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Numerical and experimental investigations of dust-plasma-asteroid interactions

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Numerical and experimental investigations of dust-plasma-asteroid interactions

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Content NUMERICALANDEXPERIMENTALINVESTIGATIONSOFDUST-PLASMA-ASTEROID INTERACTIONS by WilliamYu ADissertationPresentedtothe FACULTYOFTHEGRADUATESCHOOL UNIVERSITYOFSOUTHERNCALIFORNIA InPartialFulfillmentofthe RequirementsfortheDegree DOCTOROFPHILOSOPHY (ASTRONAUTICALENGINEERING) August2018 Copyright 2018 WilliamYu Dedication ...To my family and friends who supported me ii Acknowledgements TheroadtoearningaPhDisstrifewithmanybumps,buttheculminationofallthehardworkand knowledge have been rewarding and empowering for developing my critical thinking skills and application of basic concepts to complex problems. I’ve grown academically, professionally, and personally, but not without the love and support of many individuals in my life. Firstly, I’d like to thankmymother,Nancy,whoneverdoubtedmydecisionorcapabilitytopursueandcompletemy doctorate. She told me “All the things I have in my possession can be taken away, but no one can evertakeawayyourknowledge.” Thisisapowerfulmessagethatresonatedwithinmeasayoung child, emphasizing the importance of nurturing my mind as a life-long endeavor. Next, I’d like to thank my brother and his lovely family, Wilson, Terra and Ezri, for their unconditional support, joy and encouragement at every family gathering. Each time I visit, I come away with a renewed sense of gratitude and fulfillment in keeping family close. I want to also thank John Polansky for all his guidance in the lab and his willingness to answer questions from Japan when things go awry. A big thanks to Kevin Chou who completed his PhD along side me. To my advisor, Dr. Joseph Wang, thank you for all your patience and guidance along the way. Research into plasmaphysicshavegivenmeanewlevelofappreciationinlaboratoryexperimentsandcomputer modeling. I’dliketoalsothankYuanHuforallthelatenightdiscussionsontheintricatedetailsof plasmaphysicsandnumericalmodeling. IoweDr. EdwardRhodesahugedebtofgratitudeforall thehelpful feedback asthe outside committee member. He managesto come through forme time after time, despite the short notices I provide. Finally, I’d like to acknowledge the Department of AstronauticalEngineeringfortheopportunityandsupportduringthislongjourney. iii TableofContents Dedication ii Acknowledgements iii ListofFigures vii ListofTables xi Abstract xii Chapter 1 : Introduction 1 1.1 MotivationandObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 ExplorationofAsteroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 AsteroidDynamicsandChallenges . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 SignificanceofAsteroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4.1 PhysicalPropertiesofAsteroids . . . . . . . . . . . . . . . . . . . . . . . 3 1.4.2 Classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4.3 SurfaceProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4.4 InternalStructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 AsteroidEnvironment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5.1 SmallAirlessBody . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5.2 InfluenceoftheSun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5.3 PlasmaEnvironment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5.4 LocalPlasmaWake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.5.5 SolarRadiationPressure . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5.6 AnalogousEnvironmentsandChallenges . . . . . . . . . . . . . . . . . . 15 1.6 DustGrainCharginginCollisionlessPlasma . . . . . . . . . . . . . . . . . . . . . 16 1.6.1 SurfaceChargingTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.6.2 ProbeTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.6.3 Dust-PlasmaInteractions . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.6.4 ExperimentalDustChargingStudies . . . . . . . . . . . . . . . . . . . . . 23 1.6.5 NumericalDustChargingModels . . . . . . . . . . . . . . . . . . . . . . 26 1.6.6 RemarksonRecentDustChargingStudies . . . . . . . . . . . . . . . . . . 29 iv 1.7 DissertationOutlineandApproach . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.7.1 ResearchApproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Chapter 2 : Plasma-AsteroidInteractions: LaboratorySimulationExperiments 32 2.1 ConductingSphereCase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.1.1 ExperimentalSetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.1.2 PlasmaEnvironment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.1.3 ChargingandCurrentCollectiononAluminum . . . . . . . . . . . . . . . 37 2.2 DielectricSphereCase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.2.1 ExperimentalSetupandPlasmaEnvironment . . . . . . . . . . . . . . . . 40 2.2.2 ChargingandCurrentCollectiononAluminumOxide . . . . . . . . . . . 41 2.3 SimulationStudy: ExperimentalParameters . . . . . . . . . . . . . . . . . . . . . 46 2.3.1 SimulationDomainandBoundaryConditions . . . . . . . . . . . . . . . . 46 2.3.2 SimulationResultsfortheExperimentalFlowField . . . . . . . . . . . . . 47 2.4 SummaryandConclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Chapter 3 : Laboratory Simulations of Plasma-Dust Surface Charging in a Local- izedWake 53 3.1 PlasmaWakeDustChargingSetup . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.1 TargetSurfaceMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.1.2 PlasmaOperatingConditionsandScaling . . . . . . . . . . . . . . . . . . 56 3.2 PlasmaWakeExpansionResults . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3 RegolithSurfaceCharginginPlasmaWake . . . . . . . . . . . . . . . . . . . . . 64 3.4 DustChargeonRegolithSimulantSurfaceintheWake . . . . . . . . . . . . . . . 66 3.5 ExperimentalRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Chapter 4 : Plasma-Asteroid-DustTransportModel 69 4.1 GravitationalFieldModelingnearSmallAsteroids . . . . . . . . . . . . . . . . . 69 4.1.1 GravityModelingTechniques . . . . . . . . . . . . . . . . . . . . . . . . 69 4.1.2 Finite-ElementMassConcentrationApproach . . . . . . . . . . . . . . . . 70 4.1.3 SphericalBodywithFEMASCONmodel . . . . . . . . . . . . . . . . . . 71 4.2 SolarRadiationPressureonDustGrains . . . . . . . . . . . . . . . . . . . . . . . 72 4.3 DustTransportModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.3.1 SimulationDomainSetupandInitialConditions . . . . . . . . . . . . . . . 73 Chapter 5 : NumericalSimulationsofPlasma-Asteroid-DustInteractions 75 5.1 DustTransportvsChargeState . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.1.1 PlasmaEnvironmentSimulation . . . . . . . . . . . . . . . . . . . . . . . 75 5.1.2 DustTransportandDistribution . . . . . . . . . . . . . . . . . . . . . . . 78 5.2 DustTransportvs. GrainSize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.2.1 DustDistributionSimulation . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.3 DustTransportvs. Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3.1 DustDistributionSimulation . . . . . . . . . . . . . . . . . . . . . . . . . 81 v 5.4 DustTransportvs. AsteroidShape . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.4.1 PlasmaEnvironmentSimulation . . . . . . . . . . . . . . . . . . . . . . . 86 5.4.2 DustDistributionSimulation . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.5 SummaryandConclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Chapter 6 : ConclusionsandFutureResearch 92 6.1 ConclusionsandContributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 6.1.1 DustySurfaceChargingvs. IsolatedDustCharging . . . . . . . . . . . . . 93 6.1.2 AsteroidSurfaceCharging . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.1.3 DynamicsofPlasma-Asteroid-DustInteractionsvsDustTransportandDis- tribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 6.2 ProposedFutureResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 6.2.1 PlasmaDiagnosticsDevelopment . . . . . . . . . . . . . . . . . . . . . . 94 6.2.2 ParallelizationofPlasmaModel . . . . . . . . . . . . . . . . . . . . . . . 95 6.2.3 CEXandFacilityEffects . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.2.4 DustDistributionfromImpactEjectra . . . . . . . . . . . . . . . . . . . . 95 6.2.5 Time-VariantPlasmaChargingModel . . . . . . . . . . . . . . . . . . . . 96 6.2.6 ImplementCohesiveForceintoDustTransportModel . . . . . . . . . . . 96 AppendixA: LaboratoryExperimentalSetupandPlasmaDiagnostics 97 A.1 VacuumFacility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 A.2 ElectronBombardmentGriddedIonSource . . . . . . . . . . . . . . . . . . . . . 98 A.3 PlasmaDiagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 A.3.1 LangmuirProbe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 A.3.2 EmissiveProbe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 A.3.3 FaradayProbe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 A.3.4 RetardingPotentialAnalyzer . . . . . . . . . . . . . . . . . . . . . . . . . 106 A.3.5 Non-contactingElectrostaticVoltmeter . . . . . . . . . . . . . . . . . . . 108 AppendixB: Plasma-AsteroidInteractionModel 109 B.1 PlasmaSpecies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 B.2 SimulationDomainandBoundaryConditions . . . . . . . . . . . . . . . . . . . . 112 B.3 ExampleSimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 B.3.1 PlasmaEnvironmentandFieldProperties . . . . . . . . . . . . . . . . . . 114 Bibliography 117 vi ListofFigures 1.1 Positions of asteroids and comets in the inner solar system. Asteroids are yel- low dots and comets are sunward-pointing wedges. Figure credit: Paul Chodas (NASA/JPL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 CumulativesizedistributionofMBAs . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Asteroid rotation rate and rotation period vs. asteroid diameter obtained from brightnessvariationsfromhundredsofobservations. . . . . . . . . . . . . . . . . . 6 1.4 (a) Close-up image of the very rough surface of Itokawa, taken by Hayabusa1; the surface is composed mainly of a thin layer of gravel and pebbles. (b) Close- up image of the surface of 17 km Eros, taken by the NEAR-Shoemaker mission (imaged area is 12 m across); the surface consists of a deep layer of fine dust. Despite their drastically different regolith properties, Itokawa and Eros belong to thesameS-typetaxonomy. Photocredits: JAXAANDNASA . . . . . . . . . . . 7 1.5 Convergenceregion (solid crosshatch lines) for spherical harmonics with (a) exte- riorand(b)interiorBrillouinsphere . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.6 Asteroid216Kleopatra(a)polyhedralmodel(b)finite-elementmodel(1384parti- cles) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.7 Accelerationpercenterroroffinite-elementgravitymodel . . . . . . . . . . . . . . 11 1.8 Overview of solar drivers and fundamental physical processes in the lunar plasma environment, including solar wind scattering, pickup processes, wake formation andrefilling,crustalmagneticfieldinteractions,andsurfacecharging. . . . . . . . 12 1.9 Schematicoflunarchargingenvironmentnearterminatorregion . . . . . . . . . . 13 1.10 Localplasmavoidformedbysupersonicsolarwindflow . . . . . . . . . . . . . . 14 1.11 Schematicrepresentationofsolarwindexpansionintoshadowedlunarcrater . . . . 14 1.12 Chargingonaregolithsurfaceofanairlessbody . . . . . . . . . . . . . . . . . . . 18 1.13 Dust-plasmainteractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.14 Dust acoustic wave with a wavelength of0.6 cm, a frequency of15 Hz and a phasespeedof9cm/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.15 The shock wavepropagatesfrom (a) to (d) of the left part of the frames, and has a maximumspeedof1cm/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.16 Collectiveoscillationsinadustcrystalatdifferentpressures: (a)Nooscillationsat P=0.198Torr,(b)wavespropagatinginthelowercrystalplanesatP=0.185Torr and(c),(d)separatedintimeby16ms)wavefrontpropagatingatP=0.160Torr. . 25 vii 1.17 (a) Experimental configuration for dust transport on a planar surface, (b) poten- tial distributions 1 mm above the surface, (c) images showing dust transport into shadow with the beam energy at 80 eV. The labels indicate the time elapsed after turningonthebeam.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.18 Distribution function of vertical velocity of photoelectrons for a realistic model (solid curve), the unidirectional model (dotted curve), and the Maxwellian model (dashedcurve). Theyarenormalizedsothatthetotalareaunderthecurveisunity. . 27 1.19 Motionofdustgrainswithradiusof1.0,0.5,and0.1m,respectively,withinitial velocitybetween0.1and2.5m/s. (a)Realisticphotoelectronvelocitydistribution, (b)unidirectionalmodel,(c)Maxwellianmodel . . . . . . . . . . . . . . . . . . . 28 1.20 DusttrajectoriesonEroswithsunelevationangleat20 o abovelefthorizon . . . . . 29 1.21 Fate of 1.2 m particles with varying initial conditions above (a) Itokawa and (b) Eros. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.1 Surfacechargingexperimentforasphereimmersedinamesothermalplasmainside vacuumchamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2 End (left) and top view (right) schematic of experimental setup and probe scan region. Theendviewislookinginthenegative-xdirection(i.e.,towardtheplasma source). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3 Side view of conducting sphere for surface potential measurement with the Trek probe for the floating case. In the biased cases, the suspending wire connects to a powersupplyoutsideofthevacuumchamber. . . . . . . . . . . . . . . . . . . . . 34 2.4 Plasmaenvironmentinthehorizontalhalf-planearoundafloatingconductingsphere. Measurements were limited to distances greater than 6.35 mm from the surface. Thelocationoftheambientmeasurementswas18.6mmtotheleftofthesphereat y=0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.5 Near-surfacecontouroftheplasmapotentialandelectrondensityaroundthefloat- ingconductingsphere. Minimumprobe-spheredistancewas1.27mm . . . . . . . 37 2.6 Current flux of drifting argon ions and thermal electrons incident on conducting sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.7 Side view of dielectric sphere for surface potential measurement with an exposed wirebydirect-contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.8 Plasma environment around an dielectric sphere. Measurements were limited to distancesgreaterthan6.35mmfromthesurface . . . . . . . . . . . . . . . . . . . 42 2.9 Near-surfacecontouroftheplasmapotentialandelectrondensityarounddielectric sphere. Positionsforcurrentbalanceareindicatedon p . . . . . . . . . . . . . . 43 2.10 Current flux of drifting argon ions, thermal electrons and secondary electrons on dielectricsphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.11 Surface alteration of spheres after exposure to plasma source. Spheres below are clean,untestedspheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.12 Plasmasimulationaroundaconductingsphere . . . . . . . . . . . . . . . . . . . . 49 2.13 Near-fieldsimulationaroundaconductingsphere . . . . . . . . . . . . . . . . . . 50 viii 2.14 Plasmasimulationaroundadielectricsphere . . . . . . . . . . . . . . . . . . . . . 51 2.15 Near-fieldsimulationaroundadielectricsphere . . . . . . . . . . . . . . . . . . . 52 3.1 Schematicofexperimentalsetup: plasmasource,aluminumcube,theplasmaflow fieldscanregion,andasampletargetplate(locatedbelowscanregion) . . . . . . 54 3.2 Plasmawakedustchargingexperimentsetup. Positionofthetargetplateindicated bydepthsh 1 andh 2 fromthetopofcube . . . . . . . . . . . . . . . . . . . . . . . 55 3.3 Targetmaterialsforsurfacecharging . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.4 Plasmapotential,ioncurrentdensitycontours,andionvelocityvectorsath 1 andh 2 60 3.5 Iondensity,electrondensity,andelectrontemperaturecontoursath 1 andh 2 . . . . 61 3.6 ,n i ,andn e z-profilesath 1 (dottedlinerepresentsboundaryofwakeregion) . . . 63 3.7 IonenergydistributionfromRPA . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.8 JSC-1A simulant surface potential (solid lines) versus Al 2 SiO 5 smooth solid sur- face potential (dashed lines) for the h 1 and h 2 case. The potential shown is with respecttoambientplasmaflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.9 Chargingmodelforasphericaldustgrainwithincidentcurrent,I i ,andsecondary- inducedcurrent,I si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.1 Finite-elementmodeltrajectoryofaspherical1kmasteroid . . . . . . . . . . . . . 71 5.1 Plasma contours around an asteroid under average solar wind plasma and uv- inducedphotoelectrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.2 Overlaycontourofthegravityfieldandelectricfieldaroundanasteroid . . . . . . 77 5.3 Acclerationprofileonachargeddustasafunctionofaltitude . . . . . . . . . . . . 77 5.4 Dustdistributionaroundasmallasteroidforvariouschargestate . . . . . . . . . . 79 5.5 Sampledusttrajectoriesaroundasmallasteroidforvariouschargestate . . . . . . 80 5.6 Dustdistributionaroundasmallasteroidforvariousgrainsizes . . . . . . . . . . . 81 5.7 Distributionfornominalgravity . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.8 Distributionfor10xgravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.9 Distributionfor100xgravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.10 Distributionfor1000xgravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.11 Plasmapotentialcontourforanirregularly-shapedasteroid . . . . . . . . . . . . . 87 5.12 Plasmapotentialcontourforanaligned-binaryasteroidsystem . . . . . . . . . . . 87 5.13 Plasmapotentialcontourforatransverse-binaryasteroidsystem . . . . . . . . . . 87 5.14 Dustdistributionaroundanirregularly-shapedasteroid . . . . . . . . . . . . . . . 89 5.15 Aligned-binaryasteroidsystemdistribution . . . . . . . . . . . . . . . . . . . . . 90 5.16 Transverse-binaryasteroidsystemdistribution . . . . . . . . . . . . . . . . . . . . 90 A.1 Stainlesssteelvacuumchamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 A.2 Plasmasourceandelectricalconfiguration . . . . . . . . . . . . . . . . . . . . . . 98 A.3 Plasmadiagnosticsontraversingsystem. Thesuiteofprobesin(b)arefastenedto thelabel“ProbeSuite”in(a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 A.4 Langmuirprobeandelectricalschematic . . . . . . . . . . . . . . . . . . . . . . . 101 ix A.5 ExampleLangmuirprobeI-Vcurve . . . . . . . . . . . . . . . . . . . . . . . . . 102 A.6 Emissiveprobeandelectricalschematic . . . . . . . . . . . . . . . . . . . . . . . 102 A.7 ExampleemissiveprobeI-Vcurvewithinflection-pointmethod . . . . . . . . . . 103 A.8 Faradayprobeandelectricalschematic . . . . . . . . . . . . . . . . . . . . . . . . 103 A.9 Radial (i.e., the -y-axis) profile of plasma beam potential, p . Main beam is between0to4.5cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 A.10 Radialprofilesofplasmadensities. Mainbeamisbetween0to4.5cm. . . . . . . . 106 A.11 RPAandelectricalschametic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 A.12 RPAmainbeamionenergydistribution . . . . . . . . . . . . . . . . . . . . . . . 107 A.13 Treknon-contactingESVMprobe . . . . . . . . . . . . . . . . . . . . . . . . . . 108 B.1 PICloopiteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 B.2 Fluxjumpacrosstheinterfacecausedbysurfacecharging . . . . . . . . . . . . . . 111 B.3 Simulationsetupforplasmainteractionsforanilluminatedasteroid . . . . . . . . . 113 B.4 Density contours of average solar wind plasma, uv-induced photoelectron, and totalspacechargedensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 B.5 Potentialcontouraroundasteroidcalculatedbynon-homogeneousIFEsolver . . . 115 B.6 ElectricvectorfieldcalculatedbyIFE-PICplasma-asteroidinteraction . . . . . . . 116 x ListofTables 1.1 Averagesolarwindconditionsatlunarsurface . . . . . . . . . . . . . . . . . . . . 12 2.1 Referenceambientplasmaparametersforbiasedsphere,(f)-float . . . . . . . . . . 37 2.2 Ambientparameters,measuredandcalculatedsurfacepotentials,(f)-float . . . . . 40 2.3 Estimatedparametersforsurfacepotentialscalculation . . . . . . . . . . . . . . . 45 2.4 Measuredandcalculatedsurfacepotentialfordielectricsphere . . . . . . . . . . . 45 2.5 Normalizedionandelectronvelocitiesandtemperature . . . . . . . . . . . . . . . 47 3.1 Targetsurfacematerialproperties . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.2 Averageexperimentalplasmaparametersfor“ambient"conditionsinthewakeregion 57 3.3 Experimentalcasesandscalinglengths . . . . . . . . . . . . . . . . . . . . . . . . 59 3.4 AveragechargeofindividualdustgrainonregolithsurfaceQ d versuschargeofan isolateddustgrainQ d;iso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.1 Asteroidandgrainsimulationparameters . . . . . . . . . . . . . . . . . . . . . . 73 4.2 Averagesolarwindplasmaandphotoelectronparameterat1AU . . . . . . . . . . 74 4.3 SimulationparametersandinitialconditionsforESlevitateddust . . . . . . . . . . 74 B.1 Averagesolarwindplasmaandphotoelectron(at90 o SEA)parameterat1AU . . . 112 xi Abstract Asteroids are the remnants of the formation of the solar system and they constitute a wealth of information relating to evolution of the solar system. The origin of the solar system questions can only be fully addressed in the context of an ambitious program of space exploration to the asteroids. Asteroids in space are airless, dusty objects immersed in the solar wind plasma and illuminated by solar radiation. The dust grains are susceptible to the competing effects from the gravitationalforce,theelectromagneticforceandsolarradiationpressurethatculminatetoachal- lengingprobleminmitigatingtherisksofasteroidrendezvousmissions. Thisdissertationexperimentallyinvestigatedthechargingpropertiesofdustgrainsinaplasma in order to develop the first 3D model for plasma-asteroid-dust interaction and the dynamics of chargeddusttransportonaglobalscale. Laboratorymeasurementsofasimulatedplasma-asteroid surfaceprovidedthechargingmodelandthechargingparametersofconductingobjects,dielectric objectsanddustgrainsimmersedinamesothermalplasmaflow. Aplasma-asteroid-dusttransport numerical model incorporated the results of the particle-in-cell plasma-asteroid charging simula- tion with a finite-element gravitational field model and a solar radiation pressure model to deter- minethedustdistributionaroundsmallasteroidsundervariousscenarios. Theeffectsofdustparticlesareimportantconcernsforspacecraftfunctionalityandsurvivabil- ity, but there are still large uncertainties in the current knowledge of dust transport on planetary surfaces. The following statements summarize the principal finding of this dissertation: First, solar radiation pressure dominates the transport of the particles under a low charging state, while theelectrostaticforcebecomesthedominantfactorformoreextremechargingconditions. Second, xii the dust dynamics are sensitive to the sizes of the individual grains such that as the grain size is increased, the forces acting upon it are effectively attenuated and the grain becomes more tightly boundtothesurfaceonwhichitislocated. Thirdly,andintuitively,arelativelystronggravitational field acts to confine more of the dust to lower altitudes. Lastly, the asteroid shape contributes to dust transport in more complex ways, making it more difficult to predict the dust distribution. Implications of the study may advance the current understanding of the asteroid environment and improvefunctionalityoffuturespacecraftdesignforasteroidrendezvousmissions. xiii CHAPTER 1: INTRODUCTION 1.1 MotivationandObjectives Asteroids represent material that failed to get incorporated into planets when the Solar System formed. As such, they constitute a metaphorical gold mine of scientific information relating to the properties of the early Sun, astrophysical processes in the protoplanetary disk, and the early stages of planetesimal formation and evolution [1]. The fact that many asteroids (i.e. the parent bodiesofchondriticmeteorites)areundifferentiated,andthereforelargelyunalteredsincethesolar system formed, is especially important in this respect. Moreover, the differentiated asteroids (i.e. the sources of metallic and achondritic meteorites) are also of great scientific interest, as their study will shed light on our understanding of the earliest stages of planetary differentiation into cores, mantles and crusts. These scientific objectives can only be fully addressed in the context of an ambitious program of space exploration able to conduct in-situ investigations, and sample collectionreturntoEarthfromalargenumberofdifferenttypesofasteroid[2]. The endeavors of space exploration have continually challenged the limits of scientific and technical feasibility, at the benefit of humanity. In the process of discovering new worlds, new innovations foster new technologies on Earth and new perspectives spark reflection on the current stateofhumanaffairs. 1.2 ExplorationofAsteroids Asteroidsaretheremnantsoftheformationofthesolarsystemandareconsideredlargelyunaltered since then. As such, asteroids preserve the primitive material that would provide clues into the properties of the Sun, planetesimal evolution and astrophysical processes in the protoplanetary disk. Understanding the composition of the asteroids will help us determine: 1) how the solar 1 of124 1.3AsteroidDynamicsandChallenges systemwascreated;2)theevolutionofplanetarydifferentiation;and3)theoriginofEarth’swater andorganicmatter. Asteroids are believed to have formed early in our solar system’s history – about 4.5 billion yearsago–whenacloudofgasanddustcalledthesolarnebulacollapsedandformedoursunand the planets. By visiting these Near Earth Objects (NEO) to study the material that came from the solar nebula, we can look for answers to some of humankind’s most compelling questions, such as: how did the solar system form and where did the Earth’s water and other organic materials such as carbon come from? In addition to unlocking clues about our solar system, asteroids may provide clues about our Earth. By understanding more about asteroids we may learn more about past Earth impacts and possibly find ways to reduce the threat of future impacts. Future robotic missions to asteroids will prepare humans for long-duration space travel and the eventual journey to Mars. Robotic missions will provide reconnaissance information about asteroid orbits, surface composition, and even return samples to Earth for further evaluation. These robotic missions are a critical step in preparing humans to visit asteroids where we will learn about the valuable resources available in space, and further develop ways to use them in our quest for more efficient andaffordableexploration. 1.3 AsteroidDynamicsandChallenges A small asteroid is defined as one for which the gravitational force may not be the dominating force. Fornear-Earthspaceenvironment, asteroids smallerthan1 kminsizehaveatenuousgrav- itational field such that other forces must be taken into consideration. In particular, dust particles mayalsobesubjectedtoelectromagneticforceduetoplasmacharginginteractionsandsolarradi- ationpressure. Localplasma-surfaceinteractionsleadtoasteroidsurfacecharging,hence,charged dust grains on the surface could lead to levitation and transport around an asteroid. The effects of dustparticlesareimportantconcernsforspacecraftfunctionalityandsurvivability. Challengesfor accurately modeling dust dynamics arise from competing effects between electromagnetic effects 2 of124 1.4SignificanceofAsteroids (topographical features yield complex local electric field), gravity (irregular asteroids have com- plex gravitational field), and other forces. The charging state of the regolith surface will highly influencethedegreeofdustmobilization. 1.4 SignificanceofAsteroids As one of the most active research areas in planetary science, asteroids are important players in the evolution of the solar system, considered to be the remnants of terrestrial planetary formation. Current orbits of asteroids are typically different from the regions of their creation. The emphasis on understanding the composition and dynamics of asteroids may lead to clues in the origin, age and development of the planets and other celestial bodies [3]. In addition to scientific endeavors, asteroid mining ventures could offer two benefits: a burgeoning of planetary sciences, includ- ing the discovery of exotic new cosmic materials, and much cheaper space missions to explore the solar system and the distant universe [4]. Ground-based and space-based observations have immensely expanded our knowledge on asteroid characteristics, however, many physical details remainamysteryandvariouschallengesinexplorationhasyettobeaddressed[5]. 1.4.1 PhysicalPropertiesofAsteroids Asteroids are faint in the sky because they are small and only reflect sunlight from their sur- face. Therefore, it is difficult to postulate their true physical properties from remote observations. Despitethelargeuncertainties,analogousmaterialsfoundonEarthandthelunarsurfaceestablish links to ascertain characteristics of the minor celestial bodies. The main belt is the largest repos- itory of asteroids, located between the orbits of Mars and Jupiter bounded at 1.8 AU and 3.3 AU (Figure 1.1). The asteroids in the belt are aptly designated main belt asteroids (MBAs), while the population that orbits between 0.98 AU and 1.3 AU are termed near-Earth asteroids (NEAs) [3]. MBAs are typically larger than NEAs since smaller asteroids are more easily dislodged from the 3 of124 1.4SignificanceofAsteroids mainbeltorbit. ThecumulativesizedistributioninthemainbeltisdepictedinFigure1.2andhas beenreferredtoasa“fossilized”sizedistribution,suggestingthedistributionaroseearlyinhistory withminimalevolutionsince[6,7]. ThenumberofMBAslargerthan1kminsizeisestimatedat aboutonemillion. Figure 1.1: Positions of asteroids and comets in the inner solar system. Asteroids are yellow dots andcometsaresunward-pointingwedges. Figurecredit: PaulChodas(NASA/JPL) The rotational period of the body is derived from light-curve measurements through optical telescope observations. In Figure 1.3, the asteroid rotational period derived from brightness vari- ations is plotted against the diameter of objects. The observed objects include NEAs, MBAs and Marscrossingasteroids(MCAs). Forasteroidsgreaterthan200minsize,anabruptupperthresh- oldofthe“spinbarrier"maybeevidenceforinternaltensilestrengthlimitwithoutejectingmaterial [8]. Observationsinthemid-infraredtothermal-infraredgiveheatfluxmeasurementsthatprovide sizeestimatesandthermalinertiapropertiesoftheobject[5]. 4 of124 1.4SignificanceofAsteroids Figure1.2: CumulativesizedistributionofMBAs 1.4.2 Classifications The spectral properties of asteroids have been used to categorize them into the following taxo- nomic classes: S-type, C-type, and M-type. S-type asteroids are probably composed of materi- als analogous to common meteorites, the ordinary chondrites, which are moderately evolved but unmelted chondritic rocks. Moderate visual albedo reveal spectroscopic features with distinct sil- icate absorption bands, likely composed of olivine and pyroxene. They account for 15%-20% of known asteroids and dominate the near-Earth and inner belt population. C-type asteroids are estimated to be about 75% of all asteroids, located primarily in the middle and outer regions of the main belt. They are presumed to have material similar to most primitive meteorites, carbona- ceous chondrites, which contain complex organics, silicate minerals, and reduced iron and other metals, suggested by the dark, reddish spectral properties. In general, the asteroids are radially distributed, transitioning outward from S-type domain to C-type domain in the main belt. How- ever,recentstudieshaveclaimedthatlower-temperaturecarbonaceousmaterialpresentinthemain belt formed in very different locations and was later scattered into the asteroid belt. Evidence of 5 of124 1.4SignificanceofAsteroids Figure 1.3: Asteroid rotation rate and rotation period vs. asteroid diameter obtained from bright- nessvariationsfromhundredsofobservations. such scattering and radial mixing of bodies comes from both direct measurements and dynamical models[9]. Finally,M-typeclassificationwasoriginallyconsideredtobemetallicfragmentsfrom differentiated planetary cores, although recent mid-infrared spectroscopic observations have sug- gestedthemineralogytobehydratedsilicateratherthanmetal[10]. Thecurrentunderstandingof compositionbasedsolelyonspectralobservationsremainslimitedanduncertain. 