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The space environment near the Sun and its effects on Parker Solar Probe spacecraft and FIELDS instrumentation

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The space environment near the Sun and its effects on Parker Solar Probe spacecraft and FIELDS instrumentation

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Content THE SPACE ENVIRONMENT NEAR THE SUN AND ITS EFFECTS ON PARKER SOLAR PROBE SPACECRAFT AND FIELDS INSTRUMENTATION by Millan Fernando Diaz-Aguado Robison A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ASTRONAUTICAL ENGINEERING) August 2020 Copyright 2020 Millan Diaz-Aguado ii Epigraph “We are like dwarfs sitting on the shoulders of giants; we perceive more and see farther than they, but not because we have better vision, nor because we are taller than they, but because they have lifted us up and added their gigantic height to ours”[1] Bernard of Chartres iii Dedication To Alexandra and Fernando iv Acknowledgements First and foremost, I would like to thank Dr. John W. Bonnell, at the Space Sciences Laboratory, UC Berkeley; without his guidance and support this dissertation would not have been possible. This endeavor started with an e-mail and a phone call to Dr. Mike Gruntman. He welcomed me to the USC Astronautical Engineering department, and I’ve felt a Trojan ever since, even though I did all my classes online. Mike, thank you for your patience with a PhD student so far away. My journey continued shortly after that phone call, when I stopped by John’s office and asked him if he wanted to be my advisor. Without hesitation he said yes, but I did ask him again the next day to make sure he understood the commitment it would take. Again, an unequivocal yes was the answer. Eight years later I hope he has enjoyed learning and teaching me about plasma interactions with spacecraft as much as I have enjoyed learning from him. I hope we can continue writing papers, over beers at Triple Rock, and enjoying each other’s company as well as our scientific and engineering sojourns. I have also been very fortunate that my “academic advisor”, William “Bill” Donakowski helped monitor my take home exams with such great dedication and rigor. I surely miss you and our runs through the park. In addition, I would like to thank all the staff at USC Astronautical Engineering department, Marrietta Penoliar, Nicole Valdez, Dell Cuason, Norma Perry and Luis Saballos for their patience and support especially during class registration. There are many people that have helped me and welcomed me to their research facilities. First, I would like to thank Professor Stefano Nannarone, Dr. Angelo Giglia, Dr. S.J. Rezvani, and Dr. Konstantin Koshmak from the National Research Council, Basovizza, Trieste, Italy. They v produced great photoemission data, even if I had to wait a little longer than expected to get it. The research paper about the photoemission of un-annealed vs. annealed surfaces could not have happened without them. Second, Dr. JR Dennison, and his students Justin Christensen, Phillip Lundgreen, Jordan Lee, Justin Dekany, and Brian Wood from the Surface Physics Group at Utah State University deserve my most sincere gratitude. We had impacting conversations about surface properties and secondary electrons and they provided me with important secondary electron emission and backscatter electron emission data. Their contributions to the spacecraft charging community will be widely recognized. Third, Dr. Stuart Bale for his support was invaluable, both during the qualifier, thesis direction, and monetary issues, in addition to the entire Parker Solar Probe FIELDS team (David Glaser, Paul Turin, Jose Fermin, Dennis Seitz, Chris Scholtz) for making an instrument able to survive in one of the most complex environments. Fourth, I would like to extend my thanks to Marc Pulupa, Julien Forest and Dr. Jean-Charles Mateo Velez for their support on spacecraft charging modeling in Spacecraft Plasma Interaction Software (SPIS). Without their help my models would not as accurate. Last but not least, I would like to acknowledge Dr. Joseph Wang for his expert observations on spacecraft charging, testing and modeling and Dr. Kent Tobiska for sharing his knowledge of the space environment. All of my committee members, including my external committee member Dr. Aiichiro Nakano, were crucial for their feedback and I am extremely grateful to them. vi Looking further into my past, I also wanted to thank my master’s adviser from The University of Texas, Dr. Wallace Fowler. He has always believed in me and given me moral support even before this arduous journey started. On a more personal level, I would like to thank my mother, a university English professor, Alexandra Robison, for her support and for reviewing my English. Even though I’ve lived in the USA for many years, the first 15 years of my educational background were in Spanish which has hampered me, especially in writing in English. I would also like to thank my stepdad Emilio Buendia for our long talks about work and dissertation. Even though he passed away ten years ago, my father was instrumental in my education and was always there for me, especially in the hard times. My father in-law also deserves my sincere appreciation, as he arrived right before this dissertation was due, and was a great help as he cooked all the family meals while I was immersed in writing this dissertation. And last, but not least, I would like to thank my wife Dr. Dorothea Sauer and my son Thomas. Doro, your patience and encouragement got me through this. Thomas, I hope I balanced work life and personal time well and you won’t come back to me when you are 20 years old asking me why I did not spend more time with you. This research was supported in part by NASA contract number NNN06AA01C. vii Table of Contents Epigraph .......................................................................................................................................... ii Dedication ...................................................................................................................................... iii Acknowledgements ........................................................................................................................ iv List of Tables .................................................................................................................................. x List of Figures ................................................................................................................................ xi Abstract ......................................................................................................................................... xv 1 Introduction ............................................................................................................................. 1 1.1 Space Environment .......................................................................................................... 1 1.2 Spacecraft Charging ......................................................................................................... 3 1.2.1 Langmuir Probes ....................................................................................................... 5 1.2.2 Electrostatic Analyzers ............................................................................................. 5 1.3 Space Environment Missions ........................................................................................... 6 1.3.1 ISEE .......................................................................................................................... 6 1.3.2 Polar .......................................................................................................................... 7 1.3.3 Cluster ....................................................................................................................... 7 1.3.4 THEMIS .................................................................................................................... 7 1.3.5 Van Allen Probes ...................................................................................................... 8 1.3.6 MAVEN .................................................................................................................... 8 1.3.7 Solar Orbiter.............................................................................................................. 9 1.4 Parker Solar Probe ............................................................................................................ 9 1.4.1 FIELDS Instrument and Science ............................................................................ 12 1.5 Content of Dissertation................................................................................................... 13 2 Theoretical Background ........................................................................................................ 16 2.1 Probe Theory .................................................................................................................. 16 2.1.1 Thin Sheath – Child Langmuir Law ....................................................................... 19 2.1.2 Thick Sheath – Orbital Motion Equations .............................................................. 21 2.2 Spacecraft Charging Background................................................................................... 25 2.2.1 Photoemission ......................................................................................................... 28 2.2.2 Electron Current ...................................................................................................... 30 2.2.3 Ion Current .............................................................................................................. 31 2.2.4 Secondary and Backscattered Electron Current ...................................................... 32 viii 2.2.5 Thermionic Emission Current ................................................................................. 35 2.2.6 Bias Current ............................................................................................................ 37 2.3 Theoretical Summary ..................................................................................................... 38 3 Photoelectron Yields from PSP Spacecraft Materials ........................................................... 39 3.1 Introduction .................................................................................................................... 39 3.2 Experimental Setup ........................................................................................................ 41 3.3 Photoemission Results ................................................................................................... 44 3.3.1 Work Function ........................................................................................................ 45 3.3.2 Photoelectric Threshold .......................................................................................... 45 3.3.3 Normal Photoelectron Yield ................................................................................... 46 3.3.4 Photoelectron Yield vs. Incident Photon Angle ...................................................... 49 3.3.5 Electron Photoemission Under Solar Irradiation .................................................... 54 3.3.6 Analytical Fit to the Photoelectron Yield at Normal Incidence .............................. 57 3.4 Photoemission Testing and Analysis Conclusions ......................................................... 62 4 Secondary Electron and Backscattered Secondary Electrons ................................................ 63 4.1 Introduction .................................................................................................................... 63 4.2 Experimental .................................................................................................................. 67 4.3 Theoretical Models ......................................................................................................... 73 4.3.1 Secondary Electron Yield Models .......................................................................... 75 4.3.2 Backscattered Secondary Electron Yield Models ................................................... 76 4.3.3 Emitted Electron Energy Distribution .................................................................... 77 4.3.4 Ambient Electron Current Density ......................................................................... 78 4.3.5 SE Current Density ................................................................................................. 79 4.3.6 BSE Current Density............................................................................................... 79 4.3.7 Current Density per Number Density ..................................................................... 79 4.4 Results ............................................................................................................................ 80 4.4.1 Secondary and Backscattered Electron Yield ......................................................... 80 4.4.2 Electron Emission Energy Distribution .................................................................. 94 4.4.3 SE and BSE Current Densities ................................................................................ 98 4.4.4 Current Densities per Electron Number Density .................................................. 105 4.4.5 NASCAP Fit Parameters....................................................................................... 109 4.5 Secondary and Backscattered Electron Conclusions ................................................... 110 ix 5 PSP FIELDS Charging Modeling........................................................................................ 112 5.1 Introduction .................................................................................................................. 112 5.2 SPIS Software .............................................................................................................. 115 5.2.1 Spacecraft Charging Model in SPIS ..................................................................... 115 5.2.2 Simulation Geometry and Mesh ........................................................................... 118 5.2.3 Material Properties ................................................................................................ 122 5.2.4 Circuit Definition .................................................................................................. 125 5.2.5 Space Environment and Numerical Settings ......................................................... 126 5.3 Modeling Results.......................................................................................................... 130 5.3.1 Numerical Results - No Bias on FIELDS Antenna and Shield ............................ 130 5.3.2 Numerical Results – Other Sensitivity Studies ..................................................... 144 5.3.3 Numerical Results bias FIELDS Antenna and Shield – I-V Curves .................... 147 5.4 PSP FIELDS Flight Data ............................................................................................. 150 5.5 PSP FIELDS Modeling Conclusions ........................................................................... 155 6 Conclusions ......................................................................................................................... 157 References ................................................................................................................................... 161 x List of Tables Table 3-1 Work function of Metals unannealed and annealed .................................................... 45 Table 3-2 Photoelectric Thresholds of Metals unannealed and annealed .................................... 46 Table 3-3 Emission lines in the solar spectrum at 1 AU of solar cycle 21 [85] .......................... 55 Table 3-4 Integrated photoelectron current density at 0° incidence at 1 AU, at maximum and minimum solar irradiances (cycle 21) .................................................................................... 56 Table 3-5 Parameters for Analytical Fit Unannealed .................................................................. 59 Table 3-6 Parameters for Analytical Fit Annealed ...................................................................... 59 Table 4-1 Material Properties and Annealed Temperatures ......................................................... 71 Table 4-2 SE Yield Parameters ..................................................................................................... 90 Table 4-3 BSEY Fit Parameters ................................................................................................... 91 Table 4-4 Fits for Electron Emission Distribution ........................................................................ 97 Table 4-5 Average Electron Plasma Parameters at Magnetosheath, GEO and Solar Wind ........ 99 Table 4-6 Unannealed and Annealed Material SE Current Densities (μA/m 2 ) Without Reduction Due to Temperature ................................................................................................... 102 Table 4-7 Unannealed and Annealed Material BSE Current Densities (μA/m 2 ) ....................... 104 Table 4-8 Nascap-2k Fit Parameters ........................................................................................... 109 Table 4-9 Nascap-2k BSEY Fit Parameters............................................................................... 110 Table 5-1 Material Properties used in Surface Charging Calculations [52, 97, 135] ................. 124 Table 5-2 Conductivity and Resistivity Properties of Al2O3 [135]............................................. 125 Table 5-3 Expected Plasma Parameters of PSP FIELDS Space Environment [33] .................. 128 Table 5-4 Graphical representation of different Ram direction cases ....................................... 128 Table 5-5 Typical Numerical Settings for SPIS ........................................................................ 129 Table 5-6 Surface Potentials (V) for PSP FIELDS Space Environment (unannealed Nb- C103)........................................................................................................................................... 131 Table 5-7 Surface Potentials (V) for PSP FIELDS Space Environment (annealed Nb- C103)........................................................................................................................................... 131 Table 5-8 Current Source Comparison for PSP between 1AU and 0.16AU. ............................ 133 Table 5-9 – Modeled Plasma Parameters[33] at 35Rs compared to flight parameters at 35.7Rs [155-157] ........................................................................................................................ 151 Table 5-10 Model Potentials with 1 st Perihelion, Flight Potential Bias Values (Antenna - 11.6V and shield 0.1V), Flight Nb-C103 Photocurrent 2.4e-4A/m 2 .......................................... 151 xi List of Figures Figure 1-1 Electron density (#/cm 3 ) vs electron energy (eV) of different natural and laboratory plasmas [3]..................................................................................................................... 2 Figure 1-2 Parker Solar Probe in Launch Configuration with FIELDS Antennae Retracted in Launch configuration ................................................................................................................ 10 Figure 1-3 PSP Assembled ready for Integration [34] .................................................................. 11 Figure 1-4 Detail of FIELDS Antenna Instrument Deployed on PSP during Assembly.............. 12 Figure 2-1 Potential of plasma near a surface at a negative potential .......................................... 17 Figure 2-2 Orbit-Limited Current-Voltage Behavior ................................................................... 25 Figure 2-3 Schematic of spacecraft charging near the Sun: a. Negative charged spacecraft repelling electrons and attracting ions; b. positively charged spacecraft attracting electrons and repelling ions. ......................................................................................... 27 Figure 2-4 An illustration of the three step photoemission process [40] ...................................... 28 Figure 2-5 Thermionic emission current density – a. versus temperature of antenna, b., versus distance from the Sun, as compared to the annealed photoemission current density (Jph0 = 49 μA/m 2 ) .......................................................................................................................... 36 Figure 2-6 – Biased current schematic where figure a. shows the probe potential and ambient current and b. shows the probe potential and bias current [61] ...................................... 38 Figure 3-1 Measurement schematic (geometry shown for 40° of incidence): CEM and sample are scanned in angle together in order to keep the relative positions fixed. ..................... 43 Figure 3-2 Image of the photon and electron detector at the BEAR testing facility, Trieste, Italy[71] ........................................................................................................................... 44 Figure 3-3 Photoelectron yield (elec./photon) at 0° angle of incidence for W, compared to past data from Walker and Rentscheler [11] left unannealed, right annealed. ......................... 48 Figure 3-4 Photoelectron yield (elec./photon) at 0° angle of incidence for W, TaW, Nb C103, Moly TZM, Elgiloy, left unannealed, right annealed. ........................................................ 48 Figure 3-5 Photoelectron yield (elec./photon) at 0° angle of incidence for DAG-213® and TiN, left unannealed, right annealed. ..................................................................................... 49 Figure 3-6 Angular dependence of the ratio of the s-, p-polarized and total yield and their yield at normal angle of incidence (°) for Tungsten unannealed left, annealed right at 10.2eV photon energy. The secant and the cosine are also plotted. ............................................ 51 Figure 3-7 W Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed. ............................. 51 Figure 3-8 Nb-C103 Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed. ................. 52 xii Figure 3-9 TaW Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed. ................. 52 Figure 3-10 Moly TZM Photoelectron yield (electrons/photon) within the range of 9- 14eV photon energies and between 0-80° incident angles, left unannealed, right annealed ........ 53 Figure 3-11 Elgiloy Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed .................. 53 Figure 3-12 TiN Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed .................. 54 Figure 3-13 DAG-213® Photoelectron yield (electrons/photon) within the range of 9- 14eV photon energies and between 0-80° incident angles, left unannealed, right annealed ........ 54 Figure 3-14 Maximum and Minimum Solar Flux Energy Spectrum at 1 AU (Meier) [85] without line fluxes and the normal photoelectron yield of Elgiloy unannealed and annealed ........................................................................................................................................ 57 Figure 3-15 Photoelectron yield (elec./photon) at 0° angle of incidence with theoretical fit for Nb C103, left unannealed, right annealed .......................................................................... 61 Figure 3-16 Photoelectron flux vs incident photon energy at 0° angle of incidence with theoretical fit for NbC103, left unannealed, right annealed for solar maximum. ......................... 61 Figure 4-1 Schematic of the hemispherical grid retarding field analyzer (HGRFA), with the ammeters (I), ground and voltage biases[98]. ......................................................................... 69 Figure 4-2 Image of the HGRFA Hemisphere and Carrousel Sample Holder. The blue arrow indicates the direction of electrons passing through the HGRFA and incident on an electrically isolated sample mounted in a sample carousel sample block. ................................... 69 Figure 4-3 Electron range versus incident energy. (a) W, Nb-C103, Ta-W 10% and TZM. (b) TiN, Elgiloy, DAG-213® graphite epoxy composite, and amorphous C as reference. Range calculated using refs. [114, 115]. ..................................................................... 73 Figure 4-4 DAG-213® TEY, SEY, and BSEY data and model fits for an annealed sample, between 10eV and 5keV incident electron energy. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table II. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table 4-3. Yield features, 𝛿 max, ESEmax, n, m, E1, and E2 are indicated on the plot. ............................................................................................................... 81 Figure 4-5 Tungsten SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 30keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table 4-2. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table 4-3. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. ................................................................ 83 Figure 4-6 Nb-C103 SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 5keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table 4-2. BSEY fits are modeled with Eq. (A2) with fitting xiii parameters listed in Table 4-3. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. ................................................................ 84 Figure 4-7 TiN SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 5keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table 4-2. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table 4-3. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. ............................................................................................... 85 Figure 4-8 Ta-W SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 5keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table 4-2. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table 4-3. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. ............................................................................................... 86 Figure 4-9 TZM SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 5keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table 4-2. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table 4-3. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. ............................................................................................... 87 Figure 4-10 Elgiloy SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 30keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table II. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table III. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. ................................................................ 88 Figure 4-11 DAG-213® SE and BSE data and fit energy distribution, annealed sample. .......... 94 Figure 4-12 SE and BSE energy distribution fits of W, Nb-C103, TiN, Moly-TZM, Ta- W and Elgiloy. (a) Results for unannealed samples. (b) Results for annealed samples. ............. 96 Figure 4-13 Differential Electron Number Flux in different plasma environments and the SE and BSE yield of W annealed and unannealed. Flux left axis, yield right axis. Past tested W fit was added to compare with current W fits. ............................................................. 100 Figure 4-14 Primary electron, and SE current densities per electron number density for W, Nb-C103, TiN, Ta-W, TZM, Elgiloy, and DAG-213. (a) Results for unannealed samples. (b) Results for annealed samples. The dashed line indicates the electron current density. ........................................................................................................................................ 107 Figure 4-15 Primary electron, and BSE current densities per electron number density for W, Nb-C103, TiN, Ta-W, TZM, Elgiloy, and DAG-213. (a) Results for unannealed samples. (b) Results for annealed samples. The dashed line indicates the electron current density. ........................................................................................................................................ 108 Figure 5-1 SPIS General Process ................................................................................................ 116 Figure 5-2 FIELDS instruments on the spacecraft during integration and testing a. Deployed state b. Stowed state ................................................................................................... 119 xiv Figure 5-3 Spacecraft model in SPIS a. Groups (except the side TPS facing the sun) b. Mesh Spherical Volume .............................................................................................................. 120 Figure 5-4 Cross section of spacecraft model in SPIS a. y-z plane mesh grid of PSP b. surface mesh FIELDS shield ...................................................................................................... 121 Figure 5-5 Model circuit design, a. circuit with floating shield and antenna, b. biased potential difference between spacecraft and antenna and spacecraft and shield ........................ 125 Figure 5-6 Super Particle # versus Time for 35Rs. ..................................................................... 127 Figure 5-7 Plasma Potential (Volts) and spacecraft and FIELDS Potential (Volts) at 0.16AU (First Perihelion) a. y-z plane, b. x-y plane ................................................................... 134 Figure 5-8 Plasma Potential (Volts) of PSP a. and c. 9.5Rs, b. and d. 35Rs, a. and b. at 35Rs potential scales and c. and d. at 9.5Rs potential scales ...................................................... 135 Figure 5-9 Plasma Potential (Volts) of the cross-sections of the a. shield and b. antenna – at 90° ram, diameter of the spherical boundary is 16m .............................................................. 136 Figure 5-10 Plasma Potential (Volts) of PSP a. and c. 219Rs (1AU), b. and d. 35Rs (0.16AU), a. and b. at 35Rs potential scales and c. and d. at 1AU potential scales ................... 137 Figure 5-11 PSP and FIELDS Log Electron Density (log (#/m 3 )), a. 1AU and b. 0.16AU ...... 138 Figure 5-12 PSP and FIELDS Ion Density (#/m 3 ), a. 1AU and b. 0.16AU ............................... 138 Figure 5-13 PSP and FIELDS Log Photoemission Density log (#/m 3 ), a. 1AU and b. 0.16AU ........................................................................................................................................ 139 Figure 5-14 PSP and FIELDS Log SE Density log (#/m 3 ), a. 1AU and b. 0.16AU .................. 140 Figure 5-15 PSP and FIELDS Log BSE Density log (#/m 3 ), a. 1AU and b. 0.16AU ............... 141 Figure 5-16 PSP and FIELDS Log SE due to Ions Density log (#/m 3 ), a. 1AU and b. 0.16AU ........................................................................................................................................ 141 Figure 5-17 PSP TPS Shield Potential and Plasma Densities as a Function of Distance at a. 1AU (219Rs), b. 0.16AU (35Rs) and c. 0.045AU (9.5Rs) .................................................... 143 Figure 5-18 Predicted FIELDS Antenna I-V Curve with Different Shield Bias Potentials. ..... 148 Figure 5-19 Shield I-V Curve, Shield Potential with respect to spacecraft vs. Current with respect to Antenna .............................................................................................................. 149 Figure 5-20 Shield I-V Curve, Shield Current with respect to Antenna vs. Potential with respect to Antenna....................................................................................................................... 150 Figure 5-21 PSP FIELDS V1-V4 Antenna Voltage and Current Bias Time Series .................. 152 Figure 5-22 FIELDS V1-V4 Third Perihelion, First I-V Curve Sweep .................................... 153 Figure 5-23 FIELDS V1-V4 Third Perihelion, Second I-V Curve Sweep ................................ 154 xv Abstract New space environments are encountered as spacecraft reach farther into our solar system and beyond. FIELDS, a Parker Solar Probe (PSP) mission instrument launched in 2018, is being exposed to high never experienced temperatures and new plasma environments. This new environment and its interaction with the spacecraft and FIELDS instruments were studied, including the charging of spacecraft surfaces and of FIELDS sensors. These floating potentials are determined by the current balance of arriving and departing electrons, ions, and photons. All environmental and bias current sources were studied to obtain better FIELDS scientific measurements. The currents include photocurrent, ambient electron current, secondary electron (SE) current, backscattered secondary electron (BSE) current, ambient ion current, bias current and thermionic current. The theory of the ambient electron and ion, thermionic current and bias currents is discussed. Photoemission, SE and BSE theory and testing methods and results are described for samples of the new spacecraft materials used on PSP, which include new analytical fits and calculations. Finally, the charging of the PSP spacecraft and FIELDS instrument were modeled using Spacecraft Interaction Plasma Software (SPIS), a three-dimension particle in cell (PIC) self-contained code, and compared with flight results. Electron photoemission influences spacecraft surface potentials and the surrounding plasma, and many modern spacecrafts utilize new uncharacterized materials, leading to uncertainties in surface charging and plasma environments around those spacecrafts. The angle dependent photoemission properties were measured for Niobium C103 alloy, Molybdenum TZM alloy, Tantalum Tungsten alloy, Elgiloy, graphite lubricant epoxy (DAG-213®) and Titanium Nitride at the Bending for Emission Absorption and Reflectivity (BEAR) beamline. The properties xvi of Tungsten were also studied to verify the method with past data. The materials were readied as spacecraft flight materials and annealed to predicted peak flight temperatures. Results are presented for the photoelectric threshold and photoelectron yield for photon energies up to 30eV. The work function was also found for each material tested. An analytical equation was then used to fit the normal photoelectron yield for each material to help obtain photocurrents, which were calculated assuming solar illumination at 1 AU at normal incidence. In addition to photoemission, SE and BSE also influence spacecraft surface potentials and the surrounding plasma. SE and BSE often play a significant role in that current balance, and so knowledge of the SE and BSE fluxes from exposed surfaces is crucial in determining those floating potentials, especially in eclipse and for surfaces not exposed to the Sun. The yield properties for 10eV-5keV incident electron energies for all samples were measured. Both unannealed and annealed states were tested, except DAG-213®, which was only tested annealed. Standard three- parameter and four-parameter models was used to fit the BSE and SE yield data, respectively. The emitted electron energy distributions were also obtained and fit with a Chung-Everhart model for SE and a Gaussian function for BSE. The SE and BSE currents densities were calculated for different ambient plasma conditions, including at Geosynchronous Earth Orbit (GEO), in the magnetosheath, and in the solar wind at heliocentric distances from 1AU to 9.5 solar radii (0.044 AU) away from the Sun. For ready reference, the normalized primary electron, SE and BSE current densities versus ambient electron temperature were computed and plotted for Maxwellian distributions having temperatures from 1 eV to 8 keV for each of the tested materials. With the photocurrent, SE and BSE new information of the spacecraft samples, the charging of the PSP spacecraft and FIELDS electric antennas were modeled using SPIS. The model was used to find the floating potentials of the spacecraft and FIELDS antennas at different xvii distances from the Sun (from 1AU to 0.046AU). At larger distances from the Sun, the spacecraft charges negatively as the Thermal Protection System (TPS) shield is insulative at low temperatures. As the spacecraft approaches the Sun, the temperature of the TPS increases, the resistance between it and the spacecraft drops, and its photoemission increases, driving the spacecraft more positive. At the same time, an electrostatic barrier forms near the illuminated surface of the TPS and reflects the photoelectrons back leading to negative charging of some surfaces. The FIELDS antennas charge positively at all distances modeled without bias potentials. Our SPIS modeling relied on material properties of new spacecraft materials that we had obtained in previous work. As the spacecraft nears the Sun at 0.046AU, temperatures reach ~1600K, where the thermionic current could be in the same order of magnitude as the dominating photocurrent. The effect of voltage biasing between the antenna, its shield, and the spacecraft on the current balance of each surface was investigated. The model data was reduced to I-V curves to find saturation photocurrents (analysis results 52µA versus flight results 54-72 µA), and sheath resistances (analysis results of 325 kΩ versus flight results of 51 kΩ). 1 1 Introduction Space is a variable environment that can have detrimental effects on spacecraft. These effects can be divided in four different categories: plasma, ionizing radiation, neutral gas interactions and particulate impacts [2]. This research studies the relationship between both the plasma and the heat flux environment near the Sun with the Parker Solar Probe (PSP) spacecraft and its instrumentation, including the environment effects on the spacecraft and its instruments, and is centered on advancing the field of space-environment interactions with high temperature surfaces of the spacecraft through modeling and experimentation. The introduction of the space environment near the Sun and effects on spacecraft and instrumentation is divided into five primary sections. First the space environment is described briefly. The description is followed by the spacecraft charging induced by the space environment, and a historical background is included as well. The introduction also includes descriptions of past spacecraft missions which studied the space environment and its interactions with the spacecraft and their instrumentation. This is followed by a detailed explanation of the Parker Solar Probe mission, which this thesis is focused on. Subsequently, the questions addressed by this dissertation are listed. Finally, the content and structure of this thesis is described. 1.1 Space Environment Space is not an empty vacuum: it is mainly filled with plasma. Plasma is considered the fourth state of a material which can also be a gas, liquid or solid [3]. A plasma is an ionized gas with unique properties, where magnetic fields and electric fields can define the plasma flow characteristics. Plasmas exhibit collective behavior [4], which characterizes different space environments. Figure 1-1 shows the different plasma temperatures and densities found in various 2 laboratory and space environments. This dissertation focuses on the solar wind, with a few eV to 100’s eV for plasma temperature and 10 4 – 10 5 cm -3 electron densities, the plasma environments that Parker Solar Probe is experiencing [5-8]. Figure 1-1 Electron density (#/cm 3 ) vs electron energy (eV) of different natural and laboratory plasmas [3]. 