of the dissertation:
• In Chapter 2, models of dust charging in space and on a surface are developed to
study interactions of a multi-dust system.
• Chapter 3 develops experimental setups to verify the derived multi-dust capacitance
model.
• Chapter 4 discusses the experiment of JSC-1A dust charging on a dusty surface in
plasma.
• Chapter 5 compares modeling and experimental results of single dust charging and
JSC-1A dust simulant charging on a dusty surface in plasma.
• In Chapter 6, a series of numerical computer simulations are conducted to investigate
the dust dynamics in surface traveling waves and their frequency response to the
applied waves.
• Chapter 7 is the system design of an advanced EDS device for dust manipulation,
sorting and segregation.
• Chapter 8 concludes this dissertation and discusses future work.
20
Compared with previous work which focuses on single dust particle charging in plasma
and the utilization of the single dust charging model to explain charging of dusty surface,
this dissertation investigates the inter-dust capacitance model of a dust system on a dusty
surface in plasma as well as the direct measurement of surface charge density of a dusty
surface charged by plasma to obtain dust charging states. The simulation precisely models
forces exerted on a charged lunar dust particle in traveling electrostatic waves to study the
underlying physics of dust dynamics in such waves. The designed EDS device is able to
generate complicated multi-phase traveling wave patterns for dust mitigation, sorting and
segregation.
21
Chapter 2: Capacitance Modeling
2.1 Introduction
Almost all studies on dust charging are based on the single-dust-charging with OML current
collection. The objective of this work is to investigate the situation of packed dust on a
surface pictured in Fig. 2.1. Hence, in this chapter, we first study the capacitance of a dusty
surface.
Figure 2.1: Packed dust on a dusty surface
Fig. 2.2 and Eq. 2.1 shows commonly used single-dust-charging model. In this model,
one considers a single charged dust, whose electric field is shielded by the sheath sur-
rounding it. The sheath thickness is approximately the Debye lengthλ
D
. Hence, one way
to calculate the capacitance between the dust and its boundary, for a spherical dust, the
capacitance is given by Eq. 2.2 as r
d
<< λ
D
. Note the single dust charging has the same
form of a single isolated sphere in free space. This single dust charging model is widely
used to estimate charge accumulated on a dust particle [5, 79, 89].
dQ
d
dt
= C
d
dφ
d
dt
(2.1)
C
d
= 4πε
0
1
1
r
d
−
1
λ
D
≈ 4πε
0
r
d
(2.2)
22
Figure 2.2: Single dust charging
However this assumption of the single dust model clearly is not valid for a dusty plasma
situation when the inter-dust distance becomes much less than the Debye length. Also, the
single dust charging calculation is not valid for a dusty surface system.
In order to understand the capacitance of dusty surface, we compare four different sit-
uations as shown in Fig. 2.3: a) single dust in space, b) multiple dust in space, c) single
dust on a surface and d) multiple dust on a surface. This chapter presents the approximate
analytical dust capacitance models. The next chapter presents experimental validations of
the analytical capacitance models.
2.2 Capacitance Modeling
The capacitance of a system is obtained by calculating the charge to potential ratio. The
capacitance of a system is a function of the system configuration and material property.
In a dusty plasma system, the capacitance of a dust will be influenced by other dust
particles located in the sheath. Two assumptions are applied in the analysis of this chapter.
First, every single dust grain is treated as a sphere with radius r
d
. Second, we assume an
equal-potential surface on each dust particle.
23
Figure 2.3: Dust charging situation
2.2.1 A Multiple Dust System
The capacitance of a single dust is given by Eq. 2.2. The capacitance of a multiple dust sys-
tem is much more complicated than that of a single dust due to dust-to-dust interactions.
There are two kinds of capacitance in this system: self-capacitance and mutual capaci-
tance. Self-capacitance exists between the dust surface and infinity (treated as ground).
The mutual capacitance exists between the dust surfaces. The total capacitance of an object
is defined as the sum of the self capacitance and mutual capacitances between the object
and all other objects [81].
As an example, Fig. 2.4 shows a two-dust capacitor system in space for dust 1 and dust
2, especially. Hence, C
10
and C
20
are the self capacitances between the dust surfaces and
infinity. The mutual-capacitance C
12
exists between the two dust surfaces, which serve
as two electrodes in the equivalent circuit. The capacitor C
12
is charged to store electric
energy when there is a potential difference between dust 1 and dust 2. The total charge on
Dust 1 and Dust 2 depends upon the potential of both dust particles.
24
Figure 2.4: Two-dust capacitor system
Q
1
= C
10
φ
1
+C
12
(φ
1
−φ
2
) (2.3)
Q
2
= C
20
φ
2
+C
12
(φ
2
−φ
1
) (2.4)
The image charge method provides a way to calculate the self and mutual capacitance
in the system if the radii of the two dust are the same. The capacitance can be calculated
by depositing image charge on the center line of two dust particles [81]. The expressions
of self and mutual capacitance of this system are listed in Eqs. 2.5 and 2.6, whered is the
center separation between two dust particles and d > 2r
d
. It is obvious that besides dust
size, both capacitances are also functions of the distance between the centroids. The total
capacitance of any single dust (for example C
11
) is defined by the equivalent capacitance
on that dust while grounding the other, as given in Eq. 2.7.
C
10
= C
20
= 4πε
0
r
d
1−
r
d
d
+
r
2
d
d
2
−r
2
d
−
r
3
d
d
3
−2dr
2
d
+···
(2.5)
25
C
12
= 4πε
0
r
2
d
d
1+
r
2
d
d
2
−2r
2
d
+
r
4
d
d
4
−4d
2
r
2
d
+3r
4
d
+···
(2.6)
C
11
= C
10
+C
12
(2.7)
Another approach to solve the capacitance of the two-body system is to invert the elas-
tance matrix to obtain the system capacitance elements [21] in Eqs. 2.8 to 2.12. This
approach has approximately 3% error when compared with the image method discussed
above [21]. Where C
m
= 4πε
0
d and C
1
= 4πε
0
r
g1
, C
2
= 4πε
0
r
g2
are the capacitances
of single dust particle in free space. This method can be applied to calculate capacitances
when the dust system contains different dust sizes.
C
11
=
C
2
m
C
1
C
m
−C
1
C
2
(2.8)
C
22
=
C
2
m
C
2
C
m
−C
1
C
2
(2.9)
C
12
= C
21
=
C
1
C
2
C
m
(2.10)
C
10
= C
11
−C
12
(2.11)
C
20
= C
22
−C
12
(2.12)
Fig. 2.5 illustrates a more complicated 4-dust system. Each dust has its own self-
capacitance, C
i0
with respect to the ground as well as mutual capacitance, C
ij
between
any two particles. Both capacitances are functions of dust size and distance between each
26
pair. The capacitance matrix method discussed in the next section provides a convenient
approach to obtain capacitances in this more complicated dust system.
Figure 2.5: Capacitances in a 4-dust system
2.2.2 Capacitance Matrix Method
The capacitance matrix method provides a straightforward means to calculate equivalent
capacitance and charge on each node in a capacitor network.
Potential around Charges
The potential at pointp induced by an electric charge, at distanced in Fig. 2.6 with radius
r
0
is:
27
φ
p
=
Q
4πε
0
d
(2.13)
In Eq. 2.13, φ
p
is only a function of distance d ≥ r
0
if the charge Q is fixed. When
d > r
0
, φ
p
is the potential at any point in free space and when d = r
0
, φ
p
is the surface
potential of the charge with finite size. This equation can also be written in a more general
form:
φ
p
= s(d)Q (2.14)
Wheres in Eq. 2.14 is the elastance between the charge and pointp in the unit of F
−1
.
Figure 2.6: Potential field induced by a charge
The electric potential atp can be superposed linearly if there aren charged dust particles
in the system:
φ
p
=
n
X
i=1
s(d
i
)Q
i
(2.15)
28
Similarly, the surface potential of each dust particle is given in Eq. 2.16.
φ
1
= s
11
Q
1
+s
12
Q
2
+s
13
Q
3
+s
14
Q
4
+···+s
1n
Q
n
φ
2
= s
21
Q
1
+s
22
Q
2
+s
23
Q
3
+s
24
Q
4
+···+s
2n
Q
n
φ
3
= s
31
Q
1
+s
32
Q
2
+s
33
Q
3
+s
34
Q
4
+···+s
3n
Q
n
φ
4
= s
41
Q
1
+s
42
Q
2
+s
43
Q
3
+s
44
Q
4
+···+s
4n
Q
n
.
.
.
φ
n
= s
n1
Q
1
+s
n2
Q
2
+s
n3
Q
3
+s
n4
Q
4
+···+s
nn
Q
n
(2.16)
Eq. 2.17 is the matrix format of Eq. 2.16. (S) matrix is the elastance matrix, the diag-
onal term s
ii
is the self-elastance of the i-th dust particle and r
di
is the radius of the i-th
dust. The non-diagonal terms
ij
is the mutual elastance between i-th and j-th dust particles
andd
ij
is the centroid distance of this dust pair. According to Green’s theorem,s
ij
=s
ji
and
hence the (S) matrix is symmetric. (Q) vector stores the information of charge deposited
on each dust and the right hand side (φ) vector gives floating potential of each dust in
plasma.
s
11
s
12
s
13
s
14
··· s
1n
s
21
s
22
s
23
s
24
··· s
2n
s
31
s
32
s
33
s
34
··· s
3n
s
41
s
42
s
43
s
44
··· s
4n
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
s
n1
s
n2
s
n3
s
44
··· s
nn
Q
1
Q
2
Q
3
Q
4
.
.
.
Q
n
=
φ
1
φ
2
φ
3
φ
4
.
.
.
φ
n
(2.17)
Where,
s
ii
=
1
4πε
0
r
di
(2.18)
s
ij
=
1
4πε
0
d
ij
(2.19)
29
The inverse of the (S) matrix establishes the capacitance matrix (Eq. 2.20) of the mul-
tiple dust system. Therefore, Eq. 2.21 is the explicit form to calculate(Q) vector. The non-
diagonal element−C
ij
is the mutual capacitance, defined as the ratio of induced charge on
the j-th dust to the potential of i-th dust when all other dust particles are grounded. Since
the induced charge is always opposite in sign, any non-diagonal element is negative or
zero [81].
C
11
−C
12
−C
13
−C
14
··· −C
1n
−C
21
C
22
−C
23
−C
24
··· −C
2n
−C
31
−C
32
C
33
−C
34
··· −C
3n
−C
41
−C
42
−C
43
C
44
··· −C
4n
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
−C
n1
−C
n2
−C
n3
−C
44
··· C
nn
=
s
11
s
12
s
13
s
14
··· s
1n
s
21
s
22
s
23
s
24
··· s
2n
s
31
s
32
s
33
s
34
··· s
3n
s
41
s
42
s
43
s
44
··· s
4n
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
s
n1
s
n2
s
n3
s
44
··· s
nn
−1
(2.20)
Q
1
Q
2
Q
3
Q
4
.
.
.
Q
n
=
C
11
−C
12
−C
13
−C
14
··· −C
1n
−C
21
C
22
−C
23
−C
24
··· −C
2n
−C
31
−C
32
C
33
−C
34
··· −C
3n
−C
41
−C
42
−C
43
C
44
··· −C
4n
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
−C
n1
−C
n2
−C
n3
−C
44
··· C
nn
V
1
V
2
V
3
V
4
.
.
.
V
n
(2.21)
The diagonal element C
ii
of the capacitance matrix is the total capacitance of the i-th
dust particle defined as the ratio of charge to potential when all other dust particles are
grounded [81]. Eq. 2.22 is the expression ofC
ii
in terms of mutual and self-capacitance.
30
C
ii
= C
i1
+C
i2
+···+C
i(i−1)
+C
i0
+C
i(i+1)
+···+C
in
(2.22)
2.3 Approximate Calculation of Multiple Dust Particle
Charging
2.3.1 Effects of Mutual Elastance on Dust Charging
The capacitance matrix in Eq. 2.20 needs to be solved numerically. But to demonstrate the
effects of the mutual elastances induce by other dust particles in the system, we consider
a sample. As Eq. 2.20 cannot be solved analytically, four approximations are presented in
this section to obtain simplified solutions to Eq. 2.20 assuming every dust particle has the
same sizer
d
.
1. A dust is not affected by any other dust in the system.
2. The capacitance of a dust is only affected by dust withind
n
in the system.
3. A dust is sitting at the center of the system and all other dust are surrounded at d
n
,
whered
n
is the distance between a dust and its neighbors.
4. A dust is sitting in the center of the system and all other dust are surrounded at
d, where d is the average distance to the system center, considering all dust in the
system.
Where, d
n
is calculated based on the dust number density n
d
: d
n
= n
−1/3
d
for 3D
distribution and d
n
= n
−1/2
d
for 2D distribution [68]. d = 3/4L for 3D distribution and
d = 2/3L for 2D distribution calculated from uniformly distributed dust system, where L
is the radius of the system considered. This section tests a 2D distributed dust situation
with four cases stated above.
31
Approximation 1 is the single isolated dust for the dust-in-plasma situation. In approx-
imation 2, we include only the mutual capacitance from a dust particle’s immediate neigh-
bors, while the contributions from other dust particles are ignored. In approximation 3, we
assume that the mutual capacitance contribution from all dust particles to a given particle
is the same as that from its immediate neighbor. Clearly, Approximation 2 underestimates
the mutual capacitance effect while Approximation 3 overestimates the mutual capacitance
effect. In Approximation 4, we still assume that the contribution from all dust particles to
the mutual capacitance is the same. However, the mutual capacitance is calculated using
an averaged inter-dust distance
Approximation 1
In approximation 1, the(S) matrix in Eq. 2.20 becomes Eq. 2.23, where,s
11
= 1/(4πε
0
r
d
),
the self-elastance of each dust particle. In the matrix, only diagonal elements are non-zero.
The solution to self-capacitanceC
10
, normalized to4πε
0
r
d
is given in Eq. 2.24. This result
is the same as the capacitance of a singe isolated sphere in space.
s
11
0 0 0 ··· 0
0 s
11
0 0 ··· 0
0 0 s
11
0 ··· 0
0 0 0 s
11
··· 0
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
0 0 0 0 ··· s
11
(2.23)
ˆ
C
10
= 1 (2.24)
32
Approximation 2
In approximation 2, the (S) matrix is penta-dianonal as shown in Eq. 2.25 because a dust
only interacts with four neighboring dust particles in a 2D Cartesian coordinate system.
The solution toC
10
cannot be derived analytically, it will be calculated numerically.
s
11
s
12
s
12
s
12
s
11
s
12
s
12
s
12
s
11
s
12
.
.
.
s
12
s
11
s
12
s
12
s
12
s
12
s
11
s
12
s
12
s
12
s
11
.
.
.
.
.
.
.
.
.
.
.
. s
12
s
12
s
12
s
11
(2.25)
Approximation 3
In approximation 3, the diagonal elements remain the same but all non-diagonal elements
are replaced by s
12
= 1/(4πε
0
d
n
), the mutual elastance between two neighboring dust
particles. Eq. 2.27 shows the solution to the normalized self-capacitance, where
ˆ
d
n
is
normalized to dust radiusr
d
.
s
11
s
12
s
12
s
12
··· s
12
s
12
s
11
s
12
s
12
··· s
12
s
12
s
12
s
11
s
12
··· s
12
s
12
s
12
s
12
s
11
··· s
12
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
s
12
s
12
s
12
s
12
··· s
11
(2.26)
33
ˆ
C
10
=
ˆ
d
n
ˆ
d
n
+N−1
(2.27)
Approximation 4
In approximation 4, the(S) matrix has similar form as shown in approximation 2, however,
s
′ 12
= 1/(4πε
0
d), where, d in this 2D distribution case is calculated as follows: Eq. 2.28
shows the number of dust particle within an arbitrary radius D; Eq. 2.29 shows the distri-
bution function of dust at D; Eq. 2.30 calculates the average distance of dust to the center
within a control circle with radiusL. The solution to the normalized self-capacitance shows
in Eq. 2.32.
N(D) = πD
2
n
d
(2.28)
f(D) =
dN(D)
dD
= 2πDn
d
(2.29)
d =
1
N
L
Z
L
0
Df(D)dD =
1
πL
2
n
d
Z
L
0
2πD
2
n
d
dD =
2
3
L (2.30)
s
11
s
′ 12
s
′ 12
s
′ 12
··· s
′ 12
s
′ 12
s
11
s
′ 12
s
′ 12
··· s
′ 12
s
′ 12
s
′ 12
s
11
s
′ 12
··· s
′ 12
s
′ 12
s
′ 12
s
′ 12
s
11
··· s
′ 12
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
s
′ 12
s
′ 12
s
′ 12
s
′ 12
··· s
11
(2.31)
ˆ
C
10
=
ˆ
d
ˆ
d+N−1
(2.32)
34
2.3.2 Analysis of the Approximate Solutions
Fig. 2.7 shows the comparison of normalizedC
10
calculated by four approaches at different
d
n
of a 100-dust system. Fig. 2.8 is on the log scale. The self-capacitance in approximation
2 to 4 approaches to the single isolated model whend
n
increases, indicating less interaction
from other dust particles in the system. As expected, the capacitance result in approxima-
tion 4 falls between that of approximation 2 and approximation 3. In order to make a better
solution, we choose Eq. 2.32 to calculate dust capacitance using the average distance d
without numerically calculating the matrix. Eqs. 2.33 to 2.38 are results adopted to calcu-
late the capacitances.