1.4.3 SurfaceProperties It is important to note that spectral observations may only provide information of the first few micrometers of the surface. Surface properties such as the size distribution and depth of regolith grains, cohesion, and surface morphology must be obtained by in-situ investigations or analysis of sample-return. Asteroid flyby and rendezvous missions have contributed greatly to the current knowledge of the surface. Spacecraft-imaged surfaces show vastly diverse worlds between aster- oids of the same taxonomic class (Figure 1.4). Particle sizes range from sub-millimeter to meter sizedboulders. DetailedviewshavebeenlimitedtoS-typebodies,whileclose-upimagesofdark, 6 of124 1.4SignificanceofAsteroids carbonaceous asteroids have yet to be taken. A study of impactor flux history would imply abun- dant crater features, but the lack of craters has been interpreted for possible evidence of seismic shaking, gardening, and migration of surface regolith [11, 12]. Spectral investigation in search of aqueous alteration processes for the presence hydrated silicate material concludes that there may bemorewatericecontentwithinasteroidsthanpreviouslythought[13,14]. Figure 1.4: (a) Close-up image of the very rough surface of Itokawa, taken by Hayabusa1; the surface is composed mainly of a thin layer of gravel and pebbles. (b) Close-up image of the surface of 17 km Eros, taken by the NEAR-Shoemaker mission (imaged area is 12 m across); the surface consists of a deep layer of fine dust. Despite their drastically different regolith properties, ItokawaandErosbelongtothesameS-typetaxonomy. Photocredits: JAXAANDNASA 1.4.4 InternalStructure Theinternalstructureofasteroidsisinferredonlyfromindirectevidence: bulkdensitiesmeasured by spacecraft, the orbits of natural satellites in the case of asteroid binaries, and variations in the orbitalandrotationalstatesduetotheYarkovsky-O’Keefe-Radzievskii-Paddack(YORP)effect. A spacecraftnearanasteroidisperturbedenoughbytheasteroid’sgravitytoallowanestimateofthe asteroid’s mass. The shape and surface topography is resolved with a light detection and ranging instrument(LIDAR),whereascenterofgravitycanbereconciledbythermophysicalanalysiswith YORP effect, which is a torque that can modify the rotational rates and spin-axis orientations of small bodies in the solar system [15, 16]. Mass and volume allow the derivation of bulk density. 7 of124 1.5AsteroidEnvironment Thesemeasurementsindicatethatdarkbodieshaveabulkdensity(typicallyabout1.0-1.3g/cm 3 ) thatislowerthanthatofthebrightasteroids(typicallyabout2.0-2.7g/cm 3 )[5,15]. Theinternal porosity of asteroids can be inferred by comparing their bulk density with that of their assumed meteoriteanalogues. Despitethesmallnumberofstatistics,itisevidentthattheinteriorofanaster- oidgenerallyhassomedegreeofporosity. Mostasteroidshavesignificantporosity;darkprimitive asteroids seem to be more porous (> 40%) than bright ones, but the nature of this porosity is unclear. Porositygreaterthan30%istypicallyconsideredtobea“rubble-pile."Thiscouldsuggest thatlooselyconsolidatedprimitivebodiesarefundamentallyweakerthantheirS-typecounterparts, whichtendtobemorecoherent. However,smallgrainsoftheasteroidmayexhibitefficientshock compactionwhichwouldleadtoincreasedbulkdensityovertime. Compactionstrengthisthought tobemorerelevantforcollisionaloutcomesthantargetporosity[17]. 1.5 AsteroidEnvironment 1.5.1 SmallAirlessBody In general, small bodies have irregular shapes as their local gravity lacks sufficient force to pull the objects into spherical shapes; thus, orbital characteristics and navigation in close proximity of an asteroid are among the most challenging astrodynamics problems. The point mass gravita- tionalapproximationoforbitalmotionaroundlargesphericalbodiesisnotapplicabletorepresent motion around small bodies as the perturbing dynamics is no longer negligible [18, 19]. Hence, precisedescentandlandingdesigniscontingentuponanaccurateaccountoflocaldynamicsatthe target body. A classical approach models the exterior gravity field by approximating the potential in a spherical or ellipsoidal harmonic series expansion [20, 21]. The accuracy of the harmonic expansion is limited by the finite truncation of the series; however, computational requirements are relatively low. It is well known that harmonic series converge for field points outside of the circumscribing sphere (Brillouin sphere); however, the solution diverges, with errors exceeding 8 of124 1.5AsteroidEnvironment 100%havingbeenshownforfieldpointswithintheBrillouinsphere[20]. TakahashiandScheeres have remedied this issue by developing the interior Brillouin sphere to complement the conven- tionalharmonicexpansionapproachtoimprovetheaccuracyfornearsurfacedynamics,although, total mapping of the gravity field can become computationally expensive and laborious to opti- mize [22]. Figure 1.5 depicts the region of convergence for the spherical harmonic model. To estimate the gravity field contributed by the asteroid (dashed crosshatch lines), the solution con- verges outside of the Brillouin sphere. The interior Brillouin spheres (one shown in Figure 1.5b) complementtheexteriorBrillouinsolutionspacebysolvingfortheregionnearthesurface,inside oftheBrillouinspherebutexternaltotheasteroidbody. Nevertheless,itisnon-trivialtoascertain thephysicalmeaningofthemathematicalrepresentationofharmonicexpansion. Figure 1.5: Convergence region (solid crosshatch lines) for spherical harmonics with (a) exterior and(b)interiorBrillouinsphere Anotherconventionalapproachestimatestheasteroidgravityusingaconstant-densitypolyhe- dral shape model. For a given shape and bulk density, the polyhedral model calculates the exact gravitationalattractionoftheasteroid,validuptothesurfaceofthesmallbody[20]. Thismethod provides a convenient verification whether the field point is inside or outside the body, appeal- ing for surface interaction. A major drawback of the polyhedral model results from the uniform density assumption of the asteroid interior, as realistic internal structure of the small bodies has 9 of124 1.5AsteroidEnvironment unique mass distribution, potentially with large internal voids. Consequently, the high computa- tionaldemandsofapolyhedralmodelserveswellasabenchmarksolution. Parketal. developeda finite-element (FE) model of the asteroid which gives validity of the local gravity within the Bril- louin sphere, along with the capability to establish a non-uniform interior mass distribution, also referred to as the mass-concentration (MASCON) model [23]. A review of the MASCON model hasshownittohaveanaccuracywithina1%errorforthemajorityofthedomain,whiletheerror atthesurfaceisstilllessthan10%,forthecaseofasteroid216Kleopatra,relativetothepolyhedral model(Figure1.6and1.7)[24]. Figure1.6: Asteroid216Kleopatra(a)polyhedralmodel(b)finite-elementmodel(1384particles) 1.5.2 InfluenceoftheSun Thesunsteadilyemitsplasmaintheformofsolarwindionsandelectronsthatarecarriedalongthe interplanetary magnetic field lines. The Earth’s global magnetic field is capable of deflecting the incomingchargedparticles,however,thisisnotthecaseforairlessbodieslackingamagneticfield. Therefore, the lunar and asteroid surfaces directly interact with the bombarding plasma particles. The current knowledge of plasma-asteroid interactions has been based largely on observations in the lunar plasma environment (Figure 1.8) [25]. While the Moon today lacks a global magnetic field, the origin of lunar crustal magnetism is considered to be remanent magnetization carried 10 of124 1.5AsteroidEnvironment Figure1.7: Accelerationpercenterroroffinite-elementgravitymodel by sub-micron grains of metallic iron (< 1% of lunar soil by weight) [26]. The features of the lunar plasma environment were derived from observations of lunar missions. Average solar wind parametersaregiveninTable1.1,composedprimarilyofprotons(H + )andelectronswithenergies in the order of tens of eV [27, 28]. High energy burst activities are sporadic, but potentially on the order of MeVs, and originate from solar energetic particle (SEP) events such as coronal mass ejections, solar flares, or solar holes. Solar electromagnetic radiation flux also interacts with and affectsthedielectricsurface,specificallyatultraviolet(UV),extremeultraviolet(EUV),andX-ray wavelengths. Bothsolarilluminationandplasmaflowwillhaveasubstantialinfluenceonasteroid surfacecharging[29]. 1.5.3 PlasmaEnvironment Theasteroidsurfaceisdirectlyexposedtospaceplasmaenvironmentsduetoitsabsenceofasignif- icantmagneticfieldtodeflectionizedparticles,andthusischargedbyambientsolarwindplasma collection, solar radiation induced photoelectron emission, and secondary electron emission. A reviewofthelunarplasmaenvironmentprovidesabasisfortheasteroidstudy. 11 of124 1.5AsteroidEnvironment Figure1.8: Overviewofsolardriversandfundamentalphysicalprocessesinthelunarplasmaenvi- ronment, including solar wind scattering, pickup processes, wake formation and refilling, crustal magneticfieldinteractions,andsurfacecharging. Table1.1: Averagesolarwindconditionsatlunarsurface SolarWindPlasmaParameters IonDensity n i;sw 2.12–5.5510 6 m 3 ElectronDensity n e;sw 0.5–1010 6 m 3 ElectronTemperature T e;sw 5–30eV DebyeLength D;sw 5.26–57.6m IonDriftingVelocity v i;sw 392–745km/s ElectronThermalVelocity v te;sw 938–2300km/s The Moon apparently does not strongly affect the environment upstream from it, acting only as a source of rather tenuous neutral atoms as well as ions produced via photoemission, impact ionization, and charge exchange [25]. Measurements have reported typical day time lunar surface potentialsontheorderofafewtensofvoltspositiveduetophotoelectronemissionandnighttime potentials on the order of hundreds to even thousands of volts negative [30] - [35]. The effect of plasma flow is especially complex near the terminator where the transition from sunlight-driven 12 of124 1.5AsteroidEnvironment positive surface potential to the plasma-charged negative surface potential occurs [36] - [41], as illustratedinFigure1.9. Figure1.9: Schematicoflunarchargingenvironmentnearterminatorregion 1.5.4 LocalPlasmaWake Under typical conditions, the solar wind is a mesothermal plasma flow (the directed plasma flow speed is larger than ion thermal speed but less than electron thermal speed, v ti ≪ V i ≪ v te ). At theterminatorregion,thesolarwindplasmaflowsovertheruggedterrainatalowelevationangle and generates a localized plasma wake region as illustrated in Figure 1.10 [38]. A local wake formsbecauseoftheremovalofsolarwindionsandelectronsatthedayside,throughbothabsorp- tion/implantationandscattering/reflection,resultinginanearlycompleteplasmavoidimmediately downstream from the nightside. Highly mobile thermal electrons at the edge of the void expand into the region ahead of the more massive ions because of their higher thermal velocity. The resulting charge separation creates an ambipolar electric field at the wake flank to retard electron expansion and accelerate ions into the void [42] as illustrated in Figure 1.11. Local plasma wake, combinedwithlocalizedshadows,generateszig-zagdivisionsofpositivelychargedandnegatively charged regions. In the asteroid case, the localized wake will instead be a global wake; however, 13 of124 1.5AsteroidEnvironment plasma dynamics summarized for the lunar environment are applicable for the purposes of charge deposition and surface charging, nonetheless. Determining the plasma environment generated by the wake is critical to understanding the local processes, such as surface charging, electrostatic dusttransport,andspaceweathering. Figure1.10: Localplasmavoidformedbysupersonicsolarwindflow Figure1.11: Schematicrepresentationofsolarwindexpansionintoshadowedlunarcrater 1.5.5 SolarRadiationPressure Forinterplanetarydustonaheliocentricorbit,theparticleaccelerationisdeterminedbyabalance ofsolargravityforceandtheoutwardradiationpressure. Bothforcesfollowtheinversesquarelaw 14 of124 1.5AsteroidEnvironment proportionality with distance from the Sun. In general, radiation pressure does not significantly alterthenatureofmostparticlesinheliocentricorbits[43,44]. However, particles orbiting an asteroid are dominated by the asteroid’s gravity and solar tidal forces rather than direct solar gravity. Studies have found that radiation pressure is efficient at sweeping small particles from the circumasteroidal environment, at timescales on the order of a few years to 20 years [44, 45]. In certain scenarios, depending on the size of the asteroid and the current balance at the surface, particles may be electrostatically levitated at sub-escape velocities andmaybetoolarge(1m-100m)tobesweptawaybyradiationwillreaccreteonthesurface [46] Poor constraints on supply and loss mechanisms result in large uncertainties in numerical studiesofnear-surfacedustparticles. 1.5.6 AnalogousEnvironmentsandChallenges As with the plasma environment, the presence of dust grains at the asteroid surface is consid- ered analogous to the lunar dust environment. While the source and collisional history of asteroid regolith may be quite different from the processes on the lunar surface, the presence of fine par- ticles is evident and a tenuous dust cloud is predicted to envelop the asteroid [47]. During the Apollo era, dust on the Moon caused serious problems for exploration activities including vision obscuration, false instrument readings, dust coating and contamination, loss of traction, clogging ofmechanisms,abrasion,thermalcontrolproblems,sealfailures,andinhalationandirritation[48]. The severity of dust hazards was consistently underestimated in ground testing. It would appear dust adheres to everything, no matter the material. Dust mitigation is a priority for space explo- ration and additional in-situ measurements in conjunction with further development of theory and numerical model is crucial to fully assess potential hazards [49]. Surface electric fields and solar radiation pressure will have a greater influence on dust dynamics due to the weak local gravity of smallasteroids. 15 of124 1.6DustGrainCharginginCollisionlessPlasma In 1986, the soviet Vega program launched 2 spacecraft to study the dust particle spatial and mass distribution at comet 1P/Halley. Although measurements provided fruitful insight to the comet,severalinstrumentssuffereddamageandthesolararraysweredegradedduetodustimpacts inthecoma[50,51]. Despitethefactthatasteroidslackthedensecomasofcomets,similarcaution shouldbetakentomitigatedusthazards. Additionalfluxsourcesincludegalacticcosmicrays,interplanetarymeteoroids,interplanetary dustandhydrogen,andlocalizeddebris. However,inthecontextofsurfacecharging,thesesources arenegligible. 1.6 DustGrainCharginginCollisionlessPlasma Plasmas in the laboratory and in space are frequently contaminated with small, charged dust par- ticles, which increase the complexity of the plasma environment, often referred to as “complex plasma." In these environments, the particle dynamics are determined by gravity, molecular and plasma drag, radiation pressure, and electromagnetic forces [52]. Complex plasmas are fully- or partially-ionized, low-temperature gases comprised of neutral gas molecules, electrons, ions, and submicron- and micron-sized charged dust grains. The latter can be billions of times heavier than ions and acquire thousands of electron charges [53]. In the context of asteroid charging envi- ronment, dust grains are immersed in a collisionless solar wind plasma and illuminated by solar radiation. 1.6.1 SurfaceChargingTheory An object immersed in a plasma will charge in response to incident currents until it reaches a steadystate,asexpressedineq.