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THEORETICAL AND EXPERIMENTAL INVESTIGTION INTO HIGH CURRENT
HOLLOW CATHODE ARC ATTACHMENT
by
Ryan T. Downey
A Dissertation...
ii
Acknowledgements
The defense of this thesis marks the completion of the most intellectually,
emotionally, finically, an...
iii
times can be tempered by the measure of those who accompany you on the journey. My
thanks for showing this to be true....
iv
Finally, to Kristy; None of this would have been possibly without you. Nothing I
can write here can begin to approach h...
v
Table of Contents
Acknowledgements.........................................................................................
vi
5.1 Theoretical Methods ..................................................................................................
vii
7.4 Connection to Multi Channel Hollow Cathodes................................................... 167
7.5 Summary of ...
viii
List of Tables
Table 1. Ionization energy for common electric propulsion propellants.......................... 26
Tab...
ix
List of Figures
Figure 1: MPD thruster and force vectors [26].............................................................
x
Figure 22: Layout of vacuum side experimental components, Langmuir probe in
retracted position.............................
xi
Figure 42. Discharge voltage vs. flow rate, current as parameter, lower current
range. 2 mm Tantalum cathode..............
xii
Figure 58. Location and magnitude of the peak temperature of 2 mm Tantalum
cathode, vs. flow rate .......................
xiii
Figure 74 : Plasma Potential vs. Mass Flow rate, discharge current as parameter. 2
mm Tantalum cathode..................
xiv
Figure 90: Computed heavy species temperature (K) profile in a 6 mm Tungsten
cathode, 3.6 Amp discharge, 185 sccm Argo...
xv
Abbreviations
Symbols used:
D characteristic dimension/length (m)
e elementary charge (C)
q species specific elementary...
xvi
grey graybody
black blackbody
i ion, ionization
e electron
h heavy species (ion or neutral)
pe plasma electron
b Boltz...
xvii
Abstract:
This research addresses several concerns of the mechanisms controlling
performance and lifetime of high-cur...
xviii
of the discharge current, but a decreasing function of the mass flow rate. The width of the
active zone was found to...
1
Chapter 1: Introduction
In January of 2004, US president George Bush announced the new Vision for
Space Exploration (VSE...
2
metal (such as Tungsten or Tantalum), and have historically been solid rods, however in
recent years investigations into...
3
broken down into two categories, 1: high-thrust low-efficiency, and 2: low-thrust high-
efficiency. Typically category 1...
4
body (Earth, Moon or an asteroid), when the spacecraft is subject to a large gravitational
force, high thrust chemical e...
5
easy to see how high Isp electric propulsion systems are desirable from both the resource
utilization, and financial, po...
6
Chapter 2: MPD Thruster and Cathode Operation
2.1 The MPD/LFA Thruster
An MPD thruster is a type of Electric Propulsion ...
7
Figure 1: MPD thruster and force vectors [26]
the required current through thermionic emission, the current is initially...
8
support steady-state thermionic emission over a relatively large surface area. Thus the
initial startup phase is charact...
9
An electric field is created with both radial and axial components, driving current
flow between the two electrodes. For...
10
pertinent to applied field thrusters only. The relative dominance of each thrust
mechanism is still a mater of debate a...
11
Figure 3. Orificed Hollow Cathode [42]
Ions created in the collisions will make their way to the walls of the cathode w...
12
downstream end in contact with the orifice plate, and decreases at a rate inversely
proportional to distance upstream.
...
13
device once exposed to a cathode operating at temperatures > 2,500K during the MPD
discharge. All electron emission is ...
14
Figure 4. Axial temperature trends of a typical SCHC [18]
Multi-Channel Hollow Cathode:
A multi-channel hollow cathode ...
15
more common design. Several different hollow emission regions are formed by
the inter-rod spacing, see Figure 6.
In all...
16
Figure 5: Two different designs for Multi-channel Hollow Cathodes
Figure 6. Inter-rod spacing in "macaroni packet" desi...
17
Figure 7. Multi-Channel Hollow Cathode – “macaroni packet” design – side view
Upstream of the channels the neutral gas ...
18
2.3 The Importance of Temperature
MPD thrusters are driven by constant current power sources, in experimental
practice ...
19
Figure 9. Tungsten MCHC before operation in MPD thruster. Photo from reference
[65]
It is for this reason that the abil...
20
Figure 10. Tungsten MCHC after operation in MPD thruster. Photo from reference
[65]
of the cathode which emits – for a ...
21
eff
b wall2 s
wall eff wf
o
,
4
k T qE
j AT e
φ
φ φ
πε
−
= = − (2.2.1)
Where “j” is the emitted surface current density...
22
Figure 11. Sensitivity of emitted current to temperature and work function [26]
The choice of cathode material, as well...
23
hollow cathode, is termed the Internal Positive Column, or IPC (sometimes called the
Internal Plasma Column). The IPC i...
24
a neutral atom, with each collision raising the atoms internal electronic energy level and
bringing it that much closer...
25
when the electron temperature is much less than the ionization energy of the neutral
atom, and the neutral species spee...
26
plasma considered in hollow cathodes, where electron temperatures in the range of 1 to 5
have been reported, the coeffi...
27
region of cathode wall supplying single event ionizing-capable electrons is tied to the
axial profile of the radial pot...
28
the working gas, thus the role of the multi-step excitation and ionization process is
significant and must be included....
29
Assuming the electrons in the IPC have a Maxwellian distribution, it is only the
high-energy tail end of the distributi...
30
and ends at the potential of the cathode wall itself. Between these two boundaries the
sheath and pre sheath drop is ac...
31
A. Increased current density from the same emission region (to increase the
likelihood of electron-neutral collisions)
...
32
increases. A larger surface area of cathode wall will now be emitting elections, with
energy levels above the minimum n...
33
Figure 12 Equipotential Lines for flow rates, low (a), moderate (b), high (c) [18]
Figure 13. Computed electron tempera...
34
As the density in a cathode decreases, the frequency of electron impacts on an
individual atom decreases. From this we ...
35
discharge voltage and IPC length correspond with decreasing flow rate. This correlation
was first reported by Delcroix ...
36
qualitatively and quantitatively, and to determine the IPC properties for given operating
conditions (current, mass flo...
37
It is important to note here that previous works have noted these observations, but have
not produced qualitative theor...
38
discharge current and mass flow rate the MCHC would be expected to operate at a lower
discharge voltage - a relation th...
39
Chapter 3: History and State of the Art
3.1 Historical Related Research
MPD thrusters evolved from arcjet thrusters, an...
40
NASA-Jet Propulsion lab
NASA-Glenn/Lewis research Center
AVCO-Everett
Los Alamos National labs
Moscow Aviation Institut...
41
2) Polk – NASA-JPL/Princeton University [54]
Jay Polk conducted high current cathode research at JPL/Princeton Universi...
42
Although this work focused exclusively on solid rod cathodes, a detailed 1-
D/phenomenological model of the plasma shea...
43
design. The experiments included development and testing of 3 different thrusters, a 30
kw, 150 kw, and 200 kw – all th...
44
Figure 14. Active MCHC with Lithium -Barium mixture, photo from reference [65]
Figure 15. Active MCHC with Lithium only...
45
orificed hollow cathode with Xenon propellant. Large portions of work described in this
thesis have origins in the mode...
46
data point thus far (for an applied field thruster) is for a Lithium fed LFA operating at 69
percent (thrust) efficienc...
47
Figure 16. Schematic view of 250 kW Li-LFA, ALFA^2, [13]
Figure 17. Improvements over SOA, reference [13]
Applied-field...
48
originally awarded level. Target performance for ALFA2
was 60 to 63 percent efficiency,
6200s Isp, and >3 years of reli...
49
Figure 18. The six MCHC designs tested by MAI
The SOA of multi-channel hollow cathodes is somewhat harder to quantify, ...
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment
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Theoretical and Experimental Investigation into High Current Hollow Cathode Arc Attachment

  1. 1. THEORETICAL AND EXPERIMENTAL INVESTIGTION INTO HIGH CURRENT HOLLOW CATHODE ARC ATTACHMENT by Ryan T. Downey A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ASTRONAUTICAL ENGINEERING) December 2008 Copyright 2008 Ryan T. Downey
  2. 2. ii Acknowledgements The defense of this thesis marks the completion of the most intellectually, emotionally, finically, and physically trying period of my life. Due to the unusual circumstances surrounding my time and support in graduate school, much was sacrificed in the pursuit of this degree and its associated education, from time spent with friends and family, financial resources, peace of mind and personal health. Through it all, I consider my most significant accomplishment to be the education gained along the journey, not in an academic sense, but the knowledge acquired about myself, and my perspectives on the world around me. I consider this gained wisdom to be invaluable. Many people contributed to the eventual completion of this thesis, and when my legs were week, the finish line still distant, they gave me the support and encouragement without which I may not have finished the race. The fist person to thank is my advisor, Professor Dan Erwin, who provided me with the safe harbor during the storm. Thank you for our many discussions, your ongoing support and ability to provide perspective, and your commitment to seeing me complete this work. To my former colleagues at NASA’s Jet Propulsion Lab where my work started, Jay, Al, Ray and Yiangos; It was my privilege to work with some of the most talented people in the field, and I consider you all among them. My sincere thanks to my lab mates at USC, Nate and Taylor, who provided me with much discussion and support through the years, over many, many, many cups of coffee. To Anthony, who was my company on far too many late nights at the lab, providing me with insight and assistance both personal and professional; the difficulty of
  3. 3. iii times can be tempered by the measure of those who accompany you on the journey. My thanks for showing this to be true. My experiments could not have been completed without the tireless and loyal dedication of my lab assistant Paul, who brought an excitement and curiosity which served as a daily reminder of why I got into this whole mess in the first place. To Andrew Ketsdever, who stepped up to the plate when no one else would; My most sincere thanks and gratitude for all your support. To my friend and mentor Keith Goodfellow, who provided me with my first ideas of what a real rocket scientist is: I thank you for seeing something in me that I wasn’t quite sure I saw myself. In every sense of the word, both professional and personal, you are one of the finest teachers I have ever known…(not a bad rock climber either!) I hope someday to be able to do for my students what you have done for me. To Jon, who has known me longer than just about anyone: We’ve both seen many changes in each other throughout our lives, though unchanged is our love of science fiction, which fueled many of my early dreams of space. Thanks for sharing with me the experience of “the human condition”, our many Trek nights, and always having time to lend me your thoughts. Mom and Dad; For as long as I can remember you have always encouraged my crazy ideas of one day becoming a rocket scientist. When I was a child, you put up with my trying habit of taking things apart to figure out how they worked, even though I didn’t always figure out how to put them back together again. Your patience has finally come to fruition. Thanks for everything.