0 100 200 300 400 500 600 700 800 900 1000
0
0.2
0.4
0.6
0.8
1
1.2
n
−1/2
d
/rd
ˆ
C10
Approximation 1
Approximation 2
Approximation 3
Approximation 4
Figure 2.7: Normalzed self-capacitance vs normalized distance between neighboring dust
particles
C
11
=
s
11
+(N−2)s
12
(s
11
−s
12
)[s
11
+(N−1)s
12
]
(2.33)
C
12
=
s
12
(s
11
−s
12
)[s
11
+(N−1)s
12
]
(2.34)
35
10
1
10
2
10
3
10
−1
10
0
n
−1/2
d
/rd
ˆ
C10
Approximation 1
Approximation 2
Approximation 3
Approximation 4
Figure 2.8: Normalzed self-capacitance vs normalized distance between neighboring dust
particles on the log-log scale
C
10
= C
11
−(N−1)C
12
=
1
s
11
+(N−1)s
12
(2.35)
ˆ
C
11
=
ˆ
d
2
+(N−2)
ˆ
d
ˆ
d−1
ˆ
d+N−1
(2.36)
ˆ
C
12
=
ˆ
d
ˆ
d−1
ˆ
d+N−1
(2.37)
ˆ
C
10
=
ˆ
d
ˆ
d+N−1
(2.38)
At fixed
ˆ
d, the total capacitance increases while mutual and self capacitances approach
to 0 as the number of particles in the system increases. If dust particles are charged to the
same floating potential by ambient plasma, charge on each particle follows Eq. 2.39. In the
equation, compared with single dust charge in free space, there is an additional coefficient
ˆ
d/
h
ˆ
d+(N−1)
i
, causing lower charge carried by the particle in the multiple dust system,
36
which provides one possible explanation to the charge reduction of a single dust particle in
a dust system, as stated by Barkan et al. [5] and Avinash et al. [3].
Q
d
= C
10
φ =
4πε
0
r
d
ˆ
d
ˆ
d+(N−1)
φ =
ˆ
d
ˆ
d+(N−1)
C
0
φ (2.39)
2.4 Capacitance of Dusty Plasma
For a dusty plasma, the number of interacting dust is not arbitrary. Because of the Debye
shielding [3], only those dust particles with a inter-dust distance smaller thanλ
D
should be
included. And, therefore, the average inter-dust distanced = 3/4λ
D
in this case. Eqs. 2.40
to 2.42 show the derivation.
N(D) =
4
3
πD
3
n
d
(2.40)
f(D) =
dN(D)
dD
= 4πD
2
n
d
(2.41)
d =
1
N
λ
D
Z
λ
D
0
Df(D)dD =
1
4
3
πλ
3
D
n
d
Z
λ
D
0
4πD
3
n
d
dD =
3
4
λ
D
(2.42)
As a result,s
11
ands
12
in Eqs. 2.18 and 2.19 become Eqs. 2.43 and 2.44. Where,β and
α are defined in Eqs. 2.45 and 2.46, coefficients in addition to the original forms.
s
11
=
1
4πε
0
r
d
β
(2.43)
s
12
=
1
4πε
0
dα
(2.44)
37
β =
1
1−
r
d
λ
D
≈ 1 (2.45)
α =
1
1−
d
λ
D
= 4 (2.46)
The number of dust particles,N counts all dust in a Debye sphere in Eq. 2.47. Where,
n
d
is the dust volume number density. For N >> 1, N − 1 ≈ N. Then the normalized
self-capacitance of a dust particle in dusty plasma turns into Eq. 2.48. Where, r
d
and d
n
are normalized toλ
D
, and C
10
is normalized to the capacitance of a single isolated sphere
with radius ofr
d
in free space.
N =
4
3
πλ
3
D
n
d
(2.47)
ˆ
C
10
=
3
3+
3
4
ˆ r
d
π
1
ˆ
d
3
n
(2.48)
Fig. 2.9 shows the normalized self-capacitance of a dust particle in a dusty plasma sys-
tem at four sizes.
ˆ
C
10
starts to increase with the normalized effective separation
ˆ
d increases
and approaches to 1 as when dust particles are far apart, this becomes a dust-in-plasma
case. Also, the capacitance of a dust particle with smaller size in the dust system, reaches
that of isolated single at a shorter separation since the ratio of d to r
d
is larger. Fig. 2.10
plots the separation and capacitance in the log-log scale.
2.5 Dust Particles on a Surface
For a multiple-dust-on-surface system, we propose to derive the capacitance by modifying
the relative elements in the elastance matrix.
38
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
1.2
n
−1/3
d
/λD
ˆ
C10
ˆ rd = 10
−5
ˆ rd = 10
−4
ˆ rd = 10
−3
ˆ rd = 10
−2
Isolated single
Figure 2.9: Normalized self-capacitance of a dust particle in a dusty plasma system vs
normalized separation
The capacitance of a single dust-on-surface may be calculated using the method con-
cluded by Zisman [101]. Eq. 2.49 is the capacitance between a sphere and an infinitely
large flat plate [101, 92], where γ=0.5772 is Euler’s constant and h is the effective sepa-
ration between the sphere and plate, dependent upon surface roughness and dust size. A
typical value of theh tor ratio for modeling the capacitance of a single dust particle resting
on a plate is 0.2 [92]. In this situation, since the flat surface is infinitively large, it serves as
the reference ground.
C = 4πε
0
r
γ−
1
2
ln
h
r
(2.49)
The modified self-elastance of dust particles in this case becomes Eq. 2.50 and mutual
elastance remains the same as s
ij
= 1/4πε
0
d
ij
[81] as the mutual elastance is only a
function of distance between two objects. Elements in the capacitance matrix are calculated
using Eq. 2.20 as discussed previously.
39
10
−4
10
−3
10
−2
10
−1
10
0
10
−8
10
−6
10
−4
10
−2
10
0
n
−1/3
d
/λD
ˆ
C10
ˆ rd = 10
−5
ˆ rd = 10
−4
ˆ rd = 10
−3
ˆ rd = 10
−2
Isolated single
Figure 2.10: Normalized self-capacitance of a dust particle in a dusty plasma system vs
normalized separation on the log-log scale
Figure 2.11: Dust grains on a flat surface
s
ii
=
1
4πε
0
r
d
h
γ−
1
2
ln
h
r
d
i (2.50)
The following assumptions must be satisfied to use Eqs. 2.33 to 2.35 for approximate
solutions:
1. There are N dust particles involved in the capacitance interaction.
2. Each particle has the same sizer
d
.
40
Figure 2.12: Packed dust surface in the plasma environment
3. Dust particles are uniformly distributed on a surface with average inter-dust distance
d.
The coefficient β = γ−
1
2
ln
h
r
is defined in Eq. 2.50. Eqs.2.51, 2.52, and 2.53 are
capacitance results derived from capacitance matrix method, normalized to C
0
= 4πε
0
r
d
,
for aN-dust system on a surface, where, the distanced is normalized tor
d
.
ˆ
C
11
=
ˆ
d
2
β +(N−2)
ˆ
dβ
2
ˆ
d−β
h
ˆ
d+(N−1)β
i (2.51)
ˆ
C
12
=
ˆ
dβ
2
ˆ
d−β
h
ˆ
d+(N−1)β
i (2.52)
ˆ
C
10
=
ˆ
d
2
β−
ˆ
dβ
2
ˆ
d−β
h
ˆ
d+(N−1)β
i (2.53)
If β = 1, there is no extra self-capacitance gain due to a flat surface in space, and
Eqs. 2.51 to 2.53 recover Eqs. 2.36 to 2.38, which are the dust capacitances in free space
derived in the previous section.
41
2.6 Capacitance of a Dusty Surface in Plasma
Similarly, for dust particles on a dusty surface, the average inter-dust distanced = 2/3λ
D
because of a 2D dust distribution,α andβ are calculated in Eq. 2.55.
α =
1
1−
d
λ
D
= 3 (2.54)
β = γ−
1
2
ln
h
r
= 1.3817 (2.55)
The number of dust particles N in a Debye circle on a surface is given in Eq. 2.56.
Where, n
d
is the dust surface number density and d
n
= n
−1/2
d
, normalized to λ
D
in the
equation. Then
ˆ
C
10
becomes Eq. 2.57.
N = πλ
2
D
n
d
(2.56)
ˆ
C
10
=
2β
2+βπˆ r
d
1
ˆ
d
2
n
(2.57)
Fig. 2.13 shows the normalized self-capacitance of a dust particle on a dusty surface in
plasma at four sizes.
ˆ
C
10
starts to increase with
ˆ
d
n
increases and approaches toβ as when
dust particles are far apart. The capacitance of a dust particle with smaller size in the dust
system, reaches that of isolated single at a shorter separation. Fig. 2.14 plots the separation
and capacitance on the log-log scale. The capacitance of dust on a dusty surface in plasma
is different from that of a single isolated model. For instance, Tab. 2.1 shows sample
self-capacitances of dust on surface with different
ˆ
d
n
with (r
d
= 100 μm, λ
D
=10 mm,
ˆ r
d
= 0.01). The normalized capacitance of a single dust on a surface is
ˆ
C
10
= β = 1.3817.
42
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
n
−1/2
d
/λD
ˆ
C10
ˆ rd = 10
−5
ˆ rd = 10
−4
ˆ rd = 10
−3
ˆ rd = 10
−2
Isolated single
Figure 2.13: Normalized self-capacitance of a dust particle on a dusty surface in space
plasma vs normalized separation
10
−4
10
−3
10
−2
10
−1
10
0
10
−4
10
−3
10
−2
10
−1
10
0
n
−1/2
d
/λD
ˆ
C10
ˆ rd = 10
−5
ˆ rd = 10
−4
ˆ rd = 10
−3
ˆ rd = 10
−2
Isolated single
Figure 2.14: Normalized self-capacitance of a dust particle on a dusty surface in space
plasma vs normalized separation on the log-log scale
43
Table 2.1: Sample dust capacitance on a dusty surface in plasma
ˆ
d
n
0.02 0.1 0.2 0.5 1
ˆ
C
10
0.025 0.4358 0.8958 1.2715 1.3526
2.7 Conclusion
In this chapter, the capacitance of a dusty plasma and a dusty surface in plasma are dis-
cussed. Analytically, we are not able to solve for the capacitance matrix. Rather, we con-
sider two limiting approximation to bound the value of the capacitance. We have derived
an average distance as an approximation solution to inter-dust distance in a dust system.
We find that in dusty plasma, the capacitance of a dust particle is always lower than that
of a single isolated dust and the capacitance increases withn
−1/3
d
/λ
D
increases. Similarly,
the capacitance of a dust on a dusty surface in plasma is always lower than that of a single
isolated dust on a surface and the capacitance increases withn
−1/2
d
/λ
D
increases.
44
Chapter 3: Experimental Investigations
of Multi-dust System Capacitances in
Space Plasma
3.1 Introduction
To prove the theory of dust charging in a dust system, experiments have been designed to
conclude capacitances in the capacitance matrix. The capacitance of a circuit or an object
is determined by calculating the ratio of measured charge to potential. Faraday cups with
external amplifier and filter [102, 80, 82, 92, 93] are widely used to measure the charge of
dust particles. However, the potential of charged dust is almost impossible to be measured
precisely by instruments due toμm size and probe disturbance orders of magnitude larger
than dust charge.
To resolve the issues stated above, large scale metal spheres, 5” (127 mm) in diam-
eter were utilized to simulate the charging interaction of dust particles. The capacitance
of a 100 μm dust particle in free space is 5.56×10
−15
F, but if a metal sphere simulant is
employed, the theoretical capacitance is three orders of magnitudes higher, 7.07×10
−12
F,
a value much simpler to detect with existing amplifier systems. The following two impor-
tant assumptions are made to conduct the experiment.
1. Each dust surface is an equal potential surface in the surrounding electric field
2. Capacitances in the dust system are functions of geometry and proportional to size
Assumption 1 justifies using conducting spheres to simulate the equal potential dust sur-
faces and Assumption 2 makes it possible to scale down to real dust capacitance estimation
in complicated cases.
45
In the experiments, all metal spheres are in the same size and centroid distance between
each pair is made to be the same for simplification. In this situation, self elastance s
ii
and mutual elastance s
ij
in the elastance matrix (S) are uniform leading to uniform total
capacitance C
ii
and mutual capacitance C
ij
in the capacitance matrix (C). Only C
11
and
C
12
are measured in the experiment.
3.1.1 Parameter Normalization
The following normalization (in Tab. 3.1) is used to make parameters dimensionless for
comparison between calculations and experiments. Length and capacitance are normalized
to radius and capacitance in free space (dust or testing spheres), respectively, and thus
Eq. 2.20 becomes Eq. 3.1.
Table 3.1: Normalization
Experiment Calculation
ˆ r
0
=
r
0
r
0
= 1 ˆ r
d
=
r
d
r
d
= 1
ˆ
d =
d
r
0
ˆ
d =
d
r
d
ˆ
C =
C
C
0
=
C
4πε
0
r
0
ˆ
C =
C
C
d
=
C
4πε
0
r
d
ˆ s =
s
s
d
= 4πε
0
r
d
s
ˆ
C
11
−
ˆ
C
12
−
ˆ
C
13
−
ˆ
C
14
··· −
ˆ
C
1n
−
ˆ
C
21
ˆ
C
22
−
ˆ
C
23
−
ˆ
C
24
··· −
ˆ
C
2n
−
ˆ
C
31
−
ˆ
C
32
ˆ
C
33
−
ˆ
C
34
··· −
ˆ
C
3n
−
ˆ
C
41
−
ˆ
C
42
−
ˆ
C
43
ˆ
C
44
··· −
ˆ
C
4n
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
−
ˆ
C
n1
−
ˆ
C
n2
−
ˆ
C
n3
−
ˆ
C
44
···
ˆ
C
nn
=
ˆ s
11
ˆ s
12
ˆ s
13
ˆ s
14
··· ˆ s
1n
ˆ s
21
ˆ s
22
ˆ s
23
ˆ s
24
··· ˆ s
2n
ˆ s
31
ˆ s
32
ˆ s
33
ˆ s
34
··· ˆ s
3n
ˆ s
41
ˆ s
42
ˆ s
43
ˆ s
44
··· ˆ s
4n
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
ˆ s
n1
ˆ s
n2
ˆ s
n3
ˆ s
44
··· ˆ s
nn
−1
(3.1)
46
3.1.2 Methodology of Measurement
The expression of charge on the Sphere 1,Q
1
based on Eq. 2.21 is
Q
1
= C
11
φ
1
−C
12
φ
2
−···−C
1n
φ
n
(3.2)
Fig. 3.1 shows the equivalent circuit for C
11
measurement. When Sphere 2 to n are
electrically connected to the ground (φ
2
= ··· = φ
n
= 0) and the switch is at the initial
position, Sphere 1 is biased toV and its chargeQ
1
becomes what shows in Eq. 3.3.
Q
1
= C
11
V (3.3)
The switch is then flipped to the final position to discharge Sphere 1 to 0 V through an
electrometer, c
in the circuit, and total chargeQ
1
flows through the electrometer.
Figure 3.1: C
11
measuring circuit
47
The potential on the first sphereφ is to be biased by an external power supply to differ-
ent voltagesV and the corresponding chargeQ
1
is recorded each time. C
11
is obtained by
calculating the slope of theQ−V curve through least squares fitting.
Fig. 3.2 is the equivalent circuit for C
12
measurement. Sphere 1 is connected to the
ground through the electrometer and all other spheres are also grounded. At this initial
state, charge on sphere 1 is 0 (Eq. 3.4). Then the switch is flipped to the final position to
raise the potential of Sphere 2 from 0 toV through the external power supply, allowing the
induced charge on Sphere 1 at the final state to be given in Eq. 3.5. The net charge ΔQ
1
flow throughout the electrometer during the process of raisingV isC
12
V from Eq. 3.6.
The same least squares fitting method is then applied to derive the the mutual capaci-
tanceC
12
as the slope of theQ−V curve.
Figure 3.2: C
12
measuring circuit
Q
1 initial
=−C
12
0 = 0 (3.4)
48
Q
1 final
=−C
12
V (3.5)
ΔQ
1
= Q
1 initial
−Q
1 final
= C
12
V (3.6)
3.2 Experimental Setup
The capacitance measurement involves two parameters, voltage and charge. V oltage
applied to any sphere was directly measured by a multimeter, while the very low charge
on the sphere about 100 pC when charged to 20 V , required a high-precision electrometer
to reach such accuracy. The following sections discuss design and development of a high-
sensitivity electrometer for measuring low charge by integrating the discharge current of a
capacitor over time as well as setups to achieve low-charge measurement.