(1.1)[54]. Incidentcurrentdensitiesareinfluencedbyavarietyof physical processes including the collection of solar wind ions J i and electrons J e , photoelectron 16 of124 1.6DustGrainCharginginCollisionlessPlasma emission J ph , primary ion/electron induced secondary electron emission J sec , and backscattered electronemissionJ bs . ∑ k J k (ϕ s ) =J i (ϕ s )+J e (ϕ s )+J ph (ϕ s )+J sec (ϕ s )+J bs (ϕ s ) = 0 (1.1) The surface potential, ϕ s , will charge negatively, relative to ambient plasma potential, by elec- tron deposition and positively via ion deposition, photoelectron emission, secondary emission, and backscattered emission. In extreme scenarios of high-energy flux, secondary emission and backscattering will play significant roles, but under average solar conditions these processes con- tribute minimal impact [25, 55, 56]. The complexity of the problem varies greatly depending on the characteristics of the ambient plasma, the material property, and the geometry. Figure 1.12 depicts a sample charging surface with a layer of regolith. The magnitudes of the collected cur- rents are dependent on both the plasma sheath and the ambient plasma flow (e.g. a hotter plasma with a thick plasma sheath will yield a higher current flux). The plasma sheath thickness, d sh , is proportional to the plasma Debye length, D , defined by eq. (1.2), where ϵ o is the permittivity of free space, k is the Boltzmann constant, T e is the electron temperature, n e is the electron density, andeistheelementarycharge. D = √ ϵ o kT e n e e 2 (1.2) For an object whose characteristic length is much greater than the Debye length, L 0 ≫ D , the currentcollectionisalsoknownasthespace-charge-limitedcondition,andthesheathformedover theobjectisconsideredtobethin-sheath. Inthespace-charge-limitedcondition,alloftheparticles thatenterthesheatharecollected. WhenL 0 ≪ D ,thesheathformedovertheobjectisconsidered tobeathick-sheath,andonlyparticleswithinacertainimpactparametercanbecollected. Thisis alsoknownastheorbital-motion-limited(OML)condition. 17 of124 1.6DustGrainCharginginCollisionlessPlasma Figure1.12: Chargingonaregolithsurfaceofanairlessbody 1.6.2 ProbeTheory SpaceplasmascanbedescribedmostsimplyintermsoftheMaxwell-Boltzmanndistribution. As thisrepresentationlendsitselftoefficientmanipulationwhencarryingoutchargingcalculations,it is often the preferred way for describing plasmas. For an isotropic, thermal Maxwell-Boltzmann plasma,thevelocitydistributionfunctionf isgivenbyeq.(1.3) f(v) =n ( m 2kT ) 3=2 exp [ m(v V) 2 2kT ] (1.3) wherenistheambientplasmanumberdensity,misthespeciesmass,kistheBoltzmannconstant, T is the temperature of the species, v is the velocity of the species, and V is the drifting velocity [57]. Becausethemagnitudeofeachoftheincidentcurrentsineq.(1.1)isafunctionofthesurface potential,ϕ s ,thecurrentequationforeachprocessisdependentuponwhetherthesurfacepotential is positive or negative, whether the plasma is stationary or drifting, and whether the surface has a thin or a thick sheath [31, 58]. The following discussion applies to any surface immersed in a plasma,includingthesurfaceofadustgrain. For a stationary plasma with the thin-sheath model, current densities for collected ambient charged particles are calculated by eq. (1.4)-(1.9), where e is the magnitude of an elementary charge and the unperturbed species n i0 and n e0 are the respective ambient, unperturbed number densities. 18 of124 1.6DustGrainCharginginCollisionlessPlasma IONS J i =J i0 exp ( eϕ s kT i ) ϕ s > 0 (repelled) (1.4) J i =J i0 ϕ s < 0 (attracted) (1.5) ELECTRONS J e =J e0 ϕ s > 0 (attracted) (1.6) J e =J e0 exp ( eϕ s kT e ) ϕ s < 0 (repelled) (1.7) UNPERTURBEDSPECIES J i0 = en i0 √ kT i 2m i (1.8) J e0 =en e0 √ kT e 2m e (1.9) For a mesothermal drifting plasma with a thin-sheath, where is the angle of attack, the ion current densities are modified such that ion collection is dependent on the angle of attack and the ion drift velocity, V, as given by eq. (1.10)-(1.11), provided there is sufficient kinetic energy to overcometheCoulombrepulsionforce. Theelectroncurrentdensitiesarealsothermal,following eq.(1.6)and(1.7). IONS J i ≃en i V cos() ϕ s > 0 (repelled) (1.10) J i ≃en i V cos() ϕ s < 0 (attracted) (1.11) 19 of124 1.6DustGrainCharginginCollisionlessPlasma As the surface potential ϕ s grows in magnitude, the plasma sheath grows with it, collecting more current from the ambient plasma. Consequently, the thin-sheath model breaks down and surfacechargecollectionisdescribedbytheOMLthick-sheathmodel. Anattractedparticletakes a spiral trajectory towards the surface, analogous to that of a decaying orbit in astrodynamics. The equations governing OML current collection are summarized below. The ion current density collected at the surface follows eq. (1.12)-(1.14). The unperturbed ion current density J i0 can be eitherthestationaryplasmaordriftingplasmacase,describedinthethin-sheathmodel. Similarly, electron current densities are given in eq. (1.15)-(1.17). It is readily apparent that the planar (1D) solutionisconceptuallyequivalenttoathin-sheathcase[57]. Themodifyingfactorsforthecylin- drical solution and the spherical solution corresponds to the 2D and 3D current collection at the surface. Photoelectron emission current density from the surface is dependent on solar elevation angle (SEA),, expressed in eq. (1.18) for photoelectron number density, n ph , and photoelectron thermal velocity, v ph [59]. Many studies typically apply the OML thick-sheath model to perform dust charging on an isolated grain in a plasma [60, 61, 62]. The same approach may apply to the chargingofasphereinavacuumchamber. Thisisnotthecaseforthechargingofadustysurface sincethecharacteristiclengthofthesurfacecompatiblewiththethin-sheathmodel. IONS J i =J i0 exp ( eϕ s kT i ) ϕ s > 0 (repelled) (1.12) J i =J i0 8 > > > < > > > : (1+Q is ) : sphere 2 √ Q is + exp(Q is )erfc( p Q is ) : cylinder (1) : plane ϕ s < 0 (attracted) (1.13) Q is = eϕ s kT i (1.14) 20 of124 1.6DustGrainCharginginCollisionlessPlasma ELECTRONS J e =J e0 8 > > > < > > > : (1+Q es ) : sphere 2 √ Qes + exp(Q es )erfc( p Q es ) : cylinder (1) : plane ϕ s > 0 (attracted) (1.15) J e =J e0 exp ( eϕ s kT e ) ϕ s < 0 (repelled) (1.16) Q es = eϕ s kT e (1.17) PHOTOELECTRONS J ph = en ph v ph 2sin() (1.18) 1.6.3 Dust-PlasmaInteractions As previously mentioned, complex plasmas are ubiquitous throughout various cosmic environ- ments. The presence of dust particles in plasma further complicates the dynamics of the charging environmentandrequirescarefulconsiderationwhentheelectromagneticforcemustcompetewith gravity and radiation pressure. While being influenced by the ambient plasma, charged dust can alter the local plasma environment and dust-plasma interactions can lead to a variety of physical and dynamical consequences for both the dust and the plasma. The enormous mass difference between grains and plasma particles can lead to time-dependent charges that can become sev- eral orders larger for a dust particle, allowing it to influence the collective plasma behavior [63]. Althoughitisunlikelytooccurinanasteroidenvironment,dustcanalsoactasasourceofelectron fluxthroughthermionicemission,electricfieldemission,radioactivity,andexo-electronemission. 21 of124 1.6DustGrainCharginginCollisionlessPlasma Photoelectron emission can vary significantly by grain size as smaller grains can yield orders of magnitude greater in photoemission than their larger counterpart [64]. Like any object immersed inplasma,dustgrainschargetoasteadystatepotentialaccordingtoprobetheory. (a)Dust-in-plasma (b)Dustyplasma (c)Dustysurfacelayer Figure1.13: Dust-plasmainteractions Typically, dust grain radii, r d , are much smaller than the Debye length, D , and the inter- dust distance, d, in space and in laboratory plasmas. Complex plasmas can be categorized into 3 different regimes as shown in Figure 1.13: “dust-in-plasma," “dusty plasma," and “dusty surface layer." For “dust-in-plasma" case, D < d so that isolated, spherical dust grains behave similarly to a probe in a thick sheath. They collect ions and electrons from background plasma following OMLtheoryandexperienceclassicDebyeshieldingbehavior. Thebasicequationforthecharging ofanisolatedgrainis dQ dt = d dt C( d o ) =I tot ; (1.19) C = 4ϵ o r d (1.20) whereC isthedustcapacitance,I tot isthenettotalcurrentcollected, d and o arethedustsurface potentialandaverageambientplasmapotential,respectively[65]. When D ≫ d, “dusty plasma" displays collective behavior as the inter-dust distance is much shorterthantheDebyelength. Theplasmanolongershieldsthedustparticleindividually,causing charged grains to become electrically coupled. In the “dusty surface layer" scenario, grains are 22 of124 1.6DustGrainCharginginCollisionlessPlasma Figure 1.14: Dust acoustic wave with a wavelength of0.6 cm, a frequency of15 Hz and a phasespeedof9cm/s densely packed together, immersed in a collective sheath, where charging mechanisms may be more akin to solid surfaces and thin sheath model could be applicable. Recent research has made significantprogressfocusingon“dust-in-plasma"or“dustyplasma"inastationarythermalplasma orelectronbeam[53,66],butinordertobuildafullunderstandingofdust-plasmainteraction,the lattermustalsobeaddressed,particularlyunderalocalwakeenvironment. 1.6.4 ExperimentalDustChargingStudies Laboratory measurements have revealed new dynamics of plasma interactions with charged dust grains, where collective dust-plasma behavior is exhibited. For a collisionless plasma, the mean freepathofionsandelectronsaremuchgreaterthantheirspatialdistances. However,dustgrainsin a collisionless plasma will yield to ion-dust and electron-dust collisions, leading to a fundamental excitation of dusty plasma known as a dust acoustic wave (DAW) [67, 68]. The presence of dust can modify or even dominate wave propagation, wave instability, etc. Due to the extremely low phasespeed,(relativetoionandelectronthermalspeeds),andlowfrequency(typicallytensofHz in laboratories), it’s possible to capture wave structure images as Barkan et al. have observed in Figure1.14[69]. 23 of124 1.6DustGrainCharginginCollisionlessPlasma Figure 1.15: The shock wave propagates from (a) to (d) of the left part of the frames, and has a maximumspeedof1cm/s. DustacousticshocksundermicrogravityconditionswerefirstobservedwiththePKE-Nefedov experiment on board the International Space Station ISS [70]. Figure 1.15 shows the propagation of a shock wave characterized by a sharp boundary over which the dust number density increases byafactorof3,andapropagationspeedof1cm/syieldingaMachnumberof1.2–1.4. Further collective behavior in dust-plasma interaction experiments provides evidence for a dependence on neutral particle collisions. A collection of negatively charged micron size dust grains can be suspended in a plasma or plasma sheath as a result of a balance of an upward elec- trostatic force and the downward force of gravity and can form well organized structures called plasmacrystals. Thechargeddustintheseplasmacrystalsalignedtogetherintoasteady,solid-like state. Figure 1.16 presents observations of dust-acoustic-like wave propagation in a dust crystal withverticaloscillations,drivenbytheelectrodesheathofacapacitiveRFplasmaunderlowneu- tralgaspressures[71]. Theexperimentalresultsagreedqualitativelywithamodelofthecollisional two-stream instability involving the streaming of ions against dust grains. The growth rate of the 24 of124 1.6DustGrainCharginginCollisionlessPlasma Figure 1.16: Collective oscillations in a dust crystal at different pressures: (a) No oscillations at P = 0.198 Torr, (b) waves propagating in the lower crystal planes at P = 0.185 Torr and (c), (d) separatedintimeby16ms)wavefrontpropagatingatP=0.160Torr. dissipativeinstabilitydependsontheion-neutralanddust-neutralcollisionfrequencies. Thelatter increasewithincreasingneutralpressure. Inanefforttoobservedusttransportbygraincharging,Wangetal. createdlargepotentialdif- ferences near the electron beam impact/shadow boundaries in a laboratory. Electron beam energy at80eVproducedsufficientlylargeelectricfieldstotransportnegativelychargedparticlesfromthe beam-illuminatedregionintotheshadowedregiononaplanarsurface,asdepictedinFigure1.17. Dust transport is expected to happen near topographical features such as boulders and craters on thelunarsurface[72]. Surfacechargingexperimentshavespurredresearchanddevelopmentofnewchargemitigation material and techniques. Lightweight spacecraft materials are, in some cases, prone to exacerbate 25 of124 1.6DustGrainCharginginCollisionlessPlasma Figure 1.17: (a) Experimental configuration for dust transport on a planar surface, (b) potential distributions 1 mm above the surface, (c) images showing dust transport into shadow with the beamenergyat80eV.Thelabelsindicatethetimeelapsedafterturningonthebeam. chargingorarcingandmayallowtransmissionofelectromagneticinterferenceintosensitiveelec- tronics. All surface charging mechanisms must be considered as potential hazards to spacecraft functionalityandhealth[73]. 1.6.5 NumericalDustChargingModels Duetothelimitedaccesstoin-situmeasurementsandchallengesinterrestrialexperiments,numer- icalmodelsprovideapowerfulalternativetounderstanddustchargingdynamicsinamicrogravity environment. Horizon glow observed on the lunar surface by the Apollo astronauts suggests a tenuous dust population levitated above the surface. Numerical simulation of surface charging on asteroid Eros using a realistic photoelectron velocity distribution to model dust grain transport [74]. Figure1.18representsthevariousdistributionfunctionsofverticalvelocityofphotoelectrons modeled for dust levitation. Simulation results are for a realistic photoelectric VDF, a unidirec- tional model, and a Maxwellian model. The realistic VDF is an isotropic model that is broader and slower than the unidirectional model (which only emits photoelectrons vertically), while the Maxwellian model gives a broad range of velocities with a peak at zero and a mean energy of 2.2 eV. Dust motion is dependent on dust grain size and velocity distribution function (VDF), as 26 of124 1.6DustGrainCharginginCollisionlessPlasma Figure1.18: Distributionfunctionofverticalvelocityofphotoelectronsforarealisticmodel(solid curve), the unidirectional model (dotted curve), and the Maxwellian model (dashed curve). They arenormalizedsothatthetotalareaunderthecurveisunity. showninFigure1.19. Thedusttrajectoriesinthephotoelectricsheatharesimilarbetweenthereal- istic VDF model and the unidirectional model, with latter showing a smaller oscillating response withalowerpeakaltitude,particularlyforlowinitiallaunchvelocitiesofthegrains. Thisisinpart duetoaslightlythinnersheathfortheunidirectionalmodel. IncontrastfortheMaxwellianmodel, dust grains are accelerated to greater altitude and with longer oscillating period, particularly for a grain radius of 0.1 micron, reaching over 1500m in height, nearly independent of initial launch velocities. The Maxwellian VDF contains a more energetic population of electrons that results in an extended photoelectric sheath. Accordingly, a proper description of the photoelectron VDF is important to correctly understand the vertical structure of the sheath and the motion of charged dust. Colwell et al. modeled dust transport on Eros, specifically to determine the conditions that would explain dust ponds observed by NEAR-Shoemaker spacecraft [75]. They find that dust tends to collect in craters and region of shadow (Figure 1.20), which is consistent with NEAR- Shoemakerobservations. 27 of124 1.6DustGrainCharginginCollisionlessPlasma (a) (b) (c) Figure 1.19: Motion of dust grains with radius of 1.0, 0.5, and 0.1 m, respectively, with initial velocity between 0.1 and 2.5 m/s. (a) Realistic photoelectron velocity distribution, (b) unidirec- tionalmodel,(c)Maxwellianmodel Hartzelletal. analyzeddustlevitationaroundairlessbodiesandpresentednumericalresultson thefateofvariousinitialconditionofchargedgrains[76]. Byidentifyingtheequilibriaaboutwhich dustparticlesoscillated,theyprovidedasetofpredictions,includingconditionsfordustlevitation, that could be verified by future missions to airless bodies. The simulation analysis considered a constantplasmaenvironmentatthesubsolarpoint(daysideoftheasteroid). Figure1.21showsthe fate of 1.2 m dust around Itokawa and Eros from various initial velocities and initial altitudes. As the initial launching altitude approaches the surface, the probability of stable dust levitation decreases. Theinitialconditionsthatleadlevitationismoredependentontheparticlesizethanthe size of the central body; dust grains that result in levitation are drastically diminished as particle sizeincreases. 