  4. 4. iv Finally, to Kristy; None of this would have been possibly without you. Nothing I can write here can begin to approach how I feel about your tireless love and support, and so I will simply say thank you for being my greatest teacher, and, I love you.
  5. 5. v Table of Contents Acknowledgements............................................................................................................. ii List of Tables ...................................................................................................................viii List of Figures.................................................................................................................... ix Abbreviations.................................................................................................................... xv Abstract:..........................................................................................................................xvii Chapter 1: Introduction....................................................................................................... 1 1.1 The Importance of Electric Propulsion..................................................................... 2 Chapter 2: MPD Thruster and Cathode Operation ............................................................. 6 2.1 The MPD/LFA Thruster ........................................................................................... 6 2.2 Hollow Cathode Operation ..................................................................................... 10 Conventional Hollow Cathode:................................................................................. 10 Single Channel Hollow Cathode:.............................................................................. 12 Multi-Channel Hollow Cathode:............................................................................... 14 2.3 The Importance of Temperature ............................................................................. 18 2.4 Internal Plasma Column- IPC................................................................................ 22 Effects of Mass Flow Rate on Plasma Conditions.................................................... 30 IPC Control Parameters and Experimental Observations......................................... 36 Chapter 3: History and State of the Art ............................................................................ 39 3.1 Historical Related Research.................................................................................... 39 3.2 State of the Art – MCHC’s and LFA thrusters ....................................................... 45 Chapter 4: Role of This Doctoral Work............................................................................ 50 Chapter 5: Methods........................................................................................................... 52
  6. 6. vi 5.1 Theoretical Methods ............................................................................................... 52 5.2 Experimental Methods............................................................................................ 56 Langmuir Plasma Probe............................................................................................ 60 Cathode Stage ........................................................................................................... 66 Optical Pyrometery................................................................................................... 68 Cathodes.................................................................................................................... 71 Signal Processing and Data Acquisition (DAQ)....................................................... 73 Chapter 6: Single Channel Hollow Cathode model.......................................................... 75 6.1 Assumptions............................................................................................................ 75 6.2 Governing Equations .............................................................................................. 77 Conservation of Mass – Species Continuity Equation.............................................. 78 Conservation of Momentum – Species Equation of Motion .................................... 80 Conservation of Energy – General Species Energy Equation .................................. 87 Electron Energy Transport Equation ........................................................................ 89 Heavy Species Energy Transport Equation .............................................................. 92 Neutral Species Energy Equation ............................................................................. 92 Combined Heavy Species Energy Equation ............................................................. 93 Remaining Equations:............................................................................................... 94 6.3 Summary of Equations:........................................................................................... 96 6.4 Numerical Methodology......................................................................................... 98 Finite Volume Method............................................................................................ 100 6.5 Boundary Conditions by Boundary Location ...................................................... 102 Boundary 1: Gas entrance....................................................................................... 102 Boundary 2: Cathode Walls.................................................................................... 104 Boundary 3: Cathode Exit Plane............................................................................. 106 Boundary 4: Cathode Centerline:............................................................................ 106 6.6 Solution Procedure................................................................................................ 107 6.7 Connecting Theoretical Model and Experimental Work...................................... 108 Chapter 7: Experimental Results and Conclusions......................................................... 110 7.1 Cathodes................................................................................................................ 110 7.2 Observed Trends................................................................................................... 118 High-Voltage / Low-Current Discharges................................................................ 118 High-Current / Low-Voltage Discharges................................................................ 120 Plasma Data ............................................................................................................ 140 7.3 Active Zone........................................................................................................... 148 Computational Predictions:..................................................................................... 155
  7. 7. vii 7.4 Connection to Multi Channel Hollow Cathodes................................................... 167 7.5 Summary of Results.............................................................................................. 171 Magnitude of Peak Temperature:............................................................................ 172 “Hot Spot” or “Active Zone”:................................................................................. 172 Location of Peak Temperature:............................................................................... 174 Temperature Gradient:............................................................................................ 174 Discharge Voltage:.................................................................................................. 174 Power: ..................................................................................................................... 175 Electron Temperature: ............................................................................................ 176 Plasma Potential:..................................................................................................... 176 Plasma Density: ...................................................................................................... 176 Plasma Generation .................................................................................................. 176 7.5 Suggestions for Future Work................................................................................ 178 References:...................................................................................................................... 180 Appendix A:.................................................................................................................... 186 Evaluation of Governing Equations............................................................................ 186 Plasma Density, ni=ne ............................................................................................. 187 Plasma Temperature, Te.......................................................................................... 189 Plasma Potential, φ ................................................................................................. 191 Electric Field Vector, E........................................................................................... 193 Ion Current Density Vector, ji................................................................................. 194 Electron Current Density Vector, je ........................................................................ 196 Heavy Species Temperature, Th.............................................................................. 196 Neutral Gas Velocity Vector, un ............................................................................. 199 Neutral Gas Density, nn........................................................................................... 201 Boundary Conditions – Summary............................................................................... 203 Appendix B:.................................................................................................................... 206 Collision Frequencies.................................................................................................. 206 Appendix C:.................................................................................................................... 208
  8. 8. viii List of Tables Table 1. Ionization energy for common electric propulsion propellants.......................... 26 Table 2 . MPD thruster research groups ........................................................................... 40
  9. 9. ix List of Figures Figure 1: MPD thruster and force vectors [26]..................................................................7 Figure 2. Force vectors in ALFA^2 Li-LFA......................................................................8 Figure 3. Orificed Hollow Cathode [42]..........................................................................11 Figure 4. Axial temperature trends of a typical SCHC [18] ............................................14 Figure 5: Two different designs for Multi-channel Hollow Cathodes.............................16 Figure 6. Inter-rod spacing in "macaroni packet" design MCHC. Each hollow region acts as an individual SCHC. Figure from reference [65]......................................16 Figure 7. Multi-Channel Hollow Cathode – “macaroni packet” design – side view.......17 Figure 8. MCHC during operation, as seen head on. Photo from reference [65] ............17 Figure 9. Tungsten MCHC before operation in MPD thruster. Photo from reference [65]...................................................................................................................19 Figure 10. Tungsten MCHC after operation in MPD thruster. Photo from reference [65]...................................................................................................................20 Figure 11. Sensitivity of emitted current to temperature and work function [26] ...........22 Figure 12 Equipotential Lines for flow rates, low (a), moderate (b), high (c) [18].........33 Figure 13. Computed electron temperature in an orificed hollow cathode [42]..............33 Figure 14. Active MCHC with Lithium -Barium mixture, photo from reference [65]...................................................................................................................................44 Figure 15. Active MCHC with Lithium only, photo from reference[65]........................44 Figure 16. Schematic view of 250 kW Li-LFA, ALFA^2, [13]......................................47 Figure 17. Improvements over SOA, reference [13] .......................................................47 Figure 18. The six MCHC designs tested by MAI ..........................................................49 Figure 19. Vacuum chamber w/ door open – early iteration of cathode setup................58 Figure 20. Vacuum chamber, side view...........................................................................59 Figure 21: Construction of Langmuir probe end tip........................................................62
  10. 10. x Figure 22: Layout of vacuum side experimental components, Langmuir probe in retracted position..............................................................................................................63 Figure 23: Layout of vacuum side experimental components, Langmuir probe in fully extended position.....................................................................................................64 Figure 24: Electrical schematic of the Langmuir probe circuit. ......................................65 Figure 25: Langmuir probe data trace, 2 mm Tantalum cathode, 100 sccm, 35 Amp discharge. “Double Trace” effects of the voltage pulse are clearly visible ............66 Figure 26. Two-axis Stage to which the cathode is mounted ..........................................68 Figure 27. Chamber and optical pyrometer .....................................................................69 Figure 28: 10 mm diameter Tungsten cathodes and 2 mm diameter Tantalum cathodes............................................................................................................................72 Figure 29: Layout of the power supply and diagnostic electronic systems. ....................73 Figure 30. Computational zone........................................................................................75 Figure 31. Discretization scheme showing stepwise function for scalar values............100 Figure 32. Sample flow chart for theory and experimental work..................................109 Figure 33. Damaged cathode and flange........................................................................112 Figure 34. Close-up of damaged cathode ......................................................................112 Figure 35: Up close view of 6 mm Tungsten cathode, post test....................................113 Figure 36. 2 mm Tantalum and 10 mm Tungsten cathodes. Images are pre- discharge. .......................................................................................................................114 Figure 37. Comparison of exit planes of 2 mm Tantalum, and 10 mm Tungsten cathodes. Images are pre-discharge. ..............................................................................115 Figure 38. Close-up view of 2 mm Tantalum cathodes. Images are pre-discharge.......116 Figure 39: Images of the 10 mm diameter Tungsten cathode after operation at 2 kW..................................................................................................................................117 Figure 40. Dependence of peak temperature location on flow rate, for high- voltage, low-current discharge through 6 mm Tungsten cathode..................................119 Figure 41. Discharge voltage vs. flow rate, 2 mm Tantalum cathode ...........................121