3.2.1 High-sensitivity Electrometer Development
Charge Measurement Mechanism
Fig. 3.3 shows the discharge of a capacitor, initially charged to V with an external power
supply in a circuit. During the discharge process, there is electric current i(t) flowing
through the electrometer. The output reading of an electrometer does what is described
in Eq. 3.7. Due to extremely low charge and current, an amplifier is needed to generate
measurable voltage signal.
Q =
Z
t
0
i(t)dt (3.7)
Fig. 3.4 is an integrator circuit with an operational amplifier (Op Amp) as a core unit.
The input capacitorC
in
to be discharged is connected between the ground and the negative
49
Figure 3.3: Discharge circuit
input of the Op Amp. R
in
serves as an equivalent input resistor in the circuit. C
f
is the
feedback capacitor andR
f
with very large resistance (on the order of MΩ) is the feed back
resistor to automatically reset the negative input to 0 V after each measurement. The testing
capacitance or the input capacitance,C
in
andR
in
are both small compared withC
f
andR
f
,
causing a much smaller input time constant than the feedback one (τ
in
= R
in
C
in
<< τ
f
=
R
f
C
f
).
The measurement process is divided into the following two steps based on the above
conditions: 1) The charged C
in
first discharges through the input RC circuit, charging the
feedback resistor over t = 0 to t = t
1
. 2) The feedback capacitor discharges through the
feedback RC circuit, bringingV
out
to zero output duringt = t
1
tot = t
2
.
According to the ideal Op Amp model [24, 6], in Step 1,V
in
with respect to time follows
Eq. 3.8 during discharge. Expressions of current across R
in
and C
f
are shown in Eq. 3.9
and 3.10. Since current across the feedback resistor is low,i
in
(t) = i
C
f
(t). Eq. 3.11 gives
the total charge initially deposited on a sphere, proportional to C
f
and V
out
(t
1
), and not a
50
Figure 3.4: Integrator circuit
function of R
in
. Within about 10τ
in
, total charge on the sphere vanishes to 0 which is the
identity of RC circuit discharge.
V
in
(t) = V
in
(0)exp
−
t
τ
in
(3.8)
i
in
(t) =
V
in
(t)
R
in
(3.9)
i
C
f
(t) = C
f
−
dV
out
(t)
dt
(3.10)
Q =
Z
t
1
0
i
in
(t)dt =−C
f
Z
Vout(t
1
)
Vout(0)
dV
out
(t)
=−C
f
V
out
(t
1
)
(3.11)
Combining Eq. 3.8 to 3.10, the differential equation forV
out
yields,
51
dV
out
(t)
dt
=−
V
in
(0)
R
in
C
f
exp
−
t
τ
in
(3.12)
V
out
(t) =
Z
Vout(t)
Vout(0)
dV
out
(t) =
Z
t
t=0
−
V
in
(0)
R
in
C
f
exp
−
t
τ
in
dt
=
V
in
(0)C
in
C
f
exp
−
t
τ
in
−1
(0≤ t≤ t
1
)
(3.13)
In Step 2, C
f
discharges through the feedback RC circuit, bringing V
out
back to zero
output. τ
f
in the equations controls the length of discharge time, and proper values of R
f
andC
f
should be chosen to visualize theV
out
signal on an oscilloscope.
V
out
(t) = V
out
(t
1
)exp
−
t−t
1
τ
f
(t > t
1
) (3.14)
The time history ofV
out
(t) is plotted in Fig. 3.5 with values of circuit parameters listed
in Tab. 3.2. The magnitude ofV
out
sharply increases in a very short time due to small τ
in
,
10 ps in this case, and drops exponentially to 0 on the order of ms in the second step. The
spike att≈ 0 indicates the value ofV
out
(t
1
) in Eq. 3.11 for charge calculation.
Table 3.2: Component parameters and initial input voltage of the integrator circuit for
charge measurement
Parameter Value
R
in
1 Ω
C
in
10 pF
τ
in
10 ps
R
f
200 MΩ
C
f
200 pF
τ
f
40 ms
V
in
(0) 20 V
52
−0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
t, s
V
out
, V
Figure 3.5: V oltage history of the integrator circuit for charge measurement
Circuit Design and Components
An electrometer with high sensitivity has been developed to measure pC (10
−12
C)-level
electric charge on a testing capacitor. A Texas Instruments
R
OPA-129 Ultra-Low Bias
Current Difet operational amplifier, which greatly eliminates leakage current, was selected
to work as the amplification unit for low discharge current integration.
Fig. 3.6 gives the schematic design of the electrometer. There are two BNC jacks,
connected to BNC cables to shield external electrical noise, in the circuit for V
in
and V
out
signals. VS+ and VS- are two sockets, connected to external power supplies, delivering
±15 V DC voltage to power the OPA 129. R
f
and C
f
are given in Tab. 3.3 and share the
same values used in Tab. 3.2, 200 MΩ and 20 pF respectively, leading to a 40 ms time
constantτ of the feedback system.
Fig. 3.7 is the printed circuit board (PCB) designed to be etched for soldering. OPA
129 and two other passive components are surface mounted to the board.
53
Figure 3.6: Schematic of high-sensitivity electrometer
Table 3.3: Parameters of passive components used in the electrometer
Parameter Value Tolerance
R
f
200 MΩ 5%
C
f
200 pF 1%
The high-sensitivity electrometer PCB was photochemically etched. The design pattern
in Fig. 3.7 was printed on a transparency film. Covered by the film, a positively presen-
sitized copper clad was exposed under fluorescent light for about 15 minutes to active the
photoresist. The exposed sample went into MG Chemicals
R
positive developer solution to
remove photoresist on areas where copper was to be later etched. The developed copper
clad was then bathed in FeCl
3
solution for etching and liquid tin solution to coat a thin tin
layer on the copper for easy soldering. Finally, holes were drilled to mount pin and jack
connections, as shown in Fig. 3.8.
54
Figure 3.7: PCB design of high-sensitivity electrometer
Components were soldered to the PCB (Fig. 3.9) to complete assembly. All connectors
in Fig. 3.10 were clearly labeled to prevent misconnection and for easy access.
Figure 3.8: Completed PCB coated with tin and drilled holes
System Error Analysis of Charge and Capacitance Measurement
The error of charge measurement comes from two factors, the precision ofC
f
and reading
of V
out
from the oscilloscope according to Eq. 3.11. The error of charge calculated from
55
Figure 3.9: Back side of the PCB with all components soldered into position
Figure 3.10: The front side of the PCB with all connectors labeled
measurement,δQ is given in Eq. 3.15. δC
f
/C
f
= 1% is the tolerance ofC
f
. δV
out
is sub-
stituted by the precision of cursor measurement by the digital oscilloscope within different
ranges used in the experiment, tabulated in Tab. 3.4.
δQ = Q
s
δC
f
C
f
2
+
δV
out
V
out
2
(3.15)
Capacitance calculation involves processing N pairs ofQ−V data points through lin-
ear fitting and both variables involve measurement error, which would require total least
56
Table 3.4: V oltage cursor measurement precision of Tektronix
R
TDS 640A digital oscillo-
scope within different ranges
Range Precision
0 - 8 mV 0.02 mV
8 mV - 16 mV 0.04 mV
16 mV - 40 mV 0.1 mV
40 mV - 80 mV 0.2 mV
80 mV - 160 mV 0.4 mV
160mV - 400 mV 1 mV
400mV - 800mV 2 mV
800mV - 1.6 V 4 mV
1.6 V - 4 V 10 mV
4 V - 8 V 20 mV
8 V - 16 V 40 mV
squares fitting. This is a very complicated method requiring numerical simulation such as
Monte Carlo [22]. As a result, in Eq. 3.16 the error of capacitance is represented as the
average of calculated error at each point given in Eq. 3.17. The precision of the digital
multimeter used for biased voltage reading listed in Tab. 3.5
δC =
1
N
N
X
i=1
δC
i
(3.16)
δC
i
= C
i
s
δQ
i
Q
2
+
δV
i
V
i
2
(3.17)
Table 3.5: V oltage measurement precision of UNI-T
R
UT39A digital multimeter within
different ranges
Range Precision
2V - 20 V 1 mV
20 V - 200V 10 mV
57
Calibration and Testing
The electrometer was tested with a 200 pF capacitor as an input capacitor for capacitance
measurement. Fig. 3.11 is the setup, in which V
out
signal was fed into an oscilloscope for
accurate reading. TheQ−V curve is plotted in Fig. 3.12 and the capacitance of the testing
capacitor is C = 208±2.2 pF based on linear data fitting. The measured capacitance is
higher than the nominal value because of the dissipative capacitance in circuit components
such as the wires and switch. The capacitance in a single strand wire is on the order of tens
of pF per meter.
Figure 3.11: Setup for capacitance measurement test
3.2.2 Setups for Experiments
Experiments investigating electrical interactions between dust simulants were conducted in
the USC CHAFF IV stainless steel vacuum chamber, 3 m in diameter and 6 m in length.
Steel spheres, 5” (127 mm) in diameter were mounted in the vacuum chamber using PVC
pipes attached to an optical bench. Since the size of the chamber is 2 orders of magnitude
larger than that of the steel spheres, chamber walls are regarded as the reference ground at
infinity in the model. The chamber was not pumped down to vacuum as permittivities of
vacuum and air are almost the same, moreover,ε is canceled out after normalization.
58
0 2 4 6 8 10 12 14 16 18 20
0
500
1000
1500
2000
2500
3000
3500
4000
V , V
Q, pC
Measured Q
Linear fitting
Figure 3.12: Charge with error bar vs biased voltage of a 200 pF testing capacitor
Procedure of charge measurement on the sphere for calculatingC
11
1. Set the external power supply toV
2. Charge Sphere 1 by a wire connected to the power supply
3. Remove the wire after several seconds
4. Immediately discharge Sphere 1 by direct touching the surface with a wire through
the electrometer
5. Read the magnitude of the spikeV
out
on the oscilloscope for charge calculation
Procedure of charge measurement on the sphere for calculatingC
12
1. Electrically connect the surface of Sphere 1 to the electrometer
59
2. Set the external power supply toV
3. Ground Sphere 2 through a wire
4. Charge Sphere 2 by a wire which is attached to the power supply
5. Read the magnitude of the spikeV
out
on the oscilloscope to calculate charge induced
by Sphere 2
3.2.3 Experimental Cases
Up to four spheres were tested for electrical interactions in the chamber.
1. Capacitance of a single sphere in free spaceC
0
, which is used as the capacitance for
normalizations. (Fig. 3.13)
2. Total and mutual capacitances in the two-sphere case with different separations.
(Fig. 3.14)
3. Total and mutual capacitances in the three-sphere case with different separations.
Spheres are positioned to form vertices of an equilateral triangle. (Fig. 3.15)
4. Total and mutual capacitances in the four-sphere case with different separations.
Spheres are positioned to form vertices of a regular tetrahedron. (Fig. 3.16)
3.3 Capacitances of a Multi-dust System in Space
3.3.1 Results
The resulting sphere capacitance in free space based on the linear fitted Q− V curve is
C
0
= 7.94±0.08 pF. MeasuredC
11
andC
12
with uncertainties for the two, three, and four
sphere cases are tabulated in Tab. 3.6.
60
Figure 3.13: Single sphere case setup
Figure 3.14: Two-sphere case setup
Normalized total and mutual capacitances are shown in Figs. 3.17 to 3.19 compared
with those from the multiple dust charging theory. Trends of measured
ˆ
C
11
and
ˆ
C
12
match
ˆ
C
11
and
ˆ
C
12
from theoretical
ˆ
C
11
and
ˆ
C
12
well, indicating a successful approach of analyz-
ing capacitance interactions between dust particles in space. Capacitances with
ˆ
d > 4 were
not tested because it is not accurate to measure above this point with currently available
laboratory equipment. As observed in the plots,
ˆ
C
11
and
ˆ
C
12
approach 1 and 0 respectively
as
ˆ
d approaches infinity.
61
Figure 3.15: Three-sphere case setup
Figure 3.16: Four-sphere case setup
3.3.2 Error Analysis
Object capacitance must be distinguished from passive components and circuitry errors.
There are several factors that can affect the results.
Firstly, the chamber is not infinitively large, causing measurement deviation from true
capacitance values. V oltage was referenced to the chamber wall, which was connected to
electric ground of the building as a sink of electric current. Also, metal spheres used in the
experiments were manufactured by welding two hemispheres together, leaving a seam on
the equator and therefore were not perfectly spherical.
62
Table 3.6: Measured self and mutual capacitances in multiple sphere cases
a) Two-sphere case
d C
11
, pF C
12
, pF
2.2r
0
10.3±0.11 4.6±0.10
2.4r
0
9.8±0.10 3.76±0.09
3r
0
9.4±0.10 2.26±0.09
4r
0
9.10±0.09 1.73±0.06
b) Three-sphere case
d C
11
, pF C
12
, pF
2.2r
0
11.4±0.12 3.48±0.09
2.4r
0
10.7±0.11 3.07±0.09
3r
0
9.07±0.10 2.14±0.09
4r
0
8.40±0.09 1.59±0.09
c) Four-sphere case
d C
11
, pF C
12
, pF
2.2r
0
12.0±0.13 2.83±0.09
2.4r
0
11.0±0.12 2.47±0.09
3r
0
9.7±0.10 1.97±0.09
4r
0
8.61±0.09 1.32±0.09
Secondly, during the measurement of induced charge on Sphere 1, electrometer was
electrically connected to the surface at all times, which collected noise signal as an antenna.
Noise from the power grid was captured by the oscilloscope in Fig. 3.20. The dominant
frequency was about 60 Hz with an amplitude of 5.7 mV . In the error calculation of C
12
,
V
out
measurement error employed either the value in Tab. 3.4 or 5.7 mV , which ever was
higher. This is why the relative error ofC
12
is larger than that ofC
11
in Tab. 3.6.
63
2 2.5 3 3.5 4 4.5 5 5.5 6
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Two−sphere Case
ˆ
d
ˆ
C
theoretical
ˆ
C
11
measured
ˆ
C
11
theoretical
ˆ
C
12
measured
ˆ
C
12
Figure 3.17: Theoretical and measured
ˆ
C
11
and
ˆ
C
12
in the two-sphere case with different
centroid distance
ˆ
d
2 2.5 3 3.5 4 4.5 5 5.5 6
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Three−sphere Case
ˆ
d
ˆ
C
theoretical
ˆ
C
11
measured
ˆ
C
11
theoretical
ˆ
C
12
measured
ˆ
C
12
Figure 3.18: Theoretical and measured
ˆ
C
11
and
ˆ
C
12
in the three-sphere case with different
equal inter-sphere distance
ˆ
d
64
2 2.5 3 3.5 4 4.5 5 5.5 6
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Four−sphere Case
ˆ
d
ˆ
C
theoretical
ˆ
C
11
measured
ˆ
C
11
theoretical
ˆ
C
12
measured
ˆ
C
12
Figure 3.19: Theoretical and measured
ˆ
C
11
and
ˆ
C
12
in the four-sphere case with different
equal inter-sphere distance
ˆ
d
Figure 3.20: Ambient noise from the power grid collected by the sphere, frequency: 60 Hz,
amplitude: 5.7 mV
65
3.4 Conclusion
This chapter has discussed the experimental methods and setups to verify the dust capac-
itance model in space. A high-sensitivity electrometer is developed to measure pC level
charge on the large-scale dust simulants to conduct experiments for theory verification.
Experimental results show that the multi-dust capacitance model, the foundation of other
dust interaction models, is valid and matches experimental data well.
66
Chapter 4: Experimental Investigations
of Dusty Surface Charging in Plasma
4.1 Introduction
This chapter presents an experimental study to measure dust charging on a dusty surface.
The dusty surface considered is a surface with roughness on the order of a dust particle (10
μm to 1000 μm). The dust considered here in the experiment is JSC-1A. The top layer of
dust forms the regolith surface which is directly exposed to ambient plasma and maintains
electric charges as shown in Fig. 4.1. At steady state, the net current of the local dielectric
surface with surface area ΔA satisfies Eq. 4.1.
Figure 4.1: Dust layer surface potential measurement
N
X
i=1
J
i
(φ
s
)ΔA = 0 (4.1)
At each location of the dust pile in plasma, the surface charge density is defined by
Eq. 4.2 [70], reflecting how charge is concentrated over this location.
67
σ =
dQ
dA
(4.2)
On a flat surface formed by well-packed dust particles, chargeΔQ accumulated on this
area isσΔA. SubstitutingΔA with the projected area of a single dust particle on the plane,
πr
2
d
, charge on a dust particle resting on a flat surface becomes Eq. 4.3, wherer
d
is the dust
radius. The charge density, σ is determined by the surrounding plasma environment. The
method to measureσ will be discussed in the following section.
Q
d
= σπr
2
d
(4.3)
Q
d
m
d
=
σπr
2
d
4
3
πr
3
d
ρ
d
=
3σ
4r
d
ρ
d
(4.4)
For the setting, the charge to mass ratio is given by Eq. 4.4, where,ρ
d
is the mass den-
sity. The charge to mass ratio is an important parameter which reflects the dynamics of a
dust particle in the electric field, is derived in Eq. 4.4. r
d
and ρ
d
are material properties of
dust, treated as known parameters. However, σ is determined by the surrounding plasma
environment and the method of how to acquire its value is discussed in the following sec-
tion.