3 1.2 Spacecraft Charging Spacecraft surfaces are routinely exposed to intense solar photon and charged particle fluxes. Exposed surfaces emit electrons (photoelectrons, secondary and backscatter electrons) through interactions with this environment. Spacecraft surfaces that become hot as they approach a stellar body also emit electrons through thermionic emission [9, 10]. The relative potentials between the ambient of the spacecraft surfaces, Langmuir probes, and electric field antennas are determined by a balance between the ambient charged particle fluxes to the exposed spacecraft surfaces and the photoelectron and secondary electron fluxes from the surfaces, and are typically negative if the spacecraft is in the ionosphere or in eclipse and positive if the spacecraft is in the magnetosphere or interplanetary space and in sunlight [2, 11-13]. Interest in spacecraft charging was heightened by bodies in space charging up to several kilovolts [11, 14-16] as was observed on ATS-5 and later on ATS-6 satellites. During the 1960’s and 1970’s scientists began to understand the spacecraft charging environments. Chopra, Shen, Whipple, Grard, Fauerbacher, and Fitton were among the first scientists to study and understand the link between space environment and spacecraft charging. Chopra [17] studied rapid moving bodies in the atmosphere. He looked at spacecraft drag, and the electrohydronamics effects of artificial satellites, including the spacecraft floating potentials. With Shen and Chopra [9], they studied the thermionic emission of electrons from a hot body in interplanetary space. Whipple [11] looked at the behavior of the electron currents on charged SC, including the contribution of Secondary Electron (SE) emission from the surfaces. Grard [18] studied the photoelectron sheath on probes in interplanetary space, introducing the Maxwellian distribution function to describe the particle distribution behavior in the sheath. The sheath can be defined as the region where the potential of the plasma transitions to the potential of the surface of the SC. 4 In order to better understand the observed spacecraft charging, in-depth laboratory work began in the 1970’s. Scientists such as Feuerbacher and Fitton [19] studied aluminum, gold, stainless steel, graphite, vitreous carbon, Aquadag, and indium oxide among others because of their common spacecraft use. Grard [18] based his laboratory measurements on Feuerbacher and Fitton, adding aluminum oxide, LiF on Au, and compared the results with his mono-kinetic and Maxwellian approximations. During this time period, advances in photoemission testing aided our understanding of the material charging behavior in the space environment. In addition new computational techniques were developed, and there was further inflight research which culminated in the Spacecraft Charging at High Altitude (SCATHA) mission [16]. SCATHA studied the spacecraft surface charging characteristics, the response of the spacecraft to different environments, and the corrective techniques needed to avoid charging, and was in operation from Feb 1979 through May 1991 [20]. SCATHA had many instruments on board: a spacecraft surface potential monitor, a temperature controlled quartz crystal microbalance to study contamination, a charging electric effects analyzer looking for electromagnetic interference, an electric field detector composed of two 50m antennas, a spacecraft sheath fields detector composed of electrostatic analyzers, an electron gun to control the spacecraft potential, and particle and fields instrumentation which included electron and an ion particle detectors. Since the SCATHA mission, new materials have surfaced as technology has evolved and spacecraft have reached farther into space. Materials like DAG-213® (graphite lubricant in epoxy resin solution), Titanium Nitride (TiN), Beryllium Copper (BeCu) and Germanium Black Kapton (GBK) have become commonly used. These materials have different usages, i.e., GBK is used in Multi-Layer Insulation (MLI) blanket, DAG-213® and TiN are used on deployable booms for 5 their thermal optical properties. This research focuses on the charging behavior of some of these new materials, including DAG-213® and TiN. All these materials are electrically conductive to avoid localized charging and the electric field effects of insulating surfaces. Large differential electrostatic potentials on insulating spacecraft surfaces can be a source of discharges, leading to material damage and operational interference [2, 11, 13, 21]. These potentials can also be a cause of errors in the in-situ measurements for particles and electric fields, including Langmuir probes and electron analyzers (ESA). 1.2.1 Langmuir Probes Langmuir probes are commonly used in space physics to measure the local plasma density and thus help understand the Earth’s magnetosphere and solar wind environment. They consist of an electrode inserted directly into the plasma connected in series with a variable voltage source [22]. By changing the probe bias, the current as a function of bias potential can be measured, and from those current-voltage (traditionally called I-V curves) relationships, the plasma density and temperature can be determined. Alternately, the Langmuir probe’s electrode can be current biased and it’s floating potential relative to some reference measured, allowing one to measure external electric fields and floating potentials. 1.2.2 Electrostatic Analyzers In addition to Langmuir probes to study the electric fields, spacecraft have included ESAs which measure plasma between few eV and kV range. ESAs are instruments that measure the energy and angular distribution of charged particle fluxes [23]. A firm knowledge of the spacecraft and instrument floating potentials is important as it can induce electric fields that could skew the 6 measurements of these instruments: the particles could change direction due to the electric or magnetic fields of the spacecraft or could have been accelerated or decelerated to a different energy, leading to distortion of the measured flux distributions and systematic errors in the estimated plasma parameters (e.g. density, flow speed, pressure, temperature). 1.3 Space Environment Missions Space environment research missions used differential pairs of Langmuir probes readily, and include: International Earth Sun Explorer (ISEE), Polar, Cluster, Time History Events and Macroscale Interactions during Substorms (THEMIS), Van Allen Probes, Mars Atmosphere and Volatiles Evolution (MAVEN), Solar Orbiter, and Parker Solar Probe (PSP). Langmuir probes have been used on these missions, and the UCB SSL often been used in missions at the Space Science Laboratories (SSL) at University of California (UC) Berkeley as well. 1.3.1 ISEE The purposes of the ISEE mission was to study the Sun-Earth relationships at the boundaries of the magnetosphere, examine the solar wind and bow shock around the Earth, study mechanisms and motions of the plasma sheet as well as cosmic rays and solar flare emissions in the interplanetary regions at 1AU [24]. National Aeronautics and Space Administration (NASA) launched ISEE in 1978 and it was composed of three SC: ISEE-3 was a heliocentric spacecraft in an elliptical halo orbit about L1 and it studied the near-Earth interplanetary region, ISEE-2 and ISEE-1 studied the magnetosphere and coupling of the solar wind at highly elliptical geocentric orbits with ESA and Langmuir probes. These two spacecrafts remained close to each other to separate spatial from temporal fluctuations in their measurements. ISEE used vitreous carbon, a modern material, for the sensor surfaces. 7 1.3.2 Polar Polar was a NASA mission that was in launched 1996. The mission consisted of obtaining data from the active geospace polar-regions, and it had a highly eccentric and inclined orbit [25]. Polar flew through high and low altitudes around the poles. Scientists were able to determine how the solar wind enters the magnetosphere through the polar cusp in addition to the mechanisms of the ionospheric plasma outflow. The instruments on Polar measured the aurora and charged particles, and their behavior with ESA and Langmuir probes. Polar used DAG-213®, a finely divided graphite lubricant in an epoxy resin, for the Langmuir probes surfaces. 1.3.3 Cluster Cluster was a European Space Agency mission composed of four identical spacecraft in a large elliptical orbit around the Earth. While the original four spacecraft were destroyed in a launch mishap in 1996, the Cluster-2 (or Cluster-Phoenix) mission launched in 2001 and continues to return important magnetospheric data even now (2020). The formation flying spacecraft allowed scientists to further understand the interactions between the Earth and the Sun, by studying the particles from the Sun and their interactions with the Earth’s magnetic field with ESAs, Langmuir probes and other instruments [26]. The four spacecrafts map three-dimension plasma structures contained in the bow shock, magnetotail, polar cusps and auroral zones. Cluster helped to model the Earth’s magnetosphere, the interaction of the plasmasphere with Van Allen radiation belts, the Earth bow shock and ion acceleration, amongst other observations. Cluster, also used DAG-213® for their Langmuir probe surfaces. 1.3.4 THEMIS THEMIS was a mission (launched 2007), composed of five identical satellites and its objective was to understand the nature of substorm instabilities that release solar wind energy 8 stored within the Earth’s magnetotail [27]. It helped established when the substorms begin, how each individual component interacts, how the substorms power the aurora and how local disruptions mechanisms couple to global substorm. THEMIS also helped understand the variations in the flux of the Earth’s outer radiation belts. Two of the satellites were then repurposed as ARTEMIS to study the Sun interactions with the Moon, the other three remained orbiting Earth. Within THEMIS instruments, several Langmuir probes were deployed, and ESA used. THEMIS used new electrically conductive materials for their booms, like DAG-213®. 1.3.5 Van Allen Probes The Van Allen Probes was a mission designed to help us understand the Sun’s influence on Earth and near-Earth space by studying the Earth’s radiation belts on various scales of space and time with two identical satellites [28]. It was designed to explore aspects of the Sun-Earth system that directly influence life and society. The satellites were able to orbit with highly eccentric orbits through the inner and outer Van Allen belts. They helped discover the process that accelerates and transports particles in the radiation belts and quantify the loss of electrons from the radiation belts. They also aided to determine the process for the ion loss and were instrumental in understanding how the radiation belts change during geomagnetic storms. Instruments include the Electric and Waves Suite (EFW) composed of Langmuir probes, and other spectrometer and ion/electron composition experiments. Carefully chosen conductive materials to reduce potential charging were used, including Germanium Black Kapton (GeBk) for Multi-Layer Insulation (MLI) blankets and DAG-213® for the EFW probes. 1.3.6 MAVEN MAVEN is a mission designed to study Mars’ upper atmosphere, ionosphere and its interactions with the sun and solar wind [29]. The data from MAVEN will help determine what 9 caused the changes of Mars from containing abundant water and a thick atmosphere, to a dessert world with a thin atmosphere. The instrument package includes solar wind analyzers, solar energetic particle, ion composition, magnetometer and Langmuir probes. TiN conductive material was used for its Langmuir probes. TiN has also been used in Cassini [30] (a mission to Saturn) and Magnetospheric Multiscale (MMS) [31]. 1.3.7 Solar Orbiter Solar Orbiter is a recently launched (Feb 2020) mission that studies the Sun. It is designed to understand the solar activity effects in the inner heliosphere, observing it within and outside ecliptic regions at 0.28 AU[32]. The instrument package includes radio and plasma wave (RPW) antennas, solar wind analyzers and magnetometers. The antennas are exposed to the Sun and are made from Elgiloy, a Cobalt-Chromium-Nickel-Molybdenum alloy. 1.4 Parker Solar Probe PSP is a mission designed to study the Sun with in-situ measurements of the solar wind near the top of the solar corona. PSP has two main scientific goals: first, to study the coronal heating and solar wind acceleration, and second, to study the production, evolution, and transport of solar energetic particles. The mission expects to define the inner boundary conditions of the solar wind and the heliosphere [33]. Launched in Aug 2018, PSP has recently completed its fourth perihelion pass around the Sun, dropping from its initial 35 solar radii closest approach to just under 30 Rs. A key goal of this thesis project is to quantify, measure, and model the important plasma and space environment interactions aspects of the PSP FIELDS electric antenna system for the NASA PSP mission. The FIELDS experiment was selected by NASA to measure DC electric fields, plasma waves, and radio emission on PSP. 10 The PSP spacecraft will approach the Sun to within a heliocentric radius of 10 solar radii (6.86x10 6 km), exposing the PSP spacecraft and FIELDS antenna systems to over 500 times the radiant photon flux present at 1 AU. Because of this, the FIELDS electric antenna system is required to operate at temperatures above 1560 K, 5 times greater than at 1AU. The FIELDS instrument will be surrounded by solar wind plasma with densities 400 times larger than at 1AU (60 times larger than ever encountered by a spacecraft in the solar wind). This is a new operating (and survival) regime for this sort of instrument and presents several design and operational challenges. Figure 1-2 shows an oblique view of the PSP spacecraft with instruments and solar panels retracted. Figure 1-2 Parker Solar Probe in Launch Configuration with FIELDS Antennae Retracted in Launch configuration 11 The spacecraft has a thermal protection system (TPS) which will keep the spacecraft in the shadow at all times (bottom Figure 1-2). The TPS is composed of carbon-carbon foam shield, with a white alumina (Al2O3) finish for meteoroid impact protection, as seen in Figure 1-3. The spacecraft also includes large radiators that are able to dissipate large heat loads and retractable, water-cooled solar panels to avoid the long hot exposures during perihelion passes. The FIELDS antennae are located near the TPS, below the radiators. Figure 1-3 PSP Assembled ready for Integration [34] 12 Figure 1-4 Detail of FIELDS Antenna Instrument Deployed on PSP during Assembly 1.4.1 FIELDS Instrument and Science The FIELDS instrument has three major science objectives [33] 1. The instrument will trace the flow of energy that heats and accelerates the solar corona and solar wind. FIELDS will help identify how the energy from the solar atmosphere is transferred to, and dissipated in, the corona and solar wind. It will study the processes that affect the solar wind in the heliosphere. 2. FIELDS will determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind. The instrument will help determine if the solar wind sources are steady or intermittent. 3. The FIELDS instrument will explore the mechanisms that accelerate and transport energetic particles. It will help identify the roles of shocks, waves and turbulence in the acceleration of energetic particles, and the physical conditions for energetic particle acceleration. 13 The FIELDS instrument is making in-situ measurements of electric and magnetic fields, radio emissions, and shock waves that occur through the solar wind and atmospheric plasma. Figure 1-4 shows a section of the antenna, the stub and the isolated shield that help reduce the heat flux towards the spacecraft and reduce the temperature. Fluxgate and searchcoil magnetometers measure DC and higher frequency magnetic field fluctuations. The FIELDS antennas are composed mainly of Niobium C103 and Mollybdenum TZM, two refractory metals. Sapphire is also used for both thermal and electrical isolation. Another metal that was considered during the design process was Tantalum-Tungsten (Ta-W), but was not used because its density was double that of Nb-C103. 1.5 Content of Dissertation While the past 40 years of observational and theoretical work on spacecraft charging and Langmuir probe measurements have given us a good idea of how these processes work, there is still more questions to address that directly affect the FIELDS instruments and improve its measurements. This dissertation has four main objectives: 1. The first objective of this dissertation is to lay down the theoretical foundation of spacecraft charging of the PSP FIELDS instrument in its unusual large range of environmental conditions. The spacecraft charging current balance theory is revisited, including Langmuir probe theory, I-V curves, and thermionic emission is highlighted as a primary current source at 9.5 solar radii away from the Sun. 2. The second objective is to obtain angular photoemission properties of the FIELDS antennas, by testing material samples prepared similarly to spacecraft missions. Annealing effects are studied, solar cycle influences on photoemission and work functions are determined, and new 14 analytical fits are produced to obtain photocurrents. Photocurrent greatly influences the current balance of spacecraft and their instruments, and the potential of the surface, and is the primary current at 9.5 solar radii away from the Sun. 3. The third objective of this dissertation is to obtain the SE and BSE properties of the same materials used in the first objective. Again, annealing effects are studied, more modern analytical fits are used, and a new quick lookup graph to obtain SE and BSE currents dependent on environmental electron temperatures is shown. SE and BSE currents can be dominating currents on a surface in the shadow. 4. The fourth objective is to use these new material properties in SPIS, an advanced and complex spacecraft charging software, to obtain surface potentials of the PSP spacecraft and FIELDS instrument, as the presence of the spacecraft makes its surrounding environment nonuniform and complex. I-V curves are modeled, and results compared with preliminary flight data. This dissertation advances the state of the art of spacecraft charging in four innovative steps. The first is by introducing thermionic emission as primary current at 9.5 solar radii away from the Sun through analysis. The second, it is by demonstrating measured photoemission and secondary electron yields from relevant spacecraft and instrument materials that were not represented in existing literature, including annealing effects. The third step is by it combining photoemission and secondary electron yields from relevant spacecraft and instrument materials that were not represented in existing literature, including annealing effects. The fourth and last step is through the synthesis of the materials and modeling data to produce predictions of the unbiased and current- biased floating potentials both for the PSP spacecraft (done before) and the relevant elements of the FIELDS instrument, and the comparison between those predictions and the relevant in-flight 15 data (I-V curves), which has not been done before and, therefore, can be considered a valuable contribution to the state of the art of spacecraft charging. This dissertation involves a combination of theoretical analysis, computer simulations, and experimental observations. First, this thesis explains the theoretical background of spacecraft charging, and the processes that cause the charging: photoemission, thermionic emission, SE, BSE, electron current, ion current, and bias current. The theoretical section is followed by photoemission testing setups, testing results, and new analytical fits. Afterward, the SE emission and BSE testing are described, and data results shown. Subsequently, this new data is used to create a spacecraft model in SPIS, obtaining current balance including the spacecraft and FIELDS potential which is compared with the preliminary flight data. Finally, this section is followed by the conclusions and references. 16 2 Theoretical Background As previously mentioned, all spacecraft interact with their plasma environment. This plasma environment can cause surface charging on the spacecraft and/or instrumentation. In addition, if the spacecraft is exposed to the Sun, photons will interact with the surfaces, resulting in charging of spacecraft surfaces through photoemission or thermionic emission. Section 2.1 explains probe theory and leads to a better understanding of the current balance of a probe in a plasma environment through the development of formulas for the current collected by or emitted from a surface for a given potential difference between it and the environment. The plasma spacecraft charging theory is studied in section 2.2. 2.1 Probe Theory A probe immersed in a plasma must reach a current balance. That is the net current on a probe must equal to the sum of all currents on to or from the surface, which to reach balance must equal to zero; the charge density must not change over time. The following equation shows the current balance equation: 𝑑𝜎 𝑑𝑡 𝐴 =𝐼 𝑓𝑟𝑜𝑚 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 (Φ)−𝐼 𝑡𝑜 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 (Φ) 2-1 where σ is the charge density, A is the surface area, I is the current and Φ is the surface potential with respect to the plasma. Equation 2.1 is known as the I-V curve because it relates the current to a surface to the potential difference between the surface and the plasma. For the current balance to hold the potential difference between the surface and the plasma must be constant. When an electrode is immersed in a plasma and brought to a potential relative to the plasma a sheath forms around the surface. A sheath is defined as the layer where the potential of the 17 plasma transitions from surface potential to the plasma potential. This sheath often acts like a potential barrier, electrostatically confining or deflecting the more mobile species, usually electrons [35]. The transport of species between the surface and the sheath edge depends on the surface potential. Sheaths generally form around probes and spacecraft, controlling the flow of charge to and from their surfaces. Figure 2-1 shows a schematic of the potential near a flat surface. Figure 2-1 Potential of plasma near a surface at a negative potential To obtain the potential of a surface with respect to the plasma, we must first look at the steady state 1-D Poisson’s equation: 𝑑 2 Φ 𝑑𝑥 2 = 𝑞 𝑒 𝜖 0 (𝑛 𝑒 −𝑛 𝑖 ) 2-2 18 Where qe is the electron charge, ϵ0 is the permittivity, ne is the electron density and ni is the ion density. We then study the continuity and energy conservation equations to obtain the ion and electron density, assuming a mesothermal plasma, which is a plasma that is defined in the next equation: 𝑣 𝑡 ℎ𝑖 ≪𝑢 0 ≪𝑣 𝑡 ℎ𝑒 2-3 where u0 is the velocity of the spacecraft or probe, vthe and vthi are the electron and ion thermal velocities. Conservation of energy can be shown to follow Eq. 2-4: 1 2 𝑚 𝑖 𝑣 𝑖 2 (𝑥 )−𝑞 Φ(𝑥 )= 1 2 𝑚 𝑖 𝑣 0 2 2-4 where m is the mass of the electron or ion, v is the velocity of electron or ion, v0 is the velocity of the ion at the sheath, q is the particle charge and Φ is the potential with respect to the plasma. Continuity can be shown in the following equation: 𝑛 0 𝑣 0 =𝑛 𝑖 (𝑥 )𝑣 𝑖 (𝑥 ) 2-5 where ni is the ion density, n0 is the plasma density. By combining these two equations we can obtain a density equation: 𝑛 𝑖 (𝑥 )=𝑛 0 (1− 2𝑞 Φ(x) 𝑣 0 2 𝑚 𝑖 ) −1/2 2-6 The electron density is obtained using the following equation: 𝑛 𝑒 (𝑥 )=𝑛 0 𝑒𝑥𝑝 ( 𝑞 Φ(x) 𝑘 𝑏 𝑇 𝑒 ) 2-7 Where kb is the Boltzmann constant and Te is the electron temperature. In a mesothermal plasma, electrons are assumed to behave as a Boltzman fluid, while the ions are considered to be ballistic. 19 The number flux of the ion on a negative charging surface can be calculated for a positive potential surface using the following equation: Γ 𝑖 =𝑛 𝑖 𝑢 0 2-8 Where Γi is the ion flux, ni is the ion density and u0 is the spacecraft velocity (or ion velocity). The electron flux for can be found using the following equation: Γ 𝑒 =𝑛 𝑒 √ 𝑘 𝑏 𝑇 𝑒 2𝜋𝑚 𝑒 𝑒𝑥𝑝 ( 𝑞 Φ 𝑘 𝑏 𝑇 𝑒 ) 2-9 where ne is the electron density, kb is the Boltzmann constant, me is the electron mass and Te is the electron temperature. Using 2-1 for a steady state solution, we can find the potential of the surface. PSP, the main focus of this dissertation, is in a mesothermal plasma throughout its mission, near the Earth and as it approaches the Sun. The ion velocity and spacecraft velocity are very similar in magnitude at close approach, with different orientations. To obtain an accurate estimate of the ion flux, the solar wind ion velocity and spacecraft velocity should be added together. The resultant ion velocity remains greater than the ion thermal velocity but less than the electron thermal velocity. 2.1.1 Thin Sheath – Child Langmuir Law The Child Langmuir Law relates the current that flows to a surface with the sheath thickness. The thickness of the sheath determines the region where the charge is collected and the maximum current that can flow to the surface [2]. A thin sheath can be defined as a sheath whose thickness is smaller than the transverse dimensions of the spacecraft or probe. Because electrostatic shielding in unmagnetized plasmas like this example, and in weakly-magnetized plasmas like the solar wind, scales with the Debye 20 length [2], spacecraft dimensions and Debye lengths determine which limit (thin or thick) sheath to use. The thin sheath assumes that the sheath effects dominate the electron or ion effects to the surface. The following derivations assume a cold ion (Ti <<Te) and that the electrons are hot |𝑒 Φ/𝑘 𝑇 𝑒 |≪1 to be able to assume a uniform background plasma. By inserting 2.6 and 2.7 in Poisson’s equation (Eq. 2-2), we obtain: 𝑑 2 Φ 𝑑𝑥 2 = 𝑒 𝑛 0 𝜖 0 (𝑒𝑥𝑝 ( 𝑒 Φ(x) 𝑘 𝑏 𝑇 𝑒 )−(1− 2𝑒 Φ(x) 𝑣 0 2 𝑚 𝑖 ) −1/2 ) 2-10 If we simplify with the following notation [3]: 𝜒 =− 𝑒 Φ 𝑘 𝑏 𝑇 𝑒 𝜉 = 𝑥 𝜆 =𝑥 ( 𝑛 0 𝑒 2 𝜖 0 𝑘 𝑇 𝑒 ) 1 2 𝑀 = 𝑢 0 (𝑘 𝑇 𝑒 𝑀 ⁄ ) 1/2 2-11 where λ is the Debye length, and inserting back into Eq. 2-12, we obtain 𝜒 ̈ =(1+ 2𝜒 𝑀 2 ) 1/2 −𝑒 −𝜒 2-12 If we assume that the electron density is negligible near the wall, and we integrate twice we have: 4 3 𝜒 𝑤 3/4 =2 3/4 𝑀 1/2 𝑑 /𝜆 2-13 where d is the sheath thickness of a flat semi-infinite probe. By rearranging and reversing the simplifications of Eq. 2-13, we can obtain the Child Langmuir’s law: 𝐽 𝑖 =𝑒 Γ 𝑖 = 4 9 ( 2𝑒 𝑚 𝑖 ) 1/2 𝜖 0 |𝜙 | 3/2 𝑑 2 2-14 where Ji is the ion current density and d is the sheath thickness. By manipulating the equation, the Child-Langmuir law for cold ions can be expressed in the following manner: 21 𝑑 𝜆 =(4 √2 9 ( 𝑒 Φ 𝑘 𝑏 𝑇 𝑒 ) 3/2 1 𝑀 ) 1/2 2-15 For equations 2-14 and 2-15 to hold on a spherical surface, d<<r where r is the probe radius [2]. 2.1.2 Thick Sheath – Orbital Motion Equations The thick sheath model ignores all the space charge effects of the sheath on charged particle trajectories, focusing on the fields due to the charged surface itself. For the thick sheath, the right hand side of Poisson’s equation is zero, and Laplace’s equation holds[2]: ∇ 2 Φ=0 2-16 Equation 2-18 is only valid if the Debye length is much greater than the probe radius, λ>>r. For PSP the Debye lengths have a range between 8m near the Earth to 1.1m at closest approach to the Sun. 2.1.2.1 Attracted Species - Spherical surface The following derivations are from Mott-Smith and Langmuir (1920), who calculated the sheath properties and I-V relationships for a variety of probe geometries in the thick-sheath, orbit- motion-limited regime. For electrons or ions attracted to the surface, the conservation of energy can be defined as the following equation: 1 2 𝑚 𝑖 (𝑣 1,𝑟 2 +𝑣 1,𝜃 2 )= 1 2 𝑚 𝑖 (𝑣 0,𝑟 2 +𝑣 0,𝜃 2 )+𝑒 Φ 2-17 where v1,r, is the radial particle velocity at the surface of the sphere, v1,θ, is the tangential particle velocity at the surface of the sphere, v0,r, is the radial particle velocity at the sheath, v1,θ, is the tangential particle velocity at the surface of the sphere, v0 is the particle velocity at the sheath, and Φ is the potential at the surface with respect to the sheath. 22 We can then define the conservation of angular momentum 𝑚 𝑖 𝑟 𝑣 1,𝜃 =𝑚 𝑖 𝑎 𝑣 0,𝜃 2-18 where a is the radial distance to the sheath and r is the radius of the sphere. Combining 2-17 and 2-18 we obtain: 𝑣 1,𝑟 2 =𝑣 0,𝑟 2 −( 𝑎 2 𝑟 2 −1)𝑣 0,𝜃 2 +2 𝑒 𝑚 Φ 2-19 Only those particles for which v0,r >0 and 𝑣 1,𝑟 2 >0 are able to reach the collector . To obtain the current we must find the total number of ions which cross the sheath edge with these velocities: 𝐼 =4𝜋𝑁𝑒 𝑎 2 ∫ ∫ ∫ 𝑢𝑓 (𝑣 𝑟 ,𝑣 𝜃 ,𝑣 𝜑 𝜋 0 2𝜋 0 )𝑑𝑟𝑑𝜃𝑑𝜑 ∞ 0 2-20 where f is the distribution function. To simplify we need to replace 𝑣 𝜃 𝑣 𝜑 for polar coordinates 𝑣 𝑠 , ψ to obtain the function g: 𝑔 (𝑣 𝑠 ,𝑣 𝑟 )=∫ 𝑓 (𝑣 𝑟 2𝜋 0 ,𝑣 𝑠 𝑠𝑖𝑛𝜓 ,𝑣 𝑠 𝑐𝑜𝑠𝜓 )𝑑𝜓 2-21 For a Maxwellian distribution velocity, we can then find g 𝑔 (𝑣 𝑠 ,𝑣 𝑟 )= 𝑛 √2𝜋 𝑣 𝑡 ℎ 𝑒𝑥𝑝 (−(𝑣 𝑠 2 +𝑣 𝑟 2 )/2𝑣 𝑡 ℎ 2 ) 2-22 If 𝑣 1,𝑟 𝑎𝑛𝑑 𝑣 1,𝑠 are the surface velocities, then we can obtain an expression for the current: 𝐼 =4𝜋𝑁𝑒 𝑎 2 ∫ ∫ 𝑣 𝑟 𝑣 𝑠 𝑔 (𝑣 𝑠 ,𝑣 𝑟 ) 𝑣 𝑠 0 ∞ 0,𝑣 𝑟 ,0 𝑑 𝑣 𝑠 𝑑 𝑣 𝑟 2-23 By introducing 2-22 into 2-23 and integrating we obtain 𝐼 =4𝜋 𝑎 2 𝐽 0 [1− 𝑎 2 −𝑟 2 𝑎 2 𝑒 − 𝜂 𝑗 𝑟 2 𝑎 2 −𝑟 2 ] 2.24 23 where ηj is the scaled potential differential of such species and J0 is the ambient current density, and will be defined for different sources of currents in Section 2.2. The scaled potential differential is defined as: 𝜂 𝑗 =− 𝑞 𝑗 Φ 𝑘 𝑏 𝑇 𝑗 2-25 where qj is the species charge, kb is the Boltzmann constant, and Tj is the species temperature. If a>>r, then the current can be expressed in the following matter. 𝐼 (Φ)=4𝜋 𝑟 2 𝐽 0 (1+𝜂 𝑗 ) for a>>r 2-26 We can then define a shape factor for spherical probes: 𝐺 𝑗 (𝜂 𝑗 )=(1+𝜂 𝑗 ) 2-27 which would make equation 2-30: 𝐼 (Φ)=4𝜋 𝑟 2 𝐽 0 𝐺 (𝜂 𝑗 ) 2-28 2.1.2.2 Attracted Species – Cylindrical surface Following similar steps to section 2.1.3.1 (spherical surface), but using cylindrical coordinates we can define a shape factor for a>>r, 𝐺 𝑗 (𝜂 𝑗 )= 2 √𝜋 √ 𝜂 𝑗 +𝑒 𝜂 𝑗 erf( √ 𝜂 𝑗 ) for a>>r 2-29 where the error function (erf) is defined as: 𝑒𝑟𝑓 (𝑥 )= 2 √𝜋 ∫ 𝑒 −𝑡 2 𝑑𝑡 −∞ 𝑥 2-30 If ηj>2 and a>>r the shape factor can be re-written as: 24 𝐺 𝑗 (𝜂 𝑗 )= 2 √𝜋 √ 1+𝜂 𝑗 2-31 To obtain the surface current we can use a similar equation to 2-30: 𝐼 (Φ)=2𝜋𝑟𝑙 𝐽 0 𝐺 (𝜂 𝑗 ) 2-32 where r is the radius and l is the length of the cylinder. 2.1.2.3 Attracted Species – Plane surface For a plane surface, the shape factor Gj is simply 𝐺 𝑗 =1 2-33 To obtain the surface current we just use find the surface area and multiply by the ambient current density: 𝐼 (Φ)=𝐴 𝑠 𝐽 0 2-34 2.1.2.4 Repelled Species For repelled species, the current density can be defined exponentially: 𝐽 (𝜂 𝑗 )=𝐽 0 exp (𝜂 𝑗 ) 2-35 Figure 2-2 shows the qualitative behavior of the current-voltage (I-V) curves of plane, spherical and cylindrical shapes. 25 Figure 2-2 Orbit-Limited Current-Voltage Behavior 2.2 Spacecraft Charging Background Under stationary conditions a spacecraft or probe immersed in a plasma must reach a current balance. That is the net current to any exposed surface must sum to zero. [Whipple '65, Grard '73, Garrett '81, Whipple '81, Mullen et al. '86, Hastings et al. '96]. In such a situation the exposed surface floats to some finite voltage relative to the nearby plasma so that current balance can be achieved in the presence of significantly different fluxes of positive and negative particles. This relative potential is known as the floating potential of the surface. In steady state the spacecraft floating potential is determined by the balance of various charging currents to and from the spacecraft or probe. For PSP these currents are determined by the solar wind plasma environment, solar photon flux, spacecraft orientation and material properties, which depend on the floating potential. PSP is designed to be electrically conductive between all surfaces during the perihelia to obtain similar potentials throughout the spacecraft, except for specific 26 instrumentation, including the FIELDS antennas and shields that remain isolated to make electric field measurements possible. The currents which PSP and FIELDS are subjected to include photoelectron current (Iph) from photoelectron emission, ion current (II) and thermal electron current (Ie) from the plasma environment, secondary electron current (Ise) and backscattered secondary electron current (Ibse) resulting from the electrons leaving a surface due to the plasma interaction with surfaces, and thermionic electron current (Itherrm), electrons emitted from a hot body. The following equation shows the spacecraft or probe current balance (also known as the I-V curve): 𝐼 (Φ)=𝐼 𝑝 ℎ (Φ)+𝐼 𝑒 (Φ)+𝐼 𝑖 (Φ)+𝐼 𝑠𝑒 (Φ)+𝐼 𝑏𝑠𝑒 (Φ)+𝐼 𝑡 ℎ𝑒𝑟𝑚 (Φ)+𝐼 𝑜𝑡 ℎ𝑒𝑟 =0 2-36 where Iother could be other currents such as sensor bias currents. Each of these currents varies with the spacecraft or probe potential (Φ) relative to the plasma potential. s Figure 2-3 shows a schematic of a conductive spherical spacecraft or probe charging configuration for illustration purposes, qualitatively represents a three-dimensional plasma. If the spacecraft is negatively charged (case a), the plasma ions are attracted and the plasma electrons, the photoelectrons and thermionic electrons repelled. If the spacecraft is positively charged (case b), the plasma ions are repelled; the plasma electrons, the photoelectrons and the thermionic electrons are attracted. 27 Figure 2-3 Schematic of spacecraft charging near the Sun: a. Negative charged spacecraft repelling electrons and attracting ions; b. positively charged spacecraft attracting electrons and repelling ions. It is important to note that PSP is in a mesothermal plasma environment with plasma ion thermal velocities smaller than the SW (~300km/s) and spacecraft speeds (up to 197 km/s), plasma electron thermal velocities remain greater than the spacecraft and solar wind velocities. A spacecraft in a mesothermal plasma forms a wake behind it [5, 36, 37]. The plasma electron thermal velocities remain greater than the spacecraft and SW velocities. The following sections 28 describe the theoretical background on photoemission, secondary electrons, backscattered secondary electrons and thermionic emission. It also includes the electron and ion current. 2.2.1 Photoemission Photoemission is an emitted electron that escapes from a surface where an energetic photon has impacted [2, 11, 19, 38]. It is usually considered a three-step process: first the photon enters the material and collides with an electron, then the excited electron travels to the surface possibly undergoing multiple collisions, and lastly the electron has sufficient kinetic energy to leave the material, as seen in Figure 2-4 [39, 40]. For the electron to leave the surface, this kinetic energy must be greater than the material work function, defined as the difference in energy between the vacuum potential at the surface and the Fermi level at the surface. The work function depends on material properties, both what the bulk material is, and what the state of its surface is (dirty, clean, oxidized, pure, etc.). Figure 2-4 An illustration of the three step photoemission process [40] 29 Not only is photoemission dependent on material properties, but also on solar flux and the angle of incidence of the photon [18, 19, 41]. All the photoelectron flux occurs due to solar photon flux at energies greater than the work function of the material. For the FIELDS antennas, made from Nb-C103, the work function is ~4.34eV (285.7nm). The combination of the total photon flux, the solar photon spectrum, and the yield curves along with the density, temperature, and flow of the ambient plasma lead to the dominance of photoelectron currents over the other currents in the system. The saturated photoemission flux density (Jph0), adapted from [18], is shown in the following equation: 𝐽 𝑝 ℎ0 (𝐸 𝑝 )=−∫ ∫ 𝑊 (𝐸 𝑝 ,𝜃 𝑝 ℎ )𝑆 (𝐸 𝑝 ,𝜃 𝑝 ℎ )𝑑 𝐸 𝑝 𝜋 /2 −𝜋 /2 ∞ 𝜙 𝑑 𝜃 𝑝 ℎ 2-37 where W is the electron yield per photon and S is the solar photon flux, both dependent on incident photon energy Ep and the incident photon angle θph, and ϕ is the work function. These photoemission flux densities have been previously measured [18, 19, 41]. The photoemission is considered isotropic if the potential of the surface is zero or negative. The following equation is used to find the photocurrent if the Debye length is larger than the spacecraft dimensions (thick sheath approximations) and if, Φ, the surface potential, is positive, from [42]: 𝐼 𝑝 ℎ =𝐼 𝑝 ℎ0 𝐺 𝑝 ℎ (𝑎 ,𝑟 ,𝜂 𝑝 ℎ ) for Φ> 0 2-38 where Iph0 is the saturated photoelectron current, further discussed in Section 3; the factor Gph is dependent on the shape of the probe [35], as seen in Figure 2-2 and explained in section 2.1.3; the photoelectron scaled potential differential ηj shown in Eq. 2-25. 30 The cylindrical G function is used for actual flight antenna model verification. The cylinder in SPIS is considered as a thin wire, where the length l is much greater than the radius r and it is used to neglect end corrections. The saturated photoelectron current is calculated with the following equation: 𝐼 𝑝 ℎ0 =𝐴 𝑠 𝐽 𝑝 ℎ0 2-39 where As is the effective illuminated surface area, and the current density Jph0 is material dependent. If the surface potential is negative, then the photoemission current is calculated using the following equation: 𝐼 𝑝 ℎ =𝐼 𝑝 ℎ0 for Φ≤0 2-40 For FIELDS antennas and shields, composed of Nb-C103, Jph0 ranged from 139 to 49 μA/m 2 [43] depending on the material state (annealed versus unannealed) and solar cycle and activity [44]. Current flight estimated Nb-C103 Jph0 is closer to 240 μA/m 2 . The combination of the total photon flux, the solar photon spectrum, and the yield curves along with the density, temperature, and flow of the ambient plasma lead to the dominance of photoelectron currents over the other currents in the system. Further details of the photoemission for PSP-relevant materials are discussed in Section 3 which describes the laboratory photoemission portion of this dissertation. Modeling and flight results are shown in Section 5. 2.2.2 Electron Current When a probe or spacecraft is immersed in a Maxwellian plasma the equilibrium current is affected by the thermal electron current. Assuming the potential of the probe is negative relative to the nearby plasma, then thermal electron current is given by: 31 𝐼 𝑒 =𝐼 𝑒 0 exp (𝜂 𝑒 ) for Φ≤0 2-41 where Ie 0 is defined as 𝐼 𝑒 0 =𝐴𝑒 𝑛 𝑒 √ 𝑘 𝑏 𝑇 𝑒 2𝜋 𝑚 𝑒 2-42 ne is the ambient electron density, me is the electron mass, and η is defined in equation 2-25 above. If the surface potential is positive, then the electron current is calculated with the following equation: 𝐼 𝑒 =𝐼 𝑒 0 𝐺 𝑒 (𝑎 ,𝑟 ,𝜂 𝑒 ) for Φ> 0 2-43 Where the factor Ge is dependent on the shape, see Section 2.1.3, which is a function of a, the sheath radius, r, probe cylinder or sphere radius of the probe and the electron scaled potential difference ηe (Eq.2-25). 2.2.3 Ion Current In contrast with the Maxwellian electron population in the Solar Wind, the ions can be considered as a cold, nearly monoenergetic beam. The velocity of the solar wind varies depending on the distance from the Sun and solar activity, but it is in the range of 300km/s, corresponding to a proton kinetic energy of 1-2keV in the spacecraft frame. This means that the solar wind can penetrate barriers as high as 1-2kV [5], and as shown by [36, 45, 46] narrow negative potential wake forms behind a cylindrical body. From past simulations [5-8, 47] the resulting spacecraft potential has been predicted to range between a few tens of volts positive or negative depending on the distance from the Sun, solar wind speed, density, and temperature. The ions from the solar wind are able to penetrate the sheath and impinge on the spacecraft and FIELDS instrument with no significant impact from their 32 floating potentials. Given that, the definition of the ion current for both positive and negative potentials is simply: 𝐼 𝑖 =𝐴𝑒 𝑛 𝑖 𝑢 0 2-44 where A is the surface are impinged by the beam, ni is the ion number density, 𝑢 0 is the combined ram and ambient medium velocity. 2.2.4 Secondary and Backscattered Electron Current When high energy electrons (primary electrons or PE) or ions bombard a surface, secondary electrons (SE) are emitted from the surface due to kinetic impacts with the primary incident electrons and ions. Some of these incident electrons have their directions reversed by these impacts and backscatter out of the material with little or no change in energy; these electrons are called backscattered electrons (BSE). SE are formed in three steps: first the penetration of the PE and kinetic interaction to liberate low energy (few EV) SE in the bulk of the struck material; second the diffusion of the SE through the material; and third the-escape of the SE through the solid-vacuum interface [2, 11, 48]. For the FIELDS antennas, the ambient electron temperature of the solar wind is increasing from a few eV to tens of eV, in the range where the SE yield becomes greater than one, causing the departing current of SE to be greater than the arriving environment electron current. Secondary electron (ion induced) yield results in similar induced currents as the ion current due to high impact efficiencies, Isei ~ Ii [5]. As previously mentioned, and as will be shown in Sections 3 and 5, photoelectron current is the highest current on PSP, followed by SE currents at one order of magnitude smaller, reducing the influence of the material properties of SE on current balance and floating potentials. 33 BSE occur when electrons impact and enter the surface, but through collisions they eventually reverse direction to leave the material. These electrons are distinguished by the energy with which they leave the material: BSE leave with energies similar to the incident electron while SE have energies of at most a few eV [2, 11, 13, 49]. In this study, the BSE are defined as those SE backscattered with energies above 50eV[50]. While there are several inconsistent definitions of the BSE and SE populations, this definition is the most commonly used in the spacecraft charging community and is necessary to define material properties consistent with the models used in the NASCAP and SPIS charging models. The emitted SE can be approximated by an isotropic Maxwellian distribution, with a characteristic energy of Tse~2eV [13, 49, 51]. Estimates of the SE yield due to electrons have been difficult to predict theoretically from first principles. However, laboratory studies such as the one detailed in Section 4 below demonstrate that the SE yield for a given material is strictly dependent on the incoming electron energy and angle. From such experimentally determined yields, we can look at Je/ne and material dependent Jse/ne (Te) figures for Maxwellian (or other) electron energy distributions to predict at what ambient electron temperatures the SE currents are greater than the electron current [52]. This procedure is explained in more detail in Section 4.3. The SE current can be calculated 𝐼 𝑠𝑒 =𝐼 𝑠𝑒 0 𝐺 𝑠𝑒 (𝑎 ,𝑟 ,𝜂 𝑠𝑒 ) for Φ> 0 2-45 where Gse is the shape factor and Ise0 is the saturated SE current, defined as: 𝐼 𝑠𝑒 0 =𝐴 𝐽 𝑠𝑒 𝑛 𝑒 (𝑇 𝑒 )𝑛 𝑒 2-46 The scaled potential difference for SE is similar to the photoemission, as both Tse and Tph have similar characteristic energies. 