  11. 11. xi Figure 42. Discharge voltage vs. flow rate, current as parameter, lower current range. 2 mm Tantalum cathode......................................................................................121 Figure 43. Discharge voltage vs. flow rate, current as parameter, higher current range. 2 mm Tantalum cathode......................................................................................122 Figure 44: Discharge voltage vs. discharge current for a 2 mm Tantalum cathode ......122 Figure 45. Discharge voltage vs. discharge current, flow rate as parameter, low flow rate range. 2 mm Tantalum cathode ......................................................................123 Figure 46. Total Discharge Power vs. Flow rate, 2 mm diameter Tantalum cathode, with discharge current as a parameter, lower current range............................123 Figure 47: Total Discharge Power vs. Flow rate, 2 mm diameter Tantalum cathode, with discharge current as a parameter, higher current range...........................124 Figure 48: Discharge power vs. Discharge current, with mass flow rate as a parameter, lower mass flow rate range. 2 mm Tantalum cathode. ................................124 Figure 49: Discharge power vs. Discharge current, with mass flow rate as a parameter, lower mass flow rate range. 2 mm Tantalum cathode. ................................125 Figure 50. Energy input per mass throughput, 2 mm Tantalum cathode.......................125 Figure 51. Resistance of Argon plasma discharge vs. mass flow rate, discharge current as a parameter....................................................................................................127 Figure 52: Value of minimum resistance of the Argon plasma discharge, and flow rate at which minimum resistance occurs, vs. discharge current...................................127 Figure 53: Plasma resistance vs discharge current, Argon flow rate as a parameter, 2 mm Tantalum cathode.................................................................................................128 Figure 54: Axial temperature profile along 2 mm Tantalum cathode at 60 sccm flow rate .........................................................................................................................130 Figure 55. Axial temperature profile along 2 mm Tantalum cathode at 70 sccm flow rate .........................................................................................................................130 Figure 56 Axial temperature profile along 2 mm Tantalum cathode at 100 sccm flow rate .........................................................................................................................131 Figure 57. Axial temperature profile along 2 mm Tantalum cathode at 120 sccm flow rate .........................................................................................................................131
  12. 12. xii Figure 58. Location and magnitude of the peak temperature of 2 mm Tantalum cathode, vs. flow rate .....................................................................................................132 Figure 59: Peak temperature vs. mass flow rate, 2 mm Tantalum cathode ...................132 Figure 60: Location of the maximum temperature of 2 mm Tantalum cathode vs. mass flow rate ................................................................................................................134 Figure 61: Location of Peak Temperature dependence upon current, flow rate as a parameter, 2 mm Tantalum cathode...............................................................................134 Figure 62. Magnitude of peak temperature vs. discharge current, 2 mm Tantalum cathode...........................................................................................................................135 Figure 63: Wall temperature profile of 2 mm diameter Tantalum cathode at 20 Amp discharge. ..............................................................................................................136 Figure 64: Wall temperature profile of 2 mm diameter Tantalum cathode at 25 amp discharge, Argon mass flow rate as a parameter....................................................137 Figure 65: Wall temperature profile of 2 mm diameter Tantalum cathode at 90 sccm Argon mass flow rate, discharge current as a parameter......................................138 Figure 66: Wall temperature profile of 2 mm diameter Tantalum cathode at 90 sccm Argon mass flow rate, discharge current as a parameter......................................138 Figure 67. Pressure 40mm upstream inside 10 and 6 mm diameter cathode vs. flow rate. ........................................................................................................................139 Figure 68: Sample of raw data from Langmuir probe trace, 2 mm Tantalum cathode, 150 sccm, 30 Amp discharge...........................................................................140 Figure 69: Electron Temperature vs. Discharge current, Mass flow rate as parameter. 2 mm Tantalum cathode...............................................................................141 Figure 70: Plasma Density vs. Discharge current, discharge current as parameter. 2 mm Tantalum cathode.................................................................................................142 Figure 71: Plasma ionization fraction vs. discharge current at location 10 cm downstream of 2 mm Tantalum cathode........................................................................143 Figure 72: Plasma Potential (phi) and Discharge Voltage (DV) vs. Discharge Current, Mass Flow rate as parameter. 2 mm Tantalum cathode ..................................144 Figure 73: Electron temperature vs. Mass flow rate, discharge current as parameter. 2 mm Tantalum cathode...............................................................................145
  13. 13. xiii Figure 74 : Plasma Potential vs. Mass Flow rate, discharge current as parameter. 2 mm Tantalum cathode....................................................................................................146 Figure 75: Plasma Density vs. Mass Flow rate, discharge current as parameter. 2 mm Tantalum cathode....................................................................................................146 Figure 76: Plasma ionization fraction as a function of mass flow rate at location 10 cm downstream of 2 mm Tantalum cathode, discharge current as parameter..........147 Figure 77: Sample of analysis of thermionic emission profile data for active zone calculations. ...................................................................................................................149 Figure 78: Width of the active zone inside the cathode vs. mass flow rate...................150 Figure 79: Width of the active zone vs. the discharge current, parametric with mass flow rate ................................................................................................................151 Figure 80: Computed plasma density profile in 6 mm Tungsten cathode 3.3 Amp 121 Volt discharge, 215 sccm flow rate.........................................................................157 Figure 81; Damage of the rear mating flange after high power testing of the 10 mm Tungsten cathode....................................................................................................158 Figure 82: Computed neutral particle density profile in 6 mm Tungsten cathode 3.3 Amp 121 Volt discharge, 215 sccm flow rate..........................................................159 Figure 83: Computed plasma potential profile in 6 mm Tungsten cathode 3.3 Amp 121 Volt discharge, 215 sccm flow rate.........................................................................160 Figure 84: Computed electron temperature (eV) potential profile in 6 mm Tungsten cathode 3.3 Amp 121 Volt discharge, 215 sccm flow rate. ...........................160 Figure 85: Computed heavy species temperature (K) profile in 6 mm Tungsten cathode 3.3 Amp 121 Volt discharge, 215 sccm flow rate............................................162 Figure 86: Computed plasma density profile in a 6 mm Tungsten cathode, 3.6 Amp discharge, 185 sccm Argon flow rate. ..................................................................162 Figure 87: Computed neutral particle density profile in a 6 mm Tungsten cathode, 3.6 Amp discharge, 185 sccm Argon flow rate. ............................................................163 Figure 88: Computed plasma potential profile in a 6 mm Tungsten cathode, 3.6 Amp discharge, 185 sccm Argon flow rate. ..................................................................163 Figure 89: Computed electron temperature (eV) profile in a 6 mm Tungsten cathode, 3.6 Amp discharge, 185 sccm Argon flow rate...............................................164
  14. 14. xiv Figure 90: Computed heavy species temperature (K) profile in a 6 mm Tungsten cathode, 3.6 Amp discharge, 185 sccm Argon flow rate...............................................164 Figure 91: Normalized plasma parameters vs. normalized pressure. Baselined to 185 sccm case. ...............................................................................................................166 Figure 92: Normalized plasma parameters vs. normalized pressure. Baselined to 215 sccm case. ...............................................................................................................166 Figure 93: Gas flow in MCHC upstream of channels....................................................168 Figure 94: Exit plane of MCHC before, and after operation. Note the increased erosion in the central channels.......................................................................................170 Figure 95: Example of a generic computational zone grid............................................186 Figure 96: Computed plasma density profile in 6mm Tungsten cathode 3.3 amp 121 volt discharge, 215 sccm flow rate. ........................................................................208 Figure 97: Computed neutral particle density profile in 6mm Tungsten cathode 3.3 amp 121 volt discharge, 215 sccm flow rate............................................................209 Figure 98: Computed electron temperature (eV) potential profile in 6mm Tungsten cathode 3.3 amp 121 volt discharge, 215 sccm flow rate. .............................209 Figure 99: Computed plasma potential profiles in 6 mm Tungsten cathode, 3.3 Amp, 121 Volt discharge, 215 sccm flow rate...............................................................210 Figure 100: Computed heavy species temperature in 6 mm Tungsten cathode, 3.3 Amp, 121 Volt discharge, 215 sccm flow rate...............................................................210
  15. 15. xv Abbreviations Symbols used: D characteristic dimension/length (m) e elementary charge (C) q species specific elementary charge (C) n species number density (#/m3 ) λ mean free path (m), wavelength (m) εo permittivity of free space εi ionization energy ε emisivity φ work function (eV), plasma potential (V) Φs potential drop (V) η plasma specific resistivity σ collisional cross-section (m2 ) ν collision frequency (s-1 ) kb Boltzmann’s constant ki ionization rate coefficient h Plank’s constant j current density (A/m2 ) A material constant, area (m2 ) T temperature (eV or Kelvin) E electric field (V/m) Kn Knudsen Number m electron mass (kg) M heavy species mass (kg) n ionization rate density (#/sm3 ) P,P pressure (Pa) q conductive heat flux (W/m2 ) r radius (m) t time (s) u velocity (m/s) κ thermal conductivity(W/mK) Γ flux density (#/sm2 ) S inelastic collision energy loss (kg/ms3 ) Z atomic number Subscripts and Superscripts: a generic species type a b generic species type b n neutral
  16. 16. xvi grey graybody black blackbody i ion, ionization e electron h heavy species (ion or neutral) pe plasma electron b Boltzmann, beam s sheath th thermionic wall cathode wall eff effective c cathode o reference value en electron-neutral ei electron-ion eV indicates value in electron Volts K indicates value in Kelvin th thermionic wf work function Constants: kb Boltzmann’s Constant, kb = 1.3806*10-23 J/K, 8.6174*10-5 eV/K e basic electronic charge, e = 1.6*10-19 C ε0 Permittivity of free space ε0 = 8.85*10-12 C2 /Nm2 me mass of single electron, me = 9.11*10-31 kg α Richardson Constant, α = 1.2017*106 A/ K2 m2 R Gas constant, R = 8.3144 J/moleK c speed of light c = 3*108 m/s
  17. 17. xvii Abstract: This research addresses several concerns of the mechanisms controlling performance and lifetime of high-current single-channel-hollow-cathodes, the central electrode and primary life-limiting component in Magnetoplasmadynamic thrusters. Specifically covered are the trends, and the theorized governing mechanisms, seen in the discharge efficiency and power, the size of the plasma attachment to the cathode (the active zone), cathode exit plume plasma density and energy, along with plasma property distributions of the internal plasma column (the IPC) of a single-channel-hollow-cathode. Both experiment and computational modeling were employed in the analysis of the cathodes. Employing Tantalum and Tungsten cathodes (of 2, 6 and 10 mm inner diameter), experiments were conducted to measure the temperature profile of operating cathodes, the width of the active zone, the discharge voltage, power, plasma arc resistance and efficiency, with mass flow rates of 50 to 300 sccm of Argon, and discharge currents of 15 to 50 Amps. Langmuir probing was used to obtain measurements for the electron temperature, plasma density and plasma potential at the cathode exit plane (down stream tip). A computational model was developed to predict the distribution of plasma inside the cathode, based upon experimentally determined boundary conditions. It was determined that the peak cathode temperature is a function of both interior cathode density and discharge current, though the location of the peak temperature is controlled gas density but not discharge current. The active zone width was found to be an increasing function
  18. 18. xviii of the discharge current, but a decreasing function of the mass flow rate. The width of the active zone was found to not be controlled by the magnitude of the peak cathode wall temperature. The discharge power consumed per unit of mass throughput is seen as a decreasing function of the mass flow rate, showing the increasing efficiency of the cathode. Finally, this new understanding of the mechanisms of the plasma attachment phenomena of a single-channel-hollow-cathode were extrapolated to the multi-channel- hollow-cathode environment, to explain performance characteristics of these devices seen in previous research.
  19. 19. 1 Chapter 1: Introduction In January of 2004, US president George Bush announced the new Vision for Space Exploration (VSE) [49], in which he directed NASA to return humans to the lunar surface, establish a permanent human presence on the moon by 2020, and to eventually send human explorers to the Martian surface. In achieving these difficult and expansive goals with a high rate of efficiency and financial affordability, it is understood that high specific impulse propulsion technology is desirable, specifically electric propulsion (EP), solar and/or nuclear. Owing to their perforce in both thrust and specific impulse (Isp), Magnetoplasmadynamic (MPD) thrusters (also called Lorentz Force Accelerators, LFA’s) have been identified as a prime candidate for such missions as heavy lunar cargo (supporting a lunar base/outpost), piloted missions to Mars, and heavy cargo missions to Mars [62, 23, 17, 34]. Magnetoplasmadynamic thrusters have a desirable combination of high Isp (~3,000 to 10,000s) and relatively high thrust (~10 to 100N), while providing a large power processing density attractive to spacecraft designers. Although MPD/LFA thrusters provide large thrust for an EP device, they provide relatively low thrust compared to chemical systems, and so like all EP systems, they are required to have a long lifetime: thousands of hours of reliable performance. The cathodes of MPD thrusters have been identified as the primary lifetime- limiting component, thus much MPD thruster research focuses on cathode related issues. Due to the high operating temperatures of MPD thrusters, cathodes are made of refractory
  20. 20. 2 metal (such as Tungsten or Tantalum), and have historically been solid rods, however in recent years investigations into hollow cathodes, specifically Multi-Channel Hollow Cathodes (MCHC), have yielded promising results. Little literature exists discussing high-current hollow cathodes, with much of the available work coming from a program of study conducted by the Moscow Aviation Institute of former Soviet Union during the mid 1990’s. A complete understanding of the physics, lifetime and performance of MCHC devices is necessary in order to advance MPD thruster technology to the level of a reliable flight propulsion system. This research focuses on the internal plasma properties in a single channel of the multi-channel cathode, with the goals of a predictive capable model yielding internal plasma properties, which can be input into existing “cathode life models”. 1.1 The Importance of Electric Propulsion In order to make the great expanses of the solar system accessible to both robotic scientific investigation and manned exploration, it is necessary to transport resources across inter-planetary distances by means of high efficiency. All space missions are measured by a change in velocity (noted as ΔV, and read as “delta-V”), which is the total change in velocity necessary to accomplish the mission, or in-short, it is a measure of the energy necessary to achieve the mission’s propulsion goals. The choice of propulsion systems used for a particular mission is largely mission specific, with a wide array of options available to mission designers. The field of available options can be roughly
  21. 21. 3 broken down into two categories, 1: high-thrust low-efficiency, and 2: low-thrust high- efficiency. Typically category 1 propulsion systems are chemical engines (such as those carrying the space shuttle into orbit), while a significant portion of category 2 systems are Electric Propulsion (EP, such as the ion engine which propelled the Deep Space 1 mission). By far the most common form of spacecraft propulsion is the traditional chemical system, where by (usually) two propellants, the fuel (such as hydrogen) and the oxidizer (such as oxygen) are mixed together, combusted at high temperature and pressure, and then expanded via a contoured nozzle which produces thrust by gas-dynamic means. Chemical rocket engines produce large amounts of thrust, which is why all launch vehicles employ these types of systems, but they have a low Isp and so are relatively fuel inefficient. In chemical engines, energy stored in the chemical bonds of the propellants is released through the combustion process and then converted to kinetic energy, producing thrust. Thus the amount of available energy is determined by the combustion chemistry of the fuel and oxidizer. In Electric Propulsions system, the energy is produced by an external power source (batteries, solar array’s, nuclear reactor, etc.) and is transferred to the propellant producing thrust, thus (to first approximation) the amount of energy available to be converted to directed kinetic is only limited by the capability of the power supplies (and material limits). An EP system is categorized by the means by which energy is transferred to the propellant: Electrothermal, Electrostatic, or Electromagnetic. It is always desirable to achieve mission goals with the best possible use of resources and the most efficient systems available, however for lifting off of a planetary
  22. 22. 4 body (Earth, Moon or an asteroid), when the spacecraft is subject to a large gravitational force, high thrust chemical engines are exclusively required. However, once in orbit, where low thrust systems can achieve the required goals, mission designers have more options available from which to choose. It is here that the Electric Propulsion systems have their greatest impact to space exploration, for higher efficiency systems require less propellant to achieve the same ΔV. If a spacecraft now needs to carry less propellant, it can carry more cargo in the form of scientific instruments, people, power systems, etc. The propellant-efficiency of a propulsion system is measured in Specific Impulse, Isp (measured in seconds), which is a measure of how fast the engine exhaust is expelled from the thruster. Consider an individual particle in the exhaust plume; the higher the exhaust velocity of that particle, the more momentum it will add to the spacecraft. exhaust o u Isp g ≡ (0.7.1) From the rocket equation, we can see that the value of the thrusters’ specific impulse becomes exponentially important in determining the amount of propellant necessary to achieve a certain Δv: Minitial = M final e Δv Ispgo⎛ ⎝⎜ ⎞ ⎠⎟ (0.7.2) where Minitial and Mfinal are the vehicle mass prior to and after the engine burn. The current cost of launching payload into Earth orbit has been (roughly) estimated at $10,000 per kg – thus, in-space propulsion systems requiring large amounts of propellant will need pay a high price to place this propellant in orbit. From this it is
  23. 23. 5 easy to see how high Isp electric propulsion systems are desirable from both the resource utilization, and financial, points of view. Any future, large scale, sustained exploration effort will be required to make the best possible use of available resources to achieve long term viability. Electric Propulsion systems are currently the most efficient means of in-space propulsion available, thus their continued development is a key requirement for an affordable, and achievable, expanded program of space flight as described by NASA’s Vision for Space Exploration. To attempt a large scale, long term program of space exploration without means of high efficiency propulsion systems is to ensure its financial infeasibility, and ultimate failure.
  24. 24. 6 Chapter 2: MPD Thruster and Cathode Operation 2.1 The MPD/LFA Thruster An MPD thruster is a type of Electric Propulsion system, which makes use of the nature of charged particles to produce useable thrust with high efficiency. Magnetoplasmadynamic thrusters are classified as electromagnetic devices (though gasdynamic forces also play a role in the production of thrust). Electromagnetic thrusters produce a plasma and generate thrust by use of electromagnetic fields to accelerate the charged particles in a direction opposite of the spacecrafts desired vector of travel. A basic schematic drawing of an MPD thruster can be seen in Figure 1. (For further discussion of electrothermal and electrostatic systems, see [33]). A typical Self-Field MPD thruster consists of a central rod shaped cathode inside a cylindrical anode. An electrically neutral gas flows from behind the cathode and is introduced into the discharge region between the two electrodes. Initially, a high voltage is placed between the two electrodes, forming plasma by the initial breakdown of the gas, after which point a high current supply is engaged and the high voltage supply is disengaged. During initial breakdown under the high voltage, a small current flows through the plasma across the large voltage drop via enhanced field emission from a relatively cold cathode. After initial breakdown of the gas is achieved, a high current is then driven through the plasma, however since the bulk cathode is still too cold to support
  25. 25. 7 Figure 1: MPD thruster and force vectors [26] the required current through thermionic emission, the current is initially generated by small “cathode spots” on the cathode surface. These spots are characterized as small, non-stationary, highly mobile regions of intense heat (near the material boiling point) supplying electrons via a combination of field emission and thermionic emission [54]. This initial ignition of the discharge is the most destructive phase of cathode operation, as (for each cathode spot) the large heat loads on such a small amount of surface area cause the explosive release of vaporized cathode material and electrons, a process which occurs very rapidly before each emission site is terminated and another one is born at a different location. This non-stationary mode continues until the total heat provided by the many cathode spots raises the surface temperature to levels sufficient to
  26. 26. 8 support steady-state thermionic emission over a relatively large surface area. Thus the initial startup phase is characterized by large material erosion rates, three or four orders of magnitude higher than rates experienced under steady-state operation [54]. During steady state operation, current flows between the two electrodes causing the neutral gas to be ionized by collisions with electrons emitted thermioniclly from the cathode surface. This current creates an azimuthal magnetic field, which interacts with the motion of the charged particles, and a force tangent to both is created, governed by the Lorentz Force equation: Fmag = q v × B( ) in the absence of any electric field. It is for this reason that MPD thrusters are also referred to as Lorentz Force Accelerators, or LFA’s. (Historically, thrusters using gaseous propellant are called MPD’s, and those using vaporized metal propellant at called LFA’s, further discussion on this topic is found later in this paper.) Figure 2. Force vectors in ALFA^2 Li-LFA
  27. 27. 9 An electric field is created with both radial and axial components, driving current flow between the two electrodes. For qualitative description, a quick application of the right hand rule helps one see that the resultant force acts to accelerate the plasma both axially outward (termed the “blowing” force) and radially inward (termed the “pumping” force) with the total thrust created proportional to J2 . The ionization of the propellant gas creates a quasi-neutral plasma, and the Lorentz force accelerates both ions and electrons along the same force vector, thus space-charge limiting and beam neutralization are not factors in MPD thrusters as they are on other electric propulsion systems (ion, hall, etc.). Additionally, if the anode-cathode pairing is placed inside an external solenoid (co-axial with the cathode) producing a strong applied solenoidal magnetic field coaxial with the cathode, there is further plasma acceleration due to the interaction between the plasma and the applied magnetic field - this system is called an Applied Field MPD Thruster. Typically the applied field is used in “low power” systems (P < 500 kW), and is strong in magnitude in comparison to the magnetic field produced by the main discharge (BApplied>>BSelf). Several different thrust producing mechanisms have been identified in MPD thrusters [35]: 1. Self Field Acceleration (Lorentz force acceleration), 2. Gas Dynamic Acceleration 3. Swirl acceleration 4. Hall acceleration Swirl and Hall acceleration are caused by the interaction between the discharge current flowing through the plasma and the external applied magnetic field, and thus are
  28. 28. 10 pertinent to applied field thrusters only. The relative dominance of each thrust mechanism is still a mater of debate among researchers. Since the plasma acceleration mechanisms (with the possible exception of gas dynamics) play no significant discernable role in the internal physics of hollow cathodes, which is the focus of this work, there will be no further discussion of this topic. For additional related material see [33, 63, 14] 2.2 Hollow Cathode Operation Conventional Hollow Cathode: A conventional orificed hollow cathode consists of a hollow cylindrical tube with a plate on the down stream end, as seen in Figure 3. The plate has a small orifice in it, through which the plasma exits. Inside the tube is a porous Tungsten insert, impregnated with a Barium Calcium aluminate source material, for work function reduction. Before the discharge is ignited, the tube is heated to working temperature (~1,000 K) by an external source, typically a resistive heating element in physical contact with the exterior of the tube. The Barium in the insert material migrates its way up to the surface of the cathode where a layer of adsorbed oxygen and Barium atoms is formed, reducing the work function of the material. The working gas is ionized by collisions with the electrons emitted from the insert, and a quasi-neutral plasma exits through the orifice.
  29. 29. 11 Figure 3. Orificed Hollow Cathode [42] Ions created in the collisions will make their way to the walls of the cathode where they will be accelerated through the sheath potential drop and strike the surface of the insert depositing heat, recombining and then drifting off as a neutral. This process continues the heating of the cathode, and a balance between heating through ion bombardment and cooling through (mostly) thermionic emissions is attained, at which point the external heater is turned off. Adsorbates lost to evaporation are then replenished by a continuously renewing supply of Barium and Barium-Oxide, until the insert’s supply is depleted, at which point cathode temperatures rise and it has (largely) reached the end of its useful lifetime. The orifice plate serves as a physical barrier acting to retain the neutral gas inside the cathode, increasing the resonance time of any one particle and increasing the likelihood of ionization. The total pressure is nearly constant inside the cathode, and typically the ionization fraction is very low. Insert temperature levels peak at the Insert material
  30. 30. 12 downstream end in contact with the orifice plate, and decreases at a rate inversely proportional to distance upstream. Some examples of this type of cathode are the NSTAR (NASA Solar Electric Propulsion Technology Application Readiness) cathode used on the NASA Deep Space 1 ion engine, the plasma contactor used on the International Space Station, and the NEXIS (Nuclear Electric Xenon Ion System) cathode used on the NEXIS ion engine developed under Project Prometheus. Such low current cathodes have demonstrated relatively long operational lifetime in both ground and in-space testing. In one particularly significant experiment, an NSTAR type cathode, similar in configuration to the design used for the International Space Station plasma contactor, was run for 27,800 hours at an emission current of 12 Amps with a Xenon flow rate in the range of 4.2 to 4.7 sccm. Optical pyrometery measurements recorded average cathode peak temperature of 1533K during the first 23,776 hours of operation while discharging 12 Amps [53]. In comparison, MPD cathodes are required to discharge current levels up to several kilo-Amps. Hollow cathodes see space application use in many devices including Hall thruster, ion engines, and plasma contactors. Single Channel Hollow Cathode: A single channel hollow cathode (SCHC) is a simple device consisting of a single, cylindrical hollow tube, with no orifice plate or low work-function insert material, with some means of mating to the propellant feed system. In MPD thrusters, no external heating device is used to pre-heat the cathodes due to the limited usefulness of such a
  31. 31. 13 device once exposed to a cathode operating at temperatures > 2,500K during the MPD discharge. All electron emission is directly from the walls of the tube, and the plasma is generated (largely) inside the hollow region. In MPD thrusters, if the flow rate of propellant is high enough to be considered a viscous continuum, upon exiting out of a SCHC the flow is choked due to the large pressure difference between the inter-electrode space, and the cathode hollow region. Due to the open ended geometry there exists a large axial pressure gradient along the cathode, with propellant gas density dropping considerably as it approaches the cathode exit. A density distribution is established, leading to changing mean-free-paths throughout the cathode. Basic electron emission and ionization processes in a SCHC are similar to those in a traditional orificed hollow cathode, although due to the absence of a porous insert, there are no issues of Barium depletion, and useful lifetime is determined by the evaporation rate of the cathode wall itself. Experimental work on SCHC devices has shown that from the cathode exit plane, the surface temperature rises to a peak temperature at a location some distance L upstream, the temperature then falls as you proceed further upstream. This distance L is a function of the cathode size, discharge current, propellant flow rate, and choice of propellant gas, though the exact form of this function is still a matter of debate among researchers. Figure 4 shows the axial temperature profile of a typical SCHC discharge.
  32. 32. 14 Figure 4. Axial temperature trends of a typical SCHC [18] Multi-Channel Hollow Cathode: A multi-channel hollow cathode (MCHC) consists of several parallel channels of ionization, the exact geometry of which can vary depending upon design. The two most common designs are: 1. A single rod with several holes drilled parallel to the central axis, 2. A single hollow tube of diameter D, with many smaller solid rods of diameter d (where D>>d) placed inside the tube, where the channels are created by the spaces in between the rods. This is knows as a “macaroni packet” and is by far the
  33. 33. 15 more common design. Several different hollow emission regions are formed by the inter-rod spacing, see Figure 6. In all cases, the entire cathode component is commonly constructed of the same material, and is usually Tungsten (or Tungsten impregnated with a work function reducing material, such as Thorium). The two common designs are shown in Figure 5. Figure 6 shows the regions formed in construction of the macaroni packet design, where inter rod spacing creates many channels through which the gas flows. There are generally three types of channel cross sections formed, and each channel acts as an individual single channel hollow cathode as shown schematically in Figure 7. Each channel will have its own unique interaction with the plasma which is determined by the channels geometry and distance from the cathode centerline. The MCHC design is particularly well suited in an MPD thruster due to the high operating temperatures. Even though the porous Tungsten insert in the traditional hollow cathode has a lower work function, it would not survive long in the environment of an MPD, and so is not used. Instead, all the electron emission in a MCHC comes directly from the cathode wall itself. In practice, a MCHC can be thought of as several SCHC’s operating in parallel.
  34. 34. 16 Figure 5: Two different designs for Multi-channel Hollow Cathodes Figure 6. Inter-rod spacing in "macaroni packet" design MCHC. Each hollow region acts as an individual SCHC. Figure from reference [65]
  35. 35. 17 Figure 7. Multi-Channel Hollow Cathode – “macaroni packet” design – side view Upstream of the channels the neutral gas is introduced to the cathode, and at some point in the flow it develops the familiar parabolic velocity profile where the particles in the center of the flow move faster than those at the periphery. Thus, each channel will have a different mass flow rate, and therefore a different IPC (Internal Plasma Column, discussed in section 2.4). An operating MCHC is seen head-on in Figure 8. Figure 8. MCHC during operation, as seen head on. Photo from reference [65]
  36. 36. 18 2.3 The Importance of Temperature MPD thrusters are driven by constant current power sources, in experimental practice these are often arc-welding power supplies. The electron current flowing in the discharge comes largely from thermionic emission off the cathode surface, which is directly controlled by the temperature of the surface material (and work function) – thus a certain surface current density will be produced by a certain surface temperature. For current levels necessary in MPD thruster cathodes, the operating temperature of a Tungsten cathode approaches the melting temperature of the material (3680K), and thus a non-trivial amount of the material will evaporate during normal operation. Previous research has shown that at high temperatures the evaporation of cathode surface material is exponentially proportional to the surface temperature (~ eT ) [54]. For a given arc attachment area, exerting a larger force on the plasma requires a larger discharge current, which requires a higher temperature, which in turn leads to a higher evaporation rate and thus a shorter cathode lifetime. Thus (at this time) the reliable lifetime of an MPD thruster system is largely a function of the cathode temperature, indeed surface temperature is the key determinant of all thermionic cathodes. Figure 9 and Figure 10 show a MCHC before and after operation, where the result of extended operation at high temperature is very apparent.
  37. 37. 19 Figure 9. Tungsten MCHC before operation in MPD thruster. Photo from reference [65] It is for this reason that the ability to predict the temperature distribution of the cathode for given operating conditions is of prime importance, for these distributions can then be input to evaporation models and thus the useful lifetime of the cathode can be predicted. Much work in cathode research focuses on predicting and reducing the operating temperature of the cathode, following this course, two main paths have been pursued, cathode geometry and reduction in work function. For a given cathode material, it is desirable to achieve longer cathode life times by reducing the operating temperature through a reduction of the surface current density, while still maintaining total current levels and thruster performance. This is accomplished by changing the geometry such that the same discharge current is emitted by a larger surface area of the cathode. With a solid rod cathode, it is only the exterior surface area
  38. 38. 20 Figure 10. Tungsten MCHC after operation in MPD thruster. Photo from reference [65] of the cathode which emits – for a single hollow tube cathode, the interior and exterior surfaces emit, and hence the required current density is effectively reduced by a factor of two. In a MCHC, each channel acts as an individual hollow tube cathode, and thus the emission area increases significantly, enabling a reduction in the current density surface temperature, though a detailed understanding of the interaction between the plasma and the interior of a MCHC is not present in the literature. In addition to the erosion processes in the cathode, the other significant cathode mechanism strongly controlled by temperature is the thermionic emission of electrons from the material surface. All conductors will emit electron current in proportion to the temperature of the material, and material properties. This emission is governed by the well known Richardson equation for thermionic emission:
  39. 39. 21 eff b wall2 s wall eff wf o , 4 k T qE j AT e φ φ φ πε − = = − (2.2.1) Where “j” is the emitted surface current density in A/m2 , A is known as the Richardson coefficient, and is = 6x105 A/m2 /K for Tungsten [25]. Φwf is the work function (in eV) of the material (= 4.5 for pure Tungsten [25]), and Φeff is the effective work function, which is an effective reduction of the work function by an applied electric field over the surface of the material, the cathode sheath. It is clear to see that the electron current emitted from the surface of a hot cathode is very sensitive to both temperature and work function, with the latter the dominant parameter. A reduction in the work function by 0.5 eV yields greater than an order of magnitude difference in emitted current. In addition, a drop in surface temperature of 10% yields a corresponding reduction in emitted current density of 95.5 %.This sensitivity can been seen in Figure 11 (note the units in the figure). From this, it is easy see that nearly all of the emitted current of a hollow cathode comes from a relatively small region of the material wall, the region termed the “active zone” or “hot spot”. The precise definition of what constitutes the active zone varies among studies, but is generally taken as the region of cathode wall responsible some high percentage of the thermionically emitted current, typically ~70- 100%.
  40. 40. 22 Figure 11. Sensitivity of emitted current to temperature and work function [26] The choice of cathode material, as well as choice of propellant, has an influence on cathode temperature by reducing the work function of the material. Choosing a cathode material with a reduced work function, such as using Thoriated Tungsten rather than pure Tungsten, will reduce the temperature (for constant emission) - approximately 1~2% thorium is typical of such cathodes. With Tungsten cathodes, it has also been shown that by mixing a small amount of Barium with the propellant, the Barium will deposit itself as a monolayer on the Tungsten surface, and reduce the work function. 2.4 Internal Plasma Column- IPC The bulk volume of the plasma in MPD thrusters exists in the annular zone between the cathode and anode - the extension of the plasma to the interior region of the
  41. 41. 23 hollow cathode, is termed the Internal Positive Column, or IPC (sometimes called the Internal Plasma Column). The IPC is also termed the “plasma attachment area” in some literature due to its close interface in both proximity and phenomenon with the surface of the cathode. Though the IPC is of prime importance, its limits and area of coverage have been ill defined (both qualitatively and quantitatively) in MCHC literature. It is largely regarded as part of the hot spot, or active zone [18], of a thermionically emitting hollow cathode, and includes the regions of the cathode immediately upstream and downstream of the location of peak cathode temperature. This is largely due to a lack of theoretical research into such devices, as there currently is no reliable/validated model capable of qualitative and quantitative predictions of how far the plasma will penetrate upstream inside a MCHC device. The importance of the IPC can be understood through its relation to the plasma generation processes at work in the hollow region. Plasma is generated inside the cathode by the ionizing collisions between neutral atoms in the propellant stream and the thermionic (beam) electrons which are emitted from the cathode walls and then accelerated through the sheath potential into the main plasma volume. The ionization potential of the neutral gas sets a minimum energy requirement for a single ionization event to occur - thus single event ionization will only occur when electrons of high enough energy strike the neutrals, these high energy electrons coming from two sources: when thermionically emitted electrons accelerated through the sheath gaining sufficient energy, or from electrons in the high energy tail end of the distribution. In a multi-step ionization process, many separate collisions can each deliver finite amounts of energy to
  42. 42. 24 a neutral atom, with each collision raising the atoms internal electronic energy level and bringing it that much closer to ionization. Up to this point the relative contributions of single and multiple collisions to the ionization process of the hollow cathode IPC have not been well defined, largely due to lack of experimentally verified data of plasma properties in the IPC, and little information about this exists in the literature. Recent work in this area conducted at Princeton University [8], have modeled the plasma generation process in the IPC as a multi-step ionization process. Many collisions between electrons and neutral atoms result in excited atoms which do not become ions. When these atoms return to lower energy levels they emit radiation (seen as the bright glow of the plasma arc), some of which deposit energy back in the cathode walls, some of which is adsorbed by other particles of the plasma. Some radiation not adsorbed by other particles does not impact on the cathode wall, but a certain fraction of the total radiated power directed upstream out of the thruster and lost to the system – these events appear as energy losses to the system as no useful action (thrust, heat, etc) can be gained from them (with the possible exception of finding your cathode in the dark). If the plasma is optically thick, then this radiation from de-excitation will be absorbed back into the plasma. An excited atom then has a probability (as a function of time) of decaying to a lower energy level, however if the amount of time that an atom remains in an excited state is of the same order as the electron neutral collision frequency, the excited atom has a high probability of further excitation, a process which will eventually yield an ionization event. This further contributes to multi step ionization. Examining the relative contributions to the total rate of plasma generation made by both single collision and multi-collision processes can yield valuable insight. Consider
  43. 43. 25 when the electron temperature is much less than the ionization energy of the neutral atom, and the neutral species speed is much less than the electron speed. The equation for the direct ionization (single collision) rate coefficient as a function of electron temperature is then [22]: { } ( ) i e 4 heavye e o o 22 e i o 8 , 4 T i Z qqT k T e m ε π σ σ π ε πε − = = (2.3.1) Where Zheavy is the number of valence electrons in the heavy species particle, and σo is approximately the geometrical atomic cross section, of the neutral heavy species atom (the electron temperature is in units of electron Volts). Now, in the same plasma, consider ionization via a multi-step (stepwise) process. The equation for the stepwise ionization rate is expressed as: { } ( ) i e e 10 s ei i e 5 3 3 o o 1 4 Tm qg k T e g h T ε πε −⎛ ⎞ ≈ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ (2.3.2) Where g and h are the statistical weight and Planks constant, respectively. A comparison of the direct ionization rate coefficient to the stepwise rate coefficient yields: { } { } ( ) ( ) 7 7/22s 2 4 4 i e i o e e 2 22 i e o o ee o o , 4 4 k T g a m q m qI I k T g ThT hσ πε πε ⎛ ⎞ ⎛ ⎞ ≈ ≈ ≈⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠ (2.3.3) This relation shows that in plasmas with electron temperatures low in comparison to the first ionization energy of the neutral atom, the step-wise ionization process will dominate. When Te ≈ εi both processes are significant contributors to plasma generation, and when Te >> εi the direct ionization process will dominate. Thus for the type of
  44. 44. 26 plasma considered in hollow cathodes, where electron temperatures in the range of 1 to 5 have been reported, the coefficient ratio can range from 50 to 104 , The step-wise ionization rate is thus several orders of magnitude more significant than the direct ionization rate. The stepwise ionization rate coefficient can then be calculated from: { } { } i e 7/ 2s i e i e e 7/ 2 7/ 2 s e i i o e e e 8 T k T I k T T qTI I k k e T m T ε σ π − ⎛ ⎞ ≈ ⎜ ⎟ ⎝ ⎠ ⎛ ⎞ ⎛ ⎞ ≈ ≈⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ (2.3.4) The total rate of ionization is: i e 7/ 2 7/ 2 Total s e i i i i o e e e 8 1 1 TqTI I k k k k e T T m ε σ π −⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎢ ⎥ ⎢ ⎥= + ≈ + ≈ +⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦ (2.3.5) Where for Argon, we have σo = 1.9x10-21 m2 . The final ionization rate, or the number of positive ions created per second per unit volume, is given by: i Total n e e,n u u kν σ σ= = (2.3.6) Gas 1st Ionization energy (eV) 2nd Ionization energy (eV) Argon 15.76 27.64 Lithium 5.39 75.67 Hydrogen 13.59 - Xenon 12.13 21.22 Table 1. Ionization energy for common electric propulsion propellants The energy of the electrons is determined by the acceleration through the sheath field plus initial thermal energy determined by the cathode wall temperature, thus the
  45. 45. 27 region of cathode wall supplying single event ionizing-capable electrons is tied to the axial profile of the radial potential drop of the sheath. Table 1 lists the first and second ionization energy for several types of propellants commonly used in electric propulsion. Defining the IPC as the region of interior cathode volume containing the plasma and the plasma’s attachment to the cathode walls, and considering only single collision ionization, we can say that the IPC is therefore set by the region of the cathode wall(s) where the sheath voltage profile is above this minimum determined by the gas properties. Contributions to the ionization process made by the high energy electrons contained in the tail end of the electron energy distribution function will set this minimum sheath voltage somewhat lower than the ionization energy of the propellant gas. Where the sheath voltage drops below this minimum should be the end (or very near the end considering both high energy thermionic electrons in the tail end of the distribution, and some upstream diffusion) of the active zone or region of plasma generation - thus with the limits of ambipolar diffusion in a high speed neutral flow [8], this provides an upper limit to the length of the IPC. If a model can accurately predict the profile of the sheath drop, this will provide a prediction of how far the plasma will penetrate into the hollow region. Now, if one also considers setp-wise (multi-collision) ionization, the IPC can be extended a significant amount further upstream into the cathode, as individual electrons no longer need energy equal to the ionization energy of the neutral gas. It is important to note that this thesis work does include contributions made by both direct ionization, and multi-step ionization events. In experiment we observe the IPC to penetrate much further into the cathode than the point at which the sheath drop equals the ionization energy of
  46. 46. 28 the working gas, thus the role of the multi-step excitation and ionization process is significant and must be included. The nature of the IPC is both a cause and consequence of the cathode temperature, which depends upon many factors but in summary is determined by an energy balance between all processes (plasma related and otherwise) heating and cooling the cathode. From the plasma, energy is brought to the cathode by ions (mostly single ions, and a small number of double ions) and (reverse) electrons. The ions are naturally attracted to the cathode, and it is assumed that all ions which enter the sheath region will strike the cathode wall after falling through the attractive sheath drop. Each ion strike deposits a certain amount of heat in the cathode wall, proportional to the sheath drop (with the assumption of positive singly charged atoms only). {A note on nomenclature, particles in the central region of the cathode which covers all volume except the sheath region, are termed bulk plasma particles. Particles in the sheath region are termed sheath particles, and electrons thermioniclly emitted from the hot cathode wall are termed beam electrons.} For electrons, the sheath drop is repulsive, and thus in order to reach the cathode surface, plasma electrons are required to have an energy higher than the sheath drop. If we assume a Maxwellian distribution of thermal (bulk plasma) electrons, we can note the following: Once the bulk plasma electrons undergo many collisions they will have transferred most of their energy to ions and neutrals, and thus on average do not posses the required energy to reach the surface. After a certain number of collisions the electrons are said to be thermalized, and will attain some local average electron temperature below the 1st ionization potential of the working gas.
  47. 47. 29 Assuming the electrons in the IPC have a Maxwellian distribution, it is only the high-energy tail end of the distribution which can overcome the sheath drop and strike the cathode wall. It is only the high energy electrons which are within a single mean free path of the boundary between the sheath and the main plasma which are of importance here, since any electrons further away will undergo a collision leading to reduced energy and a speed in a different direction. Sheath models are usually assumed to be collisionless regions. As the sheath drop increases, electrons entering the bulk plasma have more pre- collision energy, thus once they become thermalized they are hotter (as compared to a lower sheath voltage). The average thermal electron temperature is therefore higher as one approaches the cathode exit. The main source of cathode cooling has been shown to be thermionic electron emission to the plasma [26]. A less significant amount of cooling is provided by neutral recombination on the surface, whereby an electron from the wall will combing with an ion adsorbed on the surface, releasing energy equal to the material work function plus the temperature of the wall. Once a cathode has reached steady state operation, a balance will have been achieved between the heating and cooling processes, therefore models which fail to accurately capture the nature of these processes will result in inaccurate temperature predictions. Experimental work [18] has shown that the magnitude of the sheath potential drop inside a SHCH can vary greatly with axial distance from the cathode exit. This range of potential drop across the sheath (for a given geometry and gas type) is related to the mass flow rate and the discharge current. The total cathode drop begins near the cathode exit,
  48. 48. 30 and ends at the potential of the cathode wall itself. Between these two boundaries the sheath and pre sheath drop is across the IPC, and can be approximated as purely axial along the cathode centerline, and purely radial near the wall (see Figure 12). Effects of Mass Flow Rate on Plasma Conditions Experiments have shown that reducing the gas flow rate has the effect of increasing both the IPC length and (within certain ranges of flow rate) the cathode voltage drop [18, 9]. It is believed that this effect occurs due to the reduction of neutral density which increases the beam electron mean free path and reduces the electron- neutral collision frequency, thus fewer ionizing collisions will occur for a given volume and given electron emission current off the surface. The mean free path, and electron neutral collision frequency are given by: λ = 1 nnσen = 1 nnπdn 2 2 (2.3.7) νen = nne2 m η (2.3.8) In order for the discharge to maintain the same current it must compensate for this loss of available charge carriers and increased electron mfp. Consider two possible results which can occur next:
  49. 49. 31 A. Increased current density from the same emission region (to increase the likelihood of electron-neutral collisions) B. Increased attachment area (emission region). If the discharge current is below the level required for the plasma to be fully ionized, and the discharge voltage is such that each beam electron has at most (on average) one ionizing collision, we can observe the following: Upon closer examination of option A, note that increased current density from constant emission surface area will require an increase in the sheath voltage. The larger sheath drop will reduce the work function through enhanced Schottky effect, and give added energy to ions impacting the surface, which will drive the temperature up. Both of these effects will tend to drive the thermionic emission current density to higher levels. If the sheath voltage is made high enough, beam electrons will exit with enough energy to ionize two neutrals. As the energy of the electrons exiting the sheath increases, so does the energy of the thermal electrons in the plasma, and thus a larger percentage of these will have the energy necessary to overcome the sheath potential, strike the wall and deposit even more heat. If the discharge current remains the same with a reduced flow rate, the ionization fraction will increase. Now let us examine possibility B, increased attachment area. Figure 12 shows the effects of flow rate on the IPC length, and equipotential surfaces in the volume for possibility B. It is reasonable to see that when the density decreases, the plasma faces less opposition to diffusion further upstream - if the electric field penetrates further upstream, the region of wall over which the minimum sheath drop required for ionization exists,
  50. 50. 32 increases. A larger surface area of cathode wall will now be emitting elections, with energy levels above the minimum necessary for ionizing collisions, into a larger volume of gas (with lower density due to reduced flow rate). These ions will deliver heat during wall strikes, increasing the wall temperature, and the balance will be maintained. When the electric field penetrates further upstream, the total cathode drop increases, and so does the total discharge voltage, thus additional power is again required for the cathode to emit the same current at the reduced flow rate. Further, and more importantly, one must consider the contributions made by multi- electron impact events on the ionization process. As shown by Mikellides et. al. [42], in the internal plasma of an orificed hollow cathode flowing Xenon, the average electron energy levels are well below the ionization potential for Xenon (as shown in Figure 13), and thus the contribution of ionization through multi-step excitation can be significant. This is particularly important in the cathodes of MPD thrusters, where the sheath voltage drop can be as low as a few volts [26]. This is reasonable when one considerers that such cathodes function within the range of continuum flow where the plasma is highly collisional, and each neutral atom can expect to undergo many collisions during its time in the cathode.
  51. 51. 33 Figure 12 Equipotential Lines for flow rates, low (a), moderate (b), high (c) [18] Figure 13. Computed electron temperature in an orificed hollow cathode [42]
  52. 52. 34 As the density in a cathode decreases, the frequency of electron impacts on an individual atom decreases. From this we can extrapolate that ionization via a multi-step excitation process due to collisions with many low energy electrons is less likely, and thus to maintain ionization, higher energy electrons are necessary (each electron must bring more energy to the collision). The smaller the collision frequency, the larger the necessary average electron energy. Since it is acceleration through the sheath voltage which provides energy to the electrons, the average electron energy increases with sheath voltage, which itself increases with the total voltage drop for the discharge and hence the power consumed by the discharge. From this view of the multi-step excitation process, it is easy to understand the relation between plasma density and cathode voltage. This process plays a key role to understanding the relationship between the power consumed by the discharge and the plasma density inside the cathode. As nature would have it, the increase in discharge voltage necessary for an increased plasma penetration depth is lower than that for constant plasma penetration depth and so scenario B is the one observed in experiment. Again, this is linked to the contribution made by the multi-step excitation and ionization process for lower energy electrons. Modeling of this phenomenon is clearly a complex and detailed problem, with other processes not described in this simple thought model. Mathematically, these phenomenon are detailed in the model contained in chapter 6. The plasma will maintain the discharge by whatever means consumes the least amount of power - since the means by which this occurs has been experimentally determined, what remains is to capture these trends in a predictive model. Previous experiments [18, 9] with gas and Lithium fed SCHC’s have shown that an increasing
  53. 53. 35 discharge voltage and IPC length correspond with decreasing flow rate. This correlation was first reported by Delcroix and Trindade [18] with gas cathodes, and again later by Cassady [9] while working with Lithium, though none of the researchers offered detailed explanation to the relation. A decrease in discharge voltage with increasing flow rates is also seen in orificed hollow cathodes, along with the transition from “spot mode” to “plume mode” (though it should be noted that comparison between orificed hollow cathodes and SCHC’s have inherent inaccuracies due to the complexities which arise from the presence of the orifice plate). Adding further complications the understanding, Cassady’s experiments also had to contend with the deposition of Lithium on the cathode surface, reducing the work-function. If the flow rate is reduced to the point at which it becomes free molecular, then one must consider the probability of an excited neutral atom leaving the cathode before being further excited to ionization. In this case the ion neutral collision frequency will be reduced, and thus the probability decay rate of an excited atom may not be comparable with its resonance time within the cathode, or the excitation-collision frequency. Thus the presence of electrons capable of ionizing in a single collision event become necessary, which required a larger cathode voltage drop. Further, any excited neutral atoms which leave the cathode are effectively “lost energy”, causing an increase in the demand for energy in the IPC which translated to a higher electron temperature through larger sheath voltages (and lower discharge efficiency). To date there are no SCHC models available which accurately describe the relation between discharge voltage, flow rate and IPC penetration depth. This work intends to provide substance towards a more comprehensive model of the IPC, both
  54. 54. 36 qualitatively and quantitatively, and to determine the IPC properties for given operating conditions (current, mass flow rate, cathode geometry, gas and material properties). If the plasma attachment area can be increased, the cathode temperature can be reduced by reduced surface current density. The focus of this work is on determining the total penetration depth of the IPC, the distribution of the internal plasma and its properties (plasma density, temperature, and potential, as well as properties of the neutral gas) with the intention of optimization for long cathode lifetime. IPC Control Parameters and Experimental Observations Experimental observations recorded by previous hollow cathode research has yielded several universally accepted conclusions [9, 18], the most significant among these are: 1. Increasing mass flow rate decreases IPC penetration depth. 2. Increasing cathode diameter increases the IPC penetration depth. 3. Peak cathode temperature is weakly dependent upon mass flow rate. 4. An MCHC has a lower discharge voltage than a SCHC while operating at identical discharge current and mass flow rates. 5. Discharge voltage decreases with increasing mass flow rate. 6. Discharge voltage decreases with decreasing cathode diameter. 7. Discharge voltage decreases when the plasma is confined (such as with a magnetic field)
  55. 55. 37 It is important to note here that previous works have noted these observations, but have not produced qualitative theory to explain the governing mechanisms at work. To such end, it is helpful to identify overarching trends in the data, from which larger insights can be drawn. For bullets 5 and 6, notice that if the mass flow rate is increased the flow becomes more collisional, additionally if the cathode diameter is decreased (reducing the cross sectional area through which the gas can flow) the flow density will increase also leading to more collisions. Additionally, increasing the cathode diameter and thus the cathode exit area, increases the loss of de-excitation caused radiation from the IPC to the exterior region. This loss of radiation that would have been otherwise recaptured by either the plasma or the cathode walls, is an additional energy loss from the system. Plasma confinement (bullet 7), such as that caused by the magnetic field of an applied-field thruster will also cause a more collisions by retarding diffusion. Noticing these previously reported trends one can extrapolate that operating conditions which cause the flow to be less-rarefied / more-collisional will decrease the discharge voltage (for a given current thus increasing the discharge efficiency). More is presented on this notion in the final chapter of this work. This is an important relation, because the discharge efficiency is directly proportional to the discharge voltage. Flowing the same amount of gas through a MCHC requires gas movement through many channels much smaller than a corresponding SCHC, thus the flux of flow will increase (equal mass flow over reduced total cross sectional area, comparing cathode of equal inner diameter). This means that the channel will, on average, have a higher density (more collisional) flow than the corresponding single channel. Thus, for the same
  56. 56. 38 discharge current and mass flow rate the MCHC would be expected to operate at a lower discharge voltage - a relation that has been experimentally observed [9]. An understanding of the ionization process inside the hollow cathode is key to predicting the efficiency of the system. This is because the ionization frequency of the neutral atoms is very sensitive to the electron energy (temperature), which is determined (largely) by the sheath voltage drop. The larger the voltages required for the ionization process, the less efficient the discharge because the power consumed by the discharge is of course directly proportional to the total voltage.
  57. 57. 39 Chapter 3: History and State of the Art 3.1 Historical Related Research MPD thrusters evolved from arcjet thrusters, and thus historically have used gaseous propellants, indeed early literature labels the devices as “MPD-Arcjets”. Initial research yielded promising performance in the way of produced thrust and Isp, though these thrusters were plagued by low efficiencies. Since the 1950’s many different groups have conducted research into MPD/LFA thrusters using a variety of different propellants, including Argon, Helium, Nitrogen, Lithium, Hydrogen and Ammonia among others. A brief list of MPD research groups is presented in table 2. It was eventually realized that cathodes are the major life limiting component of MPD thrusters, and so a large percentage of the available literature is naturally devoted to the study of cathodes. A brief review of notable past research into MPD and cathode research is presented, covering work by Delcroix, Polk, Goodfellow, MIA/ Tikhonov, Mikellides, and Cassidy. 1) Delcroix – University of Paris [18] Pioneering work on hollow cathodes was conducted at the University of Paris by Delcroix and Trindade [18] in the 1970’s. This is the first extensive study involving MCHC’s and was largely experimental in nature, reporting mostly qualitative observations. Delcroix et al. experimentally demonstrated that when compared to a single
  58. 58. 40 NASA-Jet Propulsion lab NASA-Glenn/Lewis research Center AVCO-Everett Los Alamos National labs Moscow Aviation Institute McDonnell Douglass Corporation Osaka University University of Stuttgart Tokyo University Princeton University University of Illinois Ohio State University Massachusetts Institute of Technology USAF United States of America United States of America United States of America United States of America Soviet Union United States of America Japan Germany Japan United States of America United States of America United States of America United States of America United States of America Table 2 . MPD thruster research groups channel cathode operating at the equivalent discharge voltage and flow rate, separation of the gas flow through a multichannel cathode would divide the current load over the channels, reduce the overall discharge voltage and the operating temperature of the cathode. This research also experimentally showed the reduction in discharge voltage accompanying an increase in the working gas density. This research was the first to introduce the notion of an active zone of the cathode, in which most of the ionization was predicted to take place. This corresponds with the hot spot, the location of peak surface temperature where thermionic electron emission is greatest. Peak surface temperatures were measured and noted to occur at locations upstream from the cathode exit plane – distance upstream was shown to be controlled by the mass flow rate. Several regimes of operation were noted, including Normal (N), Low Gas-Flow (LQ), Low-Current (LI) and High-Pressure (HP) regimes.
  59. 59. 41 2) Polk – NASA-JPL/Princeton University [54] Jay Polk conducted high current cathode research at JPL/Princeton University in the early 90’s, focusing his efforts on development of an understanding of the methods controlling cathode material reduction. Polk developed code modeling the migration and erosion of cathode material with temperature dependency. This work examined in detail the temperature driven process of cathode surface material evaporation, identifying the initial phase of the discharge ignition as the most destructive. This work built on previous research predicting that starting a “cold”, non- electron emitting, would cause the formation of many micro spots on the surface, which supplied electrons to the discharge via a combination of enhanced field emissions and the evaporation of small amounts of surface material. This process continues, depositing heat to small surface area regions of the cathode until a suitable surface temperature is reached, and the electrons necessary to sustain the discharge can be provided by thermionic emission. This provides a basis of predicting reliable cathode lifetime if one can accurately predict the operating temperature profile. 3) Goodfellow – NASA-JPL/University of Southern California [26] Also in the late 80’s/early 90’s, Keith Goodfellow conducted experimental and theoretical research into high current solid rod cathodes in gaseous propellants at Purdue University, and later at JPL/University of Southern California. This work provided reasonable temperature prediction ability for MPD thruster solid rod cathodes, including plasma/sheath modeling and cathode temperature distribution.
  60. 60. 42 Although this work focused exclusively on solid rod cathodes, a detailed 1- D/phenomenological model of the plasma sheath was developed to study interaction between the cathode surface and the plasma. Much insight can be drawn from these understandings and translated to the study of plasma interaction with hollow cathodes on the basis of similarity in both geometry and fundamental processes. This work provides a basis of the IPC phenomena description and qualitative sheath model contained in the current research. Goodfellow identified the major sources of heat deposition and rejection for hot cathodes, along with their relative significance as a function of surface temperatures. Experiments showed that the peak surface temperature was not strongly dependant upon gas flow rate, but was strongly dependant upon discharge current. Further work demonstrated the total surface area of plasma attachment to the cathode would increase with decreasing mass flow rate, along with a peak temperature located at some distance upstream from the cathode tip. 4) Moscow Aviation Institute [65] In 1994-1998 the Moscow Aviation Institute (MAI) conducted the first extensive testing of a Li-LFA (Lithium propellant Lorentz Force Accelerator) with a MCHC, testing several cathode designs, under the direction of scientific supervisor Victor Tikhonov. This work was performed with the support of Princeton University and NASA-JPL, and was limited largely to experimental research. The MIA experiments yielded a qualitative feel for more optimal MCHC design - testing of 6 different cathode geometries were reported along with performance and arc attachment dependency upon
  61. 61. 43 design. The experiments included development and testing of 3 different thrusters, a 30 kw, 150 kw, and 200 kw – all three were applied field thrusters. MIA testing also included introducing additives to the flow of Lithium propellant - significant reduction in material erosion was reported during experiments in which an amount of Barium was introduced into the discharge. It was predicted that the Barium atoms would deposit themselves on the cathode Tungsten, and this layer would reduce the work function. These predictions were verified when it was shown that the cathode operating temperature showed noticeable reduction during the Lithium + Barium runs while operating at equal discharge current, compared to the Lithium only runs. Because the Barium was heated and vaporized at an uncontrolled rate, it was not possible to obtain a detailed model of the effects of Barium addition from the data generated by the MAI experiments. 5) Mikellides – NASA-JPL [42] In the early 2000’s, the Advanced Propulsion Concepts group at NASA’s JPL began developing a detailed computational theory regarding the plasma and erosion processes of an NSTAR traditional hollow cathode. As part of this program, and based upon previous efforts conducted at Ohio State University, Ioannis Mikellides developed the IROrCa2D (Insert Region of an Orificed hollow Cathode) code modeling the plasma properties inside an NSTAR cathode, and later the IROrCa2D evolved OrCa2D code modeling the NEXIS cathode. IROrCa2D is a 2D-axisymmetric time independent code that models plasma and neutral gas interaction in the emitter region of a low current
  62. 62. 44 Figure 14. Active MCHC with Lithium -Barium mixture, photo from reference [65] Figure 15. Active MCHC with Lithium only, photo from reference[65]
  63. 63. 45 orificed hollow cathode with Xenon propellant. Large portions of work described in this thesis have origins in the model in the IROrCa2D code. 6) Cassady – Princeton University [8] Leonard Cassady working in the early-mid 2000’s at Princeton University’s Electric Propulsion and Plasma Dynamics Lab, conducted a study of single and multi-channel hollow cathodes using Lithium Propellant, influenced heavily by the MIA work of the previous decade. Although this work relies upon the somewhat imprecise approximation of the IPC modeled as block of uniform plasma with constant properties, created by the electron emission of the surrounding cathode wall assumed to be at uniform temperature, it never-the-less correctly predicts trends in the cathode voltage, temperature profile and ionization fraction as a function of current, Lithium flow rate and cathode channel diameter. Note that as of this writing, the research at MIA and Princeton University are the only relevant studies of a MCHC operating in an high power Li-LFA system environment, and are considered the current state-of-the-art in the field. 3.2 State of the Art – MCHC’s and LFA thrusters The current state of the art in MPD-type thrusters is the Lithium propellant (with Barium addition) self-field LFA with a multi-channel hollow cathode, such as those designed in the MIA study of the mid 1990’s, termed the Li-LFA [35, 1, 56]. The best
  64. 64. 46 data point thus far (for an applied field thruster) is for a Lithium fed LFA operating at 69 percent (thrust) efficiency, 5500s Isp, thruster power of 21 kW, Lithium flow rate of 10 mg/s, and an applied field of 0.24 T – this thruster used a conical rod shaped cathode [35]. Although this represents the best performance (from an efficiency and Isp point of view), this lacks the most advanced system components, specifically the cathode design, and thus is not considered SOA.For comparison, the best performance date for a Li-LFA with a multi-channel hollow cathode is the 200 kw MIA thruster, which ran at ~ 50 percent efficiency and 4200s Isp, with 192.7 kW discharge power [13]. In 2003 the Advanced Propulsion Technology Group at NASA-JPL was continuing efforts on a 0.5 MW class self-field Li-LFA [56] and associated testing facilities, designed as follow on studies to the MIA/Princeton work of the 1990’s. This work at JPL was funded under the Advanced Propulsion Concepts (APC) program and had been the slowly continuing efforts of Goodfellow and Polk for several years. Unfortunately the APC program was cut from the NASA budget later that year. In 2004-5 two proposals were made by the group for Li-LFA’s, a 250 kW applied field and the 0.5 MW self-field (shown in Figure 16), both of which were awarded under Project Prometheus, NASA’s plan to begin using Nuclear Electric Propulsion systems for deep space robotic exploration. This work was intended to advance the technology readiness level (TRL) of the Li-LFA from TRL-4 to TRL-5. A large part of this research was to focus on MCHC issues, however shortly after the award was made for the 0.5 MW thruster, it was retracted. The 250 kW thruster (termed the Advanced Lithium-fed
  65. 65. 47 Figure 16. Schematic view of 250 kW Li-LFA, ALFA^2, [13] Figure 17. Improvements over SOA, reference [13] Applied-field LFA, or simply ALFA2 , or “Alpha Squared”) funding was continued with Princeton University as the lead investigating organization, but was reduced to half of the
  66. 66. 48 originally awarded level. Target performance for ALFA2 was 60 to 63 percent efficiency, 6200s Isp, and >3 years of reliable lifetime - respectively the efficiency and Isp performance goals represented 30 and 46 percent gain over SOA (the MIA 200 kW thruster) [13]. The Phase 1 study was completed in mid 2005, although by that time many NASA programs found themselves competing for funding with the more visible components of the new VSE (namely design and construction of the Crew Exploration Vehicle, CEV). The EP components of project Prometheus were canceled in late 2005, all related research was shelved and Prometheus itself was effectively ended. By late in the fall of 2005, NASA HQ had received many complaints regarding the cancellation of project Prometheus, in particular many university research groups voiced concerns noting the numerous graduate students who’s doctoral research was funded by the program. In December, NASA decided to continue funding for the ALFA2 project at a greatly reduced level and with the stipulation that the funds be used solely to support the projects associated graduate students. Funding support would continue to the period of one calendar year, and was termed “ALFA2 Student Soft Landing”. Consequently, the ALFA2 cathode research was re-tooled and relocated from JPL to the University of Southern California, and continues as the study in this paper. Other research funded by ALFA2 Student Soft Landing continues at Caltech, Princeton, Michigan University and WPI. The phase 1 study and JPL’s proposed development of the 250 kW and 500 kW Li-LFA with MCHC are considered the next development in SOA of MPD thrusters at the system level, with the work done at MIA being the highest achieved level of MPD thruster development.
  67. 67. 49 Figure 18. The six MCHC designs tested by MAI The SOA of multi-channel hollow cathodes is somewhat harder to quantify, as there has been little detailed research into these devices operating in the relevant environments. Most of the relevant experimental data are results from the MIA studies of the mid 90’s, during which Lithium fed MCHC’s were used at power levels up to 192.7 kW. Six different cathode geometries were tried, with the “optimized” design found empirically, as shown in Figure 18. Though no comprehensive detailed theory governing the operation of the MCHC exists yet, some experimental studies have been conducted, yielding a phenomenological understanding of the devices [8, 9].

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