An experiment was designed to measure the surface potential and calculate the surface
charge density of a dust pile in plasma. In the experiment, JSC-1A [100] lunar regolith
simulant was placed on a plate inside a high vacuum chamber to be charged by a plasma
source for testing.
In the previous studies, dust charging on surfaces is measured by continuously agitating
and dropping charged dust particles into a Faraday cup [52, 92]. This method requires
complicated mechanical devices and vibration systems such as electromagnets inside the
68
vacuum chamber, and would introduce unexpected charge and charge exchange due to
collision with other dust particles while dropping to the Faraday cup.
The method presented in this chapter utilizes a non-contacting electrostatic probe to
scan the dust surface to acquire the charge based on surface potential without disturbing
the charge and potential of the dusty surface. Experiments conducted to investigate surface
dust charging involve the development of a 3D traversing system, gridded ion source and a
series of plasma diagnostic tools.
An electrostatic voltmeter makes it possible to detect the surface potential of dielectric
materials without contacting the testing surface, successfully avoiding charge exchange and
loss problems.
4.2 Approach
In Fig. 4.1, a packed dust layer with thicknessd is put on a metal plate, which is electrically
connected to the reference ground. φ
s
is the local dust layer surface potential charged by
plasma.
4.2.1 Surface Charge Calculation
The capacitance between two parallel metal plates with surface area A, separation d and
dielectric material relative permittivityε
rd
is given in Eq. 4.5.
C =
Aε
0
ε
rd
d
(4.5)
If there is only one metal plate covering one side of the dielectric material as in Fig. 4.1,
potential is not uniform on the dust layer surface and differential capacitance,C
dif
[42, 19],
is introduced in Eq. 4.6 to describe capacitance per unit area in this system. Therefore,
surface charge density can be expressed as in Eq. 4.7.
69
C
dif
=
dC
dA
=
ε
0
ε
rd
d
(4.6)
σ =
dQ
dA
=
dC
dA
φ
s
=
ε
0
ε
rd
d
φ
s
(4.7)
4.2.2 Method of Surface Potential Measurement
An electrostatic voltmeter is a vibrating capacitive probe used to detect surface poten-
tial [57] at each location with a current nulling method [101, 70, 72]. In Fig. 4.2, a capacitor
is created between the sampling surface with potentialφ
s
and the vibrating electrode biased
toV . The upper electrode is vibrating with frequencyω and amplituded
1
, forming a time
dependent gap,d = d
0
+d
1
sin(ωt) withd
1
< d
0
, between the sampling dielectric surface
and the vibrating electrode. The static separationd
0
is about 2 to 3 mm to maintain enough
accuracy.
Figure 4.2: Illustration of non-contacting surface potential measurement
The capacitance of this system is given in Eq. 4.8. Eq. 4.9 gives the current flow through
the electrode as a function of time. Only whenV is biased asV = φ
s
is there zero current
70
flow through the electrode, which establishes the underling physics of this non-contacting
current nulling method for surface potential measurement.
C =
Aε
d
0
+d
1
sin(ωt)
(4.8)
i =
d[C(V −φ
s
)]
dt
=−
Aεd
1
ωcos(ωt)
[d
0
+d
1
sin(ωt)]
2
(V −φ
s
) (4.9)
A controller connected to the probe sends electric pulses to vibrate the electrode at a
high frequency ω, sweeping the biased voltage V to match the surface potential φ
s
of the
testing surface. The controller displays the measured surface potential on an LED indicator
and also delivers the analog voltage to a BNC jack for automated data collection. The
electrostatic voltmeter system used has a range of±100 V and an accuracy of 50 mV .
4.3 Experimental Setup
Fig. 4.3 shows the experimental setup of packed dust layer charging in a vacuum chamber.
JSC-1A lunar regolith simulant is tamped to a layer with thickness d = 10 mm above a
grounding plate. A gridded electron bombardment ion source is positioned above the dust
layer surface with center line offsetz = 2” (50.8 mm). Surface potential and plasma param-
eters were probed over a region between 13” (330.2 mm) and 17” (431.8 mm), denoted as
x in the figure, away from the ion source exit.
To diagnose the plasma field above the surface, a Langmuir probe, nude Faraday probe
and emissive probe scanned local plasma to obtain electron temperature (T
e
), electron num-
ber density (n
e
), ion current density (J
i
) and plasma potential (φ
p
) at 1” (25.4 mm) above
the dust surface to eliminate interference from the plasma sheath due to the floating top
71
Figure 4.3: Experimental setup of packed dust layer charging
layer surface. The Debye length of plasma close to the surface with this ion source config-
uration is about 15 mm based on measurement. Fig. 4.4 shows the setup of various electric
probes above the test bed.
4.3.1 Vacuum System
The stainless steel vacuum chamber for this experiment in Fig. 4.5 measures 0.91 m in
diameter and 1.2 m in length with an attached cryogenic high vacuum pump.
To operate the chamber, a mechanical vane pump first roughs down the vacuum system
to 50 mTorr within 45 minutes. Then the gate valve is opened by a pneumatically driven
actuator to expose the chamber to the cryogenic pump after shutting off the mechanical
pump system. In 5 minutes, the cryogenic pump further lowers the chamber floor pressure
to 4×10
−7
Torr and is capable of pumping argon at 8,500 L/s.
72
Figure 4.4: Different probes employed for surface potential measurement and plasma diag-
nostics
4.3.2 JSC-1A Lunar Regolith Simulant
JSC-1A lunar regolith simulant was used to be charged in the experiment to study packed
dust charging on a surface. JSC-1A simulant has a dominant size distribution between 10
μm and 1 mm with densityρ
d
=2.928×10
3
kg/m
3
and relative permittivityε
rd
=4.29 [60, 71].
JSC-1A dust simulant stored at room condition absorbs water and captures air from the
environment, causing rapid eruption of air and water molecules without pretreatment when
the vacuum chamber is below 10 Torr. Under such a circumstance, dust particles fly away
from the test bed due to outgassing, leaving dents on the top surface. Fig. 4.6 and 4.7 show
the top surface of the dust test bed with 1” (25.4 mm) thickness before and after pumping,
respectively.
To avoid dust escaping from the test bed and contaminating the vacuum chamber, a
smaller dust pile of 10 cm in diameter and 10 mm in thickness was prepared. This thinner
pile (d=10 mm) facilitates air and water molecule escapement from both the top and side
without damaging the sample surface. However, if the dust layer is too thin, it is easy to
73
Figure 4.5: Vacuum chamber for experiments
be blown away during the chamber roughing process. The dust sample on the test bed is
pretreated and stored in the vacuum chamber overnight to ensure trapped water and air has
completely escaped.
4.3.3 Plasma Diagnostic Tools
Langmuir Probe
The tungsten Langmuir probe used in the experiment measures 5 mm in length and 0.5 mm
in diameter with a collecting area of 7.854 mm
2
. Fig. 4.8 is the Langmuir probe system for
plasma diagnostics.
In the schematic, the power supply amplifies a low voltage signal (-5 V to 5 V) gen-
erated from a computer data acquisition card to sweep the voltage between -30 V to 60 V
with the respect to vacuum chamber ground [29]. V oltmeters in a data logger, V
1
and V
2
,
74
Figure 4.6: Initial top surface of JSC-1A simulant sample without pretreatment
measure biased probe potential and voltage drop across the resistorR
Lp
= 5.5 kΩ, respec-
tively. Probe current at each biased potential is calculated in Eq. 4.10. In the experiment,
T
e
andn
e
come from analyzing the current-voltage plot of the Langmuir probe.
I
Lp
=
V
2
R
Lp
(4.10)
Faraday Probe
A nude Faraday probe was directly exposed to plasma flow to measure ion current density
J
i
. In Fig. 4.9, the stainless steel collecting surface faced the incoming plasma beam,
allowing for collection of axially flowing ions. The guard ring was concentric with the
collecting surface, having a gap of 2.0 mm between the two. The purpose of the guard ring
is to create a uniform sheath over the collecting surface by minimizing edge effects [51,
75
Figure 4.7: Top surface of JSC-1A simulant sample without pretreatment after pumping
down
86, 12]. The collecting surface outer diameter is 5.0 mm. Both the collecting surface and
guard ring were designed to be biased to an identical negative potential, -40 V with respect
to the facility ground.
The voltmeter in the circuit detects the voltage drop across the resistor R
Fp
with a
measured resistance of 119.1 kΩ. Ion current density is calculated in Eq. 4.11, whereA
Fp
is the collecting surface area of the nude Faraday probe.
J
i
=
V
R
Fp
A
Fp
(4.11)
76
Figure 4.8: Langmuir probe measurement system
Emissive Probe
Fig. 4.10 shows the emissive probe setup to measure local plasma potential. A piece of
tungsten with 0.5 mm in diameter is heated by 6 V AC current and emits thermionic elec-
trons. Wires are wrapped in a double-bore quartz tube with only a small tip of filament
exposed to the plasma. The filament will eventually reach the same potential of surround-
ing plasma [20, 64, 28, 85, 20].
Unlike obtaining plasma potential from the I-V curve of a Langmuir probe, plasma
potential is directly measured by the emissive probe diagnostics. The floating voltage mea-
sured by the voltmeter in the schematic is the same as plasma potential,φ
p
at this location.
In addition, direct measurement eliminates error caused by manually fitting the Langmuir
I-V curve to calculateφ
p
.
77
Figure 4.9: Nude Faraday probe measurement system
4.3.4 3D Traversing System
The 3D traversing system in Fig. 4.11 was designed and fabricated to precisely move probes
for plasma diagnostics in the vacuum chamber, covering a measuring volume of 457 mm
× 432 mm× 254 mm. Thex arm is fixed on an aluminum board, guided by a rod and two
guiding rails, and they arm is driven by the slider moving in thex direction. On thez arm,
the slider moves in thez direction with probes attached to it.
78
Figure 4.10: Emissive probe measurement system
Motion System
The traversing system built for the chamber can move in three orthogonal directions, driven
by three stepper motors. Fig. 4.12 is the design of the motion system in thex direction.
Two bearing mounts hold two ball bearings and the guiding rod. The lead screw is
driven by the stepper motor, transporting the lead screw nut and the slider linearly in the
x direction. A universal joint connects the stepper motor and the lead screw to eliminate
any stress on the system due to fabrication or misalignment of assembly. On the slider, the
channel bar that holds they axis is mounted. Stepper motors in the traversing system have
a step angle of Δθ = 1.8
◦
(200 steps per turn of the stepper motor) and with the pitch of
the lead screw system of 5 turns per inch, the traversing system has an linear resolution of
1 mil (0.0254 mm) in each direction.
79
Figure 4.11: 3D traversing system
In order to ensure all moving parts work smoothly in the vacuum environment, the
traversing system was cleaned throughly and lubricated with vacuum grease, which has
low vapor pressure and a low outgassing rate.
Control System
The control method of the traversing system is open loop control without feedback and it
accurately positions probes for plasma diagnostics in the vacuum chamber.
Fig. 4.13 is the stepper motor control diagram. Six pins, 2 to 7, on the parallel port of a
computer are used to output control signals. Each motor requires 2 signals, a square wave
signal and direction signal, processed by the stepper motor control unit in Fig. 4.14, which
has three individual control circuit boards, to drive three unipolar stepper motors. The 50%
80
Figure 4.12: Design of traversing system
duty square wave signal defines the frequency and the signal of the direction pin, 0 or 1,
provides the direction of the motor shaft turns, clock wise or counter clock wise.
The stepper motor control drive was written in LabView to output control signals from
a desktop computer. The program reads a prepared path data file, which lists coordinates of
each point to be diagnosed in the scanning region, moving probes to the designated position
by writing digital signals to I/O port 0x378, the parallel port. The RPM is adjusted by the
frequency of the square wave signal. A full cycle of the square wave corresponds to the
time which it would take the stepper motor to rotate a step angleΔθ. Real time position of
all three components are updated and displayed in the graphic user interface (GUI) of the
LabView program.
4.3.5 Data Acquisition and Control System
The data acquisition and control system is specially designed and built to control the 3D
traversing system and collect probe data automatically inside the vacuum chamber. A main
LabView interface calls all sub functions such as the stepper motor control driver, voltage
output and data logger communication, and displays real time information on the screen
81
Figure 4.13: Stepper motor control diagram
for system monitoring, including coordinates of probe location, speed of stepper motors
and the stepper motor in operation.
In the data acquisition and control flow chart (Fig. 4.15), a National Instruments
R
NI
PCI-6010 Data acquisition card in the computer outputs an analog signal to sweep the
biased voltage of the Langmuir probe through an amplifier. The Agilent
R
34970A data
logger records I-V curve information and sends data to the computer via RS 232 port for
post data processing. The data logger also collects voltage signals from the Faraday probe,
emissive probe and electrostatic voltmeter controller for further data processing.
The 3D traversing system moves all four probes in the diagram to a specific position
for diagnostics. The stepper motor control system has an open control loop for all three
motors. Since each motor turn step is synchronized with the rising edge of the square wave
and the traversing system is operating at low speed, the linear accuracy of the traversing
system is high, omitting the need for linear displacement feedback sensors such as linear
variable differential transformers (LVDT) for precision enhancement.
82
Figure 4.14: Stepper motor control unit
4.3.6 Ion Source Development
An alternative method for fabricating ion optics grids is fully developed to build up an ion
source to generate fast moving ions at around 100 km/s for experimental applications. This
method uses a photochemical etching process which fabricates the grid pattern directly
from a computer print out using computer aided design (CAD). First the grid is designed
with CAD software and the pattern is laser printed on a transparency sheet. Using photore-
sist film and a developer solution, the design pattern is then transferred to the grid material.
Finally, the material is etched in hydrochloric (HCl) acid solution to form an ion optics
grid directly corresponding to the CAD drawing. It is noticed that this method provides an
efficient and inexpensive grid production process. The entire grid manufacturing process
takes approximately 3 hours, including design pattern preparation on transparency sheets,
laminating photoresist on aluminum sheets, exposing and developing photoresist film, and
chemical etching.
83
Figure 4.15: Data acquisition and system control flow
Grid Design and Fabrication
Fig. 4.16 shows a CAD generated design of a typical ion optics grid design pattern. This
grid is 7.5 cm in diameter with hexagonally distributed grid openings and three mounting
holes and one wiring hole, which are all also photochemically etched. The grid thickness
t is 0.02” (0.508 mm), and hole size and grid spacing are selected with respect to the local
Debye length λ
d
, which is about 3.3 mm close to the discharge chamber exit, calculated
from Eq. 4.12, based on plasma parameters measured without ion optics grids (T
e
≃ 2 eV
and n
e
≃ 10
13
m
-3
). Individual grid holes must be smaller than 5λ
d
to allow a sheath to
form which covers the hole and the grid spacing must be within the plasma sheath thickness
(λ
sh
= 0.408 mm withV
tot
= 1200 V from Eq. 4.13) [4] to prevent ion current limitation.
The grid geometry is shown in Fig. 4.17, where d, D and t
w
are hole diameter, hole
spacing and web thickness respectively. The set of ion optics was fabricated after several
84
iterations to achieve better performance. The design dimensions for both grids are shown
in Table 4.1. The total grid opening area is 4 cm in diameter for enhanced beam concentra-
tion. The screen grid and acceleration grid share the sameD but different d and t
w
which
satisfy the relation described in Eq. 4.14. Figs. 4.18 and 4.19 display developed grid design
patterns attached to aluminum sheets, and Figs. 4.20 and 4.21 show the fully etched grids.
λ
D
=
r
ε
0
kT
e
n
e
e
2
(4.12)
λ
sh
= 1.02λ
D
eV
tot
kT
e
3
4
(4.13)
Figure 4.16: Design pattern of the grid
D = d+t
w
(4.14)
85
Figure 4.17: Geometry of hexagonal grid
Table 4.1: Dimensions of grid holes
Grid type d, mm D, mm t
w
, mm
Screen grid 1.0 2.0 1.0
Acceleration grid 0.5 2.0 1.5
Compared with traditional machining and laser cutting, photochemical etching has
higher accuracy and exerts no mechanical stress or heat concentration on parts, effectively
preventing deformation. The design pattern was created with CAD software and laser
printed negatively on a transparency sheet, covering the area to be eroded with black car-
bon. The pattern was then attached to a thin metal sheet of thicknesst and coated on both
sides with negative photoresist film. After 45 minutes of exposure to fluorescent light, the
grid pattern was developed in a dark room by washing away photoresist on the regions to
be etched with a developer solution. The prepared sample was next submerged in 19% HCl
86
Figure 4.18: Developed screen grid pattern
Figure 4.19: Developed acceleration grid pattern
acid solution for 15 minutes while bagged ice was added to remove the heat generated dur-
ing the chemical reaction in order to maintain steady state solution temperature to prevent
the detachment of photoresist from the metal sheet without diluting the solution.