28 of124 1.6DustGrainCharginginCollisionlessPlasma Figure1.20: DusttrajectoriesonEroswithsunelevationangleat20 o abovelefthorizon Figure 1.21: Fate of 1.2 m particles with varying initial conditions above (a) Itokawa and (b) Eros. 1.6.6 RemarksonRecentDustChargingStudies Recent experimental and numerical studies have made progress in understanding the dynamics of dust charging, yielding interesting results limited to very specific conditions. Experimental studies showed unexpected collective behavior of charged dust, however, they were conducted in conditions significantly different from the average asteroid environment. Numerical studies were abletosimulateconditionsmuchmoretypicalnearthesurfaceofasteroids,however,thesestudies were limited specifically to illuminated regions where there are photoemission and the models were constrained to a 2-D domain for spherical bodies. Hence, the available methodologies that 29 of124 1.7DissertationOutlineandApproach have contributed to the study of dust charging have not been suitable to reach an accurate view of thedusttransportnearsmallasteroids. 1.7 DissertationOutlineandApproach Whilethedynamicsofdusttransportaroundanairlessbodyhasbeenafocusedareaofresearchin recentyears,variouschallengingaspectsstillremaintobeaddressedforsmallasteroidswherethe dust dynamics is determined by the competing effects from gravitational force, electromagnetic force, and solar radiation pressure. The overall research goal is to investigate the global environ- mentaleffectsondusttransportanddistributionaroundsmallasteroidsutilizingnumericalmodels and laboratory experiments. The remaining content of the dissertation is given in the following outline: In Chapter 2, laboratory measurements of simulated plasma-asteroid surface are presented, andnumericalsimulationresultsarecompared. InChapter3,theeffectsofdustgraincharginginalocalizedplasmawakearepresented. InChapter4,aplasma-asteroid-dusttransportnumericalmodelispresentedwhichincorpo- ratestheresultsofthePICandthegravitationalfieldmodelanddustchargingmeasurements. In Chapter 5, dust transport and distribution results of the plasma-asteroid-dust model are presentedforvariousplasmaandasteroidscenarios. InChapter6,conclusionsandsuggestionsforfutureworkaregiven. The effects of dust particles are important concerns for spacecraft functionality and survivability. Implications of the study may advance the current understanding of the asteroid environment and improvefunctionalityoffuturespacecraftdesignforasteroidrendezvousmissions. 30 of124 1.7DissertationOutlineandApproach 1.7.1 ResearchApproach m d dv d dt =Q d (r 0 ;t)[E(r)+v d B(r)]+m d g a (r)+F SRP (r) (1.21) Aspects that influence dusty plasma around asteroids include: the charge state of a dust grain, the local electrostatic fields, the asteroid’s gravitational field, and the solar radiation pressure. Dynamicsofchargeddustparticlesaroundsmallasteroidsareexpressedineq.(1.21),wherem d ,r, v d ,andQ d (r 0 ;t)arethedustgrainmass,positionvector,velocityvector,andcharge,respectively. The primary focus is to determine and constrain the electric field as a function of position,E(r), the dust charge state as a function of initial positionr 0 and time, Q d (r 0 ;t), and the gravitational field,g a (r). Theapproachformodelingthedustdynamicsisorganizedinto5maintasks: Fullykineticsimulationsofplasma-asteroidinteractionsandasteroidcharging,E(r) Laboratorysimulationsofdustchargingonaregolithsurface,Q d (r 0 ;t) Laboratorysimulationsofplasma-asteroidcurrentbalanceandsurfacecharging,ϕ s Finiteelementgravitationalmodelofrealisticallyshapedasteroids,g a (r) Dust particle transport simulations incorporating gravity, solar pressure, and electrostatic forces Compared to previous work, which focused on dust dynamics of isolated grains in a localized plasma environment in 2D, this dissertation investigated the charging and transport of a dusty surfaceunderaveragesolarwindplasmaconditionsonaglobalperspectivearoundsmallasteroids witha3Dnumericalmodel. 31 of124 CHAPTER 2: PLASMA-ASTEROID INTERACTIONS: LABORATORY SIMULATION EXPERIMENTS Thischapterpresentsastudyonthechargingofsphericalobjectsimmersedinadriftingmesother- mal plasma. The gridded ion thruster simulates the solar wind ion and the electron plasma flow around a conducting or dielectric sphere. The focus of the study is to measure the field plasma parameters as a function of the surface potential of the sphere to validate current-balance theory. Fortheconductingcase,analuminumballisbiasedbetween-20Vto+20V.Forboththeconduct- ing and dielectric cases, the sphere is electrically isolated and floating in the plasma flow field. Aseriesof3D,fullykinetic,immerse-finite-elementparticle-in-cell(IFE-PIC)simulationsisalso developedforcomparisonwithandvalidationoftheexperimentalresults. 2.1 ConductingSphereCase 2.1.1 ExperimentalSetup The experimental facility discussed in Appendix A is utililzed to determine the charging and cur- rent balance at the surface of a conducting sphere immersed in a drifting mesothermal plasma of cold ions and thermal electrons. This setup simulates a conducting spacecraft traveling at 1 AU from the sun under average solar wind plasma conditions. The target surface was an alu- minum sphere with a diameter of 12.7 mm which was electrically floating or biased from -20V to +20V with respect to chamber ground. It was suspended by a wire at 25.4 cm downstream of the plasma source (x-direction) and aligned at the center of the beam. A photo and schematic of the experimental setup are shown in Figures 2.1 and 2.2. It is important to note that reference ambient parameters were taken at 6.86 cm (i.e., 10.8 times the radius of the sphere) upstream of 32 of124 2.1ConductingSphereCase the sphere center, as summarized in Table 2.1. This ambient reference point represents the unper- turbed plasma condition, which will be crucial for determining the current balance at the surface. For the floating case, the suspending wire connected to the sphere is also electrically connected to a measurement plate for the Trek electrostatic voltmeter that is located outside of the vacuum chamber (see Figure 2.3). The Trek probe is sensitive to the plasma environment and will charge up due to the flowing charged particles. Thus, it must be isolated from the ion source. For the biased cases, the suspending wire is instead electrically connected to a power supply outside the chamberandthebiasedpotentialisconfirmedbyadigitalmultimeter. Figure 2.1: Surface charging experiment for a sphere immersed in a mesothermal plasma inside vacuumchamber 2.1.2 PlasmaEnvironment The plasma environment was measured around the sphere in a horizontal planar region that stretched 101.6 mm in the axial direction and 38.1 mm in the radial direction (as shown in Fig- ure.2.2)withanemissiveprobe,anelectrostaticLangmuirprobe,andanudeFaradayprobe(only the emissive probe is shown in Figure. 2.1). In order to maneuver around the sphere, only one probe is fastened to the traversing system on an arm oriented perpendicular to the plasma flow 33 of124 2.1ConductingSphereCase Figure2.2: End(left)andtopview(right)schematicofexperimentalsetupandprobescanregion. Theendviewislookinginthenegative-xdirection(i.e.,towardtheplasmasource). Figure2.3: SideviewofconductingsphereforsurfacepotentialmeasurementwiththeTrekprobe for the floating case. In the biased cases, the suspending wire connects to a power supply outside ofthevacuumchamber. such that there is no interference along the scan path. Horizontal symmetry was assumed, so no measurementsweremadeinthepositive-ydirection. Thescanregioniswasdividedinto36mea- surement points with a spatial resolution of 12.7 mm by 12.7 mm. Additional near-surface scans were performed with the emissive and Langmuir probes that were 35.6 mm in the axial direction and 11.4 mm in the radial direction, reaching a minimum distance of 1 mm from the surface with a spatial resolution of 5.08 mm by 3.81 mm (28 points total). Due to the size of the nude Faraday probe, the ion current density could not be measured around the sphere with the same resolution. Asaresult,thenear-surfaceioncurrentdensityandthenumberdensitycannotbeprovided. 34 of124 2.1ConductingSphereCase For the electrically-floating sphere case, Figure 2.4 shows the measured contour plots of the plasmafieldpotential, p ,ioncurrentdensity,J i ,ionnumberdensity,n i ,electronnumberdensity, n e ,space-charge,n i -n e ,andelectrontemperature,T e . Notethatthemeasurementpointswithinthe sphereareomittedandthecontoursnearthespheresurfacewereapproximatedbyagraphicssoft- wareinterpolationroutine. Inaddition,thepotentialfieldcontoursarepresentedwithrespecttothe ambientreferencepotential(i.e., p = raw - amb ),asmeasuredbyanemissiveprobewhere raw is the uncorrected, raw data. This is consistent with the solar wind ambient reference where the quasi-neutralityoftheunperturbedplasmaisconsideredtobetheelectricalgroundreference. Sim- ilarplasmacontourswereplottedforbiasedsurfacepotentialsof-20V,-10V,0V,+10Vand+20V, but are not shown here. The floating case is representative of the plasma environment but with minorvariationsinthebiasedcases. Theplasmapotentialrelativetochambergroundwasconsis- tentforthenegativebiases,butasthebiaspotentialwasincreasedto+10Vand+20V, p increased proportionally, even at distances much greater than D , well beyond the plasma sheath. However, despite the different reference ambient potentials, the measured plasma potentials were consistent betweencasesrelativetotherespectiveambientpotential(variationswerewithin1V).Sincethe densities are determined as a function of the local potential and the temperature of the charged species, the reference ambient densities also vary between experimental runs and the respective field scans follow the same trends. The ion densities were consistent for each case as the bias potentials do not have sufficient energy to disturb the trajectories of the argon ions with a kinetic energyof1100eV.Electrons,howeverwerenoticeablyperturbednearthesurface,relativetotheir respectivereferenceambientdensitiesinTable2.1,wheretherewasareductionindensityforneg- atively biased sphere and an enhancement in density for positively biased sphere. In the absence ofasphere,onewouldexpecttheplasmaparametersinthefieldscanstobeconsistenttheambient conditionswithinthemainbeam. Theuniformityinthespace-chargeforallcases(withtheexcep- tion to the near-wake region) reflects the quasi-neutrality of the plasma. Likewise, surface biases havenoinfluenceontheelectrontemperature. 35 of124 2.1ConductingSphereCase (a) p ,plasmapotential (b)J i ,ioncurrentdensity (c)n i ,iondensity (d)n e ,electrondensity (e)n i n e ,space-charge (f)n e ,electrondensity Figure 2.4: Plasma environment in the horizontal half-plane around a floating conducting sphere. Measurements were limited to distances greater than 6.35 mm from the surface. The location of theambientmeasurementswas18.6mmtotheleftofthesphereaty=0. TheclosestmeasurementstothesurfaceweretakenwiththeemissiveprobeandtheLangmuir probe at a distance of 1.27 mm. Unfortunately, due to the bulky size of the Faraday probe, ion measurements were limited to 6.35 mm from the surface. Figure 2.5 providesa near-surfaceview of the plasma potential and electron density, capturing the the wake features downstream of the sphere. There are differences in the contours for the corresponding results in Figure 2.4 and Fig- ure 2.5. This is partly due to the variation of the plasma at any moment and partly because of the resolution differences between the two field measurements. Figure 2.4 had coarse resolution, so small features and perturbation were smoothed out by image interpolation. As previously noted, 36 of124 2.1ConductingSphereCase the reference ambient plasma parameters were measured 10.8 radii upstream of the sphere to rep- resent unperturbed flow field. They are summarized in Table 2.1 for the floating (first row) and biased cases. These parameters will be utilized in determining the current balance on the surface. TheDebyelengthintheplasmaenvironmentwasapproximately D =1.5mm. (a) p ,plasmapotential (b)n e ,electrondensity Figure 2.5: Near-surface contour of the plasma potential and electron density around the floating conductingsphere. Minimumprobe-spheredistancewas1.27mm Table2.1: Referenceambientplasmaparametersforbiasedsphere,(f)-float SphereBias amb [V] n i [10 13 m 3 ] n e [10 13 m 3 ] T e [eV] +6.4V(f) +8.99 4.17 2.05 1.4 -20V +9.53 3.89 5.51 0.6 -10V +8.90 3.86 3.79 1.0 0V +10.32 4.15 4.74 3.1 +10V +11.03 3.95 1.69 1.0 +20V +18.23 3.57 3.04 2.4 2.1.3 ChargingandCurrentCollectiononAluminum Todeterminethesurfacechargingbehavioroftheconductingsphereinamesothermalplasma,the incidentcurrentfluxesatsteadystatearesummedupusingthefollowingequation: ∑ k J k (ϕ s ) =J i (ϕ s )+J e (ϕ s ) = 0 (2.1) 37 of124 2.1ConductingSphereCase which is a variation of eq. (1.1) by omitting the species that are not present, i.e. photoelectrons, secondary electrons, backscattering electrons. In the absence of UV radiation, there was no pho- toemission. Primary electrons can be very efficient at producing secondary electron yield from aluminum,however,atlowincidentenergy,suchastheexperimentalstationarythermalelectrons, fewsecondariesareejectedsincetheyarebelowtheworkfunctionof4.25eVofaluminum. Previ- ousstudiesmeasuredthesecondaryelectronemissioninducedbyprimaryargonionbombardment onanaluminumsurface,resultinginayieldof0.08atanincidentenergyof1keV[77]. Thismeans there is an 8% probability of a single electron emission for each incident ion impact. Due to the low yield, secondary electrons will be ignored for current balance computation. Backscattering electronswerealsoignoredalsoduetolowelectronenergy. Ratherthansolarwindionsandelec- trons,J i andJ e represents plasma source ion and electron current densities. Figure 2.6 illustrates the current flux at the surface of the sphere. For the electrically-isolated floating potential case, Figure2.6: Currentfluxofdriftingargonionsandthermalelectronsincidentonconductingsphere the surface potential of aluminum, ϕ s , charges in response to the incident drifting ions and ther- mal electrons until the net current flux reaches zero at steady-state. Conversely, a biased sphere perturbs the plasma field in response to the induced surface potential. While there is a divergence in the plasma beam as it expands into the vacuum chamber, the drifting ion population in the core of the beam is assumed to be collimated, for simplicity. Thus, the collecting surface for ions is 38 of124 2.1ConductingSphereCase the projected area of the sphere on the ram-side,A i =r 2 , as the cold ions lack sufficient thermal energytoovercomethekineticenergyofthebeam,resultinginavoidofionsatthewake-side. In contrast,themobilityofthethermalelectronsallowsthemtoreachthesurfacefromanydirection, hence, the electron collecting surface is the surface area of the sphere, A e = 4r 2 . Consequently, the current balance eq. (2.1) must be modified to reflect the differences in the collecting area of eachspecies, ∑ k I k (ϕ s ) =I i (ϕ s )+I e (ϕ s ) =J i (ϕ s )A i +J e (ϕ s )A e = 0: (2.2) Following current collection outlined from probe theory in section 1.6.2, approximations to eq. (1.12)-(1.17) were utilized to estimate the charging acquired on the surface of the sphere. In boththefloatingandbiasedcases,plasmaparameterssummarizedinTables2.1and2.2wereused to calculate and validate the surface potential (denoted by a lower caseϕ). The measured surface potential is determined asϕ s =ϕ bias - amb . For potentials that are negative with respect to ambi- ent, the current balance results are given in eq. (2.3)-(2.5). Similarly, surface potentials that are positivewithrespecttoambientaregivenineq.(2.6)-(2.8). Notethateq.(2.8)isatranscendental equation. Therepelledspeciescarriestheexponentialtermascurrentcollectionisreducedbythat factor. The velocity term for electrons, v t;e1 , is the one-sided flux speed to the surface, as seen in eq.(1.9). I i =en i v i A i ϕ s < 0 (attracted) (2.3) I e =en e v t;e1 A e exp ( eϕ s kT e ) ; v t;e1 = √ kT e 2m e ϕ s < 0 (repelled) (2.4) ϕ s = kT e e ln [ n i v i A i n e v tes A e ] (2.5) 39 of124 2.2DielectricSphereCase I i =en i v i A i exp ( eϕ s kT i ) ϕ s > 0 (repelled) (2.6) I e =en e v t;e1 A e ( 1+ eϕ s kT e ) ϕ s > 0 (attracted) (2.7) ϕ s = kT i e ln [ n e v t;e1 A e n i v i A i ( 1+ eϕ s kT e )] (2.8) Table2.2: Ambientparameters,measuredandcalculatedsurfacepotentials,(f)-float SphereBias amb [V] v i [km/s] v t;e1 [km/s] Measuredϕ s [V] Calculatedϕ s [V] +6.4V(f) +8.99 72.6 199 -2.59 -2.40 -20V +9.53 72.6 134 -29.5 – -10V +8.90 72.6 165 -18.9 – 0V +10.32 72.6 297 -10.3 -9.96 +10V +11.03 72.5 167 -1.03 -1.37 +20V +18.23 72.3 218 +1.77 +0.82 The calculated surface potentials are in good agreement with measured surface potentials for allcasesexceptforthelargenegativelybiasedcases,-10Vand-20V.Attheselargenegativebiases, electrons do not have sufficient thermal energy to overcome the potential barrier, thus, there is a netionfluxandcurrentbalancecannotbesatisfied. Giventheenergiesoftheparticles,theplasma sourceisnotcapableofreachinganequilibriumsurfacechargingforsuchextremenegativebiases. 