34 For negative surface potential, the SE current is simply: 𝐼 𝑠𝑒 =𝐼 𝑠𝑒 0 for Φ≤0 2-47 Note that past studies of the SE yield of conductive materials at temperatures greater than 600K, have shown a decrease in yield on the order of 0.05%/K [53-55]. For the first perihelia the predicted antenna surface temperatures are ~885 K, and the yield reduced by 44% relative to results at 270-300 K; for the closest perihelia, the expected decease in SE yield is even larger, on the order of 79 % [52]. These effects were not modeled in this paper as photocurrent dominated the current balance by an order of magnitude. More in depth discussion and test data for BSE and SE are shown in Section 4.0. BSE currents are two orders of magnitude smaller than the SE currents for PSP and FIELDS, and are not a significant player in the current balance of the spacecraft. Nonetheless, the currents can be determined similarly than for SE currents with Je/ne and material dependent Jbse/ne (Te) figures to predict BSE currents: 𝐼 𝑏𝑠𝑒 =𝐼 𝑏𝑠𝑒 0 𝐺 𝑏𝑠𝑒 (𝑎 ,𝑟 ,𝜂 𝑏𝑠𝑒 ) for Φ> 0 2-48 and 𝐼 𝑏𝑠𝑒 0 =𝐴 𝐽 𝑏𝑠𝑒 𝑛 𝑒 (𝑇 𝑒 )𝑛 𝑒 2-49 For negative surface potential, the BSE current is simply: 𝐼 𝑏𝑠𝑒 =𝐼 𝑏𝑠𝑒 0 for Φ≤0 2-50 35 2.2.5 Thermionic Emission Current As PSP approaches the Sun with each orbit with a smaller perihelion, the TPS and instruments could experience sufficiently hot temperatures to undergo thermionic emission during the closest perihelion passes. For example, the predicted temperature of the exposed Nb-C103 antennas and shields of the FIELDS instrument reach 1600 K during the closest perihelia (9.8 Rs). At these temperatures some electrons have energies higher than the maximum of the potential barrier at the surface, escaping the metal, and causing a current [9, 56, 57]. This process was first discovered by Richardson, showing that electrons emitted from a hot tungsten filament is a physical process [58]. The proposition that electrons were free flowing in the metal was added later by Sommerfield [57]. This thermionic current can be calculated using the Richardson- Dushman Law of thermionic current flux, and assuming similar orbit limited behavior: 𝐼 𝑡 ℎ𝑒𝑟𝑚 =𝐴 𝑇𝑆 𝐽 𝑡 ℎ𝑒𝑟𝑚 0 𝐺 𝑡 ℎ𝑒𝑟𝑚 (𝑎 ,𝑟 ,𝜂 𝑡 ℎ𝑒𝑟𝑚 ) for Φ> 0 2-51 where ATS is the total surface area, Gtherm is a shape factor and 𝐽 𝑡 ℎ𝑒𝑟 𝑚 0 is defined as: 𝐽 𝑡 ℎ𝑒𝑟𝑚 0 = 𝐴 𝑇 2 𝑒 − 𝜙 𝑘𝑇 2-52 where A is the material specific Richardson constant, k is the Boltzmann constant, T is the surface temperature (in eV), 𝜙 is the work function of the metal, and Gtherm is the fraction of the thermionic electrons that escape as a function of surface potential, surface radius and sheath radius. The temperature of the thermionic electron leaving the surface is assumed to be 2eV, similar to SE and photocurrent electron emission temperatures. For negative potential of the spacecraft or probe, the thermionic current is independent of the potential: 36 𝐼 𝑡 ℎ𝑒𝑟𝑚 =𝐴 𝑇𝑆 𝐽 𝑡 ℎ𝑒𝑟𝑚 0 for Φ≤0 2-53 The thermionic emission current remains several orders of magnitude below the photoemission current until close approach. For FIELDS, we only have the work function of Nb- C103 [41, 52] and not the Richardson Constant, A. The analysis presented uses the value of A for pure Nb to predict the thermionic current of the antenna. The Richardson Constant A varies significantly between materials and within the same material depending on measurement method. For example, for pure Nb, two different investigation measurements gave values of A between 32.7 and 57 (A/cm 2 /K 2 ) [59]. This study used 32.7 A/cm 2 /K 2 to verify that the lowest predicted thermionic emission current was within the same order of magnitude as the photoemission. Figure 2-5 Thermionic emission current density – a. versus temperature of antenna, b., versus distance from the Sun, as compared to the annealed photoemission current density (Jph0 = 49 μA/m 2 ) Figure 2-5, a., shows the predicted thermionic electron current emitted by the antenna during the mission as the spacecraft perihelion decreases in altitude. Figure 2-5, b. shows the 37 thermionic and photoemission current density of the antenna versus the distance to the Sun. While the thermionic current from the antenna was not included in Section 5 because of issues with the current SPIS version (6.0.0), one can see that at heliocentric distances of 30-40Rs, the thermionic current is at least 4 orders of magnitude less than the photoelectron current, and so has not significant effect on the model results, for the first perihelia, but may become as significant at photoemission in the closest perihelia close to 10 Rs. 2.2.6 Bias Current From past experience on many magnetospheric and solar wind missions, the application of a negative bias current (Ib) to the probe minimizes the offset voltage due to spurious currents to the prove from the spacecraft or environment [60-63]. A negative bias current is an electron current from the spacecraft to the probe. Figure 2-6 a. shows how for zero bias current (i.e. usual floating potentials) a small change in the ambient current (Ia) translates into a large change in floating potential. Figure 2-6 b. shows how by adding a bias current, the sensitivity of the probe changes, giving a small voltage differential for the same spurious current variation. The optimal bias current and probe potential can be determined by the probe impedance R, defined as: 𝑅 =( 𝑑𝑉 𝑑𝐼 ) 𝑉 =Φ 2-54 where Φ is the probe potential. From the past definitions, we see how small impedances cause smaller errors ( ΔV) in the measurement if spurious current ( ΔI) is encountered. Sweeping this bias current on FIELDS allows one to determine the I-V curve of the antenna sheath, and thus environmental effects on the antenna and the electric field measurements. Note that SPIS is only able to model a fixed bias voltage between surfaces and then measure the current 38 flowing between those surfaces, as so the I-V curve of the antennas and spacecraft has to be pieced together from multiple runs of the model, as seen in section 5 below. Figure 2-6 – Biased current schematic where figure a. shows the probe potential and ambient current and b. shows the probe potential and bias current [61] 2.3 Theoretical Summary Section 2 presents a theoretical background into spacecraft charging and its interactions with its environment. The standard probe theory is explained, including thick and thin sheath definitions. The standard current balance equation is defined, and individual currents explained. Various currents that affect Langmuir probes, specifically those that can greatly influence FIELDS PSP probes are investigated. These include photoemission, SE, BSE, ambient electron, ambient ion, thermionic emission, and bias current. 39 3 Photoelectron Yields from PSP Spacecraft Materials The following section is based on the published paper “Experimental Investigation of Total Photoemission Yield from New Satellite Surface Materials” by Millan F. Diaz-Aguado, John W. Bonnell, Stuart D. Bale, S.J. Rezvani, Konstantin Koshmak, Angelo Giglia, Stefano Nannarone and Mike Gruntman, Journal of Spacecraft and Rockets, Jan/Feb 2019, Vol.56(1), pp.248-258. 3.1 Introduction Spacecraft surfaces are exposed to a variable space environment that includes plasma, radiation, neutral gas, and particulates [11, 19]. This exposure may cause detrimental effects on the spacecraft [12, 14-16, 19]. In particular, the solar photon flux can cause the surfaces to emit electrons through photoemission, also called photoelectrons, which is defined as an emitted electron that escaped from a surface where an energetic photon has impacted. Photoelectron induced current is usually one of the largest currents of Sun exposed surfaces influencing spacecraft charging [11, 12, 64]. Experiments designed to probe the properties of the plasma surrounding the spacecraft can also be affected by the surface charging [11, 17-19]. Space environment research missions have used Langmuir probes to measure density and potential variations in the plasma. These past, ongoing, and future missions include Polar [25], Cluster [65], Time History Events and Macroscale Interactions during Substorms (THEMIS) [27], Van Allen Probes [28], Cassini [30], Mars Atmosphere and Volatiles Evolution (MAVEN) [66], MMS (Magnetospheric Multiscale) [67], Solar Orbiter[68] and Parker Solar Probe (PSP) [69]. The Langmuir probes on these missions have used a variety of surface materials, including: DAG-213®, a finely divided graphite lubricant in an epoxy resin, used on THEMIS and Van Allen Probes; Titanium Nitride (TiN), an electrically conductive finish on Ti, used for the probes on 40 MAVEN, Cassini and MMS; Niobium C103 (Nb C103), molybdenum TZM (Titanium, Zirconium and Carbon), Tantalum Tungsten (TaW), alloys used for high temperature applications, with Nb C103 and Moly TZM to be used on PSP Langmuir probes with TaW as a backup alloy for PSP; and Elgiloy, a specialty alloy used for stacers, to be used on the Solar Orbiter probes. Samples of each of these materials are included in this study. This investigation also included Tungsten (W) to be able to replicate past experimental data and verify the methods used. The samples were prepared similarly to flight materials using the flight cleaning processes described below. The materials were then exposed to a nearly monochromatic photon beam at photon energies between 4 and 30eV and at photon incident angles between 0° (normal) and 80° (grazing). The DAG-213®, TiN, Nb C103, Moly TZM, TaW and Elgiloy were annealed at temperatures also seen in flight. Tungsten was also annealed. All measurements were repeated post-anneal. The data obtained in these measurements can be used to characterize the surfaces of instruments and spacecraft and their interactions with the space environment. This chapter presents the work function, photoelectron yield and photocurrent data (at 1 AU) for previously untested materials used under conditions that are characteristic in space missions, and not of pure unadulterated samples. First, the experimental setup, procedure and test parameters are described. Second, the test results are presented for all samples, starting with the work function, photoelectric threshold and photoelectron yield at normal photon incident, followed by the photoelectron yield as a function of the photon incident angle. Finally, the photocurrent of materials under solar illumination and an analytical fit of the yield at normal incidence are discussed. 41 3.2 Experimental Setup For this testing, the material samples were treated in the same manner as the mission materials. First, the items were bathed in a 10% by volume Crystal Simple Green to deionized water solution. They were subsequently ultrasonically cleaned for a minimum of 5 minutes, then ultrasonically rinsed in deionized water and finally dried in air. The materials tested were also annealed at temperatures similar to flight temperatures in the UHV (Ultra High Vacuum) preparation chamber of the apparatus used. The samples were placed in the UHV chamber at 10 -10 torr, for at least 2 hours before testing. Because of the specifics of the sample holder, the maximum annealing temperature was ~1470K resulting in 135K less than the expected one at closest approach of PSP, which occurs at 9.5 Sun radii away from the Sun. Annealing times and temperatures varied by sample; Nb C103, W, TaW, Moly TZM, were annealed at 1473K (1200°C) for 2 minutes, Elgiloy was annealed to 1073K (800°C) for 5 minutes and DAG-213® and TiN were annealed to 423K (150°C) for 20 minutes. Electron photoemission testing of the samples was done prior and post annealing to check for any change in photoelectron yield. All tests were conducted at the Italian CNR-IOM (National Research Council – Istituto Officina dei Materiali) beamline, BEAR (Bending magnet for Emission Absorption and Reflectivity) at the Elettra Synchrotron (Trieste, Italy)[70]. The light spot at the focal point was about 400x100μm 2 (horizontal x vertical). The photon beam of photon energy in the 2.7-30 eV (459.2-41.3nm) range was monochromatized with an energy resolution E/ E 2000 and linearly polarized with a degree of linear polarization  90%. This high degree of linear polarization allows for the measurement of the yield due to the two possible polarizations of an incident photon - s, where the electric field of the incident photon is perpendicular to the plane of incidence (and thus 42 solely in the plane parallel to the surface of the material); and p, where the electric field of the incident photon lies in the plane of incidence (and thus can have components both parallel to the surface of the material and normal to that surface). The incident photon intensity (photons/second) was measured by an absolute photodiode (AXUV100) before the yield measurements. This intensity monitor allowed one to take into account any variation in photon intensity between different runs. A six degree of freedom sample manipulator was used to change the angle of incidence of the photons on the sample. The total photoelectron emission was measured in s- and p-polarization with photon incidence angle from 0° to 80° (normal to grazing incidence). The angular step was 10° +/- 0.1°, and the photon energy range was from ~4 eV to 15 eV using 0.1 +/ -0.015 eV increments and from 15 eV to 30 eV using 0.5eV+/ -0.015 eV increments. Two kinds of detection of photo-emitted electrons were used as sketched in Figure 3-1, which included a Channel Electron Multiplier (CEM), Channeltron Sjuts KBL 15RS, which gives a count rate proportional within a multiplicative constant to the rate of electron emission and a Keithley pico-ammeter 6517A to measure the current of emitted electrons (the sample drain current) by grounding the sample through the pico-ammeter. The incidence plane is indicated in the inset (dashed area). The CEM is positioned out of incidence plane. The red and green arrows indicate the direction of the electric field of the incident light for s (red) and p (green) polarization incidence. The red arrow is pointing towards the page in the main figure and towards the left in the inset. The Channeltron is positioned out of the incidence plane in order to allow normal incident measurements while reducing spurious counts due to reflected photons. 43 Figure 3-1 Measurement schematic (geometry shown for 40° of incidence): CEM and sample are scanned in angle together in order to keep the relative positions fixed. The CEM was used to measure yields for low photon energies (2.8-8.0 eV) where the yield rate was low and thus not affected by possible non-linearity due to count pile up, while the pico- ammeter was used in the 7-30 eV range, where the yields and currents where higher. The two measurement methods were used simultaneously in the 7-8 eV region. This allowed one to normalize counts to the emission current which was assumed to be an absolute measurement of the rate of electron emission. The sample was biased to -110V to ensure saturation of the electron collection. This condition is equivalent to collecting all the electrons emitted in the 2π solid angle on the vacuum side. The overall uncertainty of the photoelectron yield was estimated to be of the 44 order of 0.5 %. Figure 3-2 shows an inner view of the experimental chamber of the BEAR beamline in which light beam, photodiodes and sample manipulator are indicated. Figure 3-2 Image of the photon and electron detector at the BEAR testing facility, Trieste, Italy[71] 3.3 Photoemission Results Sections 3.3.1 through 3.3.4 contain the presentation and discussion of the experimental results. Sec. 3.3.1 is devoted to the work function, Sec.3.3.2 to photoelectric threshold, Sec.3.3.3 to photoelectron yield and Sec. 3.3.4 to the angled photoelectron yield. In Sec. 3.3.5 the photocurrents under solar illumination at 1AU are presented. Finally, Sec.3.3.6 describes the derivation of an analytical expression of the photoelectron yield. 45 3.3.1 Work Function The normal photoelectron yield was fitted using Fowler [72] for low energies (less than 7eV) to obtain the work function. The material work functions are shown in Table 3-1. Previous measurements of Tungsten’s work function - 4.6eV [73], 4.52eV [10] and a range between 4.25eV and 4.66eV with a recommendation of using 4.55eV [59, 74], are in close agreement with this study, 4.2eV unannealed and 4.4 annealed. Past measurements of TiN’s work function, 4.2eV [75], are also close to the new estimate obtained. In addition, our data shows how a unannealed Tungsten work function is lower than the post-anneal work function. Table 3-1 Work function of Metals unannealed and annealed Sample Work function (eV) (unannealed) Work function (eV) (annealed) Nb C103 4.38 +/- 0.04 4.30 +/- 0.05 Moly TZM 4.31 +/- 0.04 4.48 +/- 0.04 Tungsten 4.20 +/- 0.04 4.40 +/- 0.04 TaW 4.35 +/- 0.04 4.20 +/- 0.04 Elgiloy 4.05 +/- 0.04 4.05 +/- 0.04 DAG-213® 5.10 +/- 0.05 4.70 +/- 0.05 TiN 4.15 +/- 0.04 4.10 +/- 0.04 3.3.2 Photoelectric Threshold The photoelectric threshold - minimum photon energy for photoelectron emission - was estimated by extrapolating the measured photoelectron yield for each material to zero yield using the Fowler method [72]. The photoelectric threshold measurements unannealed and annealed are shown in Table 3-2. All thresholds decreased post-annealing. The yield thresholds of the samples in Table 3-2 are greater than the work functions of the samples in Table 3-1 in agreement with the physical definition of their quantities. Work function 46 being the position of the Fermi level at surface and photoelectric threshold being the difference in energy between the highest occupied levels and the vacuum. Table 3-2 Photoelectric Thresholds of Metals unannealed and annealed Sample Photoelectric Threshold (eV) (unannealed) Photoelectric Threshold (eV) (annealed) Nb C103 4.87 +/- 0.05 4.72 +/- 0.05 Moly TZM 5.01 +/- 0.05 4.97 +/- 0.05 Tungsten 4.90 +/- 0.05 4.68 +/- 0.05 TaW 4.96 +/- 0.05 4.83 +/- 0.05 Elgiloy 5.00 +/- 0.05 4.47 +/- 0.04 DAG-213® 5.57 +/- 0.06 5.35 +/- 0.05 TiN 5.02 +/- 0.05 4.92 +/- 0.05 3.3.3 Normal Photoelectron Yield We define the total photoelectron yield as the average number of emitted electrons per incident photon. The yield was obtained by dividing the emission current by the electron charge and the photon rate, for each photon energy and angle of incidence. The results of the photoelectron yield of the samples are shown in the following figures. Figure 3-3 shows the comparison of photoelectron yield of Tungsten compared to past measurements showing good quantitative agreement between them. Figure 3-4 shows the photoelectron yield of Nb C103, Moly-TZM, Tungsten, TaW, and Elgiloy unannealed and post annealed at normal angle of incidence. Figure 3-5 shows DAG-213® and TiN results at a normal angle of incidence. From Figures 3-4 and 3-5 it can be observed that the photoelectron yields of the samples at low photon energies are irregular. Similar irregularities can also be found in past measurements for dirty tungsten [73, 76], implying some surface contamination of the samples. However, such a “contaminated” state of these materials represents their likely state at launch and during early 47 times in orbit. Thus, these measured properties will be reflective of the “beginning of life” (BOL) phototoelectron yields of these materials that can be expected to evolve upon exposure in space. Space is not a benign environment: it includes ion, electron, photon and atomic oxygen (AO) bombardment [64, 77, 78] in addition to other neutrals. Past laboratory tests show how samples are sensitive to surface contamination, such as water, hydrocarbons, carbides, and oxides, which could change the yield as the metals are exposed to the space environment [79]. The plasma environment could help etch the sample with ions and eliminate the contamination, react with AO and contaminate the surface further, or could cause electron stimulated desorption that alters the surface composition [80, 81]. While simple annealing of the samples at elevated temperatures cannot model all these processes, it does provide a useful guide as to the sorts of changes in the yield that will occur upon the aging of the surfaces in space. Figure 3-4 shows a large photoelectron yield variation between unannealing and annealing, compared to Figure 3-5, indicating an actual change in the sample structure. Previous Scanning Electron Microscope (SCM) images performed on unannealed and annealed W and Moly TZM show crystalline structure changes at high temperatures, with an effect of smoothing the metal surfaces [82], which could be the cause for the changing photoelectron yields. The changes in photoelectron yield for DAG-213® and TiN shown in Figure 3-4 suggest that increased temperatures from room temperature in UHV could reduce or eliminate some contamination of the surface through outgassing. 48 Figure 3-3 Photoelectron yield (elec./photon) at 0° angle of incidence for W, compared to past data from Walker and Rentscheler [11] left unannealed, right annealed. Figure 3-4 Photoelectron yield (elec./photon) at 0° angle of incidence for W, TaW, Nb C103, Moly TZM, Elgiloy, left unannealed, right annealed. 49 Figure 3-5 Photoelectron yield (elec./photon) at 0° angle of incidence for DAG-213® and TiN, left unannealed, right annealed. 3.3.4 Photoelectron Yield vs. Incident Photon Angle As explained by Whipple [11], the photoelectron yield can depend on the angle of photon incidence. For example, Juenker [83] showed that for pure Molybdenum the yield for p- polarization increases as the secant of the incidence angle up to 70°, while the yield due to s- polarization decreases as the cosine of the incidence angle. These trends are more likely to occur on single crystals, as tested by Heroux [84] and not on larger surfaces, like the ones tested in this dissertation. An irregular surface finish could have a large impact on the angular dependence of the photoelectron yield on a large surface compared to a single crystal, rather than interacting with a surface with a well-defined angle of incidence the photons on a larger surface encounter a wide range of incident angles. Figure 3-6 shows the photoelectron yield of Tungsten, where neither the s-polarized, the p-polarized nor the total yield follow the cosine nor the secant. 50 The dependence of photoelectron yield on incidence photon angle is shown in detail in Figures 3-7 through 3-13 for energy values between 9 eV and 14 eV and from 0 to 80° incidence for all materials tested. For all metals, at higher energies above 14 eV and at normal photon incidence, the photoelectron yield variation decreases and stays within an order of magnitude of that at normal incidence, as can be seen in Figure 3-4 where for all materials the yield lies between ~0.07 and ~0.15 for the annealed, and ~0.045 and ~0.017 for unannealed. Annealing effects vary by metal, but for all metals the angle of maximum photoelectron yield increased. For example, in Figure 3-6 the maximum photoelectron yield for W is near 30° photon incidence angle for unannealed, but closer to 50° photon incidence angle for post-anneal. The temperature treatment of TiN and DAG-213® did not affect the material as much compared with the annealing effects of W, TaW, Nb C103, Moly-TZM and Elgiloy, but the yield on both materials decreased. The yield of TiN decreased sharply at 80° incident angle after the temperature treatment. 51 Figure 3-6 Angular dependence of the ratio of the s-, p-polarized and total yield and their yield at normal angle of incidence (°) for Tungsten unannealed left, annealed right at 10.2eV photon energy. The secant and the cosine are also plotted. Figure 3-7 W Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed. 52 Figure 3-8 Nb-C103 Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed. Figure 3-9 TaW Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed. 53 Figure 3-10 Moly TZM Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed Figure 3-11 Elgiloy Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed 54 Figure 3-12 TiN Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed Figure 3-13 DAG-213® Photoelectron yield (electrons/photon) within the range of 9-14eV photon energies and between 0-80° incident angles, left unannealed, right annealed 3.3.5 Electron Photoemission Under Solar Irradiation The total photocurrent at 0⁰ incidence was estimated for a solar spectrum at 1 AU for maximum and minimum solar cycle [19, 85]. The yield was averaged for p- and s-polarizations as the solar photons are not polarized. The Sun’s photon flux is shown in Figure 3-14, where it is 55 easy to observe how the low energy photons (<10 eV) have a higher flux than at high energies. This means that materials with lower photoelectric thresholds will have higher photocurrents. In addition to the contribution from the continuous solar flux spectrum, the contributions due to the dominant emission lines in this energy range were also included, (Si II, C I, C IV, C II, O I, H Lyman alpha, Si III, O VI, H Lyman beta, C III). Table 3-3 shows the energy and intensity of these emission lines in the solar spectrum at 1 AU for solar maximum and minimum of cycle 21. Note that there are differences in the literature to what intensity values to use for Lyman Alpha [85-88]. This research used intensity values calculated from Meier [85]. Table 3-3 Emission lines in the solar spectrum at 1 AU of solar cycle 21 [85] Line Energy (eV) Intensity Max - Min (10 9 photons cm -2 s -1 ) Si II 6.86 152 - 126 C I 7.48 32.6 - 20.9 C IV 8.00 17.9 – 10.2 C II 9.28 12.0 – 6.15 O I 9.52 7.52 – 2.96 HLα 10.12 512 - 268 Si III 10.28 4.2 - 2.3 O VI 12.01 1.10 - 0.46 HLβ 12.09 4.75 – 2.43 C III 12.69 7.57– 3.54 The photoelectron yield at these values were obtained by interpolating the data obtained from the BEAR test. The contribution due to these lines is important to include, as they contribute significantly to the photocurrent [19, 85]. The analytical fits described in the next section were used to interpolate the observed yields to the energies predicted for the solar spectrum. Table 4 shows the integrated photoelectron current density under solar irradiation at 1 AU including emission line energies. The solar cycle variation was also included in the photocurrent calculations. The following equation was used to calculate the current density: 56 𝐽 0 =∑ 𝑆 (𝐸 )∆𝐸 𝑌 0 (𝐸 ) 30 𝐸 =𝜙 +∑𝐿 (𝐸 ) 𝑌 0 (𝐸 ) 3-1 where ϕ is the material work function, Y0 is the photoelectron yield at normal incidence, S is the solar flux as a function of energy, L is the line intensity and E is the incident photon energy. Tungsten data shows consistency with past measurements, which range from 21-81 µA/m 2 , including 50 µA/m 2 obtained on Explorer 8 [11] on November 1961, during solar cycle 19 with maximum in 1958 and minimum in 1964. The influence of H Lα on Tungsten varied on sample and environment; it was 45.6% of the total photocurrent for the unannealed sample at solar maximum, while it was only 7.6% of the total photocurrent for the annealed sample at solar minimum. On-orbit photocurrent estimates for DAG-213® are in good agreement with the calculated photocurrents, and range between 30uA/m 2 at Solar Minimum to 46uA/m 2 at Solar Maximum [61]. Note that photocurrents at different distances from the Sun scale with 1/R 2 . For Elgiloy, the current is higher for the annealed samples. This is due to enhanced yield at low energies and the higher photon flux at those energies, as shown in Figure 3-14: the unannealed Elgiloy has a higher yield at higher photon energies, but lower than the post-anneal Elgiloy at low photon energies. The photocurrent also increased for DAG-213® heating treatment. Table 3-4 Integrated photoelectron current density at 0° incidence at 1 AU, at maximum and minimum solar irradiances (cycle 21) Sample Current (µA/m 2 ) Max/Min (unannealed) Current (µA/m 2 ) Max/Min (annealed) Nb-C103 139/ 98.2 66.6/ 49.0 Moly TZM 51.9 / 26.0 36.8 / 25.0 Tungsten 81.0 / 43.6 56.2 / 45.0 TaW 78.6 / 45.2 65.8 / 50.8 Elgiloy 77.9 / 46.1 299 / 275 DAG-213® 41.7 / 20.3 45.4 / 22.7 TiN 70.1 / 47.5 61.8 / 34.2 57 Tungsten and TaW both had a decrease of their maximum photocurrent from unannealed to post annealed, but their minimum photocurrent increased slightly. Figure 3-14 Maximum and Minimum Solar Flux Energy Spectrum at 1 AU (Meier) [85] without line fluxes and the normal photoelectron yield of Elgiloy unannealed and annealed 3.3.6 Analytical Fit to the Photoelectron Yield at Normal Incidence In order to have a smooth model of the yield as a function of photon energy, the normal photoelectron yield was fitted using Fowler [72] for low energies (less than 7eV) to help find the work function, but the Fowler model does not extend to the higher energies needed to characterize photoemission under solar illumination. To facilitate the photocurrent calculations for all energies, the following empirical equation was used: 𝑌 (𝐸 )=𝑌 0_0 +𝑎 ( (𝐸 −𝜙 ) 𝐸 𝑏 ) 𝑐 (1+( (𝐸 −𝜙 ) 𝐸 𝑏 ) 𝑐 )(1+( (𝐸 −𝜙 ) 𝐸 𝑑 ) 𝑒 ) 3-2 58 where Y0_0 is the approximate photoelectron yield at the photoelectric threshold at normal incidence, E is the photon energy, ϕ is the work function, and a, Eb , c, Ed and e are parameters to fit the equation to the data. This choice is motivated by the fact that in a small range in the vicinity of the threshold the sample material can be treated as a simple system with free electrons (as in the Fowler model) while at higher energies this approximation does not hold where the band effects become important. The model also captures the qualitatively similar large-scale features of the yield curves: the steep initial rise in yield (the E b and C dependence), a plateau at a maximum yield, followed by a falloff in yield with increasing photon energy (the Ed and e dependence). Changes in parameter a have the most effect on the fit uncertainty. It is approximately the maximum yield, and ranges between 0.173 (elec./photon) and 0.21 (elec./photon) for unannealed and 0.028 (elec./photon) and 0.19 (elec./photon) for annealed. The maximum yield decreases for all samples between the unannealed and annealed fits. The parameter Eb defines the elbow of the plotted photon energy curve and c defines the initial slope, where Eb ranges between 6.90 eV and 8.5 eV for unannealed and between 6.8 eV and 10.7 eV annealed, and where c ranges between 4.8 and 7.9 unannealed and between 2.98 and 8.6 annealed. Eb increased and c decreased for all annealed samples. The parameters Ed and e help define the yield curve after maximum yield up to 30eV photon energy: Ed ranges between 9.90 eV and 23.0 eV for pre-anneal and between 14.8 eV and 24.9 eV, ranges between 1.1 and 3.34 for unannealed and between 0.583 and 7.23 annealed. Ed increased for all samples except for Moly-TZM and DAG-213®, and e increased for all parameters except for Elgiloy and DAG-213®. 59 Table 3-5 shows the parameters for each material unannealed, while Table 3-6 shows the parameters annealed. The fits of the model to the measured data were heavily weighted at low photon energies (1-10 eV) to ensure accurate photocurrent estimates, as the solar photon flux is higher at those energies as shown in Figure 3-14. The average relative error, U, between the fitted model, Y, and measured yield data, Yx, was estimated using the following formula: 𝑈 =〈|𝑙𝑜𝑔 (𝛿𝑌 +1)|〉 3-3 where the relative error δY is given by: 𝛿𝑌 = 𝑌 𝑌 𝑥 −1 3-4 Table 3-5 Parameters for Analytical Fit Unannealed Sample Y 0 (elec./photon) a (elec./photon) E b (eV) c E d (eV) e Fit Uncertainty Nb-C103 1.18e-6 0.500 8.29 4.80 10.9 2.30 0.414 Moly TZM 1.45e-7 0.300 7.30 7.68 14.0 1.50 0.262 Tungsten 1.81e-7 0.189 6.90 7.00 23.0 3.34 0.244 TaW 6.14e-7 0.420 7.70 5.80 12.0 1.60 0.358 Elgiloy 6.80e-7 0.361 7.80 6.50 12.0 1.60 0.207 DAG-213® 6.10e-8 0.198 8.00 6.20 18.6 1.32 0.151 TiN 1.35e-4 0.390 7.00 7.90 9.90 1.10 0.398 Table 3-6 Parameters for Analytical Fit Annealed Sample Y 0 (elec./photon) a (elec./photon) E b (eV) c E d (eV) e Fit Uncertainty Nb-C103 1.45e-8 0.0960 8.60 3.90 15.5 2.40 0.123 Moly TZM 5.23e-7 0.0525 6.60 4.93 24.9 2.70 0.307 Tungsten 1.78e-7 0.0450 10.7 2.98 24.9 7.23 0.072 TaW 4.53e-7 0.0540 7.15 4.30 23.0 3.20 0.135 Elgiloy 1.09e-4 0.0590 8.18 3.00 21.0 1.30 0.256 DAG-213® 1.48e-7 0.190 7.70 6.20 18.6 1.32 0.096 TiN 2.00e-7 0.290 7.05 8.60 14.8 1.28 0.350 60 We use this relative error as a measure of the goodness of fit of the model to the data as it is consistent with the weighting imposed during the fitting process: Using an absolute error measure, i.e. Y-Yx, would weight the higher yields more heavily at higher energies in the fitting of the model to the data, while this relative error measure follows the higher weighting of the yield data at lower photon energies. The values of U range from around 0.072 to 0.414, corresponding to an average relative error between 1.1 and 1.7 (i.e. +/- 10% to +/- 70%). This translates directly into the fractional error in the derived total photoelectron flux for each material as computed from the model and the solar photon flux spectrum. Figure 3-15 show the photoelectron yield of Nb-C103 and its calculated fit for both unannealed and annealed. These analytical fits also captured most of the peaks, valleys and plateaus of the differential photoelectron yield vs. incident photon energy that arise because of features in the solar emission spectrum, as shown for Nb-C103 in Figure 3-16. 61 Figure 3-15 Photoelectron yield (elec./photon) at 0° angle of incidence with theoretical fit for Nb C103, left unannealed, right annealed Figure 3-16 Photoelectron flux vs incident photon energy at 0° angle of incidence with theoretical fit for NbC103, left unannealed, right annealed for solar maximum. 62 3.4 Photoemission Testing and Analysis Conclusions The photoelectron yield, work function and photoelectric threshold of several metals used for new spacecraft applications were investigated. The processes for cleaning and preparing the samples were similar to those followed for spacecraft integration and assembly to better reflect actual spacecraft surface behavior during initial stages of space missions. Annealing of samples showed how surface preparation and exposure to new flight temperatures affects the photoelectron yield results. Large differences could be seen between the unannealed photoelectron yield of high temperature alloys compared to the annealed photoelectron yield. Lower temperature annealing had smaller effects on the samples. Incident photon angle was studied revealing different yield responses for each sample. This data might help improve spacecraft or instrument charging predictions by including angled photoelectron yield (and by definition photocurrents) that do not follow the cosine function. The photoelectron yield was fitted with an analytical fit at normal incidence to aid in the photocurrent calculations. The integrated photoelectron flux was estimated at normal incidence, and the induced surface current calculated due to solar irradiation at 1 AU. With this data and analytical fits scientists and engineers will better estimate spacecraft and instrument environmental effects like charging for current and future missions. 63 4 Secondary Electron and Backscattered Secondary Electrons The following section is based on the published paper “Experimental Investigation of the Secondary and Backscatter Electron Emission from Spacecraft Materials”, by Millan F. Diaz- Aguado, John W. Bonnell, Stuart D. Bale, Justin Christensen, Phillip Lundgreen, Jordan Lee, JR Dennison, Brian Wood and Mike Gruntman, Journal of Spacecraft and Rockets, Accepted 2/2/2020. 4.1 Introduction As previously mentioned, environment can have significant and detrimental effects on spacecraft (SC) operations [11, 12, 14-16, 79, 89], affecting the plasma measurements and causing surface charging events. Incident electrons on a surface result in secondary electrons (SE) and backscattered electrons (BSE) emission. BSE are electrons originating from the external environment which scatter with the material, and eventually reverse direction and backscatter out of the material. SE emitted electrons that originate within the material, are excited by collisions of incident electrons, and escape from a surface. SE and BSE are some of the most important surface charging mechanisms [11, 51, 90-92], which also include photoemission and ion induced SE, photoemission being one of the most dominating mechanisms while illuminated by sunlight. Large potential differentials caused by differential charging from SE and BSE have caused anomalies on spacecraft (SC) and their instruments [38, 90,19, 93], but there is still some debate on how the electron fluxes cause spacecraft charging events [70]. Based on results from the Spacecraft Charging at High Altitudes (SCATHA) mission there are several studies [89, 94, 95] that show what range of ambient electron energies cause spacecraft charging at GEO. All the studies differ in their detailed conclusions, but they agree that SE and BSE have significant effects 64 on spacecraft charging for ambient electron temperatures below 3 keV, by compensating for or even exceeding the ambient electron current and thus moderating the magnitude of charging. SE and BSE yield (SEY and BSEY) as a function of incident electron energy are available both in the literature and in the simulation packages (Nascap-2k and SPIS) [96, 97], but myriad new spacecraft materials have been introduced and used in the last decade for which no data is available, and these new materials have been the chief motivation for this study. This research studied the effects of incident electron with energies up to 5keV for Ta-W, TZM, TiN and DAG-213®. It also measured Nb-C103, Elgiloy and W to 30keV. Tungsten has been studied extensively [98] and was chosen as a benchmark material with similar refractory properties for these studies. The other new untested materials are being utilized on Langmuir probes used to measure density and potential variations in the plasma. Current missions that include these probes as part of their instrument suite include Time History Events and Macroscale Interactions during Substorms (THEMIS) [27], Van Allen Probes [28], Cassini [30], Mars Atmosphere and Volatiles Evolution (MAVEN) [29], MMS (Magnetospheric Multiscale) [31], Solar Orbiter [99] and Solar Probe Plus (SPP) now Parker Solar Probe (PSP) [33]. During the mission of PSP, the spacecraft is traveling from the Earth to 9.8 solar radii away from the Sun. Most of the bus will be protected by a carbon-carbon and alumina heat shield, except for two instruments which are exposed to the full solar flux (the FIELDS antennas and the SWEAP faraday cup). The spacecraft will orbit around the Sun, slowly decreasing its periapsis, and slowly increasing temperature of the antennas, faraday cup and shield, which are mainly composed of Nb-C103 and TZM, with Ta-W as the backup material for Nb-C103 if it would fail during initial design. The heating experienced by the surfaces will anneal them, which may change the SE yield and the energy distribution of emitted electrons and thus impact sheath properties. 65 Any change in the SEY or BSEY also influences the corresponding current, and thus spacecraft charging and floating potential. Other recent or future missions also make use of novel untested materials: The ESA Solar Orbiter mission will also study the Sun but at a higher altitude (0.25 AU) than PSP, using Elgiloy for their probes. MAVEN, a mission to study Mars, and Cassini, a mission to study Saturn, use Langmuir probes coated with TiN. THEMIS, Van Allen Probes and MMS are studying the magnetosphere and Van Allen belts with highly elliptical orbits. These spacecrafts had DAG- 213® on their probes. Studying the SE and BSE yields of these new materials will help in modeling spacecraft charging, specifically in software packages like Nascap-2K and SPIS. In order to measure the effects of annealing, the samples were characterized before and after exposure to expected flight temperatures. This study did not include SE emission testing at the peak temperatures. Because SE occurs mainly near the surface, SE yields are sensitive to surface contamination, including water, carbides, oxides and hydrocarbons that modify the yield as the samples are exposed to the space environment [51, 78, 79, 81]. Surfaces in space could be bombarded by ions, electrons, photons and atomic oxygen [38, 77, 78], in addition to other neutrals. Surfaces yields change as the surfaces are exposed to the space environment [78, 81], including ion etching which could eliminate contamination [77], AO reaction that could contaminate the surface even further, electron stimulated desorption that alters the surface composition [100, 101], or electron stimulated graphitization, a chemical change that reduces the yield of the surface [80, 81, 100]. For PSP and Solar Orbiter, the probable main effects on the yields are most likely the results of exposures to extremes temperatures and intense radiation. 