87
This process is much more streamlined and cost effective than the standard method,
such as that applied to chemically etch NASA’s NSTAR ion engine molybdenum grids [31,
27, 90, 91, 87]. Fig. 4.20 and 4.21 show the fully etched screen grid and acceleration
grid, respectively. Aluminum (Type 3003-H14) was utilized in this test case due to its
affordability and accessibility, compared with molybdenum.
Figure 4.20: Screen grid
Ion Source Configuration
To demonstrate the effectiveness of the grid fabrication process, ion optics grids were
applied to an argon ion source and measured the beam flow field. A 7.5 cm diameter
electron bombardment ionization chamber was used to generate argon plasma, over which
a stand and grid mounts were machined to enable ion optics attachment.
Fig. 4.22 shows the assembled ion source with the screen grid, acceleration grid and a
steel mesh enclosure for testing in the vacuum chamber. Fig. 4.23 shows the ion source
configuration for testing in the vacuum chamber. Ceramic spacers were installed to set
88
Figure 4.21: Acceleration grid
the acceleration-to-screen grid spacing at 1.270 mm and the acceleration grid-to-enclosure
spacing at 0.635 mm.
The ion source electrical circuit is illustrated in Fig. 4.24. Four power supplies were
used (V
fil
,V
ano
,V
bias
, and V
acc
) to operate the ion source. Power supplies for the filament
and anode were referenced to the high bias voltage and insulated by an isolation trans-
former to prevent high voltage discharge of internal circuits. Argon gas flows through the
back of the ionization chamber, and is ionized by thermal electrons boiled off of the hot
tungsten filament surface. In the region between the ring magnets and the back magnet, a
magnetic field confines electrons and gyrates them along the magnetic field lines to enhance
collisions with and ionization of the neutral argon gas. The ionization chamber is biased
to 1.1 kV above ground and the acceleration grid is set at about 200 V below the ground.
The total acceleration voltageV
tot
is the summation ofV
bias
andV
acc
. The anode cup, 40 V
higher than the ionization chamber, absorbs low energy electrons after collision to maintain
continuous ionization. The ion optics work as a pair of plasma lens to focus and accelerate
89
Figure 4.22: Assembled ion source in the enclosure
ions. The enclosure is grounded to screen the accelerated beam from the high voltage inter-
nal components and prevent potential perturbations. An external hot filament neutralizer is
placed 3 cm from the beam exit to neutralize the ion beam during operation.
Ion Optics Testing
The ion source was placed in the 0.9 m diameter, 1.2 m long stainless steel vacuum cham-
ber pictured in Fig. 4.25. The chamber is attached to a cryogenic pump which creates a
high vacuum environment with pressure on the order of 10
−6
to 10
−5
Torr with argon gas
flowing. Electrostatic probes mounted on the 3D traversing system scanned the beam flow
field.
A nude Faraday probe was directly exposed to plasma flow for ion current density
measurement [29]. The collecting surface is 8 mm in diameter with a surrounding guard
ring to minimize edge effects [86], and both were biased to -40 V with respect to ground.
An emissive probe measured potential at each data point. The probes scanned 2D ion
current density and potential contours in the longitudinal and radial directions, z and r
90
Figure 4.23: Ion source configuration
respectively in the contour plots. The origin of the coordinate system is 5 cm downstream
of the ion beam exit plane in order to measure a fully developed and sufficiently neutralized
beam as well as to protect the probes.
Figs. 4.26 and 4.27 are photos of an ion beam generated by the source in the chamber
with neutralizer off to enhance visibility. Figs. 4.28 to 4.29 give ion density and potential
contours of two cases with operating conditions listed in Table 4.2.
Ion beam plumes are clearly observed in the ion density contours with concentrated
current density close to the source exit. J
i
at the origin is at least one order of magnitude
higher than theJ
i
outside the beam, proving the set of ion optics grids are able to focus the
ion beam effectively. The potential in the beam region is between 10 V and 30 V , much
lower than the beam extraction voltageV
tot
, indicating that the ion beam is well neutralized
as shown in Figs. 4.30 and 4.31.
91
Figure 4.24: Ion source circuit
Table 4.2: Operating conditions of the ion source
Case P
c
, Torr ˙ m, sccm I
beam
, mA V
fil
, V I
fil
, A V
acc
, V
1 1.0×10
−5
3.9 6 9.5 7.3 200
2 6.3×10
−6
3.9 10 10.4 7.6 200
Case V
ano
, V I
ano
, A V
bias
, V φ
acc
, V V
tot
, V
1 44.2 0.23 1100 -200 1300
2 44.4 0.50 1100 -200 1300
Summary of Ion Source Testing
In conclusion, the ion optics fabrication method developed is efficient and cost saving; for
instance, it only takes approximately 3 hours and 20 dollars to fabricate one specifically
designed set of ion optics grids used in our study. The source is reliable to be utilized in the
vacuum chamber for plasma applications. The method has the potential to greatly decrease
both the experimental turn-around time for ion optics design and the total associated project
cost. Visual confirmation of the ion beam and performance test results show the set of ion
optics grids was properly fabricated and focuses the ion beam correctly.
92
Figure 4.25: Vacuum chamber for testing
4.3.7 Procedure of Surface Charge Density Measurement and Plasma
Diagnostics
Fig. 4.32 is the top view of the experimental setup (not to scale) to scan the dust surface
and measure plasma above that. All four probes are mounted on the frame of the traversing
system with certain separations to eliminate interference. In the xy plane, the Langmuir
probe is 1” west to the Faraday probe; the emissive probe is 1” north to the Faraday probe;
the electrostatic voltmeter probe is 2.5” north to the Faraday probe.
The following is the procedure of running a single charging case when the vacuum
chamber is already under high vacuum with the cryogenic pump exposed.
1. Start the ion source and turn on the neutralizer
2. Turn on the emissive probe filament, scan the region and return to the start point
3. Turn off the emissive probe filament
4. Move the 3D traversing system by 1” in the positivey direction
93
Figure 4.26: Side view of extracted ion beam with neutralizer off
Figure 4.27: View 2 of the extracted ion beam with neutralizer off
5. Scan the region with Langmuir probe and Faraday probe then return to the start point
6. Move the 3D traversing system by 2.5” in the negativey direction
7. Turn off the ion source and neutralizer at the same time
8. Scan the region with the electrostatic voltmeter probe and return to the start point
94
z, mm
r, mm
100 150 200 250 300 350 400 450
-200
-150
-100
-50
0
50
100
J
i
, A/m
2
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
Figure 4.28: Ion current density contour of Case 1 with neutralizer on
z, mm
r, mm
100 150 200 250 300 350 400 450
-200
-150
-100
-50
0
50
100
J
i
, A/m
2
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
Figure 4.29: Ion current density contour of Case 2 with neutralizer on
95
z, mm
r, mm
100 150 200 250 300 350 400 450
-200
-150
-100
-50
0
50
100
ϕ, V
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
-2
Figure 4.30: Potential contour of Case 1 with neutralizer on
z, mm
r, mm
100 150 200 250 300 350 400 450
-200
-150
-100
-50
0
50
100
ϕ, V
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
-2
Figure 4.31: Potential contour of Case 2 with neutralizer on
96
Figure 4.32: Top view of the experimental setup inside the chamber and relative probe
locations
4.4 Measurement of Dusty Surface Charging
4.4.1 Experimental Case
Three cases have been tested with the ion source conditions listed in Tab. 4.3 where I
beam
is the total ion current andI
neu
is the electron emission current from the neutralizer. Differ-
ent emission current settings lead to different surface potential and surface charge density
states; however, at any given location, surface potential φ
s
and surface charge density σ
depends upon the local current density rather than the overall current.
Figs. 4.33 to 4.41 show the plasma parameters as a function of the distance from the
plasma source,x,φ
p
,T
e
,n
e
,J
i
,φ
s
, from measurements. Here,v
i
,n
i
J
e
andσ are calculated
from Eq. 4.15, 4.16, 4.17 and 4.7 respectively.
v
i
=
s
2e(φ
0
−φ
p
)
m
i
(4.15)
97
Table 4.3: Operating conditions of the plasma source
Case P
c
, Torr ˙ m, sccm I
beam
, mA V
fil
, V I
fil
, A V
acc
, V
1 4.5×10
−6
4.8 5.02 9.08 8.0 200
2 6.2×10
−6
4.7 4.80 8.80 8.0 200
3 4.9×10
−6
4.9 1.88 7.00 7.0 200
Case V
ano
, V I
ano
, A V
bias
, V φ
acc
, V V
tot
, V I
neu
, mA
1 50.3 0.13 1000 -200 1200 2.90
2 50.3 0.10 1000 -200 1200 4.50
3 50.2 0.01 1000 -200 1200 6.73
n
i
=
J
i
ev
i
(4.16)
J
e
= en
e
r
kT
e
2πm
e
(4.17)
Where,φ
0
=1000 V is the total potential of argon ions when they were generated at zero
velocity in the ionization chamber of the ion source.
4.4.2 Error Analysis
The Langmuir probe data contains fitting error of about 20% for n
e
and T
e
measurements
in the experiment [99], causing fluctuation of those two parameters and calculatedJ
e
in the
plots.
Eq. 4.18 is the calculation of error propagation of σ and two measured parameters are
included. δV
s
=50 mV is the accuracy of the electrostatic voltmeter as stated in the manual
instruction. Thickness d of the JSC-1A dust sample in the equation was measured by a
ruler with resolution of δd=0.5 mm which is applied in the equation for error propagation
calculation.
98
320 340 360 380 400 420 440
−15
−10
−5
0
5
10
15
20
x, mm
φ
p
, V
Case 1
Case 2
Case 3
Figure 4.33: Plasma potential vs distance
320 340 360 380 400 420 440
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x, mm
T
e
, eV
Case 1
Case 2
Case 3
Figure 4.34: Electron temperature vs distance
99
320 340 360 380 400 420 440
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10
12
x, mm
n
e
, m
−3
Case 1
Case 2
Case 3
Figure 4.35: Electron density vs distance
320 340 360 380 400 420 440
0
1
2
3
4
5
6
7
8
9
x 10
13
x, mm
n
i
, m
−3
Case 1
Case 2
Case 3
Figure 4.36: Ion density vs distance
100
320 340 360 380 400 420 440
0
0.05
0.1
0.15
0.2
0.25
x, mm
J
e
, A/m
2
Case 1
Case 2
Case 3
Figure 4.37: Electron current density v.s. distance
320 340 360 380 400 420 440
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x, mm
J
i
, A/m
2
Case 1
Case 2
Case 3
Figure 4.38: Ion current density above the testing surface
101
320 340 360 380 400 420 440
6.85
6.9
6.95
7
x 10
4
x, mm
v
i
, m/s
Case 1
Case 2
Case 3
Figure 4.39: Ion velocity vs distance
320 340 360 380 400 420 440
5
10
15
20
25
30
35
40
x, mm
φ
s
, V
Case 1
Case 2
Case 3
Figure 4.40: Surface potential vs distance, error bar:±50 mV for all points
102
320 340 360 380 400 420 440
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
x 10
−7
x, mm
σ, C/m
2
Case 1
Case 2
Case 3
Figure 4.41: Surface charge density vs distance
δσ = σ
s
δV
s
V
s
2
+
δd
d
2
(4.18)
4.4.3 Dust Charging Results
Fig. 4.42 shows measured charge Q
d
on a dust particle. As the dust, have a distribution
of size, ranging from 10 μm to 1000 μm. In these plots, we assume several different dust
radii. The dust chargingQ
d
is calculated according to Eq. 4.3. Fig. 4.43 shows the charge
to mass ratio R
cm
, calculated using Eq. 4.4. Six Surface charge density σ, from 2× 10
−8
C/m
2
to1.4×10
−7
C/m
2
measured in the experiment, are selected.
At a known surface charging state (at fixed σ), large dust grains are able to hold more
charge; however, small dust particles react more sensitively to external electric or applied
fields sinceQ
d
is proportional to the square of dust size and R
cm
is inversely proportional
to dust size.
103
10
1
10
2
10
3
10
−18
10
−17
10
−16
10
−15
10
−14
10
−13
10
−12
r
d
, μm
Q
d
, C
σ = 2× 10
−8
C/m
2
σ = 4× 10
−8
C/m
2
σ = 7.5× 10
−8
C/m
2
σ = 1× 10
−7
C/m
2
σ = 1.2× 10
−7
C/m
2
σ = 1.4× 10
−7
C/m
2
Figure 4.42: Charge deposited on dust particles vs the radius of dust at different surface
charge density states on the log-log scale
10
1
10
2
10
3
10
−9
10
−8
10
−7
10
−6
10
−5
r
d
, μm
R
cm
, C/kg
σ = 2× 10
−8
C/m
2
σ = 4× 10
−8
C/m
2
σ = 7.5× 10
−8
C/m
2
σ = 1× 10
−7
C/m
2
σ = 1.2× 10
−7
C/m
2
σ = 1.4× 10
−7
C/m
2
Figure 4.43: Charge to mass ratio of dust particles vs the radius of dust at different surface
charge density states on the log-log scale
104
From the JSC-1A dust charging experiment, the measured charge to mass ratio ranges
from (5.1±0.3)×10
−9
C/kg to (3.6±0.2)×10
−6
C/kg and the measured dust charge ranges
from (6.3±0.3)×10
−18
C to (4.4±0.2)×10
−13
C.
Fabian et al. [30] tested charging of JSC-Mars-1 Martian regolith simulant with radius
r
d
≈ 50μm. Tab. 4.4 compares the ranges ofQ
d
andR
cm
between measured results from
the experiment and those measured by Fabian et al.. Results show that both charge and
charge to mass ratio of a dust on a dusty surface are lower than the single isolated case.
This is due to lower self-capacitance caused by dust interactions.
Table 4.4: Comparison of dust charge and charge to mass ratio
MinQ
d
, C MaxQ
d
, C
Experiment (1.57±0.08)×10
−16
(1.10±0.06)×10
−15
Fabian et al. (3.2±0.3)×10
−14
(1.28±0.03)×10
−13
MinR
cm
, C/kg MaxR
cm
, C/kg
Experiment (1.03±0.05)×10
−7
(7.1±0.4)×10
−7
Fabian et al. (2.0±0.2)×10
−5
(7.8±0.2)×10
−5
4.4.4 Discussions
Plasma potential in each case fluctuates within 5 V across the probing area in the x direc-
tion, indicating a relative stable plasma field within this 10-cm region during the whole
experiment, a ten-minute period. It is reasonable that higher total current input leads to
higher plasma potential (φ
p1
> φ
p2
> φ
p3
) close to the beam center line. As a result, ion
velocity calculated based on low ion temperature shows little change in velocity profile
along thex axis. The difference inv
i
for each case is within 200 m/s in Fig. 4.39.
In all three cases, dust surface potential (Fig. 4.40) is higher than plasma potential
(Fig. 4.33) measured by the emissive probe because in the probing area of this experimental
105
configuration, local ion current density was at least one order of magnitude higher than the
electron density. This is also observed in the ion and electron number density above the
surface in Figs. 4.36 and 4.35.
Surface potential of the top dust layer satisfies the net current density above the surface.
In the experiments, (J
i
−J
e
)
1
> (J
i
−J
e
)
2
> (J
i
−J
e
)
3
, therefore at any given location
x, φ
S1
|
x
> φ
S2
|
x
> φ
S3
|
x
. The overall trend of the three curves in Fig. 4.40 shows that
the surface potential decreases asx increases, resulting in the same trend of surface charge
densityσ. Since regions close to the source exit contain more ions than electrons compared
to those further away in Figs. 4.30 and 4.31, surface locations closer to the exit have higher
floating potentials and higher surface charge densities accordingly.
10 mm is the only possible dust layer thickness which can be tested in the current lab
vacuum facility since a thinner dust layer will not hold its shape firmly and be blown away
easily during the chamber roughing process and a thicker dust layer will trap to much air
and water vapor, causing sudden ejection of dust from the surface under vacuum. There is
no data available from the experiment showing how the sample thickness could affect the
surface potential and surface charge density.
4.5 Conclusion
In this chapter, an experiment is developed to measure the charging of a dusty layer in the
plasma environment. Surface potential and charge density of a dust layer charged by plasma
were measured by a non-contacting method without disturbing the existing electric field.
The charge deposited on single dust particles and charge to mass ratio were calculated from
the measurement by assuming different dust radii. We find that the charge to mass ratio
ranges from (5.1±0.3)×10
−9
C/kg to (3.6±0.2)×10
−6
C/kg and the dust charge ranges
from (6.3±0.3)×10
−18
C to (4.4±0.2)×10
−13
C.
106
Chapter 5: Comparison of Dust
Charging Models
5.1 Introduction
The objective of the study is to find out which charging model is more accurate. This
chapter compares the approximate dust capacitance models derived in Chapter 2 with the
measurement of JSC-1A lunar regolith simulant in Chapter 4. Additionally, the single-dust
charging measurement from previous studies [79] is also compared here.
5.2 Comparison
Tab. 5.1 shows the models and results to be compared in this section.
Table 5.1: Measurements and models for dust charging
Measurement: dust on dusty surface in plasma
Measurement: single dust charging by Sickafoose et al. [79]
Model: single dust in space
Model: single dust on surface
Model: dusty plasma
Model: dusty surface in plasma
Fig. 5.1 compares the single dust charging results by Sickafoose et al. [79] and different
models. Sickafoose’s experimental results follow the single isolated dust in space model,
which agrees with the experimental condition. The single isolated dust on surface model
shows higher charge at the same dust potentials. In the dusty plasma case, the charge on
a dust particle starts to deviate from the experimental results. In the dusty plasma case,
when dust particles stay closer to their neighbors (smaller n
−1/3
d
/λ
D
), the charge on each
107
10 10.2 10.4 10.6 10.8 11 11.2 11.4 11.6 11.8 12
4
5
6
7
8
9
10
11
x 10
−15
φ
d
, V
Qd, C
Experiment data, Sickafoose et al.
Single dust in space
Dusty plasma, n
−1/3
d
/λ
D
=0.2
Dusty plasma, n
−1/3
d
/λ
D
=0.15
Single dust on surface
Dusty surface, n
−1/2
d
/λ
D
=0.2
Dusty surface, n
−1/2
d
/λ
D
=0.15
Figure 5.1: Potential vs dust charge comparison between experimental results by Sick-
afoose et al. and different models
particle deviates more from that calculated by the single isolated model. Similarly, in the
dusty surface in plasma model, when n
−1/2
d
/λ
D
is decreasing, the charge on each particle
deviates more from that calculated by the single dust on surface model.
Figs. 5.2 and 5.3 compare the experimental results and dusty plasma models. One data
point of the surface charging experiment and one data point of Sickfoose’s result are used
in the comparison. The models used are the single dust model and dusty plasma model
(approximation 3 and 4). Approximation 3 is the overestimated calculation considering
108
all other dust particles are sitting at the distance of d
n
= n
−1/3
d
. Approximation 4 uses
the average inter-dust distance d = 3/4λ
D
to do the calculation. Plots show that all three
calculations are not applicable to the surface charging case. The single dust model ignores
all other dust around, giving the charge about two to three orders of magnitude higher
than the actual measurement. Both dusty plasma approximations fail to provide reasonable
values, showing charge on the dust lower than the elementary charge.
Figs. 5.4 and 5.5 compare the experimental results, the same as above, single dust
model and dusty surface in plasma model (approximation 2, 3 and 4). Approximation 2 is
the underestimated calculation considering the interaction form neighboring dust particles
only. Approximation 3 is the overestimated calculation considering all other dust particles
are sitting at the distance of d
n
= n
−1/2
d
. Approximation 4 uses the averaged inter-dust
distance d = 2/3λ
D
to do the calculation. Results show that both single dust model and
single dust on surface model are not applicable here for the same reason. Approximation 2
shows the charge is two orders of magnitude higher than the measurement as it only con-
siders the interaction from the closet dust. Approximation 3 fails to provide a reasonable
charge estimation, showing that the charge on the dust is lower than the elementary charge.
Approximation 4 using the averaged inter-dust distance shows the most accurate estima-
tion, 46% higher than the measurement. Hence, we consider this approximate analytical
model is applicable to calculate the charge on a dust resting on a dusty surface in plasma.
109
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
1
2
3
4
5
6
7
8
x 10
−15
n
−1/3
d
/λD
Qd, C
Experiment data, surface charging
Experiment data, Sickafoose et al.
Single dust in space
Dusty plasma, approximation 4
Dusty plasma, approximation 3
Figure 5.2: Effective separation vs dust charge comparison of surface charging experimen-
tal result (φ
d
= 10.60 V ,Q
d
= (1.26±0.13)×10
−17
C), experimental result by Sickafoose
et al. (φ
d
= 10.80 V ,Q
d
= (6.0±1.1)×10
−15
C) and different dusty plasma models
10
−3
10
−2
10
−1
10
0
10
−24
10
−22
10
−20
10
−18
10
−16
10
−14
n
−1/3
d
/λD
Qd, C
Experiment data, surface charging
Experiment data, Sickafoose et al.
Single dust in space
Dusty plasma, approximation 4
Dusty plasma, approximation 3
Figure 5.3: Effective separation vs dust charge comparison of surface charging experimen-
tal result (φ
d
= 10.60 V ,Q
d
= (1.26±0.13)×10
−17
C), experimental result by Sickafoose
et al. (φ
d
= 10.80 V , Q
d
= (6.0± 1.1)×10
−15
C) and different dusty plasma models on
the log-log scale
110
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
1
2
3
4
5
6
7
8
x 10
−15
n
−1/2
d
/λD
Qd, C
Experiment data, surface charging
Experiment data, Sickafoose et al.
Single dust in space
Single dust on surface
Dusty surface, approximation 2
Dusty surface, approximation 4
Dusty surface, approximation 3
Figure 5.4: Effective separation vs dust charge comparison of surface charging experimen-
tal result (φ
d
= 10.60 V ,Q
d
= (1.26±0.13)×10
−17
C), experimental result by Sickafoose
et al. (φ
d
= 10.80 V , Q
d
= (6.0± 1.1)× 10
−15
C) and different dusty surface in plasma
models
10
−3
10
−2
10
−1
10
0
10
−20
10
−19
10
−18
10
−17
10
−16
10
−15
10
−14
n
−1/2
d
/λD
Qd, C
Experiment data, surface charging
Experiment data, Sickafoose et al.
Single dust in space
Single dust on surface
Dusty surface, approximation 2
Dusty surface, approximation 4
Dusty surface, approximation 3
Figure 5.5: Effective separation vs dust charge comparison of surface charging experimen-
tal result (φ
d
= 10.60 V ,Q
d
= (1.26±0.13)×10
−17
C), experimental result by Sickafoose
et al. (φ
d
= 10.80 V , Q
d
= (6.0± 1.1)× 10
−15
C) and different dusty surface in plasma
models on the log-log scale
111
Tab. 5.2 shows the comparison between results of the dusty surface charging experi-
ment and four models at different three dust sizes. Packed dust conditions are used for
calculation (d
n
/λ
D
= 2ˆ r
d
, with λ
D
≃ 15 mm in the experiment). Results calculated from
the single dust model and the single dust on surface model show that charges are two orders
of magnitude higher than the measured dust charge. The dusty plasma model shows one
order of magnitude lower in dust charge. The approximate dusty surface in plasma model
developed in Chapter 2 shows the best estimation compared with experimental results with
error about +50% to +60%, more accurate than any other model compared.
Table 5.2: Comparison of dust charging models
r
d
,μm MeasuredQ
d
, C Single dustQ
d
, C Single dust on surfaceQ
d
, C
50 (5.9±0.6)×10
−16
1.1×10
−13
1.5×10
−13
100 (2.3±0.2)×10
−15
2.2×10
−13
3.0×10
−13
500 (5.9±0.6)×10
−14
1.1×10
−12
1.5×10
−12
r
d
,μm MeasuredQ
d
, C Dusty plasmaQ
d
, C Dusty surfaceQ
d
, C
50 (5.9±0.6)×10
−16
1.2×10
−17
9.3×10
−16
100 (2.3±0.2)×10
−15
1.0×10
−16
3.7×10
−15
500 (5.9±0.6)×10
−14
1.2×10
−14
8.8×10
−14
5.3 Calculation of Dust Charging on the Lunar Surface
Figs. 5.6 and 5.7 show the charge and charge to mass ratio of a dust with typical diameters,
resting on the lunar surface, densely packed with other neighboring dust (d
n
= 2r
d
) calcu-
lated by the dusty surface in plasma model, assuming the Debye length of the lunar plasma
isλ
D
≃ 10 m and the dust is charged to 10 V .
112
0 50 100 150 200 250 300 350 400 450 500
0
1
2
3
4
5
6
7
8
x 10
−17
r
d
, μm
Q
d
, C
Figure 5.6: Charge on packed lunar surface dust vs dust size
0 50 100 150 200 250 300 350 400 450 500
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10
−9
r
d
, μm
Q
d
/m
d
, C/kg
Figure 5.7: Charge to mass ratio of packed lunar surface dust vs dust size
113
5.4 Conclusion
This chapter has compared experimental results with modeling results. Experimental
results of dusty surface charging show that the approximate analytical dusty surface in
plasma model is the most accurate, about 50% to 60% higher than the measurement. In par-
ticular, the commonly used single-dust charging model is off by two orders of magnitude
since this model ignores the dust interactions when the inter-dust distance is comparable to
the dust size. The previously compared single dust measurement in Chapter 4 also shows
a charging range two orders of magnitude higher than that of the measurement from the
dusty surface in plasma.
114
Chapter 6: Modeling the Interactions of
a Charged Dust with Surface Traveling
Waves
6.1 Introduction
This and the next chapter consider the physics and applications of dust manipulation on
a dusty surface. There are two major applications of dust manipulation in space. The
first is to mitigate the effects of dust accumulation on sensitive spacecraft surface. For
instance, to maintain a clean surface, if is desirable to develop a method to regularly remove
dust particles accumulated on solar panels and thermal radiators to maintain the operating
efficiencies of the photovoltaic effect [11] and thermal radiation [13]. The second is dust
sorting and segregation for resource prospecting. For instance, it is desirable to develop a
device that can sort dust within certain size or mass ranges for in-situ resource utilization
such as sorting raw materials for constructing habitats [7] without sophisticated mechanical
systems.
Dust particles are charged electrostatically by ambient plasma and/or photoelectron
emission on the lunar surface and surfaces of asteroids. Hence, one method to is to apply
an electric field to exert electrostatic force on the particles, However, using the electrostatic
field to move dust for a significant distance requires a large potential difference as it is
not viable to us a DC electric field. Previously, Calle et al. [16, 14, 15] and Kawamoto
et al. [55, 54] have proposed the use of traveling electrostatic waves on electrodynamic
screen (EDS) devices to move dust. In this dissertation, we consider using a traveling
electrostatic wave to transport charged dust in a more complex way. In this method, the
115
dust are confined by the potential well of the traveling wave. Fig. 6.1 shows the concept of a
traveling wave on an EDS device proposed by Masuda et al. [66]. The wave is propagating
in the x direction on a substrate at two time frames, t = t
1
and t = t
2
. The electrodes
on the substrate are biased by external power supplies at different potentials over time in
order to form the traveling wave . In this dissertation, we extend the previous concept of
transporting and removing dust particles to dust sorting and segregation.
Figure 6.1: Electrostatic traveling wave propagating in thex direction at two time frames,
t = t
1
andt = t
2
6.2 Dynamics of Dust Particles
The motion of a charged dust grain in the electric field is affected by three major forces,
including the Coulomb force, dielectrophoresis force and gravity [56] as shown in Eq. 6.1.
m
d
⇀ a =
⇀ F
Coulomb
+
⇀ F
dipole
+m
d
⇀ g (6.1)
116
⇀ F
Coulomb
and
⇀ F
dipole
[94] are calculated as follows:
⇀ F
Coulomb
= Q
d
⇀ E (6.2)
⇀ F
dipole
= 4πε
0
ε
rd
−1
ε
rd
+2
r
3
d
∇
⇀ E
2
(6.3)
Where, ε
rd
is the relative permittivity of dust, r
d
is dust radius assuming a spherical
dust. The Coulomb force in Eq. 6.2 is proportional to the charge Q
d
on the dust particle,
while the dielectrophoresis force is caused by a nonuniform electric field. The latter does
not require any charge on the particle and is proportional to the cube of dust size and the
gradient of the square of local electric field strength in Eq. 6.3.
Eqs. 6.4 and 6.5 show accelerations of dust particles due to Coulomb and dielec-
trophoresis force respectively. Here the dust is assumed to be a sphere. φ is the dust
floating potential with respect to the ambient plasma.
ˆ
C in the equation is the normalized
capacitance with respect to the self capacitance of a sphere. i.e.
ˆ
C = C/C
0
,C
0
= 4πε
0
r
d
.
One notes that the Coulomb acceleration is inversely proportional to the radius of the dust
particle. The dielectrophoresis acceleration is independent upon dust size and is only a
function of local electric field as long as the material property remains unchanged.
⇀ a
Coulomb
=
Q
d
⇀ E
m
d
=
4πε
0
r
d
ˆ
Cφ
4/3πr
3
d
ρ
d
⇀ E =
3φε
0
ˆ
C
r
2
d
ρ
d
⇀ E (6.4)
⇀ a
dipole
=
4πε
0
m
d
ε
rd
−1
ε
rd
+2
r
3
d
∇
⇀ E
2
= 3ε
0
ε
rd
−1
ε
rd
+2
∇
⇀ E
2
ρ
d
(6.5)
117
6.3 Concept of Dust Manipulation on a Dusty Surface
To manipulate dust, traveling waves are generated on an EDS board to move charged or
polarized particles in the wave propagation direction. Two types of waves are considered
here. One is a three-phase sinusoidal wave. The other is a four-phase square wave on each
electrode [55, 17].
If there is no ambient plasma, EDS may be used directly to move polarized dust grains.
On the other hand, if there is an ambient plasma, the EDS device must be placed in a
Faraday cage to screen out external electrical disturbances and plasma to avoid system
breakdown.
6.3.1 Sinusoidal Electrodynamic Wave
Fig. 6.2 shows a particle conveyor driven by 3-phase sinusoidal AC voltage. Phase voltage
of A, B and C are 120
◦
out of phase. Line electrodes are aligned parallely on a dielectric
substrate, and coated with dielectric thin film to increase the break down voltage.
Figure 6.2: Three-phase EDS dust conveyor
118
Assuming the offset of neighboring electrodes isΔs, electrodes are thin, the amplitude
of the AC power supply is V
0
, and the wavelength of the traveling wave is λ = 3Δs. The
approximation of the wave propagating in the+x direction on the electrode board (Fig. 6.3)
is given in Eq. 6.6. Where,g in the figure is the gravity pointing in the negativez direction.
Figure 6.3: Propagation of potential wave on EDS
V(x,t) = V
0
cos(ωt−kx) (6.6)
Where, ω is the angular frequency of the applied sinusoidal electric field and k =
2π
λ
is the wave number. The wave velocity is given in Eq. 6.7 and by changing the angular
frequency of the AC source, different wave phase velocity can be achieved for an electrode
pattern with given spacing.
v
p
=
ω
k
=
3ωΔs
2π
(6.7)
119
If the electric field has onlyx component and the edge effect of the electrodes is ignored,
the electric field yields:
⇀ E =−∇V =−
∂
∂z
V
0
cos(ωt−kx)ˆ x =−kV
0
sin(ωt−kx)ˆ x (6.8)
The motion of a single dust particle in thex direction is described by Eq. 6.9. If the gyro
radius of charged particles is large compared with the reference length then the Coulomb
forceQ
d
E is the only dominant force exerted on dust particles.
m
d
d
2
x
dt
2
= Q
d
E
x
=−Q
d
kV
0
sin(ωt−kx) (6.9)
A solution with constant velocity to the equation above is:
v
dz
= v
p
=
ω
k
, z =
ωt
k
(6.10)
In such a situation, the sin term on the right hand side equals zero and velocity of
particles is constant, i.e. dust particles are trapped in the potential well and travel with the
phase velocity of the wave. The fundamental idea of the conveying mechanism is moving
potential wells and similarly, other traveling waves are also capable of moving dust grains
perpendicular to the parallel electrodes.
6.3.2 Multi-phase Trapezoidal Electrodynamic Wave
Since it is difficult to generate sinusoidal electrodynamic waves in space, we propose a
simplified design using a multi-phase traveling trapezoidal wave for applications on future
missions on planetary surfaces. In this approach, we apply a trapezoidal wave on elec-
trodes, with the phase shift such that, there is one rising edge and one falling edge in a
wavelength. This generates the propagating wave as shown in Fig. 6.4 on the EDS board.
120
Figure 6.4: Propagation of a trapezoidal wave with amplitudeV
0
in the x direction at two
time frames,t = t
1
andt = t
2
The distance between each pair of electrodes is Δs, the wavelength of the trapezoidal
wave is λ = 4Δs in this case. The wave propagates a quarter of the wavelength every
time step (from t = t
2
to t = t
2
in Fig. 6.4) by biasing electrodes to either V
0
or−V
0
.
Accordingly, the electric field of the rising and falling edge in the x direction is given in
Eq. 6.11, whereV
pp
= 2V
0
is the peak-peak voltage of the traveling wave.
|E
x
| =
V
pp
Δs
(6.11)
Dust with different size or mass respond to different frequencies of the electrodynamic
wave, and as a result, dust can be sorted if a certain wave frequency is applied. A better
design of biasing each electrode independently is stated in the system development chapter.
121
6.4 Dust Manipulation Simulation
There are two key factors in understanding how charged or polarized dust moves in the
electric field. The first is the electric potential distribution above the EDS substrate when a
traveling electrodynamic wave is applied. The second is dust charging different dust charge
to mass ratios responds to different traveling wave frequencies. Hence, one must choose
the appropriate frequency of the applied traveling wave to move different charged dust.
The purpose of dust motion simulation is to find out the frequency response of dust
based on the charge to mass ratio. The code developed to simulate dust manipulation is a
particle tracing code written in Fortran 95. It is compiled and run on a Linux workstation
with two 3.07 GHz Intel Xeon 6-core processors and 48 GB DDR 3 memory.
6.4.1 Case Setup
The simulation is based on a 2D case setup withx, the horizontal andz, the vertical direc-
tions in Fig. 6.5 (not to scale). The offset between two neighboring electrodes is 2 mm and
periodic in the x direction. The dimension simulated in the z direction is chosen to be 50
mm.
The applied electrodynamic traveling wave has peak-peak voltage of 1000 V , biasing
electrode to either +500 V or -500 V during the simulation. The phase of the traveling wave
is shifted by 90
◦
every quarter of the wave period T to simulate wave propagation in the
+x direction byΔs. Fig. 6.6 shows the sequence of biased potential on 4 electrodes over a
single wavelength during one period.
6.4.2 Governing Equations
Poisson’s equation (Eq. 6.12) is the governing equation to determine the potential distri-
bution and the electric field is calculated by taking the negative gradient of potential in
Eq. 6.13.
122
Figure 6.5: Simulation case setup
∇
2
φ =−
ρ
ε
0
(6.12)
⇀ E =−∇φ (6.13)
6.4.3 Discretization
A second order central difference method is applied to discretize the left-hand side of
Eq. 6.13. At each location (i,j), ∇
2
φ
i,j
is calculated with potential at the current loca-
tion and information from north, south, west and east nodal points in Eq. 6.14, where
Δ = dx = dz =0.5 mm in the simulation. Fig. 6.7 shows the geographical locations of
neighboring nodes used in the calculation for assembling the matrix.
123
Figure 6.6: Biased potential shift sequence of four electrodes over one period from t = 0
tot = T
∇
2
φ
i,j
=
φ
i−1,j
+φ
i,j−1
−4φ
i,j
+φ
i,j+1
+φ
i+1,j
Δ
2
(6.14)
6.4.4 Computational Domain
The mesh used for solving the electric potential field is 32× 100 in x and z directions
respectively to seat one wavelength (λ
w
= 32Δ = 0.016 m) of the traveling wave. Fig.6.8
is the computational domain with locations of electrodes marked with arrows.
124
Figure 6.7: Geographical locations of nodal points for the central difference method
6.4.5 Boundary Conditions
Boundary conditions atx
min
andx
max
are periodic in order to simulate a long dust manipu-
lation device. Atz
max
, the potential is set to 0 V , and it is obvious that a metal cover should
be placed above the EDS device during dust transportation to screen out plasma to avoid
direct electric interaction.
On the bottom of the mesh, z
min
, the potential of nodal points between electrodes is
determined by liner interpolation to create a smooth trend assuming the x component of
electric field is uniform between each pair of neighboring electrodes atz = 0. Fig. 6.9 plots
the boundary condition applied at z = 0 for initialization. Due to the periodic boundary
conditions in the x direction, the whole field shifts by a quarter wavelength every T/4,
therefore, no additional field calculation is required after every shift.
6.4.6 Potential Calculation
Since plasma is screened out by a metal cover to prevent arcing and short circuits, in this
scenario, charge densityρ is 0 everywhere in the simulation domain. Therefore, the matrix
form of Eq. 6.12 becomes the Eq. 6.15. The total number of unknown points in the domain
125
Figure 6.8: Mesh for computational domain, locations of electrodes are marked
is 3168, 32 in thex direction and 99 in thez direction, leading to a 3168 by 3168 pentadi-
agonal sparse A matrix in Eq. 6.15. For fast computation and convergence, the conjugate
gradient method [48] was used to solve theφ vector by iteration.
(A)
⇀ φ
i,j
= 0 (6.15)
126
0 5 10 15 20 25 30
−1000
−800
−600
−400
−200
0
200
400
600
800
1000
x, Δ
V , V
nodal point
electrode
Figure 6.9: Initial boundary condition in thex direction atz = 0
6.4.7 Electric Field Parameter Calculation
Electric field calculation is based on the solved potential distribution of the computational
domain. The electric field of internal nodes inx andz is calculated from Eqs. 6.16 and 6.17.
At the left and right boundary,E
x
is calculated in Eq. 6.18 and 6.19 because of the periodic
boundary. To keep the second order accuracy ofE
z
at the lower and upper boundary, three
consecutive nodes are included in the calculation in Eq. 6.20 and 6.21.
E
i,j
|
x
=−
φ
i+1,j
−φ
i−1,j
2Δ
(6.16)
E
i,j
|
z
=−
φ
i,j+1
−φ
i,j−1
2Δ
(6.17)
127
E
i
min
,j
|
x
=−
φ
i
min
+1,j
−φ
imax−1,j
2Δ
(6.18)
E
imax,j
|
x
=−
φ
i
min
+1,j
−φ
imax−1,j
2Δ
(6.19)
E
i,j
min
|
z
=
1
Δ
3
2
φ
i,j
min
−2φ
i,j
min
+1
+
1
2
φ
i,j
min
+2
(6.20)
E
i,jmax
|
z
=
1
Δ
−
3
2
φ
i,jmax
+2φ
i,jmax−1
−
1
2
φ
i,jmax−2
(6.21)
Similarly, the gradient ofE
2
is determined by Eqs. 6.22 to 6.27 for the dielectrophoresis
force calculation on the dust particle.
∇E
2
i,j
x
=
E
2
i+1,j
−E
2
i−1,j
2Δ
(6.22)
∇E
2
i,j
z
=
E
2
i,j+1
−E
2
i,j−1
2Δ
(6.23)
∇E
2
i
min
,j
x
=
E
2
i
min
+1,j
−E
2
imax−1,j
2Δ
(6.24)
∇E
2
imax,j
x
=
E
2
i
min
+1,j
−E
2
imax−1,j
2Δ
(6.25)
∇E
2
i,j
min
z
=
1
Δ
−
3
2
E
2
i,j
min
+2E
2
i,j
min
+1
−
1
2
E
2
i,j
min
+2
(6.26)
∇E
2
i,jmax
z
=
1
Δ
3
2
E
2
i,jmax
−2E
2
i,jmax−1
+
1
2
E
2
i,jmax−2
(6.27)
128
6.4.8 Method of Wave Propagation for Simulation
Parameters P such as E
x
, E
z
, ∇E
2
x
and ∇E
2
z
are shifted every N
shift
time steps in the
simulation to create wave propagation (Eq. 6.28) and the corresponding wave frequency is
calculated in Eq. 6.29. SinceN
shift
is inversely proportional tof,N
shift
is chosen to have
at least two digits in the simulation to maintain appropriate accuracy off and the value of
dt used is adjusted accordingly. The propagation speed of the traveling wave is calculated
in Eq. 6.30. Fig. 6.10 shows the sequence of shifting and reusing field parameter every
quarter cycle.
T
4
= N
shift
dt (6.28)
f =
1
T
=
1
4N
shift
dt
(6.29)
v
w
= fλ
w
(6.30)
Figure 6.10: Sequence of shifting field parameters of the computational domain
129
To facilitate the dust pushing process, four states of each field parameter are stored in a
3D array in the Fortran code as shown in Fig. 6.11. The third dimensionk in the figure is
the 2D field array of the computational domain at that time.
Figure 6.11: Storage of each field parameter as a 3D array in the computer memory
6.4.9 Model of Dust in Traveling Wave
Weighed Average Field Parameter at Dust Location
Parameters of a dust particle at a certain location in a Δ by Δ cell is calculated based on
area weighed average in Fig. 6.12. The dust particle in the cell divides the cell into four
sections with areas of S
1
, S
2
, S
3
and S
4
respectively. Parameters such as E and∇E
2
for
moving dust are calculated using Eq. 6.31 with information stored at four vertices of the
cell.
¯
P
d
=
S
4
Δ
2
P
i,j+1
+
S
3
Δ
2
P
i+1,j+1
+
S
2
Δ
2
P
i,j
+
S
1
Δ
2
P
i+1,j
(6.31)
130
Figure 6.12: Area weighed average parameter of a dust particle within a cell
Physical Properties of Dust
The electric charge deposited on dust does not change over time during the simulation since
the time constant of charging or discharging a dust particle is on the order of hours [92]
according to the material property. The mass density of dust is ρ
d
= 3.0× 10
3
kg/m
3
and
the relative permittivity isε
rd
= 4.0.
Dust Behavior Modeling at Boundaries
Once a particle leaves the left or right boundary, it will be relocated and forced to enter
from the opposite side automatically in the code to satisfy the periodic boundary condition
and the actual position is updated.
The EDS plate at z = 0 is treated as an infinitively large hard plate and the collision
between the dust and plate is modeled as inelastic. the coefficient of restitution, C
r
is
introduced to calculate the velocity and height post collision in Eq. 6.32 and 6.33. C
r
=
131
0.658 is employed in the simulation as a typical value for collisions of glass and silicon
dioxide spheres with a hard plate.
v
′ z
=−C
r
v
z
(6.32)
z
′ = C
2
r
z (6.33)
When dust leaves from the upper boundary of the computational domain, it is regarded
as not able to be confined by the traveling wave and the simulation terminates.
6.5 Results and Analysis
6.5.1 Electric Field
Fig. 6.13 is the static potential distribution at t = 0 with the 4 wavelengths plotted in the
x axis for better visualization, and electric field lines are also shown in the contour with
arrows indicating the direction of theE field.
The maximum and minimum potentials exit at positions where electrodes are located.
Additionally, the magnitude of the electric field is higher near the electrodes, as electric
field lines are more concentrated.
Fig. 6.14 shows the the contour ofE
2
and the its gradient of the computational domain
att = 0 with the 4 wavelengths plotted along thex axis. The gradient ofE
2
points down-
ward, creating a major dielectrophoresis force which pushes dust particles to the substrate
regardless of the charging state. According to Eq. 6.5, the dielectrophoresis force per unit
mass exerted on a particle is proportional to∇
⇀ E
2
even if the particle carries no charge.
132
6.5.2 Dust Motion
According to the results of simulations conducted, dust in the traveling wave is either
moved with the wave or trapped. There is no result showing dust leaving the boundary
fromz
max
because the dielectrophoresis force in the field has a large component in the−z
direction, confining dust. In addition, collisions with the substrate lead to loss of momen-
tum and kinetic energy in thez direction.
Fig. 6.15 is the trajectory of the dust moving with the traveling wave and Fig. 6.16
shows the position and velocity history in 4× 10
6
time steps (R
cm
= 1.0× 10
−4
C/kg,
dt = 1.0× 10
−5
s, N
shift
= 400, f = 62.5 Hz). In the x direction, the dust particle is
actuated by the traveling wave electric field and its velocity in thex direction reaches 1 m/s
and fluctuates around that velocity afterwards. The displacement in thex axis continues to
increase, indicating a steady transportation behavior in the direction of the traveling wave
in the+x direction. The dust initially bounces in thez direction and the velocity converges
to 0 m/s due to energy loss caused by collisions. Eventually, the dust particle has a height
around 0 m.
Fig. 6.17 is the trajectory of the dust trapped within the traveling wave and Fig. 6.18
shows the position and velocity history in 4× 10
6
time steps (R
cm
= 1.0× 10
−4
C/kg,
dt = 1.0× 10
−5
s, N
shift
= 5, f = 5000 Hz). In this scenario, the dust particle responds
to such a high frequency that it is trapped in thex direction betweenx = 1 mm andx = 3
mm, bouncing back and forth. Thex velocity also has a similar periodic pattern as that ofx
position. In thez direction, the dust travels on the order of a fewμm with lowv
z
observed
from the result, i.e. it is well confined on the board.
133
x, m
z, m
0 0.01 0.02 0.03 0.04 0.05 0.06
0
0.01
0.02
0.03
0.04
0.05 ϕ, V
450
400
350
300
250
200
150
100
50
0
-50
-100
-150
-200
-250
-300
-350
-400
-450
Figure 6.13: Potential distribution and electric field lines
x, m
z, m
0 0.01 0.02 0.03 0.04 0.05 0.06
0
0.01
0.02
0.03
0.04
0.05
E
2
, V
2
/m
2
1E+11
9.5E+10
9E+10
8.5E+10
8E+10
7.5E+10
7E+10
6.5E+10
6E+10
5.5E+10
5E+10
4.5E+10
4E+10
3.5E+10
3E+10
2.5E+10
2E+10
1.5E+10
1E+10
5E+09
Figure 6.14: Distribution ofE
2
and its gradient lines
134
0 5 10 15 20 25 30
0
0.005
0.01
0.015
0.02
0.025
x , m
z , m
Figure 6.15: Trajectory of moved dust, R
cm
= 1.0× 10
−4
C/kg, dt = 1.0× 10
−5
s,
N
shift
= 400,f = 62.5 Hz
0 1 2 3 4
x 10
6
0
5
10
15
20
25
30
N
step
x , m
0 1 2 3 4
x 10
6
0
0.005
0.01
0.015
0.02
0.025
N
step
z , m
0 1 2 3 4
x 10
6
0
0.2
0.4
0.6
0.8
1
1.2
N
step
v
x
, m/s
0 1 2 3 4
x 10
6
−0.3
−0.2
−0.1
0
0.1
0.2
N
step
v
z
, m/s
Figure 6.16: Position and velocity history of moved dust, R
cm
= 1.0× 10
−4
C/kg, dt =
1.0×10
−5
s,N
shift
= 400,f = 62.5 Hz
135
1 1.5 2 2.5 3
x 10
−3
0
0.5
1
1.5
2
2.5
3
3.5
4
x 10
−6
x , m
z , m
Figure 6.17: Trajectory of trapped dust, R
cm
= 1.0× 10
−4
C/kg, dt = 1.0× 10
−5
s,
N
shift
= 5,f = 5000 Hz
0 1 2 3 4
x 10
6
1
1.5
2
2.5
3
x 10
−3
Nstep
x , m
0 1 2 3 4
x 10
6
0
1
2
3
4
x 10
−6
Nstep
z , m
0 1 2 3 4
x 10
6
−0.02
−0.01
0
0.01
0.02
N
step
vx , m/s
0 1 2 3 4
x 10
6
−4
−3
−2
−1
0
1
2
3
x 10
−3
N
step
vz , m/s
Figure 6.18: Position and velocity history of trapped dust, R
cm
= 1.0× 10
−4
C/kg, dt =
1.0×10
−5
s,N
shift
= 5,f = 5000 Hz
136
6.5.3 Cut-off Frequency
A range of traveling wave frequencies that could be performed by electronic devices were
tested to investigate how dust responds to waves with differentR
cm
, ranging from 10
−9
to
10
−4
C/kg. Results show that there are two limits of frequencies, lower cut-off and higher
cut-off frequencies, between which dust is able to be transported.
Tab. 6.1 gives the corresponding f
low
and f
high
of dust with different R
cm
as well as
parameters of the traveling wave used in the simulation.
Table 6.1: Simulation results of frequency response of dust with different charge to mass
ratios
R
cm
, C/kg
f
low
f
high
, Hz v
w
, m/s dt, s N
shift
T , s
1.0×10
−9
0.5 0.008 1.0×10
−3
500 2.00
7.1 0.114 1.0×10
−3
35 1.40×10
−1
1.0×10
−8
1.3 0.020 1.0×10
−3
200 8.00×10
−1
12.5 0.200 1.0×10
−3
20 8.00×10
−2
1.0×10
−7
3.1 0.050 5.0×10
−4
160 3.20×10
−1
28 0.444 5.0×10
−4
18 3.60×10
−2
1.0×10
−6
8.9 0.1429 2.0×10
−4
140 1.12×10
−1
63 1.000 1.0×10
−4
40 1.60×10
−2
1.0×10
−5
26 0.421 1.0×10
−5
950 3.80×10
−2
250 4.000 1.0×10
−5
100 4.00×10
−3
1.0×10
−4
61 0.976 1.0×10
−5
410 1.64×10
−2
280 4.546 1.0×10
−5
88 3.52×10
−3
Fig. 6.19 is the plot of R
cm
versus f
low
and f
high
in the log-log scale. Strong linear
relations are observed from the trend on the plot. Eqs. 6.34 and 6.35 are expressions of
fitted f
low
and f
high
as power functions of R
cm
. In order to move dust effectively in the x
137
direction, the frequency applied to transport dust should meet this criterion: f
low
(R
cm
) <
f < f
high
(R
cm
). Dust with higher charge to mass ratios require higher frequencies to be
moved properly.
10
−10
10
−9
10
−8
10
−7
10
−6
10
−5
10
−4
10
−3
10
−1
10
0
10
1
10
2
10
3
f, Hz
R
cm
, C/kg
calculated f
low
fitted f
low
calculated f
high
fitted f
high
Figure 6.19: Lower and higher cut-off frequencies of dust with different charge to mass
ratios in the traveling wave
f
low
= 3164.297R
0.4245
cm
(6.34)
f
high
= 5386.814R
0.3242
cm
(6.35)
138
Eqs. 6.36 and 6.37 show relative error calculation off
low
and f
high
. Tab. 6.2 gives rel-
ative and absolute errors of frequency calculations with respect to differentR
cm
assuming
R
cm
has relative error of±20%.
δf
low
f
low
= 0.4245
δR
cm
R
cm
(6.36)
δf
high
f
high
= 0.3242
δR
cm
R
cm
(6.37)
Table 6.2: Errors of frequencies at different charge to mass ratios
R
cm
, C/kg δf
low
/f
low
δf
low
, Hz δf
high
/f
high
δf
high
, Hz
1.0×10
−9
±8.5% ±0.04 ±6.5% ±0.4
1.0×10
−8
±8.5% ±0.11 ±6.5% ±0.9
1.0×10
−7
±8.5% ±0.3 ±6.5% ±1.9
1.0×10
−6
±8.5% ±0.8 ±6.5% ±4
1.0×10
−5
±8.5% ±2 ±6.5% ±8
1.0×10
−4
±8.5% ±5 ±6.5% ±17
6.5.4 Dust Sorting Scheme
Dust sorting based onR
cm
is achievable with the understanding of dust frequency response.
For example, the following steps provide approaches to sortR
cm
= R
cm0
±δR
cm
out.
• Approach 1: fromf = 0 Hz
1. Sweep the spectrum from f = 0 to f = f
low
(R
cm0
− δR
cm
) to remove dust
withR
cm
< R
cm0
−δR
cm
2. Sweep the spectrum fromf = f
low
(R
cm0
−δR
cm
) tof = f
low
(R
cm0
+δR
cm
)
to sort out dust withR
cm
= R
cm0
±δR
cm
139
• Approach 2: fromf =∞
1. Sweep the spectrum from f =∞ to f = f
high
(R
cm0
+δR
cm
) to remove dust
withR
cm
> R
cm0
+δR
cm
2. Sweep the spectrum fromf = f
high
(R
cm0
+δR
cm
) tof = f
high
(R
cm0
−δR
cm
)
to sort out dust withR
cm
= R
cm0
±δR
cm
6.6 Conclusion
In this chapter, we studied the physics of the dust dynamics on an electrodynamic screen
(EDS) system in surface traveling waves using numerical computer simulations. Results
show a clear relation between the frequency response of a dust particle and its charge to
mass ratio: there are two cut-off frequencies as a function of dust charge to mass ratio; and
a dust particle can only respond to a frequency between the higher and lower frequencies
and follow the surface traveling wave to be transported. This frequency response result
builds up the foundation of the design of an innovative multi-phase EDS system proposed
in the next chapter.
140
Chapter 7: Design of An Electrodynamic
Screen System for Dust Manipulation
7.1 Introduction
In this chapter, we apply the knowledge gained from the last chapter to design a new
autonomous multi-phase electrodynamic screen (EDS) dust sorting system. In this new
system, the electrodes are embedded on a substrate, a dielectric board, and each electrode
is controlled individually to generate traveling wave patterns on the substrate. The previ-
ously developed three or four phase electrode device can only move dust particles at a fixed
frequency and speed at any given time. However, in the new design, each electrode on the
multi-phase board is controlled by a micro computer to be biased to a low potential (-500 V ,
state 0) or a high potential (500 V , state 1) with respect to the local ground independently.
Therefore, any wavelength, wave speed, or direction of wave propagation can be generated
by the controller at the desired location using only one electrode design pattern provided
that the number of electrodes per unit length is sufficiently high. As a result the new EDS
system is significantly more effective in manipulating charged dust particles.
7.2 System Design
The main purpose of this system is to control the potential of electrodes to generate travel-
ing electrostatic waves for moving dust particles on the screen board. In this design, there
are 256 electrodes embedded on the electrode board and each one is biased independently
to form moving potential waves on the electrode board. With this basic idea, any wave-
length, wave speed, or direction of wave propagation may be generated by the controller at
the desired position with only one electrode pattern design.
141
The fundamental concept of the EDS system is to control multiple high voltage signals
with only a few low voltage digital signals generated by a portable micro computer. The
system in Fig. 7.1 consists of a micro computer, a decoder, an external high voltage power
supply, 16 high voltage drivers and an electrode board. The system employs a micro com-
puter as the core control unit which outputs transistor-transistor logic (TTL) signals. The
decoder system translates signal from the micro computer to control 16 high voltage driver
units, which turn on and off 256 photo MOSFETs to bias the electrodes on the electrode
board to create traveling waves.
Figure 7.1: Architecture of a multi-phase EDS system
142
7.3 Components
7.3.1 Micro Computer
A commercial micro computer, the Arduino
R
MEGA in Fig. 7.2, serves as the control unit
and outputs 22 bits of data. The first 16 bits (Bit 0 to 15) are used to deliver control signal.
Information carried by Bit 16 to 19 are sent to the decoder to select high voltage drivers.
Bit 20 is the latch signal to lock the system to keep the state at that moment. Bit 21 is the
electric ground signal from the micro computer. In order to reduce wiring, only 16-bit data
is written each time to control 16 electrodes. 16 sweeps are required during one cycle to
complete state assignment to all 256 electrodes. This data output structure employs a 4-16
decoder to select 16 high voltage drivers, which directly operates 256 photo MOSFETs.
Figure 7.2: Arduino
R
MEGA micro computer by the Arduino Team
7.3.2 Decoder
Fig. 7.4 is the circuit schematic of the decoder system used to control the high voltage
drivers. Data from the micro computer flows to the decoder system through port SV1 in
the figure. First 16 bits of data connect to the first 16 pins on 16 output connectors (JP1
143
to JP16) directly and Bit 16 to 19 are fed to the 4-16 4514N decoder, which translates the
4 bits of data into 16 unique outputs to select one of the 16 output ports at a time. The
selecting signal from the decoder is delivered to Pin 17 on each JP port. One pin out of
S0 to S15 is selected every time to write 16 data bits via the corresponding port JP 1 to JP
16 according to the input state of Bits 16 to 19 (D1 to D4 on 4514N). Bit 20 from the the
decoder controls the latch (ST on 4514N) of the decoder to enable the decoding operation
or lock the states of S0 to S15. JP17 is the input power to supply the decoder system,
delivering operating power to 16 high voltage drivers through JP1 to JP16 via Pin17 and
18. A voltage regulating system, IC7805T, maintains the circuit operating voltage of the
decoder system at 5 V to provide steady voltage for all ICs.
7.3.3 High Voltage Driver
The high voltage control mechanism employs a photo MOSFET as a solid state relay to
manipulate high voltage with a digital signal as shown in Fig. 7.3. The AQV25 photo
MOSFET in the system insulates circuits with different ground references on each side
up to 1500 V , eliminating electrical interference between low voltage and high voltage
sections.
R
1
is a current limiting resistor of the input circuit which turns on or off the LEDs inside
the photo MOSFET. On the right-hand side, there are two 500 V power supplies to power
the system with output resistance R
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in
is at a low level with respect to GND 1,
the high voltage circuit is open, biasing V
out
to 500 V with respect to GND 2. When V
in
is at a high level with respect to GND 1, LEDs emit light to activate the photo sensitive
CMOSFET and close the circuit on the right to output -500 V with respect to GND 2.
There are 16 high voltage driver units altogether in the whole system, and each controls
one of the 16 electrodes. Fig. 7.5 is the circuit schematic of a single high voltage driver,
which is in charge of biasing 16 electrodes by controlling 16 photo MOSFETs with a TTL
144
Figure 7.3: Photo MOSFET solid state relay system
signal. Data from the decoder is sent to the high voltage driver through port JP1 in the
figure. There are two 74CHT563N ICs, each handling 8 bits of data, in the schematic as a
latch system. When a high voltage driver is selected by the decoder, data passes through the
latch ICs from the left side to the right side with inverted output values. 16 AQV25 photo
MOSFETs are hooked to the output ports of the latch system and operate as switches to
turn on and off the high voltage signal. Pin1 of A VQ25 is the control signal and Pin 2 is the
control circuit ground. Every Pin 6 of every AQV25 outputs a high voltage control signal
for biasing electrodes to create the traveling wave. Port JP 2 collects 16 the high voltage
signals outputed from the 16 photo MOSFETs to drive 16 electrodes on the electrode board.
Port X1-1 and X1-2 in the schematic are high voltage input connectors, supplying 500 V
and -500 V respectively to control electrodes.
145
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146
Figure 7.5: Schematic of the high voltage driver
147
7.3.4 Electrode Board
The electrode board in Fig. 7.6 (not to scale) has 256 copper electrodes connected to high
voltage drivers. In the cross-sectional view (Fig. 7.7), electrodes are well aligned on a
substrate and coated with polyurethane to increase the breakdown voltage [16, 78, 63].
Tab 7.1 lists the specifications of parts used to fabricate the electrode board.
Figure 7.6: Multi-phase electrode screen board
Figure 7.7: Cross-sectional view of the multi-phase electrode screen board with major
dimensions in mm
7.3.5 High-voltage Power System
Two external adjustable power supplies with nominal output voltage 500 V are required
to power the system. Direct high voltage DC power supplies are applicable in laboratory
testing, while on lunar or asteroid surfaces, a better approach is to use DC-DC converters to
148
Table 7.1: Part list of EDS board
Part number Part name Material
1 Insulating coating Polyurethane
2 Electrode Copper
3 Substrate Fiber glass
output high voltage from a DC battery source. Nowadays, a high voltage DC-DC converter
is capable of converting high voltage from a 30 V or below DC input and has compact size
with mass lower than 5 g, ideal for space missions.
7.4 System Operation
To use the device, traveling wave pattern design with respect to time is first programmed to
the micro computer. Next, a 5V control voltage and high voltage source is connected to the
system. Finally, the micro computer is turned on to apply traveling waves on the electrode
board for dust manipulation. By applying traveling waves with different frequencies and
wave lengths at different locations of the electrode board, dust particles with different mass
and size will respond and thus be moved and collected.
7.5 Advanced Dust Manipulation Concept
In order to manipulate dust more effectively, a 2D electrode array is introduced. In Fig. 7.8,
N × N electrodes are embedded on a dielectric board and each electrode is controlled
individually to generate traveling waves on the substrate. Compared with a parallel aligned
electrode device, which can only move dust particles perpendicular to the electrodes, each
electrode on the 2D array can be biased to low potential (state 0) or high potential (state 1)
independently at any given time, but more wiring is required. In addition, any wavelengths,
number of wavelength, wave speed and direction can be generated by the controller at
149
a desired position with only one electrode pattern design if the resolution of electrodes
(number of electrodes per unit area) is high enough.
Figure 7.8: Electrode array board
Figs. 7.9 to 7.12 show four basic dust manipulation methods on the EDS: gathering,
dispensing, linear transportation and rotation, respectively. Note that electrodes are not
displayed in the figures. Arrows show propagation of wave envelopes and dust particles
will move with the wave envelopes and remain in the shaded regions shown in the figures.
150
Figure 7.9: Gathering dust
Figure 7.10: Dispensing dust
151
Figure 7.11: Linear dust transportation
Figure 7.12: Rotation of dust
152
7.6 Conclusion
This chapter has proposed the system design of an innovative multi-phase EDS device
based on the physics of dust dynamics discussed in the last chapter. Compared with the
previous three-phase or four-phase EDS system design, this EDS system is able to control
each electrode individually by a micro computer to generate more complicated surface
traveling wave patterns to achieve dust mitigation, sorting and segregation for future space
missions on the lunar, Martian and asteroid surfaces.
153
Chapter 8: Conclusions and Future
Work
8.1 Conclusions
This dissertation has studied the charging interactions of a dusty layer in plasma. Specifi-
cally, this study has advanced the state-of-the-art in two areas.
The first is on the dust charging for a dusty layer immersed in a plasma environment.
The single isolated dust charging model is a commonly used capacitance model for dusty
surface charging with the OML current collection model for potential calculation. Previous
experiments only measured the charge and charge to mass ratio for a single dust particle
in plasma. However, the charging and capacitance model of a dust on a dusty surface in
plasma were still not understood. In this study, we first developed an analytically approx-
imate capacitance model for a dusty plasma and dust layer using the capacitance matrix
method, and validated the result with experiments. We then developed another experiment
to measure the charging of JSC-1A dust layer in plasma inside a vacuum chamber. We find
that in our experiment, the single dust charging model is no longer applicable to packed dust
charging on a dusty surface as it shows calculation results two orders of magnitude higher
than the measurement since it ignores interactions between surrounding dust particles. The
dusty surface in plasma model developed using an average distance approximation pro-
vides an accuracy of 50% to 60% compared with the measurement. This is found to be
an accurate model to predict how much charge a dust particle can carry on a dusty surface
immersed in plasma.
The second area is dust manipulation for potential applications of dust mitigation, sort-
ing and segregation on the lunar, Martian and asteroid surfaces. Previously, people only
demonstrated the application of removing dust particles accumulated on surfaces with
154
three-phase of four-phase surface electrostatic traveling waves. However, the underlying
physics of the dust dynamics in such traveling waves was not understood. In this study,
we investigated the physics of dust behavior on an EDS device using numerical computer
simulation and concluded that there are two cut-off frequencies as a function of dust charge
to mass ratio; and a dust particle can only respond to a frequency between the higher and
lower cut-off frequencies and then follow the surface traveling wave to be transported. We
also developed a new design of an EDS device using multi-phase surface traveling waves
to precisely control the dust motion. The capability of the new design includes dust miti-
gation, sorting and segregation based on charge to mass ratio.
8.2 Future Work
8.2.1 Dust Charging
Modeling
This study has developed an approximate analytical dusty surface charging model. We need
to numerically solve the capacitance matrix to have more accurate results of dust capaci-
tance interaction in dusty plasma. A possible way is to randomly place dust particles to
form a uniformly distributed dust system in a controlled domain and then precisely calcu-
late the interaction between each pair according to their locations in the domain to solve
the capacitance matrix.
Experiments
Experiments of the dust layer charging with different thickness needs to be conducted in
the future to investigate effects on the dusty surface charging state caused by the sample
layer thickness. This may require appropriate modifications to the current vacuum system.
155
A better ion source is needed in order to adjust the ambient plasma to create a wider
range of plasma parameters for the dusty surface charging investigation. Doing this may
require a computer controlled power processing unit to accurately control the ion beam
current and the neutralizer current.
A retarding potential analyzer (RPA) [49, 73] testings may be performed in the future
to have better understanding of the ion velocity and energy distributions in the vacuum
chamber for modeling dust and dusty surface charging in the plasma environment.
8.2.2 EDS Design and Fabrication
We have only developed the concept design of an EDS device based on the computer sim-
ulation, future work will need fabricate the EDS device and demonstrate the dust manipu-
lation, sorting and segregation concept through laboratory test. This may involve compact
printed circuit board design and precision fabrication.
156
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Abstract (if available)
Abstract
The objective of this dissertation is to study the charging interactions of a dusty surface in space plasma through experimental, analytical, and numerical investigations. Specifically, this dissertation investigates 1) dust charging on a dusty surface and 2) dust manipulation on a dusty surface. ❧ In the first area, an analytically approximate capacitance model for a dusty plasma and dust layer using the capacitance matrix method and an averaged inter-dust distance to account for dust interactions, has been developed. In the previous studies, the single isolated dust charging model is commonly used for dusty surface charging with the OML current collection model for potential calculation, and experiments conducted only measured the charge and charge to mass ratio for a single dust particle in plasma. Hence, the capacitance model of a dust on a dusty surface in plasma was still not understood. In our study, we first validated the capacitance model derived with experiment and then developed another experiment to measure the charging of JSC-1A dust layer in plasma inside a vacuum chamber. It is found that the single dust charging model is no longer applicable to packed dust charging on a dusty surface as it shows calculation results two orders of magnitude higher than the measurement because the interactions between surrounding dust particles were ignored. The dusty surface in plasma model developed assuming an averaged inter-dust distance approximation provides an accuracy of 50% to 60% compared with the measurement. This is found to be an accurate model to calculate the dust charging on a dusty surface immersed in plasma. ❧ In the second area, we investigated the underlying physics of dust behavior in the surface electrostatic traveling wave on an electrodynamic screen (EDS) device using numerical computer simulations. Previous studies only demonstrated the application of removing dust particles accumulated on surfaces with three-phase or four-phase surface electrostatic traveling waves without concluding the physics of the dust dynamics in such traveling waves. We found that there are two cut-off frequencies of the wave as a function of dust charge to mass ratio
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Asset Metadata
Creator
Ding, Ning
(author)
Core Title
Experimental and numerical investigations of charging interactions of a dusty surface in space plasma
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Astronautical Engineering
Publication Date
10/17/2013
Defense Date
09/14/2012
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
charging,dusty surface,OAI-PMH Harvest,plasma
Language
English
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Electronically uploaded by the author
(provenance)
Advisor
Wang, Joseph (
committee chair
), Erwin, Daniel A. (
committee member
), Goodfellow, Keith (
committee member
), Gruntman, Michael (
committee member
), Kunc, Joseph (
committee member
), Muntz, E. Phillip (
committee member
)
Creator Email
ningding.phd@gmail.com,ningding@usc.edu
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https://doi.org/10.25549/usctheses-c3-105444
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UC11289480
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usctheses-c3-105444 (legacy record id)
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etd-DingNing-1254.pdf
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105444
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Dissertation
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Ding, Ning
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texts
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(contributing entity),
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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 a...
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Tags
charging
dusty surface
plasma