2.2 DielectricSphereCase 2.2.1 ExperimentalSetupandPlasmaEnvironment The experimental setup for a dielectric sphere case was identical to the conducting, but with a sphere material of aluminum oxide (or alumina ceramic) instead. Aluminum oxide, Al 2 O 3 , is attractiveforengineeringapplicationsduetoitschemicalstability,strength,thermalandelectrical insulation characteristics, and its abundant availability. Alumina silicate does not readily come in spherical shape with the size of interest, thus aluminum oxide was chosen for the dielectric case. 40 of124 2.2DielectricSphereCase Consequently,theelectricalpropertyisnotadirectanalogtoJSC-1A,withalargerdielectriccon- stant of 9 [78]. Undoubtedly, the insulating material will have differential charging and therefore the Trek probe is not suitable for surface potential measurements as with the aluminum sphere. Instead, a single-strand, exposed wire fastened to the traversing system was used to approximate the surface potential of the dielectric sphere by direct-contact measurement, shown in Figure 2.7. Theprocedureandpositionforplasmaparametermeasurementswerethesameasthefloatingcon- Figure2.7: Sideviewofdielectricsphereforsurfacepotentialmeasurementwithanexposedwire bydirect-contact ductorcase,whilesurfacebiasesarenotapplicable. Figure2.8depictsthesameplasmaparameter contours as previously shown. The plasma potential here is slightly more positive than it is for aluminum. Other parameters are similar in the far field regions. Figure 2.9 illustrates the near- surfacepotentialandelectrondensity. Theplasmapotentialhasagreatrangeofvalues,wherethe ram-side measurements are more positive and the wake-side are more negative when compared withaconductor,asexpectedwithdifferentialsurfacecharging. 2.2.2 ChargingandCurrentCollectiononAluminumOxide Unlikewiththeconductingsphere,itisnotapplicabletoapplyfar-fieldplasmaparameterstodeter- minethecurrentbalanceforlocaldifferentialcharging. Instead,onemustconsiderthelocalcurrent flux to the surface. Additionally, secondary electron emissions are higher for insulating material than for metal targets (up to a factor of 5-10 for alkali halides) [79]. There is limited available data for insulators, particularly for low incident energies (< 10 keV), but it has been reported that 41 of124 2.2DielectricSphereCase (a) p ,plasmapotential (b)J i ,ioncurrentdensity (c)n i ,iondensity (d)n e ,electrondensity (e)n i n e ,space-charge (f)n e ,electrondensity Figure 2.8: Plasma environment around an dielectric sphere. Measurements were limited to dis- tancesgreaterthan6.35mmfromthesurface emission yields are proportional to impact velocities with energies below 40 keV. Following the work from Dietz and Sheffield (1975), secondary electron yield from ion bombardment onAl 2 O 3 was estimated to be 0.2 for incident velocities of 70,000 m/s [79]. For every 5 ions that impact at normal incidence, an average of 1 electron will be emitted. Moreover, the total electron yield has adependenceontheangleofincidence,asdescribedbyeq.(2.9),where (0)istheelectronyield atnormalincidenceangle( =0 ◦ ). Theincidentangulardependencewasobservedexperimentally for<70 ◦ . Thisisduetothefactthatanormalincidence,ionswillpenetratemoredeeplyintothe 42 of124 2.2DielectricSphereCase (a) p ,plasmapotential (b)n e ,electrondensity Figure 2.9: Near-surface contour of the plasma potential and electron density around dielectric sphere. Positionsforcurrentbalanceareindicatedon p solidwhileimpactatananglewillliberatemoreelectronsclosertothesurface,allowinganeasier escapepath. () = (0)sec() (2.9) Figure 2.10: Current flux of drifting argon ions, thermal electrons and secondary electrons on dielectricsphere Current collection on aluminum oxide sphere is illustrated by Figure 2.10. Surface potential calculation positions are indicated on Figure 2.9b, numbered 1 through 5 from ram-side to wake- sidesurface. Forpositions1and2,eq.(2.10)describesthecurrentcollectionforonlydriftingions and thermal electrons while eq. (2.11) includes the flux of secondary emission. Since secondary emission is not well-defined at glancing angles of incidence, position 3 only collects drifting ions 43 of124 2.2DielectricSphereCase described by eq. (2.10) and secondaries were not considered. Lastly, positions 4 and 5 are char- acterized by eq. (2.12), where ions approach the surface at the ion acoustic velocity, C s , from eq. (3.2), which does not have sufficient energy to induce secondary emission. For secondary emission,electronshaveatemperatureof2.2eVandanassociatedthermalspeedof248km/s. ϕ s = kT e e ln [ n i v i n e v t;e1 ] (2.10) ϕ sec = kT e e ln [ n i v i n e v t;e1 n i v sec sec() ] (2.11) ϕ s = kT e e ln [ n i C s n e v t;e1 ] (2.12) Table 2.3 summarizes the parameters for the current balance calculation and Table 2.4 sum- marizes the measured and calculated surface potential, ϕ s . The ion and electron densities were estimated by extrapolating the nearest measurement points from the field scans to the numbered positions. InthelastcolumnofTable2.4,that’sthenetpotentialwhensecondariesareincludedin thecurrentbalance,whichshouldreflectamorepositivepotentialthancolumn3. Secondaryemis- sion could net a positive surface potential when the surface has sufficient electron yield, but may notnecessarilybetruewhenimmersedinaplasmaenvironment. Sincethedriftingargonionsare generating the secondaries, surface potential resulting from secondaries alone were not estimated here. Thecalculatedresultsareingoodagreementwithdirect-contactwiremeasurementforposi- tions 4 and 5, where there is an absence of drifting ions and secondary electrons. In positions 1 through 3, measurements are more positive than the calculated ϕ s and ϕ sec . When implementing direct-contactmeasurementsinthepresenceofdriftingions,thesurfacepotentialisskewedbyion collectionoftheexposedwire,leadingtoamorepositivepotentialthantheactualsurfacepotential. Unless there is a good method to shield the incoming ions, the direct-contact method will inher- entlybeperturbedbytheplasma. Thecontributionofsecondaryemissionleadstoamorepositive 44 of124 2.2DielectricSphereCase surface potential; however, the results are not significantly influenced by the estimated electron yield. Theinfluenceonthecalculatedϕ sec fromtheangleofincidenceisnoticeablebetweenposi- tions1and2. Finally,itshouldbenotedthatthesurfacealterationsfromthebombardingionsand thermalelectronswilldrasticallychangethecurrentfluxtothesurface[79]. Figure2.11showsthe difference between the unaltered spheres compared with the tested targets, where alteration of the aluminum and the ceramic is evident. In the case of aluminum, signs of altered current collection are unmistakable after prolonged testing, as the floating potential drifts more negatively, as much as3to4volts. Table2.3: Estimatedparametersforsurfacepotentialscalculation SpherePosition n i [10 12 m 3 ] n e [10 12 m 3 ] v i [km/s] v t;e1 [km/s] ¬ 18.0 31.0 0 ◦ 72.7 166 19.6 34.3 36.9 ◦ 72.6 166 ® 9.03 18.7 90 ◦ 72.6 191 ¯ 1.60 4.70 – 2.08 229 ° 7.50 2.81 – 2.08 288 Table2.4: Measuredandcalculatedsurfacepotentialfordielectricsphere SpherePosition Measuredϕ s [V] Calculatedϕ s [V] Calculatedϕ sec [V] ¬ +0.219 -2.46 -2.12 +0.223 -2.48 -2.05 ® -2.25 -3.03 – ¯ -11.9 -10.3 – ° -10.3 -11.2 – 45 of124 2.3SimulationStudy: ExperimentalParameters Figure 2.11: Surface alteration of spheres after exposure to plasma source. Spheres below are clean,untestedspheres 2.3 SimulationStudy: ExperimentalParameters Next, the plasma-asteroid simulation model discussed in Appendix B is implemented to help explain the phenomena observed in the experiment. The IFE-PIC code is capable of modeling a conductingandadielectricsurfacebysolvingtheelectrostaticPoisson’sequationself-consistently. Ions and electrons were modeled as macro-particles and distributed “freely” in the simulation domain. Particles update the potential field which in turn updates the particle acceleration, veloc- ityandpositioneverytimestep,untilthesimulationreachesstead-state. Notincludedinthemodel aresecondaryelectronsthatmaybeemittedfromthesurfaceaswellasthebackground,unionized neutralargongas. Additionally,thesimulatedplasmaisassumedtospanoutinfinitelyintheradial direction,asopposedtocollimatedbeamintheexperimentexpandingintothevacuumchamber. 2.3.1 SimulationDomainandBoundaryConditions ThedomainsizeforIFE-PICmodelfortheexperimentalcaseisreducedto120x25x25PICcells, whichis120x1.5mmby25x1.5mmby25x1.5mminphysicalunits. Tominimizecomputational 46 of124 2.3SimulationStudy: ExperimentalParameters resources, axial symmetry is implemented with a quarter-sphere asteroid is centered at 40 cells downstream from X min . The same boundary conditions are applied as discussed in Appendix B. Particlesrepresenting plasma source electrons and ions are pre-loaded into the simulation domain and injected at X min , Y max and Z max , drifting in the positive x-direction. No photoemission was included for the experimental setup as there is no exposure to uv-illumination. To reduce round- offerrorswhenperformingcalculationswithextremelylargeorextremelysmallnumericalvalues, thegoverningequationsarenormalizedbyreferenceparameterssuchaslength,mass,temperature, potential energy, e, number density and velocity. The respective physical reference parameters are as follows: the Debye length, D = 1.5 mm, the electron mass, m e , the electron temperature, T e , the thermal energy, kT e , the electron density, n e , and the electron thermal velocity, v th;e . The normalized parameters for each species are listed in Table 2.5. The variable ^ n is the normalized density, ^ V isthedriftingvelocity, ^ v isthethermalvelocity,and ^ T isthetemperature. Table2.5: Normalizedionandelectronvelocitiesandtemperature Speices ^ n ^ V ^ v ^ T Electrons 1.0 0.0000 1.0000 1.00 Ions 1.0 0.1165 0.0013 0.25 2.3.2 SimulationResultsfortheExperimentalFlowField The plasma field for both the aluminum sphere and aluminum oxide sphere were modeled by the simulation. Figure 2.12 presents the steady-state simulation of the plasma potential, the ion density and the electron density for the floating conducting case with the same scan region as the experiment. Figure2.13showsthesameparametersforthenear-surfaceareatoresolvethedetails that were prohibitively difficult to measure with probes. The input for the dielectric constant was set sufficiently high such that charges accumulated on the surface were able to freely redistribute themselves uniformly on the sphere. The potential of the sphere floats to approximately -3.7 V, 47 of124 2.3SimulationStudy: ExperimentalParameters which is in good agreement with the experimentally measured and analytically calculated ϕ s of -2.6 V and -2.4 V, respectively. For both ion and electron densities, the wake region region in thesimulation has a sparse population incomparison with experimentalobservations. There are a couple of reasons that may explain the elevated ion densities in the vacuum chamber. First, in the presence of a neutral background population, collisions between high speed ions and slowneutral argons can result in a density of slow CEX ions and fast neutrals that was previously described in the wake charging experiments. Another possible reason for the high ion density relates to the Faradayprobeitself. ComparedwiththeEPandLP,thenudeFaradayprobehasalargercollecting area, resulting in limited resolution. When the probe is only partially eclipsed by the sphere, it would collect additional drifting ions and skews the results to a higher density. In contrast, the Langmuir probe may also be skewed to an elevated electron current collection, despite its smaller size. As the probe sweeps through its voltage bias to generate an I-V curve, plasma sheath also grows in size, thus collecting more electrons in an expanded volume, particularly in the wake region where the lower density equates to a larger Debye length. However, the more negative plasma potential measured by the EP in the wake would suggest that there is an elevated electron populationrelativetotheiondensity. Thenumericalsimulationhighlightsastarkcontrastbetween theplasmaflowandwakeregionpopulation,whilethediffuseappearanceinthelabmeasurements couldbepartiallyattributedtotheinterpolationmethodoftheimageprocessorthatwasused. Similarly,Figure2.14showsthesteady-statesimulationoftheplasmaparametersforthefloat- ing dielectric case for the large scan region and Figure 2.15 depicts the near-surface region. The inputforthedielectricconstantof9correspondstothematerialpropertyofaluminumoxide. The most significant difference in this simulation for the dielectric case is the differential potential on the surface. The surface potential is actually in very good agreement with the current balance calculationsforϕ s . Thewakeregionpotentialsarealsomorenegativeascomparedwithconduct- ing case, which is expected as the ceramic surface charges more negative locally, consistent with 48 of124 2.3SimulationStudy: ExperimentalParameters (a) p ,plasmapotential (b)n i ,iondensity (c)n e ,electrondensity Figure2.12: Plasmasimulationaroundaconductingsphere experimental results. The void of electrons in the wake is slightly larger compared with the con- ductingtargetforthesamereason. Quantitativedifferencesbetweentheexperimentandsimulation examinedfortheconductingcasealsoapplytothedielectriccase. 49 of124 2.4SummaryandConclusion (a) p ,plasmapotential (b)n i ,iondensity (c)n e ,electrondensity Figure2.13: Near-fieldsimulationaroundaconductingsphere 2.4 SummaryandConclusion A laboratory study was carried out to measure the charging of a conducting sphere and a dielec- tric sphere in a collisionless, mesothermal plasma. The surface potentials of the conducting case wereobtainedutilizingtheasuspendedwireelectricallyconnectedtoameasurementplateoutside the vacuum chamber. For the dielectric case, the surface potential was obtained by employing a direct-contactmethodwithanexposedwire. Theresultsshowedthatthesurfacepotentialscharged 50 of124 2.4SummaryandConclusion (a) p ,plasmapotential (b)n i ,iondensity (c)n e ,electrondensity Figure2.14: Plasmasimulationaroundadielectricsphere accordingtocurrentbalancetheorybyaccountingforthenetfluxofchargedspecies. Thesimula- tionresultsprovidedvalidationoftheexperimentalobservations,buildingonourunderstandingof theplasma-asteroidinteractioninalaboratorysetting. Thenumericalmodeldevelopedissuitable forextrapolatingdynamicsofplasma-asteroid-dustinteractionsinspace. 51 of124 2.4SummaryandConclusion (a) p ,plasmapotential (b)n i ,iondensity (c)n e ,electrondensity Figure2.15: Near-fieldsimulationaroundadielectricsphere 52 of124 CHAPTER 3: LABORATORY SIMULATIONS OF PLASMA-DUST SURFACE CHARGING IN A LOCALIZED WAKE Laboratory measurements are crucial to build up our knowledge of plasma-surface interactions. Previousexperimentalworkfocusedonthechargingofa“dust-in-plasma”inathermal,stationary plasma or in electron beams, where the presence of neighboring grains did not affect dust charg- ing. However, dust charging on the asteroid/lunar regolith surface is completely different from that under the “dust-in-plasma” condition. As the inter-dust distance is almost zero, the sheaths surrounding each individual dust grains overlap to form one single sheath over the surface, and hence the charging on a single dust grain is strongly affected by the presence of the neighboring dust grains. The overall goal is to try to understand the entire sequence of interactions from the global plasma environment to the local plasma interaction to asteroid surface charging and finally to dust levitation and transport. The specific objective of this chapter is to present two different aspects in the following sequence 1) the mesoscale plasma flow-surface interactions and 2) dusty surfacecharging. 3.1 PlasmaWakeDustChargingSetup This experimental study combines dusty surface charging and plasma flow effects. The intention is to simulate regolith surface charging in a localized plasma wake environment similar to that found at the lunar terminator in a laboratory. While the conditions at the lunar terminator are different than those of an asteroid environment, the lunar environment is better understood and characterized. Itservesasareferencebaselinestudywithcomparisonstolunarobservations,prior toextendingtheanalysistoasteroidstudies. Atthelunarterminator,alocalizedplasmawakewill 53 of124 3.1PlasmaWakeDustChargingSetup begeneratedbyanobstacle(suchasarockoramountain)thatblockstheplasmaflow. Thepoten- tial of the obstacle surface on the ram side is typically either close zero or slightly positive with respect to the ambient plasma due to photoelectron emission, while the potential of the regolith surfaceinthewakeregionisnegativewithrespecttotheambient. Figure3.1showsaschematicof ourexperimentalsetuptosimulatethisscenariotomeasureregolithsurfacecharginginconnection with the plasma wake. The experiments were performed in a vacuum chamber. The average solar wind plasma is simulated by a 4-cm gridded ion source which generates a mesothermal plasma. Thescanregionindicatesthelocationofthemeasuredplasmaflowfieldparameters. Figure3.1: Schematicofexperimentalsetup: plasmasource,aluminumcube,theplasmaflowfield scanregion,andasampletargetplate(locatedbelowscanregion) Togeneratealocalizedplasmawakeregion,a10.2cmx10.2cmx10.2cmgroundedaluminum cubeisplaced7.6cmdownstreamoftheplasmasource(Figure3.1bandFigure3.2a). Theleading edge of the target surface is placed behind the cube at a distance of 17.8 cm from source exit and positioned at two different depths, h 1 and h 2 (Figure 3.1b and Figure 3.2b) from the top of the cube so as to measure surface charging in different plasma wake environments. To simplify the analysis of the wake structure, we consider a 2-D plasma wake region in this study. Two Kapton covered side walls were placed on the sides of the block to limit the edge effect of plasma flux from entering the region laterally so as to ensure that the expansion is 2-D in the wake region. Measurements of field characteristics and surface charging were taken near the centerline behind 54 of124 3.1PlasmaWakeDustChargingSetup theblock,whichwefindismorethan12Debyelengthawayfromthesidewall. Hence,theeffect ofthesidewallsonthemeasurementsisminimal. (a)Sideviewinsidevacuumchamber GND Cube JSC-1A h h 1 h 2 X 1 X 2 X 3 X (b)Sideviewoftargetposition (c)Topviewfromthe+z-direction Figure 3.2: Plasma wake dust charging experiment setup. Position of the target plate indicated by depthsh 1 andh 2 fromthetopofcube 3.1.1 TargetSurfaceMaterials Surface charging is highly dependent on the electrical properties of the material. Two types of targetsurfacesareconsideredtocomparesurfacecharging: aregolithsurfaceandasoliddielectric surface placed side-by-side, as viewed in Figure 3.2c. The first is JSC-1A lunar simulant surface with a relative dielectric constant of 3.6–4.22 [80]. JSC-1A was created by Johnson Space Center fromglass-richbasaltictuffminedfromacommercialquarryattheMerriamCraterinArizona. Its compositionhasbeenmeasuredtobe46.2%SiO 2 ,17.1%Al 2 O 3 ,11.2%FeO,9.43%CaO,6.87% MgO,3.33%Na 2 O,1.85%TiO 2 ,andothertraceoxides. JSC-1Alunarsimulantmostcloselyrep- resents S-type asteroid surfaces where spectral absorption observations indicate silicate features. ThesecondisasmoothsolidaluminasilicateAl 2 SiO 5 surface,whichhasarelativedielectriccon- stantof5.6–6.8[81]. Thedielectricconstant,ortherelativepermittivity,isameasureoftheability ofamaterialtokeepelectricalchargesphysicallyseparatedbyadistance. Bydefinition,thedielec- tric constant of vacuum is 1. Electrical resistivity quantifies how easily a material resists the flow of electrical current. The loss tangent is the inherent dissipation of electromagnetic energy. The lattertwoquantitiesarebothtemperaturedependent. Inthisexperiment,theJSC-1Ahasaparticle 55 of124 3.1PlasmaWakeDustChargingSetup radius distribution of 50 20 m. The regolith surface layer thickness is measured to be 3 mm, whichisthesamethicknessasaluminasilicatesolid. Thesimilardielectricconstantsbetweenthe twomaterialswerechosentominimizethevariationinelectricalproperties. Itshouldalsobenoted thatthesedielectricmaterialshaveanaffinitytoretainmoisturefromambienthumidity,whichcan significantly alter the charging state of the surfaces. Thus, the target surfaces were placed under vacuum overnight and baked with a sheet heater (placed on the underside of the sample) prior to chargingtoensureanyabsorbedwaterwasoutgassed. Table3.1: Targetsurfacematerialproperties Properties Al 2 SiO 5 JSC-1A LunarSoil Dielectricconstant 5.6–6.8 3.6–4.22 2–11 Electricalresistivity[Ωm] 10 12 10 14 10 10 –10 13 Losstangent 0.01–0.05 0.003–0.021 0.001–0.1 (a)JSC-1Alunarsimulant (b)AluminasilicateAl 2 SiO 5 solid Figure3.3: Targetmaterialsforsurfacecharging 3.1.2 PlasmaOperatingConditionsandScaling It is not feasible to generate a plasma environment with identical properties to those of the solar wind plasma in a vacuum chamber. In particular, the operation of a plasma source in a vacuum chambermayintroduceafacilityplasmanotinherentinthelunarplasmaenvironment. Theeffects of a facility plasma in our experiment were studied both experimentally and numerically [82, 83]. 56 of124 3.1PlasmaWakeDustChargingSetup The plasma emitted by the source includes beam ions with energy of 500 eV, thermal electrons, withenergyofafeweV,andalowenergycharge-exchange(CEX)ionpopulationduetocollisions between between beam ions and unionized propellant neutrals. The CEX ions are the dominating component of the facility plasma [82]. The propellant CEX production rate is calculated from the neutraldensityn n ,beamiondensityn i ,beamionvelocityv i ,andtheCEXcollisioncross-section CEX by dn CEX dt =n n n i v i CEX (3.1) where n n and n i are determined in turn by propellant flow rate _ m and propellant utilization effi- ciency b , and CEX is a function of ion beam energy E b . Two different propellants were tested, N 2 gas and Ar gas, and we found that the CEX ion production rate for N 2 is about 40% less than Ar for the desired beam plasma parameters. ForE b = 500 eV, N 2 plasma flow can produce a dis- tinctiveplasmawakestructurebehindthecube. However,anArplasmaflowisdivergentatanion energy of 500 eV, which does not reflect the lunar terminator flow field with a 0 ◦ angle of attack. Foracollimatedplasmabeam,Arplasmahastooperateatanionbeamenergyof1100eV,which for the given experimental geometry yields a limited wake expansion behind the cube. Hence, N 2 ionswerechosentorepresentmesothermalplasmaflow. Figure3.2bshowstherelativepositionsofthetargetplatewithrespecttothecube. Theplasma parametersassociatedwiththeplasmaflowweremeasuredbothnearthesourceexitandinascan Table3.2: Averageexperimentalplasmaparametersfor“ambient"conditionsinthewakeregion AmbientConditionforPlasmaWake IonDensity n i0 4.7910 13 m 3 ElectronDensity n e0 6.5710 12 m 3 ElectronTemperature T e0 2–4eV DebyeLength D0 3.97–5.61mm IonDriftingVelocity v i0 59.0km/s ElectronThermalVelocity v te0 593–839km/s 57 of124 3.1PlasmaWakeDustChargingSetup region behind the cube. Along the beam direction (x-direction), the scan region is from x = 55 to 180mmbehindtheblock. Perpendiculartothebeamdirection(z-direction),thescanregionisfrom about20mmabovethetargetplateto75mmabovethetopedgeofthecube. Table3.2summarizes the average ion density n i0 , electron density n e0 , and electron temperature T e0 for the ambient condition of the plasma wake. Here, the ambient is defined as the condition before the plasma flow undergoes the expansion. To represent the ambient condition for the plasma wake, plasma parametersweretakenwithinthebeamcoreregionjustabovethecubeedgeattheleftscanregion boundary (at x = 55 mm, z≃ 5–25 mm, beam centerline at z≃ 14 mm). Table 3.2 also lists the plasmaDebyelength,N + 2 ionvelocity,andelectronthermalvelocitycalculatedfromthemeasured ambient plasma parameters. In the vacuum chamber, the measured ion streaming velocity and electron temperature in the wake region are v i0 ≃ 59 km/s and T e0 ≃ 2.5 eV, respectively. In a collisionlessplasma,theionacousticspeedcanbegivenaseq.(3.2). Hence,theMachnumberfor theplasmaflowintheexperimentiscalculatedineq.(3.3). C s = √ kT e m i (3.2) M Lab = v i0 C s ≃ 20 (3.3) TheaveragesolarwindconditionsaresummarizedinTable1.1,forreference. Inspace,ionand electron densities are significantly more rarefied as compared to a vacuum chamber environment. The Debye length is inversely proportional to the square root of the number density. Electrons created in the lab are less energetic than that of the solar wind electrons. Solar wind ions are hydrogen ions; for a given kinetic energy, laboratory ions are slower due to their higher mass. Electrons from a plasma source are also slower as a result of their lower temperature. For scaling analysis to relate the plasma environment in the vacuum chamber to the solar wind, we compare theplasmaflowMachnumberandtheDebyelength. Letusconsideranaveragesolarwindplasma density of 4x10 6 particles/m 3 , a plasma flow velocity of 700 km/s, and an electron temperature of 20 eV. These parameters yield a Debye length at the lunar surface of D;sw ≃ 16.6 m and an ion 58 of124 3.2PlasmaWakeExpansionResults Table3.3: Experimentalcasesandscalinglengths Cases InLaboratory InDebyelength OnLunarSurface D0 =3.97mm D;sw =16.6m h 1 95.3mm 24.0 D0 400m h 2 57.1mm 14.4 D0 240m flowMachnumberatthelunarsurfaceofM sw ≃16. Inourexperiments,theMachnumberofthe plasma flow in the vacuum chamber, M Lab , is similar to that at lunar surface, M sw . However, the Debye length in vacuum chamber is much smaller than that at lunar surface due to a much denser plasma environment. Hence, one needs to scale the spatial dimension using the Debye length in ordertorelatethemeasurementsinvacuumchambertothelunarsurfacecondition. As indicated in Figure 3.2b, h denotes the vertical depth between the target plate and the top edgeofthecube. Inthefollowingsection,wepresentmeasurementsfortargetplateplacedattwo different vertical depths, h 1 and h 2 . Table 3.3 lists the values of the vertical depths in physical unit, in terms of the Debye length D0 , and their equivalent values under typical lunar plasma environment. Under the typical lunar plasma environment, h 1 and h 2 would be approximately 400mand240m,respectively. 3.2 PlasmaWakeExpansionResults Plasma diagnostics were utilized to characterize a full set of plasma parameters in the scan region behind the block and above the JSC-1A/Al 2 SiO 5 target surface. Measured spatial distributions of plasma potential , ion current density J i , ion density n i , electron density n e , and electron temperatureT e arepresentedinFigure3.4and3.5forthetwodustsampletargetdepthsconsidered, h 1 and h 2 . Faraday probe measurements were carried out both axially (along the plasma beam direction) and radially (perpendicular to the beam direction) to obtain the ion velocity vectors shown in the second row of Figure 3.4. Figure 3.6 shows the 1-D profiles of , n i , and n e along 59 of124 3.2PlasmaWakeExpansionResults thez-axisatthreedownstreamdistancesfromthecubefortheh 1 case. (1-Dprofilesfortheh 2 case are similar). The downstream distances are X 1 = 63.5 mm (16.0 D0 ), X 2 = 102 mm (25.6 D0 ), andX 3 =140mm(35.2 D0 ). (a)h 1 =24:0 D (b)h 2 =14:4 D Figure3.4: Plasmapotential,ioncurrentdensitycontours,andionvelocityvectorsath 1 andh 2 60 of124 3.2PlasmaWakeExpansionResults (a)h 1 =24:0 D (b)h 2 =14:4 D Figure3.5: Iondensity,electrondensity,andelectrontemperaturecontoursath 1 andh 2 61 of124 3.2PlasmaWakeExpansionResults A collisionless mesothermal plasma flowing over an object generates a plasma wake due to plasma expansion [84, 85]. Behind an unbiased object, the plasma wake consists of the expan- sion waves generated at the object’s corner, and its steady-state structure is also analogous to the Prandtl-Meyer expansion fan generated by a supersonic gas flowing around a corner [85]. Under the ideal situation, the trajectories of the ions are turned in such a way that the velocity normal to each expansion fan characteristic line is always at the ion acoustic velocity C s . As the plasma expandsintothewakeregion,theelectricpotential,iondensity,andelectrondensitydecrease[85]. As the diameter of our plasma source is only 4 cm, the plasma beam above the cube is not uniform. Thebeamcenterlineispositioned14mmabovethecube. However,thedecreasein,n i , andn e in the radial direction behind the block due to plasma expansion is obvious in Figures 3.4- 3.6. Figure 3.7a and 3.7b further show the energy distribution associated with the ion velocity component in the beam direction and the radial direction, respectively. Figure 3.7a confirms that the streaming ions that flow over the block with a peak energy E b of 500 eV. Figure 3.7b shows that the radial ion distribution has a peak energy of 2.5 eV, which was measured in the wake region 25 mm below the top of the scan region (just below the top surface of the cube). While the electron temperature contour plots are noisy due to both the limitations of our plasma source and the diagnostic techniques, Figure 3.5 shows that the electron temperature in the wake region is around T e 2–3 eV. As the plasma beam undergoes expansion, the ions accelerate to C s and have energies similar the electron temperature. Due to the trajectory of drifting ions, it is unlikely theradialRPAmeasurementsaredirectlydetectingthisspecies. Perpendiculartotheplasmaflow, ions have a thermal motion similar to the neutral background gas. As the drifting ions collide with the neutrals, CEX ions born in the main beam accelerate into the wake region, also at the ion acoustic velocity. These are mostly likely particles detected radially by the RPA in the wake region. Hence, Figure 3.7b indirectly confirms that the ion velocity perpendicularly to the beam direction is centered around the ion acoustic velocity C s , consistent with the energy associated withtheexpansionofamesothermalplasmainthewake. 62 of124 3.2PlasmaWakeExpansionResults Figure3.6: ,n i ,andn e z-profilesath 1 (dottedlinerepresentsboundaryofwakeregion) (a) Energy distribution of N 2 plasma beam ions measuredaxiallyintheambientregion (b)EnergydistributionofN 2 CEXionsmeasured radiallyinwakeregion Figure3.7: IonenergydistributionfromRPA 63 of124 3.3RegolithSurfaceCharginginPlasmaWake 3.3 RegolithSurfaceCharginginPlasmaWake We next show surface charging measurements that were observed on a target surface of JSC-1A simulantaswellasonasmoothsoliddielectricsurfaceofAl 2 SiO 5 intheplasmawake. Figure3.8 shows the results of the surface potential with respect to the ambient plasma measured by a Trek non-contactingESVM.TheregiononthetargetsurfacemeasuredbytheTrekprobeisfrom25to 130 mm behind the cube. Based on a normal distribution and deviations, the statistical error bars reflecta95%confidencelevelonthemeasuredsurfacepotential. Figure 3.8: JSC-1A simulant surface potential (solid lines) versus Al 2 SiO 5 smooth solid surface potential (dashed lines) for the h 1 and h 2 case. The potential shown is with respect to ambient plasmaflow. The solid Al 2 SiO 5 dielectric surface in the plasma wake is negatively charged with respect to the ambient plasma. For theh 1 case (surface position: 24 D0 below the cube edge and 6.25 D0 – 32.5 D0 behind the cube), the surface potential ranges from s -6 to -5 V. For the h 2 case (surface position: 14.0 D0 below the cube edge and 6.25 D0 –32.5 D0 behind the cube), s is less negative than that in the h 1 case, ranging from s -2.5 V to -0.5 V. For both cases, s 64 of124 3.3RegolithSurfaceCharginginPlasmaWake is more negative at the end closer to the cube. These results are consistent with the plasma flow field in the wake. The floating potential of the target surface is determined by the current balance accordingtoprobetheoryeq.(1.4)-(1.17). Inamesothermalplasmaflow,theionflowtothetarget surfaceissignificantlyreducedbythecubeinfrontoftheionbeamwhiletheelectronsstillfollow the random thermal motion. This leads to more negative charging for those positions that are at larger vertical distance h below the cube edge and at closer horizontal distance to the cube. The measured s is consistent with the current balance calculation utilizing the measured parameters atthebottomlocationoftheplasmascanregioninthez-directioninFigure3.4and3.5. ThepotentialoftheJSC-1Aregolithsurfaceintheh 1 caseissimilartothatofthesoliddielec- tric surface. However, the regolith surface potential in the h 2 case significantly differs from the soliddielectricsurface,rangingfromabout0Vatthenearendtoalmost6Vpositivewithrespect totheambientatthefarend. Thesurfacepotentialdifferencebetweenthesoliddielectricsurfaceandtheregolithsurfacein the h 2 case may be explained by the effect of microscale features of the regolith surface on ion collection. On a regolith surface, the current collection is through the surface of each individual dustparticle. Inamesothermalplasmaflow,ioncurrentcollectionissensitivelyinfluencedbythe surface orientation with respect to the ion streaming direction. In theh 1 case, ion impingement is primarily along the normal direction of the surface. Hence, the surface area that collects ions is similarforboththeregolithsurfaceandthesolidsurface. Therefore,theregolithsurfacepotential and the solid surface potential are also similar. In theh 2 case, the ions impinged the surface with an angle of attack because the plate is in a shallow wake. Hence, each dust particle will have a fraction of the surface facing the ion streaming direction. Therefore, ion current collection by the regolith surface is enhanced by the ram side dust surface facing the ion stream. The enhanced ion currentcollectionleadstoamorepositivefloatingpotentialfortheregolithsurface. 65 of124 3.4DustChargeonRegolithSimulantSurfaceintheWake 3.4 DustChargeonRegolithSimulantSurfaceintheWake Itisalsointerestingtoestimatetheaveragechargeofindividualdustgrainsonthesamplesurface. Dingetal. [86]studiedthechargingofindividualdustgrainsforapositivelychargeddustysurface. Following the same approach, let’s consider a spherical dust grain for the two different charging Figure 3.9: Charging model for a spherical dust grain with incident current, I i , and secondary- inducedcurrent,I si models depicted in Figure 3.9. On a dusty layer of thicknessd layer , with permittivityof free space ϵ o andrelativedielectricconstantϵ rd ,thelocalsurfacechargedensity is = dQ dA = dC dA s = ϵ o ϵ rd d layer s : (3.4) Thechargeaccumulatedonasingledustgrainwitharadiusr d onthesurfaceis Q d =r 2 d : (3.5) From the above two equations, we can derive the average charge per dust particle on the regolith surfacefromthemeasuredJSC-1Asimulantsurfacepotential s . Mostpastlaboratorymeasurementsondustcharginghavebeencarriedoutforasingleisolated dustgrain. Mostmodelingstudiesinvolvingdustchargingonthelunarsurfacealsoutilizedsingle dustgrainchargingmodelsorresults. Incontrasttothedustysurfacechargingmodelineq.(3.5), an isolated grain is not characterized by the collective mutual capacitance from nearby dust but ratheracapacitancebetweenthesurfaceandfreespace/vacuumchamberwallinwhichthemedium 66 of124 3.5ExperimentalRemarks isonlythevacuum. Hence,forcomparison,wealsocalculatedthechargeaccumulatedonasingle isolateddustgrainwiththesameradiusr d andthesamedustpotential s from Q d;iso = 4ϵ o r d s : (3.6) The results are compared in Table 3.4. We find that, at the same negative charging potential, the charge of a single isolated dust grain is about a factor of 50 greater than that of an individual dust grain on a regolith surface. The measurements in [86] show that, at the same positive charging potential, the charge of a single isolated dust grain is about two orders of magnitude greater than that of an individual dust grain on a regolith surface. The results in this chapter further confirm ourpreviousconclusionthatthechargestoredbyanindividualdustgrainonaregolithsurfacewill be significantly reduced as compared with that of a single isolated dust particle. The dust charge reduction on a regolith surface is due to the reduction of the dust’s self-capacitance as a result of dust-dustinteractions[86]. Table 3.4: Average charge of individual dust grain on regolith surface Q d versus charge of an isolateddustgrainQ d;iso Case s [V] Q d [10 16 C] Q d;iso [10 16 C] h 1 -5.00 -5.54.0 -278111 h 2 4.03 4.53.2 22490 3.5 ExperimentalRemarks Laboratory experiments were carried out to measure lunar regolith surface charging in a local- izedplasmawake. Theseexperimentswerescaledtoapproximatelyreflectlunarsurfacecharging behind a mountain at the lunar terminator under average solar wind conditions. The charging of aJSC-1AsimulantsurfaceisalsocomparedagainstthatofasmoothsolidAl 2 SiO 5 dielectricsur- faceundersimilarplasmawakeconditions. Inadeepwakewheretheionflowisalmostnormalto 67 of124 3.5ExperimentalRemarks the surface, the potential of a regolith surface is similar to that of a solid dielectric surface. How- ever, in a shallow wake where ions impinge the surface at a small angle of attack, the potential of a regolith surface can be significantly more positive than that of a solid dielectric surface. The resultssuggestthationcurrentcollectionbyaregolithsurfacecanbequitedifferentthanthatbya soliddielectricsurfaceinaplasmawakeenvironment. Asioncurrentcollectioninamesothermal plasma flow is sensitively influenced by the surface orientation, the ram side fraction of the dust surfacecan enhanceoverallion current collectionby interceptingthe streaming componentof the incidentionflux,resultinginamorepositivepotentialthanthatofasolidsurface. Theresultsalso showed that, at the same negative charging potential, the charge on an isolated dust grain is about 50timesgreaterthanthatofadustgrainontheregolithsurface. Adetailedmodelingstudytaking into account of the microscopic geometric features of a regolith surface is essential in order to quantitatively predict the current collection and charging of a regolith surface. Laboratory results areutilizedtodevelopnumericalsimulationsandputconstrainsonphysicalparameters. 68 of124 CHAPTER 4: PLASMA-ASTEROID-DUST TRANSPORT MODEL Inanefforttomodelthedynamicsbetweenthesolarwindplasma,asteroidsurfaceanddustgrains near a small asteroid, it’s important to account for all the forces acting on a dust grain in that environment. The equation of motion of a charged particle around a small object in space, again, isasfollows: m d dv d dt =Q d (r 0 ;t)[E(r)+v d B(r)]+m d g a (r)+F SRP (r) (4.1) Previous chapters have addressed the electric field,E(r), with the fully kinetic IFE-PIC plasma- asteroidmodel,thechargestateofdust,Q d (t),withlaboratorysimulationoflocalizedwakesurface charging,andthesurfacepotential,ϕ s ,withlaboratorysimulationofasphereimmersedinplasma. Inthischapter,thegravitationalfieldofanasteroid,g a (r)isaddressedaswellasthedusttransport model to incorporate all the competing effects, including the solar radiation pressure, F SRP (r). Notethattheaboveequationdoesnotapplytothesituationwhereinter-dustcollisionsdominatethe process. For an unmagnetized asteroid, the electrostatic equation of motion of a charged particle issimplifiedtothefollowing: m d dv d dt =Q d (t)E(r)+m d g a (r)+F SRP (r) (4.2) 4.1 GravitationalFieldModelingnearSmallAsteroids 4.1.1 GravityModelingTechniques When a dust grain is sufficiently far away from the asteroid, one may use a zeroth-order gravity model for the asteroid. Assuming a spherical, homogenous body, the gravitational field from 69 of124 4.1GravitationalFieldModelingnearSmallAsteroids asteroidmaybesimplifiedasthatfromapointsource:g a (r) = r 3 r,whereristhedistancefrom dust to asteroid center and is the standard gravitational parameter, defined as the product of the gravitational constant G and the mass of the asteroid M. However, near the asteroid, the effects from the irregular shape and non-homogenous internal density on gravitational force cannot be ignored. Developing an accurate gravity field model of asteroids is a challenging astrodynamics task. Conventional approaches to gravity-modeling include spherical and ellipsoidal harmonic expansion series. For objects approaching a spherical geometry, harmonic expansion is a very goodapproximationofthegravityfieldoutsidetheBrillouinsphere[20,21]. However,duetothe variabilityofthedensityandirregularitiesofasteroidbodies,classicalharmonicexpansionmodel havelimitedapplicationwitherrorsdemonstratedexceeding100%. Auniform-densitypolyhedral shapemodelapproachoffersaccuratesolutionuptothesurfaceofthebody,however,thismethod is computationally intensive and does not to address internal variations [20]. The methodology developed by Park et al., a finite-element (FE) model of the asteroid gives validity of the local gravity within the Brillouin sphere, along with the capability to establish a non-uniform interior massdistribution,[23]. 4.1.2 Finite-ElementMassConcentrationApproach The finite-element mass concentration approach utilizes discrete spherical mass elements repre- sented as point sources. The relative positions between these particles are fixed and rotate in circular motion about a common spin axis with constant angular velocity. The positions of these particlesinthebody-fixedframearedenotedas i ,fori=1,2,3,...,N. Theexternalgravitational accelerationisgivenby ∇U m = @U @r = N ∑ i=1 Gm i jjr i jj 3 (r i ) (4.3) 70 of124 4.1GravitationalFieldModelingnearSmallAsteroids where G is the gravitational constant, m i is the mass of the i th particle, andr is the field position vector. Inessence,thefinite-elementmodelisacircular-restrictedN+1bodyproblem,where“N” denotesthenumberofparticlesthatmakeuptheasteroid. The“1"denotesthedustgrain[24]. 4.1.3 SphericalBodywithFEMASCONmodel TheorbitaltrajectoryresultshowninFigure4.1isanFEMASCONmodelforaspherical,homoge- nous body of 1 km in size with 5975 elements. Nominal trajectory denotes a point source model. To avoid any overlap of mass elements, spherical particles fill the internal volume in a hexagonal close packing scheme, proven to be the densest possible packing of equal spheres for a packing density of 74% [87]. This would imply an asteroid porosity of 26% and a bulk density of 2.22 g/cm 3 . For modest computational demand, FE MASCON methodology provides reasonable accuracy in the simplest approach, making it an ideal candidate for gravitational field estimation. ThetrajectoryoftheFEmodelshowninaredisthemanifoldof10orbitalperiods. Figure4.1: Finite-elementmodeltrajectoryofaspherical1kmasteroid 71 of124 4.2SolarRadiationPressureonDustGrains 4.2 SolarRadiationPressureonDustGrains The effect of solar radiation pressure on dust grains are not negligible relative to the gravitational and electrostatic forces. In the method presented by Hamilton and Burns [44], radiation pres- sure follows the same inverse square radial dependence as solar gravity. Thus, radiation force is oftenexpressedasproductofdimensionlessquantity andtheSun’sgravitationalforce[43]. For sphericalparticles,theradiationforcecanbecalculatedbyeq.(4.4). F SRP (r) = s a 2 ^ { (4.4) = 3L s 16 s c Q pr d r d = 5:77x10 5 Q pr d r d (4.5) Solar parameters are defined as standard gravitational parameter s and luminosityL s at distance a. Thevariablecisthespeedoflight. Dustpropertiesaredefinedincgsunitsasgrainmassdensity d , grain radiusr d , and radiation pressure optical coefficient Q pr . Photographs and sample return showparticlesonasteroidsrangefrommicron-sizedfinestocm-sizedpebbles. Previousstudiesof radiationpressureonparticlestypicallytakeQ pr =1,assumingcompleteradiationabsorption. The numericalvaluegivenineq.(4.5)representssolarparametersataheliocentricdistanceof1AU. 4.3 DustTransportModel The dust transport model incorporates the results of IFE-PIC simulation, dust charging measure- ments,andgravitationalfieldmodel. Thedynamicsofchargeddustmotionineq.(4.2)aremodeled in a 3-D PIC particle push scheme similar to the IFE-PIC approach. Gravitational field is repre- sented by the FE MASCON model and effects from other bodies are not considered. Dielectric surfaces are expected to have a charge time ≪ 1 s [25], so the electric field E(r) and surface potential s are assumed to be at steady-state and spatially dependent. While the dust charge Q d isexpectedtobetime-dependentasafunctionofthelocalcurrentbalance,thismodelassumesthe 72 of124 4.3DustTransportModel charge to be time-invariant throughout the dust transport simulation, determined by the asteroid surfacepotentialasafunctionofinitiallocalposition,Q(r 0 ). Solarradiationpressureinfluenceon grainsisincorporatedintothismodel. Theequationofmotionforthisdusttransportmodelshould berewrittenas m d dv d dt =Q d (r 0 )E(r)+m d g a (r)+F SRP (r): (4.6) 4.3.1 SimulationDomainSetupandInitialConditions The domain size for dust transport model is the same as IFE-PIC model, 120 x 30 x 30 PIC cells, for a total of 108,000 cells, with the same asteroid position, at x = 40. For an axially symmetric setup, a particle reflection boundary condition is applied at Y min , and Z min and particle rejection at all other boundaries. At the asteroid surface interface, a charged dust particle rebounds at a randomly-defined oblique plane (that is, the surface normal vector is perturbed) with a coefficient of restitution of 0.8 while the asteroid rotation also imparts momentum at the point of impact. The model considered an asteroid size of 28 m, similarly sized to the near-Earth asteroids 1998 KY26,2004FH,367943Duende,and2014RC.Asteroidanddustcharacteristicsforthemodelare summarized in Table 4.1, whereas the plasma characteristics are summarized in Table 4.2. At the givenbulkandgraindensities,thismodelconsidersanasteroidalinternalstructurewithauniform andisotropicmicroporosityof27%[5,17]. Effectsfromotherbodiesarenotconsidered. Table4.1: Asteroidandgrainsimulationparameters Asteroidgeometry spherical,28m Graingeometry spherical Solardistance 1AU(NEA) Bulkdensity 2.8g/cm 3 Graindensity 3.0g/cm 3 Coefficientofrestitution 0.8 Grainsize 20m Rotationalperiod 7.6hrs Dielectricconstant 4.0 Thesimulationconsidersinitialconditionsforanelectrostatically-levitateddustgrainfromthe surfacewithzeroinitialvelocityintheabsenceofinter-graincohesion. Thedustgrainsonadusty 73 of124 4.3DustTransportModel surface charge to the same local ϕ s as determined by the plasma-asteroid interaction model and weresampleduniformlyfromtheasteroidsurfaceateverytimestep. Foreachtimestep,200parti- clesweresampledandthenumberofdustparticlesreached4–8millionatsteady-state. Initially at rest, dust particles are subsequently mobilized electrostatically by E(r) for four charge-mass ratio cases, first is the neutral case (∥Q/m∥ = 0 C/kg), followed by laboratory measurement cases asmentionedinChapter3,thedustysurfacechargingmodel,Q d (∥Q/m∥110 7 C/kg)andthe isolated charging model, Q iso (∥Q/m∥ 110 4 C/kg), and lastly by increasing dust charge to 1000xgreaterthanQ iso (∥Q/m∥110 1 C/kg),effectivelyraisingtheelectrostaticforcerespec- tively. Simulation parameters are summarized in Table 4.3. The simulated dust distributions are discussedinthenextchapter. Table4.2: Averagesolarwindplasmaandphotoelectronparameterat1AU Species Numberdensity Driftvelocity Thermalvelocity Temp Debyelength n[cm 3 ] v d [km/s] v t [km/s] T [eV] D [m] S.W.Electron 8.7 468 1450 12 8.73 S.W.Ions 8.7 468 31 10 7.97 Photoelectron 64 N/A 622 2.2 1.38 Table4.3: SimulationparametersandinitialconditionsforESlevitateddust Domainsize Meshsize Meshlength ∥Q d =m d ∥cases 120x30x30 1 1.38m 0C/kg Simulationtime Timestep Sim. walltime 10 7 C/kg 200mins 0.2sec 10–20hrs 10 4 C/kg #ofdustparticles 4–8million 10 1 C/kg 74 of124 CHAPTER 5: NUMERICAL SIMULATIONS OF PLASMA-ASTEROID-DUST INTERACTIONS The previous chapters defined the environment that a charged dust particle is subjected to near a small asteroid. To further examine the dynamics of forces acting upon asteroidal dust grains on a global scale, parameters observed from the charging experiments were implemented into the asteroid-dust-transport simulation model, along with the gravitational field model and solar radiationpressuremodelonasphericalgrain. Specifically,laboratorymeasurementsprovidedthe parameterstomodelthechargestateofagrainonadustysurface(inconjunctionwithisolateddust charging model) and validated the plasma-surface interaction through current-balance analysis. This study considers the effects of charging, grain size, gravity and asteroid shape have on the dustdistributioninthecircumasteroidalzone. Allsimulationsutilizedaxialsymmetrywhereonly a quarter of the sphere is modeled, but the results were reflected along the xz-plane to show a hemisphereforviewingconvenience. 5.1 DustTransportvsChargeState 5.1.1 PlasmaEnvironmentSimulation Thesteady-stateresultsoftheplasmasimulationareshowninFigure5.1fortheplasmapotential, average solar wind ions, average solar wind electrons, uv-induced photoelectrons. As a result