66 In order to best capture the temperature effect for these materials in their flight configuration, the samples (from the same vendors and lots as the missions mentioned previously) were prepared similarly to flight materials using cleaning and storing processes described in the experimental section. Once cleaned, the samples were then exposed to an electron beam at normal incidence. The Total Electron Yield (TEY) and BSE yields (BSEY) were measured, and SEY were obtained through subtraction. All the samples were then heat-treated at temperatures similar to maximum flight temperatures to anneal them. The yield measurements were then repeated for all samples, except for DAG-213®, to search for differences in the samples, and its effects on SEY and BSEY. It is important to emphasize that the data presented here could be of interest not only to the spacecraft charging community [11, 14, 38, 79, 91], but to a much broader audience. Additional applications of electron emission include scanning electron microscopy (SEM)[80, 102, 103], particle accelerators[100], photomultiplier tubes (PMTs), ion thrusters, plasma deposition, semiconductor metal-oxide interfaces, and nanodielectrics. and the multipactor effect[104]. However, the processes and theoretical steps followed here are primarily directed to the spacecraft charging community, plasma modeling, and analysis. For example, the process of preparing the samples is very different, as the spacecraft charging community is interested in following the steps of material preparations used in specific space missions, and not necessarily of pure samples of the pristine material itself[101]. In addition, the spacecraft charging and SEM communities most often use operational definitions of TEY, SEY and BSEY based on emission energy rather than the definitions used more commonly in the surface physics community based on the origin of the emitted SE and BSE 67 as outlined in the opening paragraph of the Introduction. In particular, the material definitions in the preeminent spacecraft charging modeling codes, including NASCAP and SPIS, define the electron yield properties in terms of the operational definitions of SEY and BSEY with BSE identified as electrons emitted with energies >50 eV[11, 50, 91, 102, 105]. The details of the experimental setup and test results are described below. First, the experimental setup of the Electron Emission Test (EET) Chamber at Utah State University (USU)[106] is explained, followed by the theoretical models used[92]. Next, the experimental results are shown for SEY, BSEY and TSEY for the materials tested, including the theoretical fits. The SE and BSE energy distribution are also shown. Subsequently, the SE and BSE current densities are calculated for different ambient plasma, and a conclusion is reached. 4.2 Experimental All tests were conducted at room temperature in the EET Chamber by the USU Materials Physics Group [98, 106]. The test system uses a fully encased hemispherical grid retarding field analyzer (HGRFA)[107]. The yield measurements were made using ~10 electron beam pulses per beam energy. Pulses (3μs for low incident electron energies < 5 keV and 30μs for higher incident electron energies) at typical beam currents of 1-10 nA were incident on 8-12 mm 2 surface areas; this is 0.3-6 fC/mm 2 (or 2·10 3 to 4·10 4 electrons/mm 2 ) per pulse. Even though the samples in this research were conductive, the sample was flooded for a few seconds with both ~5 eV electrons and ~5 eV photons between each pulse to dissipate accumulated sample charge[107-109],. The biased hemispheres capture the emitted electrons. The HGRFA detector is capable of measuring yields within +/-2% accuracy. By biasing the retarding grid to 0V, the total yield is measured by detecting all electrons. Biasing the retarding grid to -50V allows for only the BSE to reach the detector. The ratio between the incident and emitted charges were then integrated to obtain the 68 Total Electron Yield (TEY) and BSEY. The samples were not biased during these measurements to ensure that the low energy SE and BSE reached the collector. The SEY are determined by subtracting the BSEY from the TEY. The SE emission spectra was determined with the same HGFRA by scanning the voltage of the retarding grid through a range of voltages. The emission spectra were determined for a range of incident electron energies to be able to distinguish the SE at low energies with the BSE which are similar in shape, peak location and height of peak energies to the incoming electrons. The shape of the distributions functions 𝑔 𝑆𝐸 (𝐸 𝑆𝐸 ) and 𝑔 𝐵𝑆𝐸 (𝐸 𝑆𝐸 ) are very largely independent of the incident energy or even what the source incident energy is, as incident energy only affects the emission spectra amplitudes through the energy-dependent yield, 𝜎 (𝐸 )=𝛿 (𝐸 )+ 𝜂 (𝐸 ). The rough validity of this assumption has been shown experimentally in [107, 110], and theoretically by Chung and Everhart [111]. Figure 4-1 shows a schematic of the HGRFA hemispheres and sample setup [108], where A is the inner grid used to provide the uniform electric field and shield from unwanted edge effects, B is the biased grid used to discriminate electron energies coming from the sample, and C is the collector. The HGRFA resolution is ~2 eV, with additional contributions from the thermal spread of electron sources and electronics for an estimated instrument resolution of ~2.4±0.2 eV. Figure 4- 2 shows an image of the HGRFA and the rotating sample holder inside the EET chamber. 69 Figure 4-1 Schematic of the hemispherical grid retarding field analyzer (HGRFA), with the ammeters (I), ground and voltage biases[98]. Figure 4-2 Image of the HGRFA Hemisphere and Carrousel Sample Holder. The blue arrow indicates the direction of electrons passing through the HGRFA and incident on an electrically isolated sample mounted in a sample carousel sample block. 70 The tungsten sample is a high purity bulk refractory material. Nb-C103 niobium sample which is a highly refractory Nb-Hf-Ti alloy typically used in aerospace components and other high temperature environments. TiN is an extremely hard high temperature ceramic material, often used as a coating on metals; this sample was a 2 μm N thick coating on a Ti substrate. The Ta-W sample is a bulk Ta refractory material with ~10% W alloying. Molybdenum TZM is a standard Mo alloy, used in applications that require high strength and creep resistance at elevated temperatures. Elgiloy® is a high temperature non-magnetic Co-Cr-Ni-Mo alloy. DAG-213® is a thermosetting resin-bonded graphic dry film lubricant coating formulated from processed microcrystalline graphite and epoxy resin, often used in space applications as a black thermal control material. Relevant properties of the materials are listed in Table 4-1. The samples were treated similarly to materials used during flight missions, except for the first step, where samples were cut to fit the holder. Due to limited resources, only one sample was tested for each material (one annealed, one unannealed), except for DAG-213® which was only tested annealed. An ultrasonic methanol bath was then used to clean the surfaces. This step is usually done before assembly of parts to clean any manufacturing and handling contaminants. Immediately afterwards, the samples were baked-out at ~373K at <10 -6 Torr for >48 hours prior to all yield measurements to minimize absorbed water and volatile contaminates, including handling and manufacturing contaminants. Afterwards, the samples were stored in a dry nitrogen glove box. Instruments before flight are often stored and purged in dry nitrogen, or controlled environments (clean rooms) before launch. Finally, the samples were placed inside the EET chamber (base pressure 10 -7 to 10 -8 Torr) for >48 hrs prior to electron yield measurements, simulating the space pressure environment. 71 Table 4-1 Material Properties and Annealed Temperatures Sample Composition (% mass) Surface Contam. Surface Roughness (µm) Density, ρm (g-cm -3 ) Mean Atomic Number, 𝒁̅ Mean Atomic Weight, 𝑴 𝑨 ̅̅̅̅̅ Work- Function, ϕ (eV) Ann. Temp. (°C) W W (99.98%) C(5%), O(1%) ≤0.2 19.3 74 183.85 4.55 1200 Nb-C103 Nb(89%), Hf(10%), Ti(1%) C(8%), O(2%), Rb(2%) ≤0.2 8.85 43.91 101.02 4.1* 1200 TiN Ti(77%), N(23%) C(3%) ≤0.1 5.22 14.5 30.94 4.2 180 Ta-W 10% Ta(90%), W(10%) C(5%), O(1%), Fe(0.1%) ≤0.1 16.9 73.1 181.20 4.2* 1200 TZM Mo(99.3%), Ti(~0.5%), Zr(~0.08%) C(5%), O(2%) ≤0.5 10.3 42.0 95.94 4.3* 1200 Elgiloy Co (40±1%), Cr (20±1%), Ni (15±1%), Fe (~15%), Mo (7±1%), Mn (2±0.5%), Si ~1.2% C(3%), O(3%) ≤0.5 8.30 27.28 59.25 4.3* 800 DAG- 213® Graphite (~10%) / bisphenol epoxy resin (C18H18O3)n (~90%) composite none <0.1% ≤1 0.98 3.77 7.07 ~4.7 (epoxy band gap) 180 * Work functions for alloys are found with a Vegard-like approach, if not specifically available in the literature, using values in [112] Surface morphology studied with scanning electron microscopy (SEM) found smooth (though not atomically smooth) surfaces with vertical features less than ½ µm high (except for DAG-213®) (see Table-4-1). W, TZM, and DAG-213® had ~2-10 µm wide irregular patches; Nb- C103, TiN, Ta-W, and Elgiloy exhibited additional striations from machining or polishing. These rough surfaces may supress the electron yields somewhat, but are not expected to have large effects (except for DAG-213®), since the height-to-lateral aspect ratio is typically less than 50%. Energy 72 Dispersive X-Ray Spectroscopy (EDS) analysis (see Table-I) confirmed the alloy composition, with other contaminants noted in Table-4-1. All materials had C and O surface contamination evident, suggesting thin organic contamination layers; other contaminates were often contentrated in particulates. Contamintion, especially organic layers or oxide layers, can have significant effects on electron yields which are difficult to predict. After initial testing, the materials tested were annealed by exposure to temperatures experienced during realistic flight: Nb-C103, TZM and W were annealed at 1473K (1200°C), Elgiloy was annealed at 1073K (800°C) and DAG-213® and TiN were annealed at 423K(180°C). All materials were annealed in a vacuum furnace in a quartz tube at <7.5x10 -5 torr. to avoid oxidation. Such annealing or flight exposure could be expected to remove contamination or smooth the surfaces[113]. Figure 4-3 shows the electron range for the materials studied here, as well as that of amorphous graphitic carbon for comparison. Ranges were calculated using methods detailed in Wilson [114, 115]. 73 Figure 4-3 Electron range versus incident energy. (a) W, Nb-C103, Ta-W 10% and TZM. (b) TiN, Elgiloy, DAG-213® graphite epoxy composite, and amorphous C as reference. Range calculated using refs. [114, 115]. 4.3 Theoretical Models The data obtained by the lab experiments were fitted parametrically with well-established theoretical models. SEY curves were fitted using a four-parameter semi-empirical model [92, 98]. BSEY curves were fitted using a three-parameter empirical model [92, 98]. Electron emission (b ) (a) 74 spectra were fit as the sum of a Chung-Everhart model for the emitted SE energy distributions and a Gaussian function for the BSE energy distribution [92, 111]. These theoretical models are important tools for estimating spacecraft outgoing currents and therefore potentials under varying space plasma conditions. Often spacecraft charging is simulated using standard charging codes such as Nascap-2K or SPIS [96, 97]. In this study, the ambient, SE, and BSE current densities were calculated using a standard model for electron emission from negatively or zero biased surfaces [2]. Electron yield is an incident energy-dependent measure of the interactions of incident electrons with a material and characterizes the number of electrons emitted per incident electron. The total electron yield (TEY), 𝜎 (𝐸 0 ), is defined as the ratio of total emitted electron flux to the incident flux, 𝜎 (𝐸 0 )≡𝑁 𝑜𝑢𝑡 𝑒 − 𝑁 𝑖𝑛 𝑒 − ⁄ = 𝛿 (𝐸 0 )+ 𝜂 (𝐸 0 ) 4-1 It is separated into two terms, the secondary electron yield (SEY), 𝛿 (𝐸 0 ), and backscattered electron yield (BSEY), 𝜂 (𝐸 0 ). Some researchers use the term “secondary yield” to mean the same thing as TEY without differentiating between the two mechanisms which produce emitted electrons; see for example Ref. [102]. This fails to adequately model electron yield, and often creates confusion, so it is important to distinguish between the two as is done in this dissertation. Sections 4.3.1-4.3.3 describe the parametric models used to fit the observed TEY, SEY, BSEY, and emitted electron energy distributions. These parametric models provide significantly higher accuracy representations of the SEY and BSEY [98] for current flux calculations than those using standard Nascap-2K fit parameters for SEY and BSEY [96] which are listed in section 4.4.3. 75 4.3.4-4.3.6 show the electron, SE and BSE current density calculation equations for different mission plasma environments. Section 4.3.7 shows the equation used to plot normalized current density versus ambient electron temperatures. 4.3.1 Secondary Electron Yield Models SEY describes electrons emitted from the material which originate within the material and are excited through inelastic collisions with the incident electrons; operationally SE are defined as electrons with emission energies <50 eV. Experimentally, SEY is determined by subtracting the BSEY from the TEY. There were several different fits studied for each material, including Sternglass[55], Dionne[116] and Hastings[2] fits, as reviewed by Lundgreen[117]. All of the sample SE yields shown in Figures 4-3 to 4-10 were fit using a four-parameter semi-empirical equation in reduced format derived from a 1D scattering model for the SE in the material [106]: 𝛿 (𝐸 0 )= 𝛿 𝑚𝑎𝑥 [1−𝑒 −𝑟 𝑚𝑎𝑥 ] ∙( 𝐸 0 𝐸 𝑚𝑎𝑥 ) 1−𝑛 ∙[1−𝑒 (−𝑟 𝑚𝑎𝑥 ∙( 𝐸 0 𝐸 𝑚𝑎𝑥 ) 𝑛 −𝑚 ) ] 4-2 where E0 is the primary electron incident energy. Fitting parameters include 𝛿 𝑚𝑎𝑥 , 𝐸 𝑚𝑎𝑥 , and two power law coefficients n and m related to the low energy and high energy slopes of log-log plots of SEY such as Figure 4-4. 𝑟 𝑚𝑎𝑥 is a parameter dependent on n and m and fully determined by normalization of the fitting function. Details of the fitting function and parameters are given in [117]. This model is functionally similar to a model by Sims used with the SPIS code [118]. 76 4.3.2 Backscattered Secondary Electron Yield Models BSEY describes electrons emitted from the material which originate from the incident beam; operationally BSE are defined as electrons with emission energies >50 eV. Many BSE interact with the material largely through elastic (or nearly-elastic) collisions and are emitted with energies near the incident energy, E0. Other BSE undergo one or more quasi-elastic collisions, but still escape with energies higher than most SE. An extended three-parameter empirical model has been developed to model BSEY[106, 117]: 𝜂 (𝐸 0 )= { 0 𝑖𝑓 𝐸 0 ≤50𝑒𝑉 𝑙 𝑜𝑔 ( 𝐸 0 50𝑒𝑉 ) 𝑙𝑜𝑔 ( 𝐸 𝑚𝑎𝑥 50𝑒𝑉 ) 𝜁 (𝐸 ) 𝑖𝑓 50𝑒𝑉 <𝐸 0 <𝐸 𝑚𝑎𝑥 𝜁 (𝐸 ) 𝑖𝑓 𝐸 0 ≥𝐸 𝑚𝑎𝑥 } 4-3 where ζ is defined as 𝜁 (𝐸 0 ;𝜂 𝑚𝑎𝑥 ,𝜂 0 ,𝐸 peak ) =𝑒 (𝜂 𝑚𝑎𝑥 −𝜂 0 )𝑒 −(𝐸 0 /𝐸 peak ) +𝜂 0 4-4 Epeak is the energy where the BSE yield peaks, ηmax is the yield value at Epeak, and η0 is the high energy asymptotic value at energies ≫Epeak. This has the same functional form as an empirical model proposed by Prokopenko and LaFroamboise [42]. The single-parameter NASCAP fit to BSEY sets Epeak=5 keV and 𝑒 (𝜂 𝑚𝑎𝑥 −𝜂 0 )= 0.1 , with 𝜂 0 specified through the fitting parameter Zeff for an effective atomic number [96]. A similar relation for the SPIS BSEY fit differs slightly from NASCAP fit only above 10 keV [97]. As a first approximation, Zeff can be set to the mean atomic number averaged over the stoichiometry for non-elemental materials, 𝑍 ̅ (see Table 4-9) [96, 97]. 77 4.3.3 Emitted Electron Energy Distribution The normalized TE emission spectrum is the weighted sum of the normalized SE and BSE spectra 𝑑𝑛 𝑇𝐸 (𝐸 𝑆𝐸 ) 𝑑𝐸 =(1−𝑓 𝐵𝑆𝐸 )⋅𝑔 𝑠𝑒 (𝐸 𝑆𝐸 )+ 𝑓 𝐵𝑆𝐸 ⋅𝑔 𝐵𝑠𝑒 (𝐸 𝑆𝐸 )+𝑦 0 4-5 Where 𝐸 𝑆𝐸 is the energy of the electron leaving the surface, 𝑓 𝐵𝑆𝐸 is the fraction of emitted electrons that are BSE. 𝑦 0 is a small offset to correct for instrumental effects and equal to the BSEY at E=0. Emission spectra typically have two main peaks corresponding to SE and BSE, modeled by the normalized distribution functions 𝑔 𝑠𝑒 (𝐸 𝑆𝐸 ) and 𝑔 𝐵𝑠𝑒 (𝐸 𝑆𝐸 ), respectively. Representative energy distributions of emitted electrons are shown in Figs. 4-11 and 4-12. The shape of the distributions is very largely independent of the incident energy (or even what the source the incident energy is); incident energy only affects the emission spectra amplitudes through the energy-dependent yield, 𝜎 (𝐸 0 )=𝛿 (𝐸 0 )+ 𝜂 (𝐸 0 ). Multiplying the normalized distributions Equations 4-5, 4-6 or 4-7 by their corresponding yields gives the absolute electron emission spectra. Comparison of the parameter 𝑓 𝐵𝑆𝐸 to the ratio 𝜂 (50𝑒𝑉 )/𝜎 (50𝑒𝑉 ), provides a measure of the errors introduced in low energy yields from the operationally distinction SE and BSE at 50 eV. The normalized SE distribution, 𝑔 𝑠𝑒 (𝐸 𝑆𝐸 ), rises quickly from zero emitted energy to a peak energy at 𝐸 𝐶𝐸 = 1 3 Φ, usually between 1 eV and 3 eV; it then decays more gradually back to zero at higher energies. The Chung-Everhart model [111] describes this emitted SE energy distribution, which is[117]: 𝑔 𝑆𝐸 (𝐸 𝑆𝐸 )={ 6∙(𝐸 𝑆𝐸 Φ ⁄ ) [1+(𝐸 𝑆𝐸 Φ ⁄ )] 4 } . 4-6 78 Φ is the vacuum energy surface barrier for emission, which is the work function for a conductor [107, 111] or the electron affinity for dielectrics and semiconductors[119-121]. For SE to escape a material, the electron must have enough energy to cross this vacuum barrier. The BSE distribution has an upper cutoff above E0, set by elastically scattered primary electrons, with a tail at lower energies for incident electrons that undergo one or more lower energy inelastic collisions. The measured BSE distribution is a convolution with an instrumental broadening function. This is typically modeled as a normalized Gaussian with width ∆𝐸 𝑆𝐸 as[106, 117]: 𝑔 𝐵𝑆𝐸 (𝐸 𝑆𝐸 )={[2𝜋 ∙(∆𝐸 𝑆𝐸 ) 2 ] −1/2 ∙𝑒𝑥𝑝 [ (𝐸 𝑆𝐸 −𝐸 0 ) √2(∆𝐸 𝐸 ) ] 2 } 4-7 The approximation of the BSE distribution as such a Gaussian largely neglects contributions to the BSE distribution due to quasielastic scattered electrons, which are usually only on the order of 10% of BSE electrons. 4.3.4 Ambient Electron Current Density The electron current density was calculated using [2] 𝑗 𝑒 =−𝑞 𝑒 2𝜋 𝑚 𝑒 2 ∫ 𝐸 𝑒 𝑑 𝐸 𝑒 ∞ 𝐸 ∗ ∫ 𝑠𝑖𝑛𝜃𝑑𝜃 𝑓 (𝐸 𝑒 ) 𝜋 0 4-8 where qe is the electron charge, me is the electron rest mass, f(Ee) is the energy distribution function of the incoming electrons with energy Ee, and Ѳ is the angle from surface normal of incident electrons. The lower bound of the distribution 𝐸 ∗ is 𝐸 ∗ =| 0 𝑉 𝑠 ≤0 𝑞 𝑒 𝑉 𝑠 𝑉 𝑠 >0 for a surface potential, 𝑉 𝑠 . The energy distribution function can be defined as a single Maxwellian distribution: 79 𝑓 =𝑛 𝑒 ( 𝑚 𝑒 2𝜋 𝑘 𝐵 𝑇 𝑒 ) 3/2 𝑒𝑥𝑝 (− 𝐸 𝑒 𝑘 𝐵 𝑇 𝑒 ) 4-9 where ne is the electron number density of the plasma environment, Te is the electron plasma temperature, and 𝑘 𝐵 is the Boltzmann constant. 4.3.5 SE Current Density The SE current densities were calculated using the following equation [2]: 𝑗 𝑆𝐸 =−𝑒 2𝜋 𝑚 𝑒 2 ∫ 𝑑 𝐸 𝑠𝑒 ∞ 0 ∫ 𝐸 𝑒 𝑑 𝐸 𝑒 ∞ 𝐸 ∗ ∫ 𝑠𝑖𝑛𝜃𝑑𝜃 𝑔 𝑠𝑒 (𝐸 𝑆 𝐸 ,𝐸 𝑒 ) 𝛿 1𝐷 (𝐸 𝑒 ,𝜃 ) 𝑓 (𝐸 𝑒 ) 𝜋 0 4-10 where me is the electron mass, f(Ee) is the energy distribution function of the incoming electrons with energy Ee, δ1D(Ee,θ) is the SE yield as a function of Ee found in Equation 4-1, g(Ese, Ee) is the normalized emission spectrum of SE with energy ESE due to incident electrons with energy Ee, and Ѳ is the angle from surface normal. 4.3.6 BSE Current Density The BSE current densities were calculated using [51]: 𝑗 𝐵𝑆𝐸 =−𝑒 2𝜋 𝑚 𝑒 2 ∫ 𝐸 𝑒 𝑑 𝐸 𝑒 ∞ 𝐸 ∗ ∫ 𝑠𝑖𝑛𝜃𝑑𝜃𝜂 (𝐸 𝑒 ) 𝑓 (𝐸 𝑒 ) 𝜋 0 4-11 where η(Ee) is the percent of electrons backscattered at the fraction x of incident energy Ee. 4.3.7 Current Density per Number Density Different missions will encounter different ambient plasma parameters, which are characterized by the ne and Te. The integrals in Equations 4-8, 4-10 and 4-11 are not a function of ne which is independent of E. For ready reference to aid scientists and engineers in the probe or spacecraft charging design process, current densities are divided by ne and are plotted versus Te. The following equation shows the electron current density divided by the number density: 80 𝑗 𝑒 𝑛 𝑒 ⁄ =−𝑞 𝑒 2𝜋 𝑚 𝑒 2 ∫ 𝐸 𝑒 𝑑 𝐸 𝑒 ∞ 𝐸 ∗ ∫ 𝑠𝑖𝑛𝜃𝑑𝜃 𝑓 ′(𝐸 𝑒 ) 𝜋 0 4-12 where f’(Ee)=f(Ee)/ne. Similarly, the SE current density and BSE current densities can be divided by ne : 𝑗 𝑆𝐸 𝑛 𝑒 ⁄ =−𝑞 𝑒 2𝜋 𝑚 𝑒 2 ∫ 𝑑 𝐸 𝑠𝑒 ∞ 0 ∫ 𝐸 𝑒 𝑑 𝐸 𝑒 ∞ 𝐸 ∗ ∫ 𝑠𝑖𝑛𝜃𝑑𝜃 𝛿 (𝐸 𝑒 ,𝜃 ) 𝑔 𝑠𝑒 (𝐸 𝑠𝑒 ,𝐸 𝑒 ) 𝑓 ′(𝐸 𝑒 ) 𝜋 0 4-13 and 𝑗 𝐵𝑆𝐸 𝑛 𝑒 ⁄ =−𝑞 𝑒 2𝜋 𝑚 𝑒 2 ∫ 𝑑 𝐸 𝑏𝑠𝑒 ∞ 0 ∫ 𝐸 𝑒 𝑑 𝐸 𝑒 ∞ 𝐸 ∗ ∫ 𝑠𝑖𝑛𝜃𝑑𝜃 𝜂 (𝐸 𝑒 ,𝜃 ) 𝑔 𝐵𝑆𝐸 (𝐸 𝐵𝑆𝐸 ,𝐸 𝑒 )𝑓 ′(𝐸 𝑒 ) 𝜋 0 4-14 4.4 Results The following sections describe the TE, SE and BSE yields from the samples tested, including the TE, SE and BSE energy distributions and currents calculated for different ambient plasma parameters. The annealing effects varied by material and plasma environment. 4.4.1 Secondary and Backscattered Electron Yield The results of the TEY, SEY, and BSEY are shown in Figures 4-4 to 4-10. Note these are log- log plots used to emphasize the effects of the power law fitting parameters n and m at lower and higher energies, respectively. DAG-213®, shown in Figure 4-4, did not have a unannealed sample tested. Tungsten, Nb-C103, TZM, Ta-W, Elgiloy, and TiN are shown in Figures 4-5 to 4-10, respectively. In each of these figures, the yield of the unannealed sample is shown in plot (a) and that of the annealed sample in plot (b). Residual plots (c) show the percent change in yield due to annealing, for example [(𝜎 𝑎𝑛𝑛𝑒𝑎𝑙𝑒𝑑 −𝜎 𝑢𝑛𝑎𝑛𝑛𝑒𝑎𝑙𝑒𝑑 ) 𝜎 𝑢𝑛𝑎𝑛𝑛𝑒𝑎𝑙𝑒𝑑 ⁄ ]. 81 Figure 4-4 DAG-213® TEY, SEY, and BSEY data and model fits for an annealed sample, between 10eV and 5keV incident electron energy. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table II. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table 4-3. Yield features, 𝛿 max, ESEmax, n, m, E1, and E2 are indicated on the plot. It is important to note that at low energies (10eV-50eV) errors can be rather great, estimated to be up to ±20% of the plotted yields at energies <30eV. A major source of errors in lower energy SEY and BSEY is the use of the conventional engineering definition employed in charging codes that categorizes electrons emitted with energies >50eV as BSE and those with energies <50eV as SE; obviously this definition fails to have any meaning for electron with incident energies <50eV. Comparison of the parameter 𝑓 𝐵𝑆𝐸 to the ratio 𝜂 (50𝑒𝑉 )/𝛿 (50𝑒𝑉 ), as discussed in Section 4.4.1, suggests that the errors introduced with the use of low energy yields from the operationally distinction between SE and BSE at 50 eV employed in both measurements and yield fitting functions is negligible for the studies here above incident energies above 53 eV. These low energy errors can also be due to electron dynamics, as primary and SE are affected by stray and non-uniform electric and magnetic fields inside the chamber. The chamber is fitted with a two layer sleeve of μ-metal magnetic shielding to reduce ambient magnetic field 82 inside the chamber by a factor of ≳10 [119], but other magnetic fields from the instrumentation could still induce errors. These disturbances to the electron trajectories lead to two major sources of errors: the number of electrons from the electron gun missing the target, and the number of electrons not captured by the grid [122]. In other words, not all electrons leaving the gun impact the sample, and not all the SE and BSE leaving the sample hit the grid, especially at low energies. Use of a (nearly) fully enclosed hemispherical detector captures and measures nearly all emitted electrons, except ~1-2% that can escape via a drift tube that allows incident electrons to reach the sample [119], thereby allowing this detection scheme to make high accuracy yield measurements, on the order of 2-3% for conductors and ~5% for insulators [107, 108]. 83 Figure 4-5 Tungsten SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 30keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table 4-2. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table 4-3. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. (b ) (a) (c) 84 Figure 4-6 Nb-C103 SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 5keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table 4-2. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table 4-3. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. (b ) (a) C (c) 85 Figure 4-7 TiN SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 5keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table 4-2. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table 4-3. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. (b ) (a) (c) (b) 86 Figure 4-8 Ta-W SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 5keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table 4-2. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table 4-3. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. (b ) (a) (c) 87 Figure 4-9 TZM SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 5keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table 4-2. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table 4-3. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. (b ) (a) (c) 88 Figure 4-10 Elgiloy SE, BSE and TSE yields and model fits for incident electron energies between 10eV and 30keV. SEY fits are modeled with Eq. (A1) with fitting parameters listed in Table II. BSEY fits are modeled with Eq. (A2) with fitting parameters listed in Table III. (a) Unannealed sample. (b) Annealed sample. (c) Percent difference between annealed and unannealed samples. (b ) (a) (c) 89 Table 4-2 summarizes the SE yield fit parameters for all samples, based on the four- parameter semi-empirical Equation 4-1. These include 𝛿 max, the maximum SE yield, ESEmax, the incident electron energy where 𝛿 max occurs, and two power law coefficients n and m related to the low energy and high energy slopes of log-log plots of SEY such as Figure 4-4. The crossover energies, E1 and E2, defined as where the SE yield equals unity are also listed, as is the normalization constant rmax. These yield features are identified in Figure 4-4. Similarly, Table 4-3 summarize the BSE yield fit parameters for all samples, based on the three-parameter empirical Equation 4-3. The maximum sample SE yield, 𝛿 max, changes between unannealed versus annealed samples of the materials, as noted in Table 4-2. The maximum yield increased for Elgiloy, Molly TZM, Nb-C103, and Tungsten, with annealing of the sample, while it decreased or remained within the error of the unannealed sample for Ta-W and TiN. The residual curves of Figures 4-5 to 4-10 (c) demonstrate how both the TSEY, SEY and the BSEY have changed due to annealing. Shaded regions in Figures 4-5 to 4-10 (c) are bounded by the mean residuals for each yield ±1 standard deviation (SD) of the residuals. Together, these provide a useful way to highlight energies at which statistically significant changes occur due to annealing. As expected, the relative changes are largest for BSE data (blue) where yields are small. In addition, Table 4-2 shows differences in E1 and E2 for annealed versus unannealed samples. E1 increases with annealing on Ta-W and Elgiloy, while it decreases on W, Nb- C103, and remains the same for TiN. E2 increases for all samples except for Nb-C103, which decreases. 90 Table 4-2 SE Yield Parameters Sample δmax [ δ max 𝑎 −δ 𝑚𝑎𝑥 𝑢 δ max 𝑢 ] * (%) ESEmax (eV) [ 𝛥𝐸 𝑺𝑬𝒎𝒂𝒙 𝑎 −𝛥𝐸 𝑆𝐸𝑚𝑎𝑥 𝑢 𝛥𝐸 𝑺𝑬𝒎𝒂𝒙 𝑢 ] (%)* n m E1 (eV) [ 𝐸 1 𝑎 −𝐸 1 𝑢 𝐸 1 𝑢 ] (%)* E2 (keV) [ 𝐸 2 𝑎 −𝐸 2 𝑢 𝐸 2 𝑢 ] (%)* rmax W Unannealed 1.50±0.1 13 230±30 52 1.41±0.08 0.60±0.07 35±1 -2.8 1.10±0.1 100 1.23±0.7 W Annealed 1.70±0.1 350±50 1.52±0.06 0.53±0.05 34±1 2.20±0.1 1.25±0.6 Nb-C1O3 Unann. 1.80±0.1 11 300±30 -11 1.53±0.04 0.46±0.02 43±2 -21 1.70±0.1 -4.7 1.23±0.5 Nb-C1O3 Annealed 2.00±0.1 270±50 1.56±0.04 0.43±0.03 34±2 1.62±0.1 1.33±0.5 TiN Unannealed 2.30±0.1 2 260±30 -4 1.64±0.04 0.41±0.03 27±1 0.00 1.72±0.07 0.58 1.12±0.5 TiN Annealed 2.35±0.08 250±30 1.65±0.02 0.41±0.01 27±1 1.73±0.07 1.12±0.3 Ta-W 10% Unann. 2.30±0.1 0 260±30 8 1.47±0.06 0.44±0.05 18±1 28 2.9±0.1 3.5 1.47±0.7 Ta-W Annealed 2.30±0.07 280±30 1.48±0.03 0.46±0.02 23±1 3.0±0.1 1.36±0.5 TZM Unannealed 2.20±0.05 0 240±30 17 1.59 ±0.06 0.35±0.1 38±1 -39 2.1±0.1 9.5 1.79±0.8 TZM Annealed 2.20±0.05 280±10 1.54 ±0.02 0.48±0.02 23±1 2.3±0.1 1.30±0.4 Elgiloy Unann. 1.90±0.1 11 300±50 20 1.62±0.06 0.49±0.04 33±2 9.1 1.60±0.1 29.3 1.07±0.5 Elgiloy Annealed 2.10±0.1 360±30 1.63±0.04 0.45±0.03 36±2 2.07±0.1 1.14±0.5 DAG-213® Annealed. 2.00±0.05 NA 240±50 NA 1.60±0.04 0.45±0.03 33±1 NA 1.45±0.07 NA 1.20±0.6 * Values greater than uncertainties in italics 91 Table 4-3 BSEY Fit Parameters Sample E SE max (eV) [ 𝐸 𝑝𝑒𝑎𝑘 𝑎 −𝐸 𝑝𝑒𝑎𝑘 𝑢 𝐸 𝑝𝑒𝑎𝑘 𝑢 ]* η max [ 𝜂 𝑚𝑎𝑥 𝑎 −𝜂 𝑚𝑎𝑥 𝑢 𝜂 𝑚𝑎𝑥 𝑢 ]∗ η0 [ 𝜂 𝑜 𝑎 −𝜂 𝑜 𝑢 𝜂 𝑜 𝑢 ] * W Un. 4000±4000 0.23±0.3 0.229±0.018 W 1200°C 3000±2000 -25% 0.29±0.02 +29% 0.273±0.016 +19% Nb-C103 Un. 4200±1900 0.221±0.014 0.2297±0.0086 Nb-C103 1200°C 20000±30000 +380% 0.26±0.03 +18% 0.23±0.10 +0.1% TiN Un. 290±90 0.157±0.010 0.132±0.011 TiN 180°C 800±400 +176% 0.171±0.011 +9% 0.14±0.017 +6% Ta-W 10% Un. 3000±4000 0.31±0.03 0.27±0.10 Ta-W 1200°C 2500±1600 -17% 0.30±0.12 -3% 0.27±0.04 0% Molly TZM Un. 3000±3000 0.210±0.017 0.19±0.04 Molly TZM 1200°C 4000±4000 +33% 0.24±02 +14% 0.19±0.18 0% Elgiloy Un. 2000±1300 0.206±0.015 0.177±0.017 Elgiloy 800°C 1400±1100 -30% 0.186±0.019 -10% 0.17±0.014 -4% DAG-213®180°C 520±140 0.145±0.011 0.067±0.018 * Values greater than uncertainties in italics 92 All these differences will influence the material behavior in different ambient plasma, by changing the current induced by SEY and BSEY, as shown in Section 4.4.3. The effects of relative changes of the SE and BSE fitting parameters on threshold charging have been quantified; it was found for the specific cases studied there that changes in 𝛿 max followed by changes in ESEmax, had the greatest effects on charging for several different representative space plasma environments [92]. Yield data for the composite material DAG-213® is shown in Figure 4-4. As is expected [123] the yields are more similar to bisphenol epoxy yields, which constitute the vast majority of the composite material, than the yields of graphitic carbon, which have a low maximum yield typically just above unity at low Emax, near 200 eV [108]. Note that the probe beam does not cause the sample to exhibit signs of charging due to the ~10% conductivity microcrystalline graphite content that enhances conductivity in the sample and dissipates the charge from the probe beam. Figure 4-5 shows the results for W, where annealing has the effect of increasing the peak of the SEY curve (maximum yield) by ~13% and increasing the slopes at the lower (~13%) and higher energies (~180%). The maximum BSEY decreased ~25% due to annealing at higher energies. Annealing of the sample also has the effect of decreasing the incident energy where BSEY is greater than the SEY. This effect is also observed in other samples, including Nb-C103 and Elgiloy shown in Figure 4-6 and Figure 4-10. Figure 4-6 shows Nb-C103, with a modest ~11% increase in the maximum SEY yield and a ~11% decrease in ESEmax, while the slope at lower energies remains constant and increases at higher energies. BSEY also increased due to annealing. 93 Note, there is evidence for two peaks in the unannealed Nb-C103 BSEY curve, one near 150 eV and one at much higher energies. The presence of two BSE peaks is even more evident in the annealed curve Fig. 4-6(b). A possible explanation for this has been proposed by Wilson for similar studies of a series of thin graphitic carbon layers with increasing thickness deposited on Au substrates [124]; there, the lower energy BSE observed at ~170 eV can be clearly attributed to the C layers and a higher energy peak attributed to the Au substrate. The more pronounced double peak for annealed Nb-C103 is consistent with the observation (see Table 4-1) that this sample has approximately twice the carbon and oxygen contamination layers observed for other films. Similar, though less pronounced, double peaked BSEY curves are observed for Ta-W [Figure 4- 8(a-b)] and unannealed TZM [Figure 4-9(a)], suggesting similar organic contamination layers for these samples. Figure 4-7 shows TiN, where the annealing effects on SEY were very small, compared to other samples tested. The annealing temperature of TiN was much lower than the other samples and might have affected the amount of cleaning and smoothing on the sample. The effects on BSEY were larger, increasing Emax for the annealed sample. In Figure 4-8 there are two peaks in the BSEY unannealed samples of Ta-W, probably due to contamination of the surface (as discussed above). The BSEY double peak structure for the Ta-W sample is significantly reduced after annealing. This double peak structure is even evident in the TEY curve. During annealing of the surface in vacuo, contamination is removed leading to a smooth single TEY peak, very similar in shape and form to the unannealed sample. Annealing cleaning and smoothing surface effects have been previously explored for W and Moly-TZM [113] with a scanning electron microscope (SEM). This double peak and removal of contamination is also observed in Ta-W and TZM, shown in Figure 4-9. 94 The Elgiloy SEY and BSEY results are shown in Figure 4-10. The annealing increased the maximum yield and the slopes have also increased at higher and lower incident energies. Annealing increased the BSEY. 4.4.2 Electron Emission Energy Distribution The SE and BSE energy distributions were measured for all samples for a range of incident electron energies. As an example, Figure 4-11 shows the normalized SE and BSE energy distribution (number of particles emitted per unit energy per incident electron, dn/dE) of DAG- 213® at a representative incident energy of 53eV along with the fitted Chung-Everhart (SE) and Gaussian (BSE) models. As expected, the BSE Gaussian fits have a very reproducible maximum of 53.67 ± 0.04 eV (see Table 4-3), close to the incident electron energy of ~53eV and a BSE peak width of 2.59 ± 0.05 eV, in agreement with the instrumental resolution estimated in Sec. 4-2. Figure 4-11 DAG-213® SE and BSE data and fit energy distribution, annealed sample. 95 The energy distribution in Figure 4-11 has been normalized such that the area under the curve is equal to unity. Absolute yield distributions are obtained by multiplying the normalized distribution by the energy-dependent yield, 𝛿 (𝐸 0 ). Recall, by convention, electrons with emission energies <50eV are considered SE, while everything at higher emission energies is considered BSE. Comparison of the parameter 𝑓 𝐵𝑆𝐸 to the ratio 𝜂 (50𝑒𝑉 )/𝛿 (50𝑒𝑉 ), provides a measure of the errors introduced in low energy yields from the operationally distinction SE and BSE at 50 eV employed in both measurements and yield fitting functions. Values for 𝑓 𝐵𝑆𝐸 are consistently higher than the ratio 𝜂 (50𝑒𝑉 )/𝛿 (50𝑒𝑉 ), by about a factor of 2; this is consistent with the notion that about half of BSE electrons with a Gaussian distribution of width would be measured as BSE by a detector with finite resolution Δ𝐸 𝐸 . At incident energies below 50 eV, the measured BSEY is typically in the range of 0.01 to 0.04, at or below the instrumental resolution of yields; this is related to the offset yo for the BSEY energy distribution (see Table 4-4). No significant changes in 𝑓 𝐵𝑆𝐸 are observed as a result of annealing. Figure 4-12 shows the normalized distribution dn/dE of W, Nb-C103, TiN, Moly-TZM, Ta-W and Elgiloy. Figure 4-12(a) shows the results from the unannealed samples, and Figure 4- 12(b) those from the annealed samples. In each case, the peak at low energies (below 10 eV) is from the SE energy distribution and that near 53 eV is from the BSE energy distribution. The shapes of the curves are very similar, although the relative contributions from SE and BSE differ somewhat from material to material as characterized by the differences in the parameter 𝑓 𝐵𝑆𝐸 and the ratio 𝜂 (50𝑒𝑉 )/𝛿 (50𝑒𝑉 ) listed in Table 4-4. 96 Table 4-4 shows the parameters of the SE Chung-Everhart model fits. This table also shows the energy of the peak of the SE energy distribution (kBTse, in eV) of the SE distribution. The measured values of kBTSE were within the range of values measured for metals in prior experiments of 1.3 to 2.5eV[110]. Annealing had at most modest effects on TSE of the samples. The energy of maximum number of SE did not change due to annealing (≤3%) by an amount larger than the uncertainties for most samples, the exceptions being that it increased for Elgiloy by ~7% and decreased for W by ~8%. Figure 4-12 SE and BSE energy distribution fits of W, Nb-C103, TiN, Moly-TZM, Ta-W and Elgiloy. (a) Results for unannealed samples. (b) Results for annealed samples. 97 Table 4-4 Fits for Electron Emission Distribution Sample Chung-Everhart SE fit Gaussian BSE fit ϕ (eV) kB TSE (eV) [ 𝑇 𝑆𝐸 𝑎 −𝑇 𝑆𝐸 𝑢 𝑇 𝑆𝐸 𝑢 ]∗ 𝜂 (𝐸 0 ) 𝛿 (𝐸 0 ) 𝑓 𝐵𝑆𝐸 [ 𝑓 𝐵𝑆𝐸 𝑎 −𝑓 𝐵𝑆𝐸 𝑢 𝑓 𝐵𝑆𝐸 𝑢 ]∗ E 0 (eV) Δ𝐸 𝐸 (eV) * y 0 (eV) -1 W Unannealed 4.79±0.09 1.63±0.02 3.5% 4.8%±0.7% 53.63±0.18 2.6±0.3 0.0004 ± 0.0006 W (1200°C) 4.54±0.13 1.50±0.03 -8% 2.9% 5.8%±0.7% +21% 53.48±0.13 2.8±0.3 0.0008 ± 0.0005 Nb-C1O3 Un. 4.68±0.16 1.56±0.06 3.5% 6.5%±0.8% 53.47±0.15 2.9±0.3 0.0005 ± 0.0007 Nb-C1O3 (1200°C) 4.74±0.07 1.61±0.02 +3% 2.9% 6.6%±0.7% +2% 53.96±0.13 2.3±0.2 0.0008 ± 0.0006 TiN Un. 4.55±0.4 1.57±0.4 3.1% 10%±2% 53.75±0.14 2.9±0.6 -0.0012 ± 0.0006 TiN (180°C) 4.51±0.07 1.60±0.02 +2% 2.4% 6.1%±1.1% -41% 53.7±0.2 2.8±0.4 -0.0002 ± 0.0009 Ta-W 10% Un. 4.74±0.10 1.59±0.02 1.2% 8.3%±1.1% 53.74±0.12 2.8±0.3 -0.0010 ± 0.0009 Ta-W (1200°C) 4.73±0.09 1.57±0.02 -1% 2.2% 5.9%±0.7% -30% 53.77±0.11 2.45±0.19 0.0014 ± 0.0004 TZM Un. 4.67±0.10 1.59±0.03 2.7% 6.4%±0.6% 53.63±0.10 2.47±0.18 0.0004 ± 0.0005 TZM (1200°C) 4.71±0.09 1.61±0.02 +1% 3.0% 6.2%±0.6% -3% 53.80±0.11 2.44±0.18 0.0013 ± 0.0004 Elgiloy Un. 4.49±0.19 1.47±0.07 5.7% 5.4%±0.9% 53.62±0.19 2.4±0.3 0.0018 ± 0.0006 Elgiloy (800°C) 4.68±0.11 1.57±0.03 +7% 4.0% 6.0%±0.7% +11% 53.37±0.13 2.7±0.2 0.0009 ± 0.0005 DAG-213® (180°C) 4.72±0.09 1.57±0.02 3.4% 5.9%±0.9% 53.83±0.15 2.4±0.3 0.0008 ± 0.0006 Mean Value 53.67 ± 0.04 2.59 ± 0.05 0.0005 ± 0.0002 * Values greater than uncertainties in italics 98 As shown by Chung-Everhart [111] kBTSE is directly proportional to the material’s work function Φ, as kBTSE = ⅓Φ. Agreement between work functions estimated as a fitting parameter and from the peak position were in very good agreement, within 0.01 eV or less (except for annealed TiN). The estimated work function for annealed W—the effective calibration standard for this study— using this relation determined from energy spectra using this relation (see Table 4-4, column 2) was in excellent agreement with previous measurements and recommendations of 4.55eV [43, 59, 74, 112]. TiN, Nb C103, TZM, TaW and Elgiloy estimated work functions are ~0.38 eV or 9% larger than prior measurements and ~0.4 eV or ~10% larger than estimates found with a Vergard-like approach from tabulated elemental work functions (see Table 4-1, column 8) [112]. DAG-213®’s estimated work function was similar to past measurements [43], and approximately equal to the band gap energy for typical epoxy materials. Annealing also varied the BSE energy spectra compared to the unannealed samples. The material-dependent fraction of BSE in the emission spectra, fBSE, varied due to annealing. fBSE increased for W and Elgiloy, while it decreased for Ta-W and TiN. Table 4-4 shows the parameters of the BSE Gaussian model fit. 4.4.3 SE and BSE Current Densities The current due to SE was calculated for all materials in different space environments, such as GEO experienced mostly by Van Allen Probes and the magnetosheath experienced by MMS in their high eccentricity orbits. The current was also calculated in the solar wind at 1AU, 0.72AU, 0.25AU experienced by Solar Orbiter and even closer to the Sun 9.5Rs by PSP. Table 4-5 shows the electron temperature and number density of these plasma environments. The GEO plasma environment is considered a two-electron population plasma [2]. The current calculations for the 99 magnetosheath use average electron temperatures at 7.8eV which is in the same order of magnitude to as the SEY population of 1-2 eV. Other environments not included are the plasmasphere and the ionosphere with few eV of electron population. While the densities in each region are quite high, the temperatures are lower than the value of E1 for these materials, leading to insignificant SE and BSE fluxes in those environments. Figure 4-13 shows on the left axis the ambient differential electron number flux versus electron energy in these different plasma environments. The SEY of the annealed and unannealed W sample is shown on the right axis of Figure 4-13. The annealed W SE yield curve is not consistently larger or smaller than the unannealed one, making the W annealed and unannealed SE current densities behave differently (larger/smaller) depending on the incident electron environment. In contrast, the BSE yield curve (at least above 100 eV) is consistently larger for annealed W (not so for the other samples), which makes the BSE currents always larger for the annealed sample in all environments. Table 4-5 Average Electron Plasma Parameters at Magnetosheath, GEO and Solar Wind Electron Density (cm -3 ) Electron Temperature (eV) Current Density ( μA/m 2 ) 1 AU 6.93 8.14 1.06 0.75AU 13.51 10.41 2.34 0.25AU 116.12 22.95 3.28e2 9.5Rs 4022 84.87 1.98e3 GEO 0.78 0.31 550 8680 1.26 Magnetosheath 17 7.76 2.55 100 A W SEY curve fit from past experiments [125] was also added to compare with the new fits. The new tested unannealed W yield fits are comparable with [125], but not equal, with a SEY peak at similar incident electron energy but smaller. The slope on the right side of [125] is similar to that of the unannealed sample, and steeper on the low energy side of the peak. These variations are probably due to different surface treatment prior to testing. Similar studies of W available in the literature [126-130] show a wide variance in measured yield curves; such large differences are common in the literature as even modest variations on surface contamination, surface morphology, instrumentation calibration for absolute yields are often not Figure 4-13 Differential Electron Number Flux in different plasma environments and the SE and BSE yield of W annealed and unannealed. Flux left axis, yield right axis. Past tested W fit was added to compare with current W fits. 0.01 0.1 1 10 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 1.E+11 1.E+12 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 Yield (elec./elec.) d Γ/dE (#/(cm²*eV*s)) Electron Energy (eV) Electron Flux (1AU) Electron Flux (0.72AU) Electron Flux (20Rs) Electron Flux (9.5Rs) Electron Flux (GEO Average SCATHA) Electron Flux (35Rs) Electron Flux (Magnetosheath) SE Yield W Unannealed SE Yield W Annealed BSE Yield W Unannealed BSE Yield W Annealed SE Yield W - Past Data 101 well documented or taken into account [131]. This makes comparison of absolute yields from different studies challenging [108]. The annealed sample showed clear differences in maximum peak, and slopes before and after the peak, as seen in Figure 4-12. The maximum yield occurs at a greater electron energy for the annealed sample. Current densities of [125] are lower at electron energies below the peak for both annealed and unannealed W. The current density of past measured W has larger current densities above the peak. Table 4-6 shows the SE current densities calculated for the unannealed and annealed samples, at electron plasma environments described in Table 4-5; fit results for a previous study of a clean technical W sample at USU are also listed. Annealed W current densities were within 10% of current densities for these previous tests, while unannealed W was within 25% of the previous observed current densities. This suggests that annealing had a significant effect of the W yields, perhaps by driving off contamination. The resulting SE currents differences between unannealed and annealed samples are material and environment dependent. While annealed W has larger SE currents for all environments compared to unannealed, the annealing effects of Nb-C103, TiN, TZM, and Elgiloy influences the SE currents in a non-consistent way, as shown in Table 6. In contrast with W, unannealed Ta-W has larger SE currents for all plasma environments compared to annealed. For PSP, not only does the electron flux and temperature change at different distances from the Sun, but the temperature of the sample increases significantly as the spacecraft approaches perihelion. Temperatures of the FIELDS antennas will reach more than 1500K (from author’s thermal analysis). 102 The SE current densities shown in Table VI are estimates for the samples at ambient temperature. Past tests by Sternglass [55], McDonnell [132] showed how metal samples of platinum, tantalum and carbon, decreased their SEY by 0.07, 0.06 and 0.05 % per Kelvin, in contrast with the BSE which hardly changed with high temperature testing. Estimates of Nb, Mo, Ta and W [53] point to an approximate reduction of 37%, 27%, 31% and 33% of the SE yield at elevated temperatures close to 1400K. More recent investigations [54] indicate a reduction of 31% for TiN for temperature close to 673K. Taken together, these eight studies of high temperature conducting materials all have a negative temperature coefficient of change for SEY, with a reasonably consistent value of 0.05%±0.03% per Kelvin. Other authors have seen small changes in SEY of conducting materials due to changes in sample temperature. Gonzalez saw small changes in yield from room temperature to 10K for a Table 4-6 Unannealed and Annealed Material SE Current Densities (μA/m 2 ) Without Reduction Due to Temperature Sample 1AU 0.72AU 0.25AU 9.5Rs GEO Magentosheath Previous W measuements 0.60 1.51 28.7 2930 1.44 1.39 W Unannealed 0.74 1.77 28.5 2416 1.16 1.74 W (1200°C) 0.63 1.55 27.2 2661 1.39 1.48 Nb-C1O3 Unannealed 0.56 1.41 26.8 2887 1.55 1.31 Nb-C1O3 (1200°C) 0.60 1.51 28.4 2955 1.38 1.64 TiN Unannealed 0.68 1.72 33.2 3548 1.57 1.59 TiN (180°C) 0.70 1.77 34.1 3625 1.55 1.63 Ta-W 10% Unannealed 0.83 2.06 37.8 3711 1.72 1.93 Ta-W (1200°C) 0.78 1.93 35.2 3507 1.71 1.82 TZM Unannealed 0.54 1.47 35.1 5095 2.99 1.24 TZM (1200°C) 0.77 1.91 34.7 3423 1.60 1.80 Elgiloy Unannealed 0.61 1.51 27.6 2820 1.36 0.91 Elgiloy (800°C) 0.58 1.45 27.5 3031 1.60 1.35 DAG-213 (180°C) 0.66 1.65 30.5 3014 1.26 1.55 103 sputtered clean, lab prepared sample of Cu [133]. Patino also saw very small changes in SEY for a single crystal Ni between 300K and 600K [134] . By contrast, changes in electron yields of semiconductors or insulators with band gap energies on the order of inelastic collisions experienced by primary electrons during the SE creation process, might well be expected to have larger variations in yield with sample temperature; this is loosely analogous to the differences in the thermal gradients in electrical conductivity of conductors to semiconductors/insulators. Few studies of such variations in yield with sample temperature for semiconductors/insulators have been made and are largely inconclusive[119]. The two studies of conductors cited above could suggest that SEY of conductors is not intrinsically affected by the temperature to a large extent, but that variations observed here were due to high temperature changes in the surface properties of materials from exposure to extremes in temperature. In this research samples were polycrystalline in nature, not sputtered clean; changes in room temperature yields of four samples were investigated after prolonged exposure ~1400K under vacuum. Even though some of the materials tested are different from these past data, except W and TiN, these trends of decreased SEY at hot temperatures would reduce the influence of SE induced currents. As spacecraft approach the Sun, the solar photon flux increases, increasing the photocurrent, and increasing the surface temperature. This increase in temperature decreases the SE current densities. Table 4-6 does not show this reduction of current density due to temperature, but it does show the annealing effects on current densities at different environments. Unannealed W has larger SE current densities at 1AU, 0.75AU, 0.25AU and Magnetosheath than annealed W. Unannealed Nb-C103 has larger SE current densities for all plasma environments compared to annealed sample. Annealed TiN has larger SE current densities for GEO and the Magentosheath, and the SE current densities are the same for 1AU, 0.72AU, 104 0.25AU and 9.5Rs. Even though designers will not use TiN or DAG-213® for instruments exposed to the Sun as close as 9.5Rs, PSP has many instruments protected by the Sunshield during close encounters with the Sun which maintain temperatures below 150°C, which are exposed to the plasma environment but not the solar photon flux. Annealed Ta-W has larger SE currents for all plasma environments compared to unannealed. Annealed TZM has larger SE current densities at 1AU, 0.72AU and Magnetosheath, similar SE currents at 0.25AU, and smaller SE currents at 9.5Rs and GEO. Annealed Elgiloy has higher SE current densities for all plasma environments except for GEO, which is equal to the unannealed Elgiloy. Table 4-7 Unannealed and Annealed Material BSE Current Densities (μA/m 2 ) Sample 1AU 0.72AU 0.25AU 9.5Rs GEO Magentosheath W Unannealed 7.88E-06 6.82E-05 1.36E-02 6.07 1.12E-02 1.38E-05 W (1200°C) 1.58E-05 1.36E-04 2.72E-02 12.05 2.10E-02 2.78E-05 Nb-C1O3 Unannealed 9.77E-06 8.46E-05 1.69E-02 7.57 1.45E-02 1.72E-05 Nb-C1O3 (1200°C) 8.32E-06 7.21E-05 1.44E-02 6.42 1.20E-02 3.29E-05 TiN Unannealed 2.47E-05 2.13E-04 4.15E-02 16.21 1.46E-02 4.35E-05 TiN (180°C) 1.29E-05 1.12E-04 2.21E-02 9.30 1.13E-02 2.27E-05 Ta-W 10% Unannealed 1.99E-05 1.72E-04 3.44E-02 15.10 2.49E-02 3.48E-05 Ta-W (1200°C) 2.23E-05 1.93E-04 3.85E-02 16.93 2.80E-02 3.93E-05 TZM Unannealed 1.21E-05 1.05E-04 2.09E-02 9.23 1.56E-02 2.13E-05 TZM (1200°C) 1.76E-05 1.52E-04 3.03E-02 13.31 2.16E-02 3.09E-05 Elgiloy Unannealed 1.62E-05 1.40E-04 2.78E-02 12.15 1.88E-02 2.85E-05 Elgiloy (800°C) 1.32E-05 1.14E-04 2.28E-02 9.97 1.54E-02 2.33E-05 DAG-213 (180°C) 2.21E-05 1.90E-04 3.67E-02 13.70 9.26E-03 3.90E-05 105 Table 4-7 shows the BSE current densities of the unannealed and annealed W, Nb-C103, TiN, Ta-W, TZM, and Elgiloy. DAG-213® current densities are shown only for annealed as the author only had one sample already annealed. The BSE current densities are at least two orders of magnitude smaller than the SE current densities, and changes in BSE currents due to annealing effects would not affect the current balance. Annealed W has larger BSE current densities for 0.25AU, 9.5Rs, and GEO than unannealed W. Unannealed Nb-C103 has larger BSE current densities for 0.25AU, 9.5Rs, but smaller for GEO than annealed Nb-C103. Annealed TiN has larger BSE current densities for 0.25A, 9.5Rs and GEO than unannealed TiN. Unannealed Ta-W has smaller BSE current densities for 0.25AU, 9.5Rs, but larger for GEO than annealed Ta-W. Annealed TZM has larger BSE current densities for 0.25AU 9.5Rs and GEO than unannealed TZM. Unannealed Elgiloy has larger BSE current densities for 0.25AU, 9.5Rs, but smaller for GEO than annealed Elgiloy. 4.4.4 Current Densities per Electron Number Density The electron current densities per number density were calculated for single Maxwellian plasma from 1eV to 8keV ambient plasma electron temperatures. The SE and BSE current densities per number density were also calculated from 1eV to 8keV ambient plasma electron temperatures. The SE and BSE electron current densities per number densities are plotted in Figure 4-14 and Figure 4-15 respectively. Fig.4-14 shows how the materials between ~20eV (first crossover) and ~1.2keV (second crossover) have a larger SE current than primary electron current. The annealing effects can be seen in the currents, both in the total current density per number density as well as the points where the SE currents are greater than the primary currents. The annealing has small first crossover 106 changes, except for TZM, which decreased by 24eV and Nb-C103 which decreased by 5eV. The annealing effects are greater at the second crossover, were it increases for W, TZM and Elgiloy by values greater than 400eV, but decreases for Nb-C103 and TiN by 50eV. TaW had no large crossover changes. Fig. 4-15 shows how the BSE current densities per number densities are very small at temperatures lower than 30eV, compared to the primary current densities per number densities. As the electron temperature increases to 8keV, the BSE current densities per number densities have only one order of magnitude difference from the SE current densities per number densities. 107 Figure 4-14 Primary electron, and SE current densities per electron number density for W, Nb-C103, TiN, Ta-W, TZM, Elgiloy, and DAG-213. (a) Results for unannealed samples. (b) Results for annealed samples. The dashed line indicates the electron current density. 108 Figure 4-15 Primary electron, and BSE current densities per electron number density for W, Nb-C103, TiN, Ta-W, TZM, Elgiloy, and DAG-213. (a) Results for unannealed samples. (b) Results for annealed samples. The dashed line indicates the electron current density. 109 For a quick estimate of the current balance calculation of an isolated surface in space (in the shade), an engineer or scientist may assume a temperature and from the plots estimate the primary electron current, the SE current and the BSE current. Note that the primary electron currents will have an opposite sign to the SE and BSE currents in the current balance equation. 4.4.5 NASCAP Fit Parameters This section shows the Nascap-2k parameter fits for all samples. Table 4-8 shows the SE yield parameter fits. Table 4-9 shows the BSE parameter fits. Table 4-8 Nascap-2k Fit Parameters δ max E max (keV) b 1 (Å) n 1 b 2 (Å) n 2 W Un. 1.81 0.276 1.21 0.577 1 1.79 W 1200°C 1.83 0.266 0.787 0.368 1 1.58 Nb-C103 Un. 1.81 0.269 1.16 0.584 1 1.78 Nb-C103 1200°C 1.97 0.252 0.867 0.46 1 1.71 TiN Un. 2.3 0.236 0.807 0.416 1 1.83 TiN 180°C 2.35 0.227 0.728 0.378 1 1.78 Ta-W 10% Un. 2.35 0.24 0.912 0.546 1 1.71 Ta-W 1200°C 2.31 0.247 0.733 0.42 1 1.57 Molly TZM Un. 2.19 0.216 1.13 0.84 1 1.81 Molly TZM 1200°C 2.22 0.229 0.744 0.485 1 1.63 Elgiloy Un. 1.96 0.253 0.66 0.487 1 1.69 Elgiloy 800°C 2.09 0.314 1.19 0.411 1 1.78 DAG-213®180°C 1.97 0.19 2.03 0.99 1 1.95 110 4.5 Secondary and Backscattered Electron Conclusions TE, SE, BSE and yields were measured and fitted for different sample materials for seven materials of particular relevance to spacecraft in high-temperature, high flux environments. The SE and BSE normalized energy distribution were also measured and fitted. The initial samples tested were unannealed and in conditions typical for spacecraft materials at launch; subsequent tests were conducted after annealing to high temperatures representative of the Parker Solar Probe mission, which might be expected to drive off contamination and even smooth rougher surfaces through thermal annealing. Small, but potentially significant, changes in the materials electron emission properties were observed. The results show how the SEY and BSEY characteristics of the materials can evolve through exposure to extreme environments typical of these new close-to- Table 4-9 Nascap-2k BSEY Fit Parameters Sample 𝑍 ̅ Z eff η0 [ 𝜂 𝑜 𝑎 −𝜂 𝑜 𝑢 𝜂 𝑜 𝑢 ]* W Un. 74 10.5±1.5 0.155±0.016 W 1200°C 74 16.4±1.8 0.210±0.015 35% Nb-C103 Un. 44.1 8.9±1.3 0.137±0.015 Nb-C103 1200°C 44.1 11.0±1.7 0.160±0.018 17% TiN Un. 14.5 5.2±0.8 0.087±0.012 TiN 180°C 14.5 5.7±0.7 0.096±0.010 10% Ta-W 10% Un. 73.1 16.4±2.3 0.201±0.019 Ta-W 1200°C 73.1 15.0±1.4 0.198±0.012 2% Molly TZM Un. 41.8 6.2±0.8 0.102±0.011 Molly TZM 1200°C 41.8 9.1±1.0 0.14±0.012 37% Elgiloy Un. 27.3 8.9±1.0 0.137±0.012 Elgiloy 800°C 27.3 8.0±1.0 0.126±0.012 -8% DAG-213®180°C 4.1 3.5±0.8 0.058±0.014 * Values greater than uncertainties in italics 111 the-Sun missions, as observed in the SE and BSE current density calculations. The SEY and BSEY were used to calculate current densities in different plasma environments, showing how the annealing effects of the materials varied depending on the environment. The current densities per number densities were also plotted for primary electrons, SE, and BSE to aid in the design of instruments and spacecraft. Even though photoemission is a dominating spacecraft charging process, especially for illuminated surfaces, SE and BSE play an important role. Based on these results, it is important for spacecraft designers to incorporate both induced changes of materials properties and materials induced changes to the plasma environment in their spacecraft charging calculations as they can affect equilibrium potentials [6, 81]. Engineers and scientists who use codes such as Nascap-2k or SPIS for spacecraft charging assessments could benefit from use of the material data presented in this dissertation. 112 5 PSP FIELDS Charging Modeling The following section is based on the paper “Parker Solar Probe FIELDS instrument charging in the near Sun environment” by Millan F. Diaz-Aguado, John W. Bonnell, Stuart D. Bale, Joseph Wang and Mike Gruntman, Journal of Geophysical Research, Space Physics, to be submitted. 5.1 Introduction As mentioned in the introduction, Langmuir Probes have been used extensively in space environment research missions to measure the density and plasma potential variations of the environment with respect to the probes [11, 25-31, 33, 35, 99]. For accurate probe measurement, it is important to be able to measure and predict the plasma effects on the instrument and spacecraft charging environment [11, 18, 19, 95]. Knowledge of the photoemission (photon induced electron emission from a surface), secondary electron emission (electron or ion induced electron emission from surface), backscattered electrons are crucial to understand the charging behavior of the probes. In addition, the exposed surfaces at close distances to the Sun, increase in temperature to a point where thermionic emission becomes a primary current source. PSP is a mission to study the Sun which includes the FIELDS instrument that measures the magnetic fluctuations and electric fields, plasma wave spectra and polarization properties, the spacecraft floating potential and solar radio emissions[33]. PSP is the spacecraft to visit closest to the Sun, operating at distances between 1AU and 0.046 AU away from the Sun. Due to this large range of heliocentric distances experienced by PSP, the environmental conditions and interactions also vary greatly. For example, at closest approach, 0.046 AU (9.8 solar radii), the FIELDS antennas are exposed to over 500 times the radiant photon flux present at 1 AU (i.e. ≈0.5 MW/m 2 ). Because of this, the FIELDS electric antenna system is required to operate at temperatures above 113 1570 K, 4 times greater than at 1AU. Furthermore, the FIELDS instrument is surrounded by solar wind plasma with densities predicted to be 580 times larger than at 1AU (60 times larger than ever encountered by a spacecraft in the Solar Wind), ranging from around 7 cm -3 to over 4000 cm -3 , and electron and ion temperatures stretching from just under 10 eV to nearly 100 eV. This is a new operating (and survival) regime for this sort of instrument and presents several design and operational challenges. This paper studies the FIELDS antennas, the PSP thermal shields, and their interaction with each other and the environment in one of the most recent perihelia passes at ~ 38 Rs (Sept 2019), as well as during the closest perihelia that will occur later in the mission. Note that the closest approach SPIS analysis has been done at 9.5 Rs, while the currently planned closest approach is 9.8 Rs. Previous spacecraft charging models have considered the PSP spacecraft, including the Thermal Protection System (TPS), the spacecraft radiators, and the bus, but they have omitted the FIELDS antennas [5-7, 135]. These past authors did not have the necessary information to model the antennas as there weren’t any probe surface properties available to them, and the final geometry of these thin (0.0031m diameter) 2m long probes were unknown at the time of those modeling efforts. Those supporting data are now available, allowing us to predict the interactions of those antennas with both the solar and plasma environment, as well as the various elements of the SC. Full scale numerical simulations are needed to estimate the spacecraft and antenna potentials due to the complexity of even a grossly simplified representation of the spacecraft and antennas embedded in the non-uniform plasma and charged particle environment surrounding the spacecraft. An estimate for antennas under solar wind and solar light without the spacecraft would give erroneous predictions due to the proximity of the spacecraft, FIELDS antennas and shield. 114 There are many software codes available to simulate the interaction between the environment and the spacecraft: EMSES, iPic3D, LASP, PTetra, Multiutility Spacecraft Charging Analysis Tool (MUSCAT), National Aeronautics and Space Administration (NASA) Charging Analyzer Program (NASCAP) and Spacecraft Plasma Interaction Software SPIS[47]. The two most commonly available and user-friendly software codes for spacecraft charging are: Nascap- 2k, only for US citizens, and SPIS. These modern spacecraft charging simulators trace their origins back to some of the earliest attempts to model the electrodynamical behavior of collisionless plasmas. Such plasma simulations were introduced by many, including Dawson and Buneman in the late 1950’s and early 1960’s [136]. As computers advanced, their efforts were followed by many others, notably by Katz in the field of spacecraft charging simulations (Systems Science and Software) who spearheaded the development of NASCAP in the 1970’s [50, 91]. More recently, the European Space Agency has funded ONERA (National Office of Aerospace Research Studies) and Artenum to develop the Spacecraft Plasma Interaction Analysis and Simulation Toolkit or Spacecraft-Plasma Interaction System (SPIS), with large contributions by [137-139]. In addition to SPIS and NASCAP, MUSCAT has also gained traction at JAXA (Japanese Aerospace Exploration Agency), led by Mengu Cho, Muranaka and Hosoda [140-142] . For this effort, SPIS was chosen over NASCAP and MUSCAT because it is an open source software allowing for the ready inclusion of the novel material properties and surface geometries of the PSP FIELDS antennas and spacecraft, and because training sessions in the use and adaptation of SPIS were readily available to the whole community. The main purpose of this paper is to evaluate the effect of environmental conditions on the operation of the PSP FIELDS antennas, quantifying their effects on measurements of the solar 115 wind plasma structure and dynamics. The results of a SPIS model are compared with initial flight data from FIELDS. First, the SPIS software package is explained, followed by environments explored and materials used specific to FIELDS and PSP. Next, an I-V curve was modeled to predict the optimal bias current for instrument accuracy and sensitivity. Finally, the variation of the model results with plasma and solar environment are discussed and compared to relevant flight data. 5.2 SPIS Software The PSP charging models shown below were implemented using the SPIS package[97]. New materials and material properties were added to the SPIS database in order to more accurately model the PSP spacecraft and FIELDS antennas. All relevant contributions (ambient plasma parameters, material PE, SE, and BSE yields) have been included except that of thermionic electron emission in the models of closest solar approach (9.5 Rs). While the current version of SPIS (SPIS 6.0.0) allows for the specification of thermionic emission from most types of surfaces, it unfortunately cannot do so for the type of surface used to model the FIELDS antenna (thin wire). Throughout the development of the PSP and FIELDS antenna models shown below, the SPIS Forum has been a great resource, providing significant support for the addition of new features, and insight into the use of existing features to model what was desired. 5.2.1 Spacecraft Charging Model in SPIS SPIS provides a modeling framework to build up the antenna and spacecraft geometry and materials, the plasma environment and the interaction between them. It then uses Vlasov-Poisson equations to self-consistently solve for the potential distribution, including the potentials on the FIELDS antenna, FIELDS shield and spacecraft surfaces. 116 Figure 5-1 shows a simplified block diagram of the SPIS package. SPIS is an electrostatic unstructured 3D mesh, particle in cell (PIC), plasma modeling software package. It uses JAVA, making it highly modular. The software begins with geometry and mesh generation. This is accomplished by using GMSH, which is a 3D open source software, and which encompasses the first three blocks shown in Fig. 5-1. Figure 5-1 SPIS General Process The materials for all exposed surfaces are then selected, and the electrical circuits connecting all the surfaces are then defined. The plasma properties and model environment are then chosen, the simulation run to convergence for the particle distribution fields, and the results viewed with various post processing utilities. SPIS uses a numerical method to model Vlasov’s and Poisson’s equations to obtain the spacecraft or probe potential Φ, as well as the charge density and potential distribution throughout the simulation volume. For example, the time independent Vlasov equation is shown in the following equation: 117 𝒗 ∙∇𝑓 + 𝑞 𝑚 (𝑬 +𝒗 ×𝑩 )∙ 𝑑𝑓 𝑑 𝒗 =0 5-1 Where v is the velocity of the particle, f is the distribution function, E is the electric field, B is the magnetic field, q is the particle charge, m is the particle mass. To obtain the potential of the spacecraft or probe, we use Poisson’s equation: ∇ 2 Φ=− 𝜌 𝘀 0 =− ∑ 𝑞 𝑛 𝑖 𝑖 𝘀 0 5-2 where ε0 is the permittivity and the current is the summation of different particle densities, where n is the number density given by the following distribution function equation: 𝑛 (𝑥 ,𝑡 )=∫𝑓 (𝒙 ,𝒗 ,𝑡 )𝑑 3 𝑣 5-3 where x is the position of the particle, v its velocity, t is the time elapsed. The software uses a particle-in-cell, or PIC approach, in which it is important to specify a sufficiently small simulation time step Δt. This Δt should be selected to ensure that the fastest particles in the simulation move less than one simulation cell in a single time step. It should also be smaller than the plasma characteristic timescale, or the plasma period Tp=1/ωpe, where ωpe is the plasma frequency, and can be calculated using the following equation: 𝜔 𝑝𝑒 =8.93𝑥 10 3 𝑛 𝑒 1/2 5-4 For PIC simulations, the plasma Δt should be less than 0.2Tp to ensure proper modeling of the electric fields and avoid modeling erroneous electron oscillations. SPIS offers the use of various velocity distribution functions, f, for the particles. For ambient electron, photoemission, SE and BSE, an isotropic, non-drifting Maxwellian distribution function was used: 118 𝑓 (𝑣 )= 𝑛 (√2𝜋 𝑣 𝑡 ℎ ) 3 𝑒𝑥𝑝 (−𝑣 2 /2𝑣 𝑡 ℎ 2 ) 5-5 where vth is the average thermal velocity. While past observational results have found that the ambient electron distributions are better described by heavy-tailed Kappa distributions rather than a Maxwellian [46, 143-147], prior modeling efforts have utilized Maxwellian electrons, and so our study will as well to better facilitate comparison with those prior modeling results. From this modeling framework and results, various case studies in different operational regimes are used to provide a full set of predictions for antenna, spacecraft, and antenna-spacecraft plasma interactions on PSP FIELDS. 5.2.2 Simulation Geometry and Mesh As shown in Figures 5-2 and 5-3, the PSP spacecraft and FIELDS antennas have unique shapes, driven by the requirement to protect the thermally sensitive portions of the instruments and spacecraft from the radiant heat of the Sun. PSP’s sun facing side consists of a thermal protection system (TPS, or sun and heat shield) that protects the rest of the spacecraft. The TPS is attached to a Ti frame that holds the spacecraft radiators and four of the FIELDS antennas. As shown in Figure 5-2, the FIELDS antennas and shields were first stowed along the spacecraft body in order to fit them within the launch fairing and secure the, against launch loads and vibration. They were later deployed and are exposed to the solar flux and solar wind. The FIELDS antennas had their own small Sun shields near the spacecraft to be able to reduce the heat flux going from the antennas to the instrument electronics. We model and analyze the deployed state of the antennas in what follows. 119 Figure 5-2 FIELDS instruments on the spacecraft during integration and testing a. Deployed state b. Stowed state As shown in Fig. 5-3, a simplified geometry was used in SPIS for the spacecraft body, TPS, FIELDS shield and antenna. A 1 m diameter and 1 meter long, cylinder with similar outside surfaces was used for the spacecraft (in actuality it is hexagonal). The solar arrays were not modeled, as this paper was mostly concerned about the FIELDS antennas. The solar arrays were not modeled, as the arrays were folded nearly completely down along the body of the spacecraft, mostly in the shade at 35Rs, and the dominating current of the spacecraft was the photoemission of the TPS. The radiators were modeled as a cone, with the top diameter of 1 m, bottom diameter of 2 m, and 1 m tall. The TPS was also modeled as a flattened cone, with a thickness of 0.12 m, 2.48 m bottom diameter, 2.44 m top diameter. The Alumina face shield on the TPS was modeled as a thin 0.1mm layer covering the entire Sun facing side of the TPS. A FIELDS antenna was modeled as 1-D wire, as the diameters are much smaller than the length, 0.0032m diameter versus 2m 120 length. The FIELDS Sun shield was modeled as a trigonal trapezohedron (0.32m long, 0.02m wide), with similar surface exposures as the two thin welded elements of the actual Sun shields. Figure 5-3 Spacecraft model in SPIS a. Groups (except the side TPS facing the sun) b. Mesh Spherical Volume Because of meshing convergence difficulties due to geometries of the model, only one shield and one antenna were modeled, and several cases run with different orientations of the ram velocity, 90° and 180°, at the first perihelion (35Rs), to reveal any differences in charging that could arise from the relative orientation of the antenna, the SC, the ram ion flow, and the spacecraft wake. Figure 5-3 b shows the unstructured simulation mesh, with a size of 1m at the spherical outer boundary, 10cm at the spacecraft, 8cm at the TPS, 1cm at the shield and antenna and 3cm at the antenna. The spacecraft model is centered within a 16-m radius simulation volume, at least twice the ambient electron Debye length, and tens of times the effective Debye lengths of the photoelectron and SE populations. Table 5-3 in section 5.2.5 shows the ambient Debye length at different distances from the Sun, ranging between 8m at 1AU to 1.1m. Figure 5-3 also shows the x,y,z axis, with the z axis aligned with the spacecraft away from the Sun, y axis aligned with the antenna, and x forming a right-handed triad with y and z. A finer mesh was used for 9.5Rs to 121 ensure that the Debye length was greater than the mesh cell near the spacecraft, ensuring that the grid was less than half the Debye length in the sheath. Table 5-5 in numerical settings section (5.2.5) shows the grid size. Figure 5-4 Cross section of spacecraft model in SPIS a. y-z plane mesh grid of PSP b. surface mesh FIELDS shield Figure 5-4 a. shows a closeup of the spacecraft, FIELDS shield and antenna mesh grid. Figure 5-4 b. shows the FIELDS shield surface grid. Because the antenna was modeled as a 1D wire, it is difficult to show the grid surrounding the wire, but a denser grid can be seen on the lower right side of Figure 5-4a. 122 5.2.3 Material Properties Table 5-1 shows the modeled properties of the antenna and spacecraft materials, including photocurrent, SE yield properties, backscattered electron properties, and conductivity (bulk and surface). The antenna and antenna shield both consist of Nb-C103, the TPS shield consists of Al2O3 (alumina), the TPS of Carbon-Carbon foam, the radiators were coated with black conductive paint (BWCondPaint), the spacecraft was mostly covered in conductive black Kapton Multi Layered Insulation (MLI) blanket and few white conductive radiators. Even though the spacecraft had a complex surface consisting of louvers, radiators and other instrumentation, it was mostly blanketed with MLI, and thus modeled in such a way. The radiators were finished in highly emissive conductive paint to dissipate the heat but covered with MLI blanketing inside to reduce the heat interaction with the hot TPS. The ion SE yield properties of Nb-C103 were not known at the time of publishing, instead the properties of Aluminum were used. Given that the ion current is small, this assumption has no significant effect on the modeling results. The average solar photon spectra between solar maximum and solar minimum were used with the yield curves for both the annealed and unannealed Nb-C103 to estimate the antenna and shield photoemission. The photocurrents can vary by up +/-17% for the unannealed Nb-C103 and +/-15% for the annealed Nb-C103, depending on solar activity [41]. As explained in Section 4, SE yield test data errors at low energies (below 30eV) can be rather large (up to +/-20%). The test data give SE yield of ~1 below 30eV, while the fits used follow the “universal law of SE yield” from Lin and Joy [148] and past yield data from Reimer [102], show that all material yields are generally below 1. The universal law of SE yield can be calculated by knowing the maximum yield and incident energy at maximum yield for many 123 materials. It is important to note that the materials tested were not single crystal, lab prepared materials, but materials handled similarly to spacecraft materials. It is difficult to obtain SE test data at primary electrons below 30eV as the SE and BSE energies become similar and are hard to discriminate, and chamber effects start introducing errors in the data. Even though these test uncertainties occur at low primary electron temperatures, the yield fittings are still considered within commonly used past theoretical fits [148], and past yield data [102]. The method use was by comparing the slopes of the theoretical pure Nb and Nb-C103 before maximum annealing and finding small rising slope differences (average difference of 1%), the mayor difference is in the maximum yield and incidence electron energy at maximum yield. Table 5-2 shows the variable conductivity of Al2O3 due to temperature. As the spacecraft nears the Sun, the temperature of the Alumina increases, and its conductivity increases, improving the electrical connection between the illuminated and shadowed portions of the TPS and spacecraft. In addition, as explained in section 4.4.3, there is an expected reduction of SE yield of Nb-C103 as temperature rises of 0.05%/K. 124 Table 5-1 Material Properties used in Surface Charging Calculations [52, 97, 135] SC Radiators TPS Foam TPS- Shield FIELDS Shield and Antenna Node # 0 0 0 1 Antenna 2/ Shield 3 Material BlackKapton BWCondPaint Carbon Foam Al 2O 3 NbC103 Unannealed NbC103 Annealed Diaelectric Constant 9.6 Thickness(m) 1e-4 Bulk Conductivity (Omega -1 m -1 ) Cond Cond Cond *** Cond Cond Effective Atomic Number 5 6.1 4.5 10.2 44.1 44.1 Delta-Max 2.1 1.42 0.93 6.4 1.81 1.97 E-Max (keV) 0.15 0.26 0.28 0.45 0.269 0.252 Range 1 (Angstrom) 71.48 1 180 5 0.733 0.867 Exponent 1 0.6 1.7 0.45 0.1 0.584 0.46 Range 2 (Angstrom) 312.1 1.3 312 1 1.0 1.0 Exponent 2 1.77 0.7 1.95 2.5 1.78 1.71 Proton Yield 0.455 0.287 0.455 0.68 0.244** 0.244** Proton Max (KeV) 140 1000 80 60 230** 230** Photoemision (A/m2) 5.00E-06 N/A N/A 7.80E- 05 1.18e-4* +/-0.204e-4 5.75e-5* +/-0.09e- 4 Surface Resistivity (omega/square) Cond Cond Cond *** Cond Cond Richardson Dushman Constant N/A N/A N/A N/A 37.2 37.2 Work function N/A N/A N/A N/A 4.48 4.35 *Average solar min/max photocurrent **Properties not available at the time of publication, used Aluminum instead ***Used Table 2 for Al2O3 conductive properties as they are thermally dependent, and therefore dependent on distance to the sun 125 Table 5-2 Conductivity and Resistivity Properties of Al2O3 [135] Alumina Electrical Properties Bulk Conductivity (Ω -1 m -1 ) Surface Resistivity (Ω/square) 0.045AU (Previous Final Perihelion), 9.5Rs Cond. Cond. 0.1AU (Science Ops.), 20Rs Cond. Cond. 0.16AU (First Perihelion), 35Rs 1E-06 Cond. 0.25AU, 54Rs 6.00E-09 6.00E+11 0.73AU (Venus) 155Rs 1.00E-15 1.00E+19 1AU, 215Rs 1.00E-15 1.00E+19 5.2.4 Circuit Definition As shown in Fig. 5-5, the charging model consists of 4 different groups of surfaces, or nodes: spacecraft, Radiators and TPS- foam were node 0, TPS-Sun is node 1, FIELDS Shield is node 2, FIELDS antenna is node 3. As shown in Table 5-1, the spacecraft, Radiators and TPS foam are considered all to be Node 0. Node 1 is the TPS shield and is connected to Node 0 through a variable resistor, which is dependent on the electrical properties of alumina, as shown in Table 5-2. Node 2 is the antenna and Node 3 is the antenna shield. Figure 5-5 Model circuit design, a. circuit with floating shield and antenna, b. biased potential difference between spacecraft and antenna and spacecraft and shield The models were run in two configurations: First, Node 2 and Node 3 were free floating for all environmental cases; Second, Node 0 and Node 3 and Node 0 and Node 2 were connected 126 with a variable differential voltage for the first perihelion pass environments in order to model the conditions during the inflight bias current sweeps. As noted above, the SPIS circuit module is not able to model a bias current between nodes, so the bias sweep was modeled using a fixed set of bias voltages for which the current flowing between the surfaces was measured, as described below in Section 5.3.2. 5.2.5 Space Environment and Numerical Settings PSP is exposed to the solar wind plasma environment near the Sun’s equatorial plane. Table 5-3 summarizes the predicted parameters of that plasma environment during various phases of the PSP mission [33]. The response of the ambient electrons, PE, and SE to the potential structures around the spacecraft and antennas was modeled using PIC. The ions (solar wind protons) were also modeled using PIC. SPIS uses super-particles injected in each cell to represent dynamics of individual groups of particles. For this analysis, super-particle numbers per cell ranged between 10 and 15 for electrons and ions, 5 for photoelectrons, 3-2 for SE, 1-2 for BSE and ion induced SE, totaling 9.3 million super-particles for 35Rs, and 16.4 million super-particles for 9.5Rs. Figure 5-6 shows the number of super particles run in the model for a typical 35Rs run. Steady state was reached around 1e-4 sec. The usual computational run-time was 8 hours for 35Rs. At 1AU the computational time was at least 4 days due to the small conductivity between the TPS shield and the spacecraft. It is also important to note the increased solar flux at 9.5Rs on the spacecraft, as it is ~500x the photon flux seen at near Earth, at 1 AU. This environment increases the temperature of the exposed materials, and as previously mentioned in 2.2.5, 4.4.3 and 5.2.3, the temperature increase changes their spacecraft charging behavior. 127 Figure 5-6 Super Particle # versus Time for 35Rs. To account for the large changes in PSP orbital velocity from aphelion to perihelion, the solar wind ion velocity in the spacecraft frame was modeled differently depending on the distance from the Sun. As the spacecraft nears perihelion, this velocity increases due to the Keplerian increase in PSP orbital velocity, as shown in Table 5-3. Table 5-4 shows different ram directions (0°, 90° and 180°) in the x-y plane were studied at 35Rs, in order to discern any aspect-dependent charging effects on the antennas or spacecraft. Table 5-5 shows the major numerical inputs from the SPIS runs and typical mesh size. The timestep (Dt) where held smaller than usual because the mesh had tetrahedron angles smaller than 60deg. The capacitance of the spacecraft was held at 2x10 -10 F, but was varied to slow/speed up 0.E+00 1.E+06 2.E+06 3.E+06 4.E+06 5.E+06 6.E+06 7.E+06 0.0E+00 5.0E-05 1.0E-04 1.5E-04 # Super Particles Time (sec) Number_of_elec1 Number_of_ions1 Number_of_photoElec Number_of_secondElec_True_from_ambiant_electrons Number_of_secondElec_from_ambiant_protons Number_of_secondElec_BS_from_ambiant_electrons 128 modeling results. Table 5-3 also shows the electron plasma frequency, Debye lengths and electron gyrofrequencies. Table 5-3 Expected Plasma Parameters of PSP FIELDS Space Environment [33] Plasma Parameter Units 1 AU 219 Rs 0.72 AU (Venus) 155Rs 0.25AU 54Rs 1st Perihelion 35Rs Science Ops 20Rs Final Per. 9.5Rs Electron Density cm -3 6.93 13.5 116 281 881 4022 Proton Temperature eV 8 11.2 30.7 39.9 55.8 87.1 Electron Temperature eV 8.14 10.4 23 31.8 48.3 84.3 Magnetic Field Intensity nT 5.8 9.72 67 157 476 2102 Solar Wind Speed km/s 363 349 308 292 273 250 Spacecraft Velocity km/s 15.8 30.6 74.4 96.8 134 197 Debye Length m 8 6.5 3.3 2.5 1.7 1.1 Electron Plasma Frequency kHz 23.7 33.1 96.9 150.9 267.1 570.8 Electron Gyroradius m 1660 1119 241.2 121.3 49.3 14.8 Table 5-4 Graphical representation of different Ram direction cases Table 5-5 shows the major numerical inputs from the SPIS runs and typical mesh size. The timestep (Dt) was held smaller than usual because the mesh had tetrahedron angles smaller than 60deg. The capacitance of the spacecraft was held at 2x10 -10 F, but was varied to slow/speed up modeling results. Table 5-3 also shows the electron plasma frequency, Debye lengths and electron gyrofrequencies. 129 Table 5-5 Typical Numerical Settings for SPIS Various sensitivity studies were also conducted on the PSP FIELDS model. The model was ran without SE yield at different distanced from the sun. Photoemission sensitivity is investigated in the annealed versus unannealed models. Electron and ion densities variations were also investigated. The removal of the magnetic field is also modeled. In addition to modeling the free-floating potentials (Fig. 5-5 a), the authors also explored the current-voltage (I-V) curve for the FIELDS antenna with different shield potentials (Fig. 5-5 b). An I-V curve study was done at first perihelion with un-annealed Nb-C103 material properties by varying the bias voltages between the antenna, the shield, and the SC. Thirty-six cases were studied for antenna and shield voltage offsets relative to spacecraft floating potential from -10V to +10V in increments of 5 V, along with unbiased antenna and shield cases in order to determine the 1AU - 35Rs 9.5Rs Electron Dt 5e-8 1e-8 Electron Duration 5e-8 1e-8 Ion Dt 5e-7 1e-7 Ion Duration 5e-7 1e-7 SE and Photoem. Dt 5e-8 1e-8 SE and Photo Duration 5e-8 1e-8 Plasma Dt 5e-7 1e-7 Plasma Duration 5e-7 1e-7 Ion/Electron Super Particle/cell 10-15 10-15 Photoemission Super particle/cell 5 5 SE Super particle/cell 4 4 SE Ion Super particle/cell 3 3 Sphere Mesh Size 1 m 1 m Spacecraft Mesh Size 0.1 m 0.03 m TPS Mesh Size 0.09 m 0.04 m Shield Mesh Size 0.01 m 0.01 m Antenna Mesh Size 0.03 m 0.03 m 130 interdependent I-V curves of those surfaces, and to obtain the optimal setting for the antenna bias current. The author would like to note that the current closest approach is 9.8Rs, compared to the modeling results shown at 9.5Rs which has higher photon flux, and therefore estimated 6% higher photoelectron currents. 5.3 Modeling Results 5.3.1 Numerical Results - No Bias on FIELDS Antenna and Shield Table 5-6 and Table 5-7 the floating potentials (i.e. potential of surface relative to the potential of the outer simulation boundary fixed at 0V) of the SC, Radiators, TPS, FIELDS antenna and FIELDS shield, for heliocentric distances and predicted plasma conditions from 1AU to 0.0495AU (9.5Rs), and for both un-annealed and annealed photoelectron and SE yields. All runs included a Z-directed magnetic field with a variable magnitude as seen in Table 5-3. Inclusion of this field had little effect on the spacecraft and FIELDS instrument potentials from models with no magnetic field. Studies by [32] showed how ~30 times the magnetic field expected for Solar Orbiter (0.25AU) changed the potential of the Radio and Plasma Wave (RPW) antennas by few volts. In these runs, one can see that the potential of the spacecraft and TPS were highly dependent on the conductance of the Alumina. At closer distances to the Sun, the TPS and spacecraft floated to similar potentials as shown in Table 5-6 and Table 5-7. At Earth and Venus where the Alumina temperature is predicted to be significantly lower, the Alumina’s resistance is significantly higher, and this significant isolation resistance allows the shadowed spacecraft to charge negative as the current from the ambient electrons and SE is higher than the ambient ions, while the illuminated 131 TPS charges positive due to high photoelectron currents. Table 5-6 also shows the effect of changes in the ram direction of the solar wind as described in Table 5-4, and of reductions of SE yield due to temperature increases of the surface. Unfortunately, when modeling SPIS with the annealed Nb-C103 properties, the SE yield reduction due to surface temperature was not functioning properly. Table 5-6 Surface Potentials (V) for PSP FIELDS Space Environment (unannealed Nb-C103) Table 5-7 Surface Potentials (V) for PSP FIELDS Space Environment (annealed Nb-C103) 1 AU 0.72 AU (Venus) 0.25AU 1st Perihelion Science Ops Final Per. SC N/A -14.5 0.75 6.25 0.60 -13.1 Radiator N/A -14.5 0.75 6.25 0.60 -13.1 TPS Foam N/A -14.5 0.75 6.25 0.60 -13.1 TPS Shield N/A 6.43 4.70 6.35 0.60 -13.1 FIELDS Shield N/A 15.6 6.45 9.1 5.75 -4.79 FIELDS Antenna N/A 20.5 7.15 13.5 13.0 7.8 The proximity of the ion wake negative potential to the antenna at Ram 0° had small effects on the antenna - a few tenths of a volt of change on top of the floating potential. The direction of the ion flow had very little influence on the floating potentials of any of the surfaces. This isn’t 219 Rs (Earth) 155 Rs (Venus) 54 Rs 35 Rs RAM 0°/90°/180° 35 Rs (SEY Red.) 20 Rs 9.5 Rs 9.5 Rs (SEY Red.) SC -12.4 -14.5 0.90 6.63/6.63/6.05 6.05 0.65 -13.0 -12.8 Radiator -12.4 -14.5 0.90 6.63/6.63/6.05 6.05 0.65 -13.0 -12.8 TPS Foam -12.4 -14.5 0.90 6.63/6.63/6.05 6.05 0.65 -13.0 -12.8 TPS Shield 14.8 6.75 4.85 6.35/6.40/6.25 6.25 0.65 -13.0 -12.8 FIELDS Shield 23.0 21.8 9.60 11.8/12.2/12.5 12.5 8.75 0.92 1.4 FIELDS Antenna 29.3 27.5 13.8 17.5/17.9/17.5 17.5 16.3 14.9 14.8 132 surprising given the 3 orders of magnitude difference between the dominant photoelectron, SE, and ambient electron currents and the ion currents. The cases run with annealed material properties tabulated in Table 5-6 show the floating potential of the shield and antenna lower than the un-annealed cases as expected: the spacecraft material properties and dimensions stayed constant, while the PE yield of the antenna and shield materials were reduced by annealing, decreasing their floating potentials; as less electrons leave the shield and antenna surfaces, the potential becomes less positive to maintain current balance. Spacecraft floating potential does not depend significantly upon the FIELDS antenna and shield characteristics and their floating potentials, by comparing Table 5-6 with Table 5-7. The spacecraft floating potentials were within past predicted models, except for 9.5Rs which was a little more negative. In detail, [135] modeled the slow and fast Solar Wind at different heliocentric distances, predicting spacecraft floating potentials at 0.25AU between -0.1V and 12.4V, at 35Rs between 1.0V and 8.0V, and at 9.5Rs between -0.4V and -12.6V. For the 35Rs, the spacecraft potential predictions are within past models, but for the 9.5Rs case, the potential of the spacecraft is more negative. In addition, [135] also modeled an extreme, post shock-case, with a spacecraft floating potential prediction of -31V. Table 5-8 shows the current source comparison between 1AU (215Rs) and 0.16AU (35Rs) for unannealed Nb-C103. At 219Rs the total currents are two order of magnitude smaller than at 35Rs. The photocurrent is dominating in both cases, by two orders of magnitude at 219Rs and by one order of magnitude at 35Rs. The SE current is two orders of magnitude smaller at 219Rs compared to 35Rs, which is only one order of magnitude smaller for the entire spacecraft, including the antennas. The ion current is two orders of magnitude smaller than the photocurrent at 1AU, while it is up to three orders of magnitude smaller at 0.16AU. The SE due to ions are in 133 the same order of magnitude as the ion current. The BSE currents are also small, several orders of magnitude smaller than the photoemission and not an important factor in the current balance in both environments. Table 5-8 Current Source Comparison for PSP between 1AU and 0.16AU. PSP FIELDS Antenna Only Current Units in Amps 1AU 219Rs 0.16 AU 35Rs 1AU 219Rs 0.16AU 35Rs 0.16AU (Reduced SEY) Total Collected -3.8E-04 -1.6E-02 -7.6E-07 -3.0E-05 -3.0E-05 Total Emitted -3.8E-04 -1.6E-02 -7.6E-07 -3.0E-05 -3.0E-05 Collected Electron -7.4E-06 -7.9E-04 -3.7E-08 -1.2E-06 -1.0E-06 Collected Ion 1.9E-06 6.5E-05 1.5E-09 7.0E-08 1.1E-07 Collected Photoelectron -3.6E-04 -1.4E-02 -7.0E-07 -2.8E-05 -2.8E-05 Collected SE -4.9E-06 -1.0E-03 -2.5E-08 -1.6E-06 -1.3E-06 Collected BSE -1.5E-07 -6.5E-06 1.0E-10 -3.5E-08 -1.3E-08 Collected SE Ion -1.2E-06 -3.8E-05 -4.5E-10 -2.0E-08 -2.0E-08 Emitted Photoelectron -3.7E-04 -1.5E-02 -7.4E-07 -2.9E-05 -2.9E-05 Emitted SE -6.3E-06 -1.2E-03 -2.6E-08 -1.4E-06 -9.0E-07 Emitted SE Ion -1.6E-06 -3.9E-05 -5.9E-10 -1.5E-08 -1.7E-08 As explained in the materials section, the high temperature on the antennas could have effects on their potentials by reducing the SE current. The potential differences are shown in Table 5-6, while the currents are shown in Table 5-8. The SE currents are reduced on the FIELDS antenna by 44% at 35Rs because of the SE yield reduction due to temperature, but with similar potential results. The spacecraft potential is negative at 219Rs as it is isolated from the TPS shield, compared to the positive charging of the TPS and FIELDS instrument. At 35Rs, the TPS shield becomes more conductive, making the spacecraft dependent on the photocurrent of the TPS and charge positive. Figure 5-7 shows the potential in volts on two slices through the simulation domain at steady state, allowing one to see both the surface potentials on the spacecraft, TPS, antenna, and 134 shield, along with the potential distribution in the plasma surrounding those surfaces during the first perihelion at 35Rs. The spacecraft charges positively at about 6.25 V, while the antenna and shield float even more positive (+17.5 V and +11.8 V relative to outer simulation boundary, respectively). Negative potential wells with a depth of -3.2 V form in front of the TPS and a negative potential well of depth of -3.25V in the ion wake of the spacecraft, not as deep to those previously found at 9.5Rs by [5, 7, 135]. These wells do differ in depth and dimension from those observed in previous studies because previous studies focused on 9.5Rs, while this research focused on 35Rs. At 35Rs, the photoemission fluxes are lower as the solar flux is lower, the electron and ion density and temperature, are lower, which translate also to lower SE fluxes. That said, [5, 7, 135] found the negative potential well in front of the TPS was less deep than the wake potential well. Figure 5-7 Plasma Potential (Volts) and spacecraft and FIELDS Potential (Volts) at 0.16AU (First Perihelion) a. y-z plane, b. x-y plane Figure 5-8 shows these differences in a comparison between our runs at 35Rs and 9.5Rs. Note that the color scales for the potential are different between the two cases in order to show the 135 extent and depth of the potential wells. In these cases, [135] predicted negative wake potential wells charging from -20V to -36V, compared to -23.9V in Figure 5-6, but their plasma parameters varied from the ones in this study with their densities ranging from 1.2x10 3 cm -3 to 4.1x10 4 cm -3 , electron temperatures ranging from 48.6eV and 59.7eV, and ion temperatures ranging from 40.5eV to 223.1eV. Figure 5-8 Plasma Potential (Volts) of PSP a. and c. 9.5Rs, b. and d. 35Rs, a. and b. at 35Rs potential scales and c. and d. at 9.5Rs potential scales The plasma potential around the shield (a.) and the antenna (b.) are shown in Figure 5-9, for the antenna at 90° RAM. The antenna and shield wakes at 0° RAM case join the wake of the spacecraft and therefore not discernable and more negative. Similarly to the TPS in Figure 5-5, a 136 negative potential well forms in front of the shield and the antenna. Note that the well in front of the antenna is not as negative as the shield and TPS. The wake from the significant proton flow (solar wind plus PSP orbital velocity) can also be seen. Note that the well in front of the antenna is not as negative as the shield and TPS. Figure 5-9 Plasma Potential (Volts) of the cross-sections of the a. shield and b. antenna – at 90° ram, diameter of the spherical boundary is 16m Figure 5-10 to 5-15 show the plasma characteristics and the near spacecraft plasma environment of a cross-section of the PSP and the antenna at 1AU (219Rs), on the left, and at 0.16AU( 35Rs) on the right. Figure 5-10 shows the plasma potential of PSP and the antenna in Volts. The negative potential well in front of the TPS and antennas are not seen at 1AU compared to 0.16AU. The wake potentials are also different due to a different angle of attack of the ions, and lower density of the ions at 1AU. The TPS shield and the spacecraft are isolated from each other at 1AU and charging at different potentials. At 35Rs the TPS shield and spacecraft charge to similar potentials. The FIELDS antennas decrease their potential. All potentials are shown in Table 5-6. 137 Figure 5-10 Plasma Potential (Volts) of PSP a. and c. 219Rs (1AU), b. and d. 35Rs (0.16AU), a. and b. at 35Rs potential scales and c. and d. at 1AU potential scales Figure 5-11 shows the Log electron plasma charge density. The electron density increases as the spacecraft approaches the Sun. The electron density figure at 1AU (left) is smoother due to a larger scale, compared to the 35Rs figure (right) which has a much smaller scale. Figure 5-11 shows the ion density. The wake is seen in both 1AU and 0.16AU, but as the velocity of the spacecraft increases, the wake has a larger ram component. The ion density is shown with a linear scale to better capture the wake structure. A low-density ion region forms opposite the impinging ions from the ram and solar wind. Higher electron mobility leads to negative space charge filling 138 the wake, which forms a negative potential area, as seen in previous simulations [5, 7]. The negative potential well in front of the TPS supported by PE and SE populations, as well as the one in the wake supported by ambient, PE, and SE electrons, repel ambient electrons, leading to reduced ambient electron densities in those locations, as seen in Figure 5-11 b. Figure 5-11 PSP and FIELDS Log Electron Density (log (#/m 3 )), a. 1AU and b. 0.16AU Figure 5-12 PSP and FIELDS Ion Density (#/m 3 ), a. 1AU and b. 0.16AU 139 Figure 5-13 shows the photoelectron density. The photoelectron density is much higher for 0.16AU as expected, as it is closer to the Sun. The photoelectrons produced fill the wells in front of the TPS and to a lesser degree, the antenna well. Figure 5-14 shows the SE charge density. The SE density is one order of magnitude smaller than photoelectron density at 0.16AU. Figure 5-13 PSP and FIELDS Log Photoemission Density log (#/m 3 ), a. 1AU and b. 0.16AU It is important to note that near the antenna and TPS, the photoelectron density is one order of magnitude greater than the SE density, and two orders of magnitude greater than the ambient electrons and ions. Compared to the spacecraft, the antenna and its shield are exposed to the Sun and are photoelectron current dominated. The photoemission electron density (~1e10 1/m 3 ) is the highest of all particle densities by at least an order of magnitude within a region several meters away from the spacecraft and antennas. Figure 5-13 shows how the photoelectrons at 35Rs occupy the environment near the spacecraft, compared to that at 1AU, where it concentrates mainly on the TPS and the antenna. Similarly, Figure 5-14 shows the electrons occupying the near spacecraft environment at 35Rs, in contrast to 1AU, where a singular structure forms around it. The SE 140 concentrate in front of the TPS shield, near the antenna, close to the side of the spacecraft and in the wake. It is significant to note that the Debye lengths are smaller at 35Rs than at 1AU. Figure 5-14 PSP and FIELDS Log SE Density log (#/m 3 ), a. 1AU and b. 0.16AU Figure 5-15 shows the BSE charge density, at two orders of magnitude smaller than photoelectron density. The BSE are attracted to the TPS shield and antennas which are charging positive at both 1AU and 0.16AU. Figure 5-16 shows the ion SE charge density, also at two orders of magnitude smaller than the photoelectron charge density. At 1AU the ions hit the left corner of the spacecraft, causing a small ion SE source. At 35Rs, the ions impact a larger surface, showing a larger ion SE source on the spacecraft. This difference is due to the greater ram velocity at 35Rs. 141 Figure 5-15 PSP and FIELDS Log BSE Density log (#/m 3 ), a. 1AU and b. 0.16AU Figure 5-16 PSP and FIELDS Log SE due to Ions Density log (#/m 3 ), a. 1AU and b. 0.16AU Figure 5-17 show the particle densities in front of the TPS as a function of distance for 1AU, 0.16AU and 0.045AU. The TPS shield is located at -0.2m. They also include the potential as a function of distance. For 0.16AU and 0.045 AU the potential in front of the spacecraft has virtual cathodes (negative potential wells as shown in Figures 5-8, 5-9 and 5-10). Space-charge- limited currents which cause this virtual cathode are determined by the PSP spacecraft sheath. They have been studied extensively by many authors, including Langmuir [149]. Bohm [150], Crawford and Cannara [151], Prewett and Allen [152], Marese et al. [153], Wang and Lai [154]. Figure 5-17 show that the minimum of these wells occur when the density of the photoelectrons 142 (plus other negative charge densities) become larger than the ion charge density, creating an inflection of the potential in the Poisson’s equation, as shown in eq. 5-2. This inflection does not occur at 1AU. Please note that at 9.5Rs the densities have some small oscillations on the densities near the shield which could be caused by too large of a timestep. Figure 5-18 shows the position of the negative well in front of the TPS, and the Debye lengths of the plasma thermal electron, the photoelectron and SE near the TPS versus the distance of the spacecraft with respect to the Sun. The location of the negative well gets closer to the TPS as the spacecraft nears the Sun. This occurs at a rate not dependent on the ambient thermal electron Debye lengths. It is closer to the SE and photoemission SE current reduction rates as the spacecraft approach the Sun. Furthermore, the SPIS results show the collected current from photoelectrons, as they return to a positive potential antenna. On an isolated free-floating antenna (i.e. without shield or spacecraft nearby), both ends would have similar values. However, photoelectrons from the shield are attracted to the antenna, making the collected current density of the antenna near the shield larger. In other words, this photoelectron current to the antenna from the shield changes the current balance and final free-floating potential of the antenna. 143 Figure 5-17 PSP TPS Shield Potential and Plasma Densities as a Function of Distance at a. 1AU (219Rs), b. 0.16AU (35Rs) and c. 0.045AU (9.5Rs) 144 Figure 5-18 TPS Negative Well Position, including the Thermal Electron, Photoemission, SE Debye Lengths versus the Distance from the Sun In addition, the modeling results show the net current density of the antenna, where the tip has positive current density while the area near the shield has negative current density. This negative density is mostly due to photoelectrons and, in a smaller influence, SE both attracted from the shield. To reduce the influence of this current from the shield on the antenna’s floating potential, a voltage bias is imposed between the shield and antenna, with the results shown in section 5.3.2. 5.3.2 Numerical Results – Other Sensitivity Studies Various sensitivity analysis were conducted on the PSP FIELDS model to find both the main current source contributor and verify the model. A variation on electron and ion density, ion velocity, photocurrent and magnetic field were introduced in the modeling parameters at both 1AU and 35Rs. The previous section showed the differences in currents between the photoelectron yield of the FIELDS Nb-C103 annealed versus unannealed. The potentials clearly showed a dependence on the photocurrent yield, but there was also a change in the SE yield due to annealing, 0 1 2 3 4 5 6 7 8 9 0 0.2 0.4 0.6 0.8 1 1.2 Length (m) Distance From the Sun (AU) Thermal Electron Debye Length Photoelectron Debye Length Secondary Electron Debye Length Location of TPS Min. Negative Well 145 even though this change was less prominent (as seen in section 4.4.3). Multiple runs were performed at 1AU and 0.16 AU (35Rs) with a variation of environmental inputs. The models were run with a variation of the distance from the Sun to vary photon flux, and hence photoemission, while keeping the electron and ion densities and velocities the same. The 1AU model (nonconductive TPS) was run at 0.7AU, double the photon flux, and hence the Sun exposed surface photoemission, and at 1.4AU, half the photon flux. At 0.7AU the photoemission current and hence the total currents doubled. The TPS shield and FIELDS antenna and shield remained positive and attracted the electrons. Their potential though decreased by a few volts (~3 to 5V). The spacecraft potential remained equal as the electron and ion environment were not changed and the TPS and the spacecraft are isolated from each other. At 1.4AU, there was half the photon flux than at 1AU, photocurrent also halves, decreasing the number of electrons emitted which reduces the potential of the surface. The photoelectron density decreases with respect to other electrons at 1AU. Photon flux variation was also ran at 35Rs with different results, simulating the photon flux at 53Rs and 27Rs while maintaining plasma densities constant. At 35Rs, the potential of the surfaces was greater than at 53Rs and continued to increase at 27Rs. The photoelectrons increased, which increased the potential. The model was run with no SE yield to confirm that the SE current was not a predominant influence on the potential during close encounters. At 35Rs it was found that the SE yield did not influence the potential charging greatly (minus a few millivolts on the antenna and minus one volt on the spacecraft), as the antenna, the shield and the spacecraft were charging positive, and the emitted electrons were attracted by the positive potential surfaces. At 1AU, the SE had a greater influence on the surface potentials, but just by a few volts (~2V). If the SE yield is removed, the 146 spacecraft potential decreases by a few volts (~3V), the TPS shield decreased by half a volt, the antenna reduced its potential by five volts. The models were also run with a variation of electron and ion density while keeping the photoemission constant. At 1AU, the model was run with higher ambient plasma density (by one order of magnitude). The higher density of the plasma causes the potential of the antenna, the TPS shield and the spacecraft to decrease, showing a dependency on the ambient thermal electron density. The model was also run with an order of magnitude smaller of ambient plasma density. In comparison with the higher density, the potential increased by tens of volts for the spacecraft, TPS shield, and antenna. At 35 Rs (0.16AU) similar electron and ion density variation was performed. When the electron and ion density were doubled, the potentials decreased by few volts on the spacecraft, TPS and the antenna. The model was then run with the density halved. The potentials of the spacecraft and the antennas increased by a few volts. At 35Rs the TPS shield is conductive, making the TPS shield and spacecraft float at the same potential. As explained in section 5.3.1, the magnetic field was also modified from expected values to see no changes at either 1AU, 35Rs nor 9.5Rs. The gyroradius of the electrons remains much larger than the spacecraft and FIELDS antenna dimensions. Changes in the magnetic field do not affect PSP and FIELDS charging. Finally, the model was run at 35Rs with the finer mesh of 9.5Rs in order to do a comparison run. The currents and potentials were compared. The model found that for the spacecraft the difference in the total collected and total emitted current to be 0%, while for the FIELDS antenna the total collected current and emitted current difference was 0.3%. The maximum error on the spacecraft was of 3% for the collected SE, while for the FIELDS antenna it was 31% of the collected SE ion. This contrast was probably due to the reduction of the super particles which was 147 done in order to be able to run the models in a shorter period of time. These errors had little effect on the total current and final potential of the antenna during the I-V curve models, and with the lower number of super-particles the models ran faster with the author’s limited computing resources. The plots shown in the previous section were created using runs with larger number of super particles to decrease the maximum current errors down to 7%. The average potential errors were small, with an overall average of 2.9%, and a maximum error of 8.9% on the spacecraft. This sensitivity study of varying the photoemission yield, SE yield, electron and ion densities reinforced the importance of knowing the material properties of the PSP and FIELDS shield and antenna. Material properties of the TPS shield at high temperatures and photoemission and SE yields must be known to predict the plasma environment near the spacecraft and instrument. 5.3.3 Numerical Results bias FIELDS Antenna and Shield – I-V Curves The following numerical results were completed with the flight estimated Nb-C103 saturation photoelectron current density of 2.4µA/m 2 under solar illumination at 1 AU compared with the laboratory estimate of 1.18 µA/m 2 [Diaz-Aguado et al., 2020]. Figure 5-18 shows the modeled I-V curves of the antenna at 1 st perihelion, or ~35Rs. This curve was obtained by sweeping the bias voltages between the antenna and spacecraft from -10V to 10V, and the shield and spacecraft from -10V to 10V in 5V increments, and measuring the steady-state currents that flowed between each of the surfaces. The curve for the antenna shows similarities to the theoretical I-V curve shown in Figure 2-2 for cylindrical probe. 148 Figure 5-18 Predicted FIELDS Antenna I-V Curve with Different Shield Bias Potentials. The recommended bias current to ensure optimal sensitivity of the probe is between -52.1 µA and -33.7 µA with respect to the spacecraft. The slopes of all the I-V curves were similar and did not significantly change depending on the shield potential and correspond to a sheath resistance of ~ 325 kΩ. The space potential at the antenna (with respect to infinity) is ~ -5V, described by the first elbow of the I-V curve, and the saturated current is -53µA, shown as the current plateau of the I-V curve as the voltage decreases. The modeled resulting photocurrent of the antenna is - 60µA. During flight the shield was maintained at a potential difference with respect to the antenna through a fixed controlled voltage, at 0.1V with respect to the antenna. Figure 5-19 shows the I- V curve of the shield, current of the shield with respect to the spacecraft versus the potential of the shield with respect to the antenna. From this graph, spacecraft engineers can deduce the current draw from the spacecraft to the shields. -6.0E-05 -5.0E-05 -4.0E-05 -3.0E-05 -2.0E-05 -1.0E-05 0.0E+00 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 Antenna Current (A wrt S/C) Antenna Potential (V wrt S/C) Shield 10V Shield 5V Shield 0V Shield -5V Shield-10V Shield Free Floating 149 Figure 5-19 Shield I-V Curve, Shield Potential with respect to spacecraft vs. Current with respect to Antenna Figure 5-20 shows a special I-V curve of the shield, specifically the current of the shield with respect to the antenna versus the potential of the shield with respect to the antenna. Even though the shield and antenna are physically and electrically isolated from each other in the model, there is an interaction of their plasma sheaths due to their proximity. This interaction behaves like a plasma channel and therefore a current can flow between them. To reduce this current, a shield potential can be chosen depending on the antenna potential, i.e., if the antenna is at -5V bias, a - 1V shield potential with respect to the antenna would give us a small -2.4µA current (compared to -51 µA with free floating shield). Such voltage biasing allows for more accurate measurements by reducing the current between the shield and the antenna. It can be deduced from Figure 5-20 that this “base conductance” has an impedance of ~240 kΩ. This data could help the engineers and scientist select the necessary bias voltage for the shield to reduce spurious currents from the shield to the antenna. -6.0E-05 -5.0E-05 -4.0E-05 -3.0E-05 -2.0E-05 -1.0E-05 0.0E+00 1.0E-05 2.0E-05 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0 Current wrt Spacecraft (A) Potential wrt to Antenna (V) Antenna 10V Antenna 5V Antenna 0V Antenna -5V Antenna -10V Antenna Free Floating 150 Figure 5-20 Shield I-V Curve, Shield Current with respect to Antenna vs. Potential with respect to Antenna 5.4 PSP FIELDS Flight Data As mentioned in the last section, during the mission it was observed that the photocurrent yield of the Nb-C103 was 240 µA/m 2 at 1AU, more than double the value of the highest predicted from ground testing 118 µA /m 2 (unannealed) at an average of the max/min solar cycle. At the time of the flight measurement, the Sun was near solar minimum (3 rd quarter 2019), near the end of cycle 24. The flight ambient plasma parameters at 35Rs are shown in Table 5-9. These parameters and the observed photocurrent values were introduced in the SPIS model, results shown in Table 5-10. Flight results suggest that the potential of the antenna charge more negative than the predicted potentials. The negative potential well that forms in front of the antenna is not as negative in SPIS (as can be observed in Figure 5-7 b. compared to the shield Figure 5-7 a). In addition, if this larger Nb-C103 flight photoemission current compared to tested data remains -8.0E-05 -6.0E-05 -4.0E-05 -2.0E-05 0.0E+00 2.0E-05 4.0E-05 6.0E-05 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0 Current wrt to Antenna (A) Potential wrt to Antenna (V) Antenna 10V Antenna 5V Antenna 0V Antenna -5V Antenna -10V Antenna Free Floating 151 unchanged during annealing of the Nb-C103, it will reduce the influence of the thermionic emission current in the current balance during closest approach at 9.8Rs. Table 5-9 – Modeled Plasma Parameters[33] at 35Rs compared to flight parameters at 35.7Rs [155-157] 1st Perihelion (Predicted) 1 st Perihelion (Data) Plasma Parameter Units 35 Rs 35.7 Rs Electron Density cm -3 281 300-500 Proton Temperature eV 39.9 8.6-12.9 Electron Temperature eV 31.8 8.6-12.9* Magnetic Field Intensity nT 157 70 to -90 Solar Wind Speed km/s 292 300 to 500 Spacecraft Velocity km/s 96.8 95.7** Debye Length m 2.5 1.29-1.58* Ion Acoustic Velocity km/s 78 40.6-49.7* *Assuming ion and electron temperature are similar in value **Calculated from orbit parameters Table 5-10 Model Potentials with 1 st Perihelion, Flight Potential Bias Values (Antenna -11.6V and shield 0.1V), Flight Nb-C103 Photocurrent 2.4e-4A/m 2 During these first perihelia, the FIELDS antennas were current biased before the sweeps between –9.7 and -9.8 uA/antenna with the shield at 0.1V potential bias with respect to the antenna. After the sweep a bias was held at -10 uA/antenna. The antenna and shield potential predictions are not the same as the flight data, probably due slight differences in plasma environment characteristics and geometrical differences between the model and the actual spacecraft. However, 1st Perihelion (flight photocurrent no bias) 1 st Peihelion (flight photocurrent, bias) Final Per. 9Rs (flight photocurrent, no bias) SC 7.03 7.20 -13.0 Radiator 7.03 7.20 -13.0 TPS Foam 7.03 7.20 -13.0 TPS Shield 7.17 7.35 -13.0 FIELDS Shield 16.1 -4.33 2.95 FIELDS Antenna 22.5 -4.39 19.5 152 there is sufficient qualitative and semi-quantitative agreement between the model and inflight results to allow for comparison between them. Figure 5-21 shows the time series of the antenna voltage of and antenna bias current to the FIELDS PSP V1 through V4 antennas near perihelion during the third encounter, on September 1, 2019. On the left axis the voltage measured is shown, while on the right axis the current sweep values are shown. There were four coplanar antennas measured, the results of the off plane fifth antenna are not shown. Figure 5-21 PSP FIELDS V1-V4 Antenna Voltage and Current Bias Time Series During the third perihelion there were four sweeps, two on V1 and V2 and two on V3 and V4. The first sweep performed on V1 and V2 was done with a current sweep between -100µA and 0 µA. The voltage of all four antennas relative to spacecraft ground was measured at each step in the sweep. Like the first sweep, the second sweep was performed on V3 and V4 between -100µA and 0 µA. The third sweep was a smaller sweep, between -14 µA and 3.5 µA on V1 and 153 V2. Finally, the fourth sweep was performed similarly between -14 µA and 3.5 µA on V3 and V4. Figure 21 also shows how the potentials of the fixed bias antennas during the current sweep change by a few volts, which could indicate a change in the spacecraft potential, influenced by the additional current required to support the biasing of the sweeping antennas. The inflight potential with respect to the spacecraft of the probes ranged between 2.9V and -1.9V compared to SPIS of 15.3 V. Figure 5-22 shows the PSP FIELDS antenna I-V curves for the first two sweeps. Figure 5- 16 shows the antenna I-V curves for the second two sweeps. By comparing Figure 5-22 with Figure 5-18 from SPIS analysis, there are similarities worth mentioning, as the saturated current of the flight antennas are -52 µA, compared to the flight, between -54 µA and -72 µA. The space potential at the probe with respect to infinity is -4.3V for the data and -5V for the analysis. Figure 5-22 FIELDS V1-V4 Third Perihelion, First I-V Curve Sweep 154 The slopes of the I-V curve (or sheath impedances, as explained in 2.6, eq. 2-54) do differ, data giving an impedance of 51 kΩ, while the analysis gives a sheath impedance of 325 kΩ. These differences could be caused by the environmental differences between the analysis and the actual plasma environments, shown in Table 5-7, and geometrical differences between the shield and the antenna modeled versus flight. Figure 5-23 shows another I-V curve forming at significant positive bias currents. As the bias current increases the antenna potential with respect to the spacecraft increases and then runs off towards the positive rail, probably due to saturation of the ambient electron current. This second I-V curve could be the signature of the I-V curve of the spacecraft sheath as described by [158] for a Langmuir probe inside the spacecraft sheath, with an impedance value of 1 MΩ. Figure 5-23 FIELDS V1-V4 Third Perihelion, Second I-V Curve Sweep 155 5.5 PSP FIELDS Modeling Conclusions The PSP spacecraft and FIELDS antennas were modeled using SPIS software to predict their potential and current interactions with the environment. Results predict the FIELDS antennas charging positive for all cases. The plasma potentials show the ion wake and negative potentials in front of the TPS, as previously predicted. These wells also are seen around the FIELDS shield. The antenna had a shallower negative potential well surrounding the cylinder, but similar negative potential due to ion wake It is important to note, the spacecraft potential predictions were within past estimates, except at 9.5Rs, which was closer to an extreme solar wind event. Modeling with PIC thermal electrons is suggested at 9.5Rs and closer to improve model predictions. The FIELDS antenna and shield I-V curves were shown for different shield potentials. An antenna bias current of -5V to 5V is suggested for optimal measurement sensitivity. SPIS was also able to model the I-V curve between two electrically isolated surfaces, which were nevertheless coupled with each other through their sheath interactions. Based on those results, a negative voltage bias of the shield with respect to the antenna is recommended to reduce the spurious currents from the shield to the antenna. Model results were then compared with initial flight results. The saturation photoelectron current of Nb-C103 was found to be larger than laboratory values by a factor of 2. The SPIS model was run with these new properties and compared the results with flight values. Flight I-V curves were plotted and compared to the analysis, finding current saturations to be within the same order of magnitude and observing similar potentials with respect to infinity. The slopes of the I-V curve (and therefore the sheath impedances) differed greatly. Even though it was found that FIELDS antenna potentials to be more negative than predicted when not current biased, spacecraft charging 156 engineers, and therefore scientists, could benefit by obtaining the I-V curves during the design process using SPIS. 157 6 Conclusions The space environment effects on PSP FIELDS instrument has been described, including new state of the art for spacecraft charging. A review of spacecraft charging theory was first examined and applied to PSP new plasma environment. The review was followed by a photoemission investigation of unannealed and annealed spacecraft materials, which include W, TaW, Nb-C103, TZM, Elgiloy, TiN and DAG-213®. This investigation incorporated new material data, including material work function, and theoretical fits. It was followed by an SE and BSE study campaign, a large contributor to spacecraft charging, especially in shadowed surfaces. Thermionic emission was also added as a potential current source at high temperatures. Lastly, the data was used to produce a spacecraft charging model in SPIS, obtain predictions and compare with flight data. This dissertation showed new spacecraft charging state of the art. Whereas thermionic emission was previously a primary current in lab settings, it introduced thermionic emission as a primary current at 9.8Rs for Nb-C103 used on the FIELDS antenna, as shown in a current vs. distance from the Sun plot. It also showed results from measured photoemission and secondary electron yields from relevant spacecraft and instrument materials that were not represented in existing literature, including annealing effects. The dissertation also advanced the state of the art by combining the yield measurements with the relevant environmental data to estimate their impact on the charging of the PSP spacecraft and FIELDS antenna elements, finding the floating potentials of the un/annealed Nb-C103. Finally, it synthesized the materials and modeling data to produce predictions of the unbiased and current-biased floating potentials both for the PSP spacecraft and the relevant FIELDS instrument, which has never been done before. 158 The theory of spacecraft charging of PSP in the solar wind was explored, which is in an unusual large range of environmental condition, due to the large changes in the solar flux and plasma temperatures and densities. Currents that affect spacecraft floating potentials were studied, including photocurrent, SE and BSE currents, ambient electron and ion currents, thermionic current, and bias current. Thermionic, photocurrent, SE currents and BSE currents are material dependent which lead to their further study to be able to model PSP and FIELDS. The photoelectron yield, work function and photoelectron threshold were measured on the un-annealed and annealed samples of previously untested spacecraft materials. The processes for cleaning and preparing the samples were similar to actual spacecraft integration to better reflect spacecraft surface behavior. The samples were annealed to investigate the effect of high flight temperature exposures of these materials. Large differences were observed between the annealed high-temperature alloys and the un-annealed samples. The incident photon angle revealed different responses for each sample, which do not follow the cosine or secant dependence that one would expect from simple, first-principles models for the dependence of photoemission on photon incidence angle. A photoelectron yield fit was used to calculate the surface normal photocurrent at 1AU at solar maximum and minimum. Future scientists and engineers will better estimate photocurrent with these analytical fits, and normal and angled photon yield data, as well as thermionic emission current with the work function. This dissertation used the Nb-C103 photoemission properties to model in SPIS the PSP FIELDS instrument. Following the photoelectron yield investigation, the TE, SE and BSE yields were measured for the same samples. Prepared similarly as the previous test campaign, the samples were cleaned and tested. All samples were annealed at temperatures similar to PSP flight predictions except for the single DAG-213® sample that was annealed in the previous testing campaign. The SEY and 159 BSEY characteristics are shown to evolve through high temperature exposures, also seen in the SE and BSE current densities. These affects varied by plasma environment. A ready reference current SE and BSE density per number density was given for all samples for primary electrons to aid spacecraft charging engineers and scientists in the design process. The SEY and BSEY calculations for Nb-C103 were then used in SPIS for FIELDS charging analysis. Finally, SPIS software was used to model PSP and the FIELDS instrument to predict their potential and current interactions with the environment at different solar radii away from the Sun. The spacecraft was modeled, including the FIELDS shield and antenna composed of Nb-C103. An I-V curve at 35Rs was obtained from the analysis acquiring current saturations, slope, and space potentials of the antenna and shield with respect to infinity. The I-V curve and floating potentials were then compared with flight potentials. Even though there were disparities in both the potential and the I-V curve slopes, SPIS was able to obtain useful results, proving that modeling future Langmuir probes before launch could benefit spacecraft charging engineers and scientists. This research helped identify further developments needed to continue improving spacecraft charging modeling in the Solar Wind near the Sun environment. Properties of materials at temperature should be explored, which include SE and thermionic emission. Past experiments have shown a decrease of SE yield as temperature increases. The Richardson-Dushman constant should be obtained for the materials exposed to the Sun, i.e. Nb-C103. In addition, modeling of the thermionic emission will also be important for the current balance of the antennas, their shields and understating the plasma environment around them. In lab photoelectron temperature measurements should be obtained for materials used in PSP. This research assumes material photoelectrons and SE have similar temperatures, but this hypothesis has not been tested. 160 Modeling all four antennas and the Solar Probe Cup should also be considered for a better characterization of the plasma environment near the spacecraft and instruments. In conclusion, new spacecraft charging data from W, TaW, Nb-C103, TZM, Elgiloy, TiN and DAG-213® were presented, including photoyield, work function, SEY, and BSEY. Novel analytical fits were created for photocurrent calculations. New SEY and BSEY fits were applied for better yield estimates and therefore current estimates. Thermionic emission theory was introduced to understand spacecraft charging behavior at close approach of the Sun, with surfaces at high temperatures, a new application. SPIS was used to predict PSP spacecraft and FIELDS instrument potentials and currents, including an I-V curve to best estimate the antenna behavior during current sweeps. The modeling results were then compared with flight data. This dissertation advances the spacecraft charging community’s knowledge in near Sun environments, benefiting both engineers and scientists, and obtained the necessary tools to predict the charging behavior of the FIELDS instrument. 161 References [1] Salisbury, J., Metalogicon (no. Chapter 4). Mansfield Center: Martino Publishing, 2015. [2] Hastings, D. and Garrett, H., Spacecraft-Environment Interactions (Cambridge atmospheric and space science series). New York: Cambridge University Press, 1996. [3] Goldston, R. and Rutherford, P., Introduction to Plasma Physics. Philadelphia: Institute of Physics Publishing, 1995. [4] Chen, F. F., Introduction to Plasma Physics and Controlled Fusion, 2nd Edition ed. New York: Plenum Press, 2010. [5] Ergun, R. E., Malaspina, D. M., Bale, S. D., McFadden, J. P., Larson, D. E., Mozer, F. S., Meyer- Vernet, N., Maksimovic, M., Kellogg, P. J. and Wygant, J. R., "Spacecraft charging and ion wake formation in the near-Sun environment," Physics of Plasmas, vol. 17, no. 7, p. 072903, 2010, doi: 10.1063/1.3457484. [6] Donegan, M. M., Sample, J. L., Dennison, J. R. and Hoffmann, R., "Spacecraft Coating-Induced Charging: Materials and Modeling Study of Environmental Extremes," Journal of Spacecraft and Rockets, vol. 47, no. 1, pp. 134-146, 2010, doi: 10.2514/1.40882. [7] Guillemant, S., Genot, V., Mateo-Velez, J.-C., Ergun, R. and Louarn, P., "Solar wind plasma interaction with solar probe plus spacecraft," Annales Geophysicae, vol. 30, no. 7, p. 1075, 2012, doi: 10.5194/angeo-30-1075-2012. [8] Guillemant, S., Genot, V., Velez, J.-C. M., Sarrailh, P., Hilgers, A. and Louarn, P., "Simulation Study of Spacecraft Electrostatic Sheath Changes With the Heliocentric Distances From 0.044 to 1 AU," IEEE Transactions on Plasma Science, vol. 41, no. 12, pp. 3338-3348, 2013, doi: 10.1109/TPS.2013.2246193. [9] Shen, C. S. and Chopra, K. P., "Thermionic Screening of Bodies in Atmosphere and Interplanetary Space - NASA - TM -X-50226," Journal of the Atmospheric Sciences, vol. 20, no. 5, pp. 359-365, 1963. [10] Dushman, S., "Thermionic Emission," Reviews of Modern Physics, vol. 3, no. 1, pp. 190-190, 1931, doi: 10.1103/RevModPhys.3.190.2. [11] Whipple, E. C., "Potential of Surfaces in Space," Report on Progress of Physics, vol. 44, pp. 1197- 1250, March 1981, doi: 10.1088/0034-4885/44/11/002. 162 [12] Lai, S. T. and Tautz, M. F., "Aspects of Spacecraft Charging in Sunlight," IEEE Transactions on Plasma Science, vol. 34, no. 5, pp. 2053-2061, 2006, doi: 10.1109/TPS.2006.883362. [13] Lai, S. T., Fundamental of spacecraft charging: spacecraft interactions with space plasmas. Princeton, N.J.: Princeton University Press, 2012. [14] DeForest, S. E., "Electrostatic Potentials Developed by ATS-5," Photon and Particle Interactions with Surfaces in Space, ed. R Grard, Proceedings of the 6th Eslab Symposium, Noordwijk, The Nedetherlands, pp. 263-267, 1972. [15] Olsen, R., "Observation of Differential Charging Effects on ATS-6," Journal of Geophysical Research, vol. 86, no. A8, pp. 6809-6819, August 1 1983. [16] McPherson, D. A., Cauffman, D. P. and Schober, W. R., "Spacecraft Charging at High Altitudes: SCATHA Satellite Program," Journal of Spacecraft and Rockets, vol. 12, no. 10, pp. 621-626, 1975, doi: 10.2514/3.57027. [17] Chopra, K. P., "Interactions of Rapidly Moving Bodies in Terrestrial Atmosphere," Reviews of Modern Physics, vol. 33, no. 2, pp. 153-189, 1961, doi: 10.1103/RevModPhys.33.153. [18] Grard, R. J. L., "Properties of the satellite photoelectron sheath derived from photoemission laboratory measurements," Journal of Geophysical Research, vol. 78, no. 16, pp. 2885-2906, 1973, doi: 10.1029/JA078i016p02885. [19] Feuerbacher, B. and Fitton, B., "Experimental Investigation of Photoemission from Satellite Surface Materials," Journal of Applied Physics, vol. 43, no. 4, pp. 1563-1572, 1972, doi: 10.1063/1.1661362. [20] Stakkestad, K. and Fennessey, R., "SCTHA Mission Termination Report," ed. NASA Technical Reports Server: NASA, 1993, pp. 453-469 [21] Garrett, H. and Whittlesey, A. C., Guide to Mitigating Spacecraft Charging Effects. Hoboken, N.J.: Wiley, 2012. [22] Amatucci, W. E., Koepke, M. E., Sheridan, T. E., Alport, M. J. and Carroll, J. J., "Self‐cleaning Langmuir probe," Review of Scientific Instruments, vol. 64, no. 5, pp. 1253-1256, 1993, doi: 10.1063/1.1144074. [23] Gomez, R., "Simulation and Optimization of ESA Designs for Space Plasma Missions," D. T. Young, Ed., ed: ProQuest Dissertations Publishing, 2011. [24] Escoubet, C. P., Pedersen, A., Schmidt, R. and Lindqvist, P.-A., "Density in the magnetosphere inferred from ISEE 1 spacecraft potential," Journal of Geophysical Research: Space Physics, vol. 102, no. A8, pp. 17595-17609, 1997, doi: 10.1029/97JA00290. 163 [25] Gurnett, D. A., Persoon, A. M., Randall, R. F., Odem, D. L., Remington, S. L., Averkamp, T. F., Debower, M. M., Hospodarsky, G. B., Huff, R. L., Kirchner, D. L., Mitchell, M. A., Pham, B. T., Phillips, J. R., Schintler, W. J., Sheyko, P. and Tomash, D. R., "The Polar plasma wave instrument," Space Science Reviews, vol. 71, no. 1-4, pp. 597-622, 1995, doi: 10.1007/BF00751343. [26] Gustafsson, G., BostrÖM, R., Holback, B., Holmgren, G., Lundgren, A., Stasiewicz, K., ÅHlÉN, L., Mozer, F. S., Pankow, D., Harvey, P., Berg, P., Ulrich, R., Pedersen, A., Schmidt, R., Butler, A., Fransen, A. W. C., Klinge, D., Thomsen, M., FÄLthammar, C. G., Lindqvist, P. A., Christenson, S., Holtet, J., Lybekk, B., Sten, T. A., Tanskanen, P., Lappalainen, K. and Wygant, J., "The Electric Field and Wave Experiment for the Cluster Mission," Space Science Reviews, vol. 79, no. 1, pp. 137-156, 1997, doi: 10.1023/A:1004975108657. [27] Bonnell, J. W., Mozer, F. S., Delory, G. T., Hull, A. J., Ergun, R. E., Cully, C. M., Angelopoulos, V. and Harvey, P. R., "The Electric Field Instrument (EFI) for THEMIS," Space Science Reviews, vol. 141, no. 1, pp. 303-341, 2008, doi: 10.1007/s11214-008-9469-2. [28] Wygant, J. R., Bonnell, J. W., Goetz, K., Ergun, R. E., Mozer, F. S., Bale, S. D., Ludlam, M., Turin, P., Harvey, P. R., Hochmann, R., Harps, K., Dalton, G., McCauley, J., Rachelson, W., Gordon, D., Donakowski, B., Shultz, C., Smith, C., Diaz-Aguado, M., Fischer, J., Heavner, S., Berg, P., Malsapina, D. M., Bolton, M. K., Hudson, M., Strangeway, R. J., Baker, D. N., Li, X., Albert, J., Foster, J. C., Chaston, C. C., Mann, I., Donovan, E., Cully, C. M., Cattell, C. A., Krasnoselskikh, V., Kersten, K., Brenneman, A. and Tao, J. B., "The Electric Field and Waves Instruments on the Radiation Belt Storm Probes Mission," Space Science Reviews, vol. 179, no. 1, pp. 183-220, 2013, doi: 10.1007/s11214-013-0013-7. [29] Andersson, L., Ergun, R. E., Delory, G. T., Eriksson, A., Westfall, J., Reed, H., McCauly, J., Summers, D. and Meyers, D., "The Langmuir Probe and Waves (LPW) Instrument for MAVEN," Space Science Reviews, vol. 195, no. 1, pp. 173-198, 2015, doi: 10.1007/s11214-015-0194-3. [30] Gurnett, D. A., Kurth, W. S., Kirchner, D. L., Hospodarsky, G. B., Averkamp, T. F., Zarka, P., Lecacheux, A., Manning, R., Roux, A., Canu, P., Cornilleau-Wehrlin, N., Galopeau, P., Meyer, A., Boström, R., Gustafsson, G., Wahlund, J. E., Åhlen, L., Rucker, H. O., Ladreiter, H. P., Macher, W., Woolliscroft, L. J. C., Alleyne, H., Kaiser, M. L., Desch, M. D., Farrell, W. M., Harvey, C. C., Louarn, P., Kellogg, P. J., Goetz, K. and Pedersen, A., "The Cassini Radio and Plasma Wave Investigation," Space Science Reviews, vol. 114, no. 1, pp. 395-463, 2004, doi: 10.1007/s11214- 004-1434-0. [31] Torbert, R. B., Russell, C. T., Magnes, W., Ergun, R. E., Lindqvist, P. A., LeContel, O., Vaith, H., Macri, J., Myers, S., Rau, D., Needell, J., King, B., Granoff, M., Chutter, M., Dors, I., Olsson, G., Khotyaintsev, Y. V., Eriksson, A., Kletzing, C. A., Bounds, S., Anderson, B., Baumjohann, W., Steller, M., Bromund, K., Le, G., Nakamura, R., Strangeway, R. J., Leinweber, H. K., Tucker, S., Westfall, J., Fischer, D., Plaschke, F., Porter, J. and Lappalainen, K., "The FIELDS Instrument Suite on MMS: Scientific Objectives, Measurements, and Data Products," Space Science Reviews, vol. 199, no. 1-4, p. 105, 2016. 164 [32] Guillemant, S., Maksimovic, M., Hilgers, A., Pantellini, F., Lamy, L., Louarn, P., Genot, V., Owen, C. J., Mateo-Velez, J.-C., Sarrailh, P., Hess, S. L. G. and Vecchio, A., "A Study of Solar Orbiter Spacecraft-Plasma Interactions Effects on Electric Field and Particle Measurements," IEEE Transactions on Plasma Science, vol. 45, no. 9, pp. 2578-2587, 2017, doi: 10.1109/TPS.2017.2731054. [33] Bale, S. D., Goetz, K., Harvey, P. R., Turin, P., Bonnell, J. W., Dudok de Wit, T., Ergun, R. E., Macdowall, R. J., Pulupa, M., Andre, M., Bolton, M., Bougeret, J. L., Bowen, T. A., Burgess, D., Cattell, C. A., Chandran, B. D. G., Chaston, C. C., Chen, C. H. K., Choi, M. K., Connerney, J. E., Cranmer, S., Diaz-Aguado, M., Donakowski, W., Drake, J. F., Farrell, W. M., Fergeau, P., Fermin, J., Fischer, J., Fox, N., Glaser, D., Goldstein, M., Gordon, D., Hanson, E., Harris, S. E., Hayes, L. M., Hinze, J. J., Hollweg, J. V., Horbury, T. S., Howard, R. A., Hoxie, V., Jannet, G., Karlsson, M., Kasper, J. C., Kellogg, P. J., Kien, M., Klimchuk, J. A., Krasnoselskikh, V. V., Krucker, S., Lynch, J. J., Maksimovic, M., Malaspina, D. M., Marker, S., Martin, P., Martinez-Oliveros, J., McCauley, J., McComas, D. J., McDonald, T., Meyer-Vernet, N., Moncuquet, M., Monson, S. J., Mozer, F. S., Murphy, S. D., Odom, J., Oliverson, R., Olson, J., Parker, E. N., Pankow, D., Phan, T., Quataert, E., Quinn, T., Ruplin, S. W., Salem, C., Seitz, D., Sheppard, D. A., Siy, A., Stevens, K., Summers, D., Szabo, A., Timofeeva, M., Vaivads, A., Velli, M., Yehle, A., Werthimer, D. and Wygant, J. R., "The FIELDS Instrument Suite for Solar Probe Plus," Space Science Reviews, vol. 204, no. 1-4, p. 49, 2016, doi: 10.1007/s11214-016-0244-5. [34] Whitman, E., "Parker Solar Probe, as seen in a cleanroom at Astrotech Space Operations in Titusville, Florida," ed: Credit: NASA/Johns Hopkins APL, 2018. [35] Mott-Smith, H. M. and Langmuir, I., "The theory of collectors in gaseous discharges," Physical Review, vol. 28, no. 4, pp. 727-763, 1926, doi: 10.1103/PhysRev.28.727. [36] Wang, J. and Hastings, D. E., "Ionospheric plasma flow over large high‐voltage space platforms. II: The formation and structure of plasma wake," Physics of Fluids B: Plasma Physics, vol. 4, no. 6, pp. 1615-1629, 1992, doi: 10.1063/1.860070. [37] Wang, J. and Hu, Y., "The Breakdown of the Fluid Approximation for Electrons in a Plasma Wake," Journal of Geophysical Research: Space Physics, vol. 123, no. 10, pp. 8797-8805, 2018, doi: 10.1029/2018JA025743. [38] Garrett, H. B., "The charging of spacecraft surfaces," Reviews of Geophysics, vol. 19, no. 4, pp. 577-616, 1981, doi: 10.1029/RG019i004p00577. [39] Hufner, Photoelectron Spectroscopy, Principles and Applications. New York: Springer, 2003. [40] Wooten, F., Optical Properties of Solids. New York: Academic Press, 1972. [41] Diaz-Aguado, M., Bonnell, J. W., Bale, S. D., Rezvani, S. J., Koshmak, K., Giglia, A., Nannarone, S. and Gruntman, M., "Experimental Investigation of Total Photoemission Yield from New 165 Satellite Surface Materials," AIAA Journal of Spacecraft and Rockets, vol. 56, no. 1, pp. 248-258, 2019, doi: 10.2514/1.A34245. [42] Prokopenko, S. M. L. and LaFroamboise, J. G., "High-Voltage Differential Charging of Geostationary Spacecraft," Journal of Geophysical Research, vol. 85, no. A8, pp. 4125-4131, 1980, doi: https://doi.org/10.1029/JA085iA08p04125. [43] Diaz-Aguado, M., Bonnell, J. W., Bale, S.D., Rezvani, S.J., Koshmak, K., Giglia, A., Nannarone, S., Gruntman, M. , "Experimental Investigation of Total Photoemission Yield from New Satellite Surface Materials," Accepted by the AIAA Journal of Spacecraft and Rockets, June 2018, 2018. [44] Sternovsky, Z., Chamberlin, P., Horanyi, M., Robertson, S. and Wang, X., "Variability of the lunar photoelectron sheath and dust mobility due to solar activity," Journal of Geophysical Research: Space Physics, vol. 113, no. 10, 2008, doi: 10.1029/2008JA013487. [45] Engwall, E., Eriksson, A. I. and Forest, J., "Wake formation behind positively charged spacecraft in flowing tenuous plasmas," Physics of Plasmas, vol. 13, no. 6, 2006, doi: 10.1063/1.2199207. [46] Guillemant, S., "Study and simulations of spacecraft/plasma interaction phenomena and their effects on low energy plasma measurements," Université Paul Sabatier-Toulouse III, 2014. [47] Marchand, R., Miyake, Y., Usui, H., Deca, J., Lapenta, G., Matéo-Vélez, J. C., Ergun, R. E., Sturner, A., Génot, V., Hilgers, A. and Markidis, S., "Cross-comparison of spacecraft-environment interaction model predictions applied to Solar Probe Plus near perihelion," Physics of Plasmas, vol. 21, no. 6, 2014, doi: 10.1063/1.4882439. [48] Shih, A., Yater, J., Hor, C. and Abrams, R., "Secondary electron emission studies," Applied Surface Science, vol. 111, pp. 251-258, 1997. [49] Hachenberg, O. and Brauer, W., "Secondary Electron Emission from Solids," Advances In Electronics And Electron Physics, vol. 11, pp. 413-499, 1959, doi: 10.1016/S0065-2539(08)60999- 3. [50] Katz, I., Parks, D. E., Mandell, M. J., Harvey, J. M., Wang, S. S. and Roche, J. C., "NASCAP, a Three-Dimensional Charging Analyzer Program for Complex Spacecraft," IEEE Transactions on Nuclear Science, vol. 24, no. 6, pp. 2276-2280, 1977, doi: 10.1109/TNS.1977.4329206. [51] Lai, S. T., "Spacecraft charging: incoming and outgoing electrons," CERN Yellow Report, vol. 2, pp. 165-168, 2013, doi: 10.5170/CERN-2013-002.165. [52] Diaz-Aguado, M. F., Bonnell, J. W., Bale, S. D., Christensen, J., Lundgreen, P., Lee, J., Dennison, J. R., Dekany, J., Wood, B. and Gruntman, M., "Experimental Investigation of the Secondary and 166 Backscatter Electron Emission from New Spacecraft Surface Materials," AIAA Journal of Spacecraft and Rockets, vol. TBD, no. TBD, 2020. [53] Warnecke, R., "Secondary Emission of Pure Metals," Journal de Physique, vol. 6, pp. 269-280, 1936. [54] Michizono, S., Saito, Y., Suharyanto, Y., Yamano, S. and Kobayashi, S., "Secondary electron emission of sapphire and anti-multipactor coatings at high temperature," Applied Surface Science, vol. 235, no. 1, pp. 227-230, 2004, doi: 10.1016/j.apsusc.2004.05.131. [55] Sternglass, E. J., "Backscattering of Kilovolt Electrons from Solids," Physical Review, vol. 95, no. 2, pp. 345-358, 07/15/ 1954. [56] Reimann, A. L., Thermionic emission. J. Wiley & sons, inc., 1934. [57] Modinos, A., "Theory of thermionic emission," in Surface Science Letters vol. 115, ed: Elsevier B.V., 1982, pp. A117-A117. [58] Richardson, O. W., "The Emission of Electrons from Tungsten at High Temperatures: An Experimental Proof that the Electric Current in Metals is Carried by Electrons," Science (New York, N.Y.), vol. 38, no. 967, p. 57, 1913, doi: 10.1126/science.38.967.57. [59] Fomenko, V. S., Handbook of Thermionic Properties. New York: Plenum Press Data Division, 1956. [60] Pedersen, A., Cattell, C., Fälthammar, C., Formisano, V., Lindqvist, P., Mozer, F. and Torbert, R., "Quasistatic electric field measurements with spherical double probes on the GEOS and ISEE satellites," Space Science Reviews, vol. 37, no. 3, pp. 269-312, 1984, doi: 10.1007/BF00226365. [61] Pedersen, A., "Solar wind and magnetosphere plasma diagnostics by spacecraft electrostatic potential measurements," Annales Geophysicae, vol. 13, no. 2, pp. 118-129, 1995, doi: 10.1007/s00585-995-0118-8. [62] Laakso, H., Aggson, T. and Pfaff, R., "Plasma gradient effects on double-probe measurements in the magnetosphere," Annales Geophysicae, vol. 13, no. 2, pp. 130-146, 1995, doi: 10.1007/s00585- 995-0130-z. [63] Cully, C. M., Ergun, R. E. and Eriksson, A. I., "Electrostatic structure around spacecraft in tenuous plasmas," Journal of Geophysical Research: Space Physics, vol. 112, no. A9, pp. n/a-n/a, 2007, doi: 10.1029/2007JA012269. 167 [64] Garrett, D. H. a. H., Spacecraft-Environment Interactions (Cambridge atmospheric and space science series). New York: Cambridge University Press, 1996. [65] Gustafsson, G., BostrÖM, R., Holback, B., Holmgren, G., Lundgren, A., Stasiewicz, K., ÅHlÉN, L., Mozer, F. S., Pankow, D., Harvey, P., Berg, P., Ulrich, R., Pedersen, A., Schmidt, R., Butler, A., Fransen, A. W. C., Klinge, D., Thomsen, M., FÄLthammar, C. G., Lindqvist, P. A., Christenson, S., Holtet, J., Lybekk, B., Sten, T. A., Tanskanen, P., Lappalainen, K., Wygant, J., Rymd- och, p., Skolan för elektro- och, s., Tidigare, I., Alfvénlaboratoriet and Kth, "The Electric Field and Wave Experiment for the Cluster Mission," Space Science Reviews, vol. 79, no. 1, pp. 137-156, 1997, doi: 10.1023/A:1004975108657. [66] Andersson, L., Ergun, R. E., Delory, G. T., Eriksson, A., Westfall, J., Reed, H., McCauly, J., Summers, D., Meyers, D., Institutet för rymdfysik, U., Uppsala, u., Fysiska, s. and Teknisk- naturvetenskapliga, v., "The Langmuir Probe and Waves (LPW) Instrument for MAVEN," Space Science Reviews, vol. 195, no. 1, pp. 173-198, 2015, doi: 10.1007/s11214-015-0194-3. [67] Torbert, R. B., Russell, C. T., Magnes, W., Ergun, R. E., Lindqvist, P. A., LeContel, O., Vaith, H., Macri, J., Myers, S., Rau, D., Needell, J., King, B., Granoff, M., Chutter, M., Dors, I., Olsson, G., Khotyaintsev, Y. V., Eriksson, A., Kletzing, C. A., Bounds, S., Anderson, B., Baumjohann, W., Steller, M., Bromund, K., Le, G., Nakamura, R., Strangeway, R. J., Leinweber, H. K., Tucker, S., Westfall, J., Fischer, D., Plaschke, F., Porter, J., Lappalainen, K., Institutet för rymdfysik, U., Teknisk-naturvetenskapliga, v., Uppsala, u. and Fysiska, s., "The FIELDS Instrument Suite on MMS: Scientific Objectives, Measurements, and Data Products," Space Science Reviews, vol. 199, no. 1-4, p. 105, 2016. [68] Vaivads, A., Eriksson, A. I., André, M., Blomberg, L. G., Wahlund, J. E., Bale, S. D., Rymd- och, p., Skolan för elektro- och, s. and Kth, "Low-frequency electric field and density fluctuation measurements on Solar Orbiter," Advances in Space Research, vol. 39, no. 9, pp. 1502-1509, 2007, doi: 10.1016/j.asr.2006.10.011. [69] Bale, S. D., Goetz, K., Harvey, P. R., Turin, P., Bonnell, J. W., Dudok de Wit, T., Ergun, R. E., Macdowall, R. J., Pulupa, M., Andre, M., Bolton, M., Bougeret, J. L., Bowen, T. A., Burgess, D., Cattell, C. A., Chandran, B. D. G., Chaston, C. C., Chen, C. H. K., Choi, M. K., Connerney, J. E., Cranmer, S., Diaz-Aguado, M., Donakowski, W., Drake, J. F., Farrell, W. M., Fergeau, P., Fermin, J., Fischer, J., Fox, N., Glaser, D., Goldstein, M., Gordon, D., Hanson, E., Harris, S. E., Hayes, L. M., Hinze, J. J., Hollweg, J. V., Horbury, T. S., Howard, R. A., Hoxie, V., Jannet, G., Karlsson, M., Kasper, J. C., Kellogg, P. J., Kien, M., Klimchuk, J. A., Krasnoselskikh, V. V., Krucker, S., Lynch, J. J., Maksimovic, M., Malaspina, D. M., Marker, S., Martin, P., Martinez-Oliveros, J., McCauley, J., McComas, D. J., McDonald, T., Meyer-Vernet, N., Moncuquet, M., Monson, S. J., Mozer, F. S., Murphy, S. D., Odom, J., Oliverson, R., Olson, J., Parker, E. N., Pankow, D., Phan, T., Quataert, E., Quinn, T., Ruplin, S. W., Salem, C., Seitz, D., Sheppard, D. A., Siy, A., Stevens, K., Summers, D., Szabo, A., Timofeeva, M., Vaivads, A., Velli, M., Yehle, A., Werthimer, D., Wygant, J. R., Institutet för rymdfysik, U., Uppsala, u., Fysiska, s. and Teknisk-naturvetenskapliga, v., "The FIELDS Instrument Suite for Solar Probe Plus," Space Science Reviews, vol. 204, no. 1- 4, p. 49, 2016, doi: 10.1007/s11214-016-0244-5. 168 [70] Sarno‐Smith, L. K., Larsen, B. A., Skoug, R. M., Liemohn, M. W., Breneman, A., Wygant, J. R. and Thomsen, M. F., "Spacecraft surface charging within geosynchronous orbit observed by the Van Allen Probes," Space Weather, vol. 14, no. 2, pp. 151-164, 2016, doi: 10.1002/2015SW001345. [71] ed, 2016. [72] Fowler, R. H., "The Analysis of Photoelectric Sensitivity Curves for Clean Metals at Various Temperatures," Physical Review, vol. 38, no. 1, pp. 45-56, 07/01/ 1931. [73] Rentschler, H. C., Henry, D. E. and Smith, K. O., "Photoelectric Emission from Different Metals," Review of Scientific Instruments, vol. 3, no. 12, pp. 794-802, 1932, doi: 10.1063/1.1748900. [74] Langmuir, I., "The Effect of Space Charge and Residual Gases on Thermionic Currents in High Vacuum," Physical Review, vol. 2, no. 6, pp. 450-486, 1913, doi: 10.1103/PhysRev.2.450. [75] Westlinder, J., Sjöblom, G. and Olsson, J., "Variable work function in MOS capacitors utilizing nitrogen-controlled TiNx gate electrodes," Microelectronic Engineering, vol. 75, no. 4, pp. 389- 396, 11// 2004, doi: https://doi.org/10.1016/j.mee.2004.07.061. [76] Hinteregger, H. E. and Watanabe, K., "Photoelectric Cells for the Vacuum Ultraviolet," Journal of the Optical Society of America, vol. 43, no. 7, pp. 604-608, 1953, doi: 10.1364/JOSA.43.000604. [77] Gineste, T., Belhaj, M., Teyssedre, G. and Puech, J., "Investigation of the electron emission properties of silver: From exposed to ambient atmosphere Ag surface to ion-cleaned Ag surface," Applied Surface Science, vol. 359, pp. 398-404, 2015, doi: 10.1016/j.apsusc.2015.10.121. [78] Davies, R. E. and Dennison, J. R., "Evolution of Secondary Electron Emission Characteristics of Spacecraft Surfaces," Journal of Spacecraft and Rockets, vol. 34, no. 4, pp. 571-574, 1997, doi: 10.2514/2.3252. [79] Lai, S. T., "The Role of Surface Condition in the Yields of Secondary Electrons, Backscattered Electrons, and Photoelectrons From Spacecraft," Plasma Science, IEEE Transactions on, vol. 41, no. 12, pp. 3492-3497, 2013, doi: 10.1109/TPS.2013.2282372. [80] Seiler, H., "Secondary electron emission in the scanning electron microscope," Journal of Applied Physics, vol. 54, pp. R1-R18, 1983. [81] Dennison, J. R., "Dynamic Interplay Between Spacecraft Charging, Space Environment Interactions, and Evolving Materials," Plasma Science, IEEE Transactions on, vol. 43, no. 9, pp. 2933-2940, 2015, doi: 10.1109/TPS.2015.2434947. 169 [82] Brodu, E., "Thermal radiative properties and behavior of refractory metals, highly textured metallic coatings and pyrolytic boron nitride on C/C composite for the Solar Probe Plus mission," 2014. [83] Juenker, D. W., Waldron, J. P. and Jaccodine, R. J., "Vectorial Photoelectric Effect in Clean Molybdenum," Journal of the Optical Society of America, vol. 54, no. 2, pp. 216-223, 1964, doi: 10.1364/JOSA.54.000216. [84] Heroux, L., Manson, J. F., Hinteregger, H. E. and McMahon, W. J., "Photoelectric Yields for Oblique Incidence of Extreme Ultraviolet Radiation," Journal of the Optical Society of America, vol. 55, no. 1, pp. 103-104, 1965, doi: 10.1364/JOSA.55.000103. [85] Meier, R., "Ultraviolet spectroscopy and remote sensing of the upper atmosphere," Space Science Reviews, vol. 58, no. 1, pp. 1-185, 1991, doi: 10.1007/BF01206000. [86] White, O. R., Rottman, G. J. and Livingston, W. C., "Estimation of the solar Lyman alpha flux from ground based measurements of the Ca II K line," Geophysical Research Letters, vol. 17, no. 5, 1990, doi: 10.1029/GL017i005p00575. [87] Lean, J. L., and A. Skumanich, "Variability of the Lyman alpha flux with solar activity," Journal of Geophysical Research: Space Physics, vol. 88, no. A7, pp. 5751-5759, 1983, doi: doi:10.1029/JA088iA07p05751. [88] Morton, D. C. W., Kenneth G., "The Solar Lyman-Alpha Emission Line," Astrophysical Journal, vol. 133, 1961, doi: 10.1086/147062. [89] Olsen, R., "A threshold effect for spacecraft charging," Journal of Geophysical Research, vol. 88, pp. 493-499, 1983. [90] Whipple, E. C., Jr., "The equilibrium electric potential of a body in the upper atmosphere and in interplanetary space - NASA-TM-X-55368," ed: Sponsoring Organization: NASA Goddard Space Flight Center, 1965. [91] Katz, I., Mandell, M. J., Jongeward, G. A. and Gussenhoven, M. S., "The Importance of Accurate Secondary Electron Yields in Modeling Spacecraft Charging," ed. La Jolla, C. A.: S-Cubed, 1986. [92] Dennison, J. R., Hoffmann, R. C. and Abbott, J., "Triggering Threshold Spacecraft Charging with Changes in Electron Emission from Materials," in 45th AIAA Aerospace Sciences Meeting and Exhibit, ed: American Institute of Aeronautics and Astronautics, 2007. [93] Rubin, A. G., Garrett, H. B. and Wendel, A. H., "Spacecraft Charging on ATS-5," M. A. Air Force Geophysics Lab Hanscom Afb, Ed., ed, 1980. 170 [94] Reagan, J., Nightingale, R., Gaines, E., Meyerott, R. and Imhof, W., "Role of energetic particles in charging/discharging of spacecraft dielectrics," J. Reagan, Ed., ed, 1981. [95] Mullen, E. G., Gussenhoven, M. S., Hardy, D. A., Aggson, T. A., Ledley, B. G. and Whipple, E., "SCATHA survey of high‐level spacecraft charging in sunlight," Journal of Geophysical Research: Space Physics, vol. 91, no. A2, pp. 1474-1490, 1986, doi: 10.1029/JA091iA02p01474. [96] Mandell, M. J., NASCAP programmer's reference manual [microform] / M.J. Mandell, P.P. Stannard, and I. Katz. Washington, DC] : [Springfield, Va.: [Washington, DC] : National Aeronautics and Space Administration ; [Springfield, Va. : National Technical Information Service, distributor, 1993], 1993. [97] Thiebault, B., Mateo Velez, J-C. Forest, J., Sarrailh, P., "SPIS 5.1 User Manual," 2013. [98] Christensen, J., "Electron Yield Measurements of High-Yield, Low-Conductivity Dielectric Materials," J. R. Dennison, F. Edwards and D. M. Riffe, Eds., ed: ProQuest Dissertations Publishing, 2017. [99] Vaivads, A., Eriksson, A. I., André, M., Blomberg, L. G., Wahlund, J. E. and Bale, S. D., "Low- frequency electric field and density fluctuation measurements on Solar Orbiter," Advances in Space Research, vol. 39, no. 9, pp. 1502-1509, 2007, doi: 10.1016/j.asr.2006.10.011. [100] Cimino, R., Commisso, M., Grosso, D. R., Demma, T., Baglin, V., Flammini, R. and Larciprete, R., "Nature of the decrease of the secondary-electron yield by electron bombardment and its energy dependence," Physical review letters, vol. 109, no. 6, p. 064801, 2012, doi: 10.1103/PhysRevLett.109.064801. [101] Chang, W. Y., Dennison, J. R., Kite, J. and Davies, R. E., "Effects of Evolving Surface Contamination on Spacecraft Charging," Proceedings of the 38th American Institute of Aeronautics and Astronautics Meeting on Aerospace Sciences, vol. Paper AIAA-2000-0868, 2000. [102] Reimer, L., Scanning Electron Microscopy: Physics of Image Formation and Microanalysis, 2nd ed. Berlin, 1998. [103] Reimer, L., "Scanning Electron Microscopy: Physics of Image Formation and Microanalysis," vol. 45, ed. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. [104] Lundgreen, P. and Dennison, J. R., "Strategies for Determining Electron Yield Material Parameters for Spacecraft Charge Modeling," in Applied Space Environments Conference, ed. Los Angeles, CA: AIAA, 2019. [105] Space Engineering: Multipaction Design and Test, Standard, ESA-ESTCE, ESA-ESTCE, Standardization, E. C. f. S., 2013. 171 [106] Chang, W. Y., Dennison, J., Nickles, N. and Davies, R. E., "Utah State University Ground-based Test Facility for Study of Electronic Properties of Spacecraft Materials," in Proceedings of the 6th Spacecraft Charging Technology Conference, 9-2000 ed. Air Force Research Laboratory Science Center, Hanscom Air Force Base, MA, 2000, pp. 73-77. [107] Hoffmann, R. C., "Electron-induced electron yields of uncharged insulating materials," 2010. [108] Dennison, J., J. Christensen, J. Dekany, C.Thomson, N. Nickles, R.E. Davies, M. Belhaj, K. Toyoda, A. R. Khan, K. Kawasaki, S. Inoue, . Montero, M. E. Dávila and L.Olano, "Absolute Electron Emission Calibration: Round Robin Tests of Au and Polyimide," in Proceedings of the 14th Spacecraft Charging Technology Conference, ed. Noordwijk, Netherlands, Space Research and Technology Centre of the European Space Agency (ESA/ESTEC),: AIAA, 2016. [109] Hoffmann, R. C. and Dennison, J. R., "Methods to Determine Total Electron-Induced Electron Yields Over Broad Range of Conductive and Nonconductive Materials," IEEE Transactions on Plasma Science, vol. 40(2), pp. 298-304, 2012 2012, doi: 10.1109/TPS.2011.2178251. [110] Hachenberg, O. and Brauer, W., "Secondary Electron Emission from Solids," in Advances in Electronics and Electron Physics vol. 11, L. Marton and C. Marton, Eds., ed: Academic Press, 1959, pp. 413-499. [111] Chung, M. S. and Everhart, T. E., "Simple calculation of energy distribution of low‐energy secondary electrons emitted from metals under electron bombardment," Journal of Applied Physics, vol. 45, no. 2, pp. 707-709, 1974, doi: 10.1063/1.1663306. [112] Michaelson, H. B., "Work Functions of the Elements," Journal of Applied Physics, vol. 21, no. 6, pp. 536-540, 1950, doi: 10.1063/1.1699702. [113] Brodu, E., "Thermal radiative properties and behavior of refractory metals, highly textured metallic coatings and pyrolytic boron nitride on C/C composite for the Solar Probe Plus mission," Ecole doctorale Energie Environment, Universite de Perpignan, Perpignan, 2014. [114] Wilson, G., Starley, A. and Dennison, J. R., "Electron Range Computational Tool for Arbitrary Materials Over a Wide Energy Range," in 15th Spacecraft Charging Tech. Conf., ed. Kobe, Japan, 2018. [115] G. Wilson, A. S., L. Phillipps and J. R. Dennison, "A Predictive Range Expression: Applications and Limitations," IEEE Trans. on Plasma Sci., vol. TBD, no. TBD, p. TBD, 2019. [116] Dionne, G. F., "Origin of secondary‐electron‐emission yield‐curve parameters," Journal of Applied Physics, vol. 46, no. 8, pp. 3347-3351, 1975, doi: 10.1063/1.322061. 172 [117] Phil Lundgreen, J. C., and JR Dennison, "Comparison of Models for Materials Parameters Used in Spacecraft Charging Codes," IEEE Trans. on Plasma Sci., vol. TBD, p. TBD, 2019. [118] Sims, A. J., "Electrostatic Charging of Spacecraft in Geosynchronous Orbit," F. Defence Research Agency, Ed., ed, 1992. [119] Nickles, N., "The role of bandgap in the secondary electron emission of small bandgap semiconductors: Studies of graphitic carbon," J. R. Dennison, Ed., ed: ProQuest Dissertations Publishing, 2002. [120] Baroody, E. M., "A theory of secondary electron emission from metals," Physical Review, vol. 78, no. 6, pp. 780-787, 1950, doi: 10.1103/PhysRev.78.780. [121] Balcon, N., Payan, D., Belhaj, M., Tondu, T. and Inguimbert, V., "Secondary Electron Emission on Space Materials: Evaluation of the Total Secondary Electron Yield From Surface Potential Measurements," Plasma Science, IEEE Transactions on, vol. 40, no. 2, pp. 282-290, 2012, doi: 10.1109/TPS.2011.2172636. [122] Wang, J., Pu Wang, M., Belhaj, J. C. M. and Velez, J. C. M., "Modeling Facility Effects on Secondary Electron Emission Experiment," Plasma Science, IEEE Transactions on, vol. 40, no. 10, pp. 2773-2780, 2012, doi: 10.1109/TPS.2012.2211041. [123] Matthew Robertson, J. C., Greg Wilson and JR Dennison, "Electron Yield of a Carbon-composite Nanodielectric," in American Physical Society Four Corners Meeting, ed. Colorado State University, Fort Collins, CO, 2017. [124] Wilson, G., Robertson, M., Lee, J. and Dennison, J., "Electron Yield Measurements of Multilayer Conductive Materials," 2018. [125] Christensen, J., "Electron Yield Measurements of High-Yield, Low-Conductivity Dielectric Materials," Masters Thesis, Physics, Utah State University, Logan, UT, 2017. [126] Ahearn, A. J., "The Emission of Secondary Electrons from Tungsten," Physical Review, vol. 38, no. 10, pp. 1858-1870, 1931, doi: 10.1103/PhysRev.38.1858. [127] Reimer, J. A., Vaughan, R. W. and Knights, J. C., "Proton Magnetic Resonance Spectra of Plasma- Deposited Amorphous Si: H Films," Physical Review Letters, vol. 44, no. 3, pp. 193-196, 1980, doi: 10.1103/PhysRevLett.44.193. [128] Petry, R. L., "Secondary Electron Emission from Tungsten, Copper and Gold," Physical Review, vol. 28, no. 2, pp. 362-366, 1926, doi: 10.1103/PhysRev.28.362. 173 [129] Krefft, H. E., "Critical primary velocities in the secondary electron emission of tungsten," Journal of the Franklin Institute, vol. 204, no. 4, pp. 537-539, 1927, doi: 10.1016/S0016-0032(27)91436- 7. [130] Whetten, N. R., "Cleavage in High Vacuums of Alkali Halide Single Crystals—Secondary Electron Emission," Journal of Applied Physics, vol. 35, no. 11, pp. 3279-3282, 1964, doi: 10.1063/1.1713210. [131] Lundgreen, P. and Dennison, J. R., "An analysis of Variations in Published Secondary Electron Yield Measurements of Copper," in Four Corner Section Meeting of the American Physical Societry, ed. Salt Lake City, UT, 2016. [132] McDonnell, L., Powell, B. D. and Woodruff, D. P., "Temperature dependent peaks in secondary electron emission spectra," Surface Science, vol. 40, no. 3, pp. 669-682, 1973, doi: 10.1016/0039- 6028(73)90151-9. [133] Gonzalez, L. A., Angelucci, M., Larciprete, R. and Cimino, R., "The secondary electron yield of noble metal surfaces," AIP Advances, vol. 7, no. 11, 2017, doi: 10.1063/1.5000118. [134] Patino, M. I., Wirz, R. E., Raitses, Y. and Koel, B. E., "Angular, temperature, and impurity effects on secondary electron emission from Ni(110)," Journal of Applied Physics, vol. 124, no. 9, 2018, doi: 10.1063/1.5025344. [135] Donnegan, M. M., Davis, V. A. and Mandell, M. J., "Surface Charging Predictions for Solar Probe Plus," in Spacecraft Charging Technology Conference vol. 134, ed. Pasadena, 2014. [136] Birdsall, C. K. and Langdon, A. B., Plasma Physics via Computer Simulation. New York: Taylor & Francis, 2005. [137] Forest, J., Eliasson, L. and Hilgers, A., "A new spacecraft plasma interactions simulation software, PicUp3D /Spis," J. Forest, Ed., ed, 2001, pp. 515-520. [138] Hilgers, A., Clucas, S., Thiebault, B., Roussel, J. F., Mateo-Velez, J. C., Forest, J. and Rodgers, D., "Modeling of Plasma Probe Interactions With a PIC Code Using an Unstructured Mesh," IEEE Transactions on Plasma Science, vol. 36, no. 5, pp. 2319-2323, 2008, doi: 10.1109/TPS.2008.2003360. [139] Roussel, J. F., Rogier, F., Dufour, G., Mateo-Velez, J. C., Forest, J., Hilgers, A., Rodgers, D., Girard, L. and Payan, D., "SPIS Open-Source Code: Methods, Capabilities, Achievements, and Prospects," IEEE Transactions on Plasma Science, vol. 36, no. 5, pp. 2360-2368, 2008, doi: 10.1109/TPS.2008.2002327. 174 [140] Hosoda, S., Muranaka, T., Kuninaka, H., Kim, J., Hatta, S., Kurahara, N., Cho, M., Ueda, H., Koga, K. and Goka, T., "Laboratory Experiments for Code Validation of Multiutility Spacecraft Charging Analysis Tool (MUSCAT)," IEEE Transactions on Plasma Science, vol. 36, no. 5, pp. 2350-2359, 2008, doi: 10.1109/TPS.2008.2003973. [141] Muranaka, T., Hosoda, S., Kim, J.-H., Hatta, S., Ikeda, K., Hamanaga, T., Cho, M., Usui, H., Ueda, H., Koga, K. and Goka, T., "Development of Multi-Utility Spacecraft Charging Analysis Tool (MUSCAT)," IEEE Transactions on Plasma Science, vol. 36, no. 5, pp. 2336-2349, 2008, doi: 10.1109/TPS.2008.2003974. [142] Mengu, C., Sumida, T., Masui, H., Toyoda, K., Jeong-Ho, K., Hatta, S., Wong, F. K. and Bao, H., "Spacecraft Charging Analysis of Large GEO Satellites Using MUSCAT," IEEE Transactions on Plasma Science, vol. 40, no. 4, pp. 1248-1256, 2012, doi: 10.1109/TPS.2012.2187074. [143] Halekas, J. S., Delory, G. T., Lin, R. P., Stubbs, T. J. and Farrell, W. M., "Lunar Prospector observations of the electrostatic potential of the lunar surface and its response to incident currents," Journal of Geophysical Research: Space Physics, vol. 113, no. A9, 2008, doi: 10.1029/2008ja013194. [144] Leitner, M., Vörös, Z. and Leubner, M. P., "Introducing log‐kappa distributions for solar wind analysis," Journal of Geophysical Research: Space Physics, vol. 114, no. A12, pp. n/a-n/a, 2009, doi: 10.1029/2009JA014476. [145] Maksimovic, M., Zouganelis, I., Chaufray, J. Y., Issautier, K., Scime, E. E., Littleton, J. E., Marsch, E., McComas, D. J., Salem, C., Lin, R. P. and Elliott, H., "Radial evolution of the electron distribution functions in the fast solar wind between 0.3 and 1.5 AU," Journal of Geophysical Research: Space Physics, vol. 110, no. 9, p. <xocs:firstpage xmlns:xocs=""/>, 2005, doi: 10.1029/2005JA011119. [146] Gloeckler, G. and Fisk, L. A., "Anisotropic beams of energetic particles upstream from the termination shock of the solar wind," The Astrophysical Journal, vol. 648, no. 1, pp. L63-L66, 2006, doi: 10.1086/507841. [147] Pierrard, V. and Lazar, M., "Kappa Distributions: Theory and Applications in Space Plasmas," Solar Physics, vol. 267, no. 1, pp. 153-174, 2010, doi: 10.1007/s11207-010-9640-2. [148] Lin, Y. and Joy, D. C., "A new examination of secondary electron yield data," Surface and Interface Analysis, vol. 37, no. 11, pp. 895-900, 2005, doi: 10.1002/sia.2107. [149] Langmuir, I., "The Interaction of Electron and Positive Ion Space Charges in Cathode Sheaths," Physical Review, vol. 33, no. 6, pp. 954-989, 1929, doi: 10.1103/PhysRev.33.954. [150] Guthrie, A., "The characteristics of electrical discharges in magnetic fields," R. K. Wakerling, Ed., 1st ed. ed. New York: McGraw-Hill, 1949. 175 [151] Crawford, F. W. and Cannara, A. B., "Structure of the Double Sheath in a Hot‐Cathode Plasma," Journal of Applied Physics, vol. 36, no. 10, pp. 3135-3141, 1965, doi: 10.1063/1.1702938. [152] Prewett, P. D. and Allen, J. E., "The Double Sheath Associated with a Hot Cathode," Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990), vol. 348, no. 1655, pp. 435-446, 1976, doi: 10.1098/rspa.1976.0048. [153] Ketsdever, A. and Micci, M., Micropropulsion for Small Spacecraft. Reston: American Institute of Aeronautics and Astronautics, 2000. [154] Wang, J. and Lai, S. T., "Virtual Anode in Ion Beam Emissions in Space: Numerical Simulations," Journal of Spacecraft and Rockets, vol. 34, no. 6, pp. 829-836, 1997, doi: 10.2514/2.3295. [155] Kasper, J. C., Bale, S. D., Belcher, J. W., Berthomier, M., Case, A. W., Chandran, B. D. G., Curtis, D. W., Gallagher, D., Gary, S. P., Golub, L., Halekas, J. S., Ho, G. C., Horbury, T. S., Hu, Q., Huang, J., Klein, K. G., Korreck, K. E., Larson, D. E., Livi, R., Maruca, B., Lavraud, B., Louarn, P., Maksimovic, M., Martinovic, M., McGinnis, D., Pogorelov, N. V., Richardson, J. D., Skoug, R. M., Steinberg, J. T., Stevens, M. L., Szabo, A., Velli, M., Whittlesey, P. L., Wright, K. H., Zank, G. P., Macdowall, R. J., McComas, D. J., McNutt, R. L., Pulupa, M., Raouafi, N. E. and Schwadron, N. A., "Alfvénic velocity spikes and rotational flows in the near-Sun solar wind," Nature, vol. 576, no. 7786, pp. 228-231, 2019, doi: 10.1038/s41586-019-1813-z. [156] Bale, S. D., Badman, S. T., Bonnell, J. W., Bowen, T. A., Burgess, D., Case, A. W., Cattell, C. A., Chandran, B. D. G., Chaston, C. C., Chen, C. H. K., Drake, J. F., de Wit, T. D., Eastwood, J. P., Ergun, R. E., Farrell, W. M., Fong, C., Goetz, K., Goldstein, M., Goodrich, K. A., Harvey, P. R., Horbury, T. S., Howes, G. G., Kasper, J. C., Kellogg, P. J., Klimchuk, J. A., Korreck, K. E., Krasnoselskikh, V. V., Krucker, S., Laker, R., Larson, D. E., Macdowall, R. J., Maksimovic, M., Malaspina, D. M., Martinez-Oliveros, J., McComas, D. J., Meyer-Vernet, N., Moncuquet, M., Mozer, F. S., Phan, T. D., Pulupa, M., Raouafi, N. E., Salem, C., Stansby, D., Stevens, M., Szabo, A., Velli, M., Woolley, T. and Wygant, J. R., "Highly structured slow solar wind emerging from an equatorial coronal hole," Nature, vol. 576, no. 7786, pp. 237-242, 2019, doi: 10.1038/s41586- 019-1818-7. [157] McComas, D. J., Christian, E. R., Cohen, C. M. S., Cummings, A. C., Davis, A. J., Desai, M. I., Giacalone, J., Hill, M. E., Joyce, C. J., Krimigis, S. M., Labrador, A. W., Leske, R. A., Malandraki, O., Matthaeus, W. H., McNutt, R. L., Mewaldt, R. A., Mitchell, D. G., Posner, A., Rankin, J. S., Roelof, E. C., Schwadron, N. A., Stone, E. C., Szalay, J. R., Wiedenbeck, M. E., Bale, S. D., Kasper, J. C., Case, A. W., Korreck, K. E., Macdowall, R. J., Pulupa, M., Stevens, M. L. and Rouillard, A. P., "Probing the energetic particle environment near the Sun," Nature, vol. 576, no. 7786, pp. 223-227, 2019, doi: 10.1038/s41586-019-1811-1. [158] Olson, J., Brenning, N., Wahlund, J. E. and Gunell, H., "On the interpretation of Langmuir probe data inside a spacecraft sheath," Review of Scientific Instruments, vol. 81, no. 10, 2010, doi: 10.1063/1.3482155.

Abstract (if available)

Abstract New space environments are encountered as spacecraft reach farther into our solar system and beyond. FIELDS, a Parker Solar Probe (PSP) mission instrument launched in 2018, is being exposed to high never experienced temperatures and new plasma environments. This new environment and its interaction with the spacecraft and FIELDS instruments were studied, including the charging of spacecraft surfaces and of FIELDS sensors. These floating potentials are determined by the current balance of arriving and departing electrons, ions, and photons. ❧ All environmental and bias current sources were studied to obtain better FIELDS scientific measurements. The currents include photocurrent, ambient electron current, secondary electron (SE) current, backscattered secondary electron (BSE) current, ambient ion current, bias current and thermionic current. The theory of the ambient electron and ion, thermionic current and bias currents is discussed. Photoemission, SE and BSE theory and testing methods and results are described for samples of the new spacecraft materials used on PSP, which include new analytical fits and calculations. Finally, the charging of the PSP spacecraft and FIELDS instrument were modeled using Spacecraft Interaction Plasma Software (SPIS), a three-dimension particle in cell (PIC) self-contained code, and compared with flight results. ❧ Electron photoemission influences spacecraft surface potentials and the surrounding plasma, and many modern spacecrafts utilize new uncharacterized materials, leading to uncertainties in surface charging and plasma environments around those spacecrafts. The angle dependent photoemission properties were measured for Niobium C103 alloy, Molybdenum TZM alloy, Tantalum Tungsten alloy, Elgiloy, graphite lubricant epoxy (DAG-213®) and Titanium Nitride at the Bending for Emission Absorption and Reflectivity (BEAR) beamline. The properties of Tungsten were also studied to verify the method with past data. The materials were readied as spacecraft flight materials and annealed to predicted peak flight temperatures. Results are presented for the photoelectric threshold and photoelectron yield for photon energies up to 30eV. The work function was also found for each material tested. An analytical equation was then used to fit the normal photoelectron yield for each material to help obtain photocurrents, which were calculated assuming solar illumination at 1 AU at normal incidence. ❧ In addition to photoemission, SE and BSE also influence spacecraft surface potentials and the surrounding plasma. SE and BSE often play a significant role in that current balance, and so knowledge of the SE and BSE fluxes from exposed surfaces is crucial in determining those floating potentials, especially in eclipse and for surfaces not exposed to the Sun. The yield properties for 10eV-5keV incident electron energies for all samples were measured. Both unannealed and annealed states were tested, except DAG-213®, which was only tested annealed. Standard three-parameter and four-parameter models was used to fit the BSE and SE yield data, respectively. The emitted electron energy distributions were also obtained and fit with a Chung-Everhart model for SE and a Gaussian function for BSE. The SE and BSE currents densities were calculated for different ambient plasma conditions, including at Geosynchronous Earth Orbit (GEO), in the magnetosheath, and in the solar wind at heliocentric distances from 1AU to 9.5 solar radii (0.044 AU) away from the Sun. For ready reference, the normalized primary electron, SE and BSE current densities versus ambient electron temperature were computed and plotted for Maxwellian distributions having temperatures from 1 eV to 8 keV for each of the tested materials. ❧ With the photocurrent, SE and BSE new information of the spacecraft samples, the charging of the PSP spacecraft and FIELDS electric antennas were modeled using SPIS. The model was used to find the floating potentials of the spacecraft and FIELDS antennas at different distances from the Sun (from 1AU to 0.046AU). At larger distances from the Sun, the spacecraft charges negatively as the Thermal Protection System (TPS) shield is insulative at low temperatures. As the spacecraft approaches the Sun, the temperature of the TPS increases, the resistance between it and the spacecraft drops, and its photoemission increases, driving the spacecraft more positive. At the same time, an electrostatic barrier forms near the illuminated surface of the TPS and reflects the photoelectrons back leading to negative charging of some surfaces. The FIELDS antennas charge positively at all distances modeled without bias potentials. Our SPIS modeling relied on material properties of new spacecraft materials that we had obtained in previous work. As the spacecraft nears the Sun at 0.046AU, temperatures reach ∼1600K, where the thermionic current could be in the same order of magnitude as the dominating photocurrent. The effect of voltage biasing between the antenna, its shield, and the spacecraft on the current balance of each surface was investigated. The model data was reduced to I-V curves to find saturation photocurrents (analysis results 52µA versus flight results 54-72 µA), and sheath resistances (analysis results of 325 kΩ versus flight results of 51 kΩ).

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Creator Diaz-Aguado Robison, Millan Fernando (author)

Core Title The space environment near the Sun and its effects on Parker Solar Probe spacecraft and FIELDS instrumentation

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Astronautical Engineering

Publication Date 06/26/2021

Defense Date 03/24/2020

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

Tag OAI-PMH Harvest,photoemission,plasma environment,secondary electron emission,spacecraft charging,spacecraft charging model

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Gruntman, Mike (committee chair), Bale, Stuart (committee member), Bonnell, John (committee member), Nakano, Aiichiro (committee member), Wang, Joseph (committee member)

Creator Email diazagua@usc.edu,mfdiazaguado@hotmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-322325

Unique identifier UC11665929

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Legacy Identifier etd-DiazAguado-8624.pdf

Dmrecord 322325

Document Type Dissertation

Rights Diaz-Aguado Robison, Millan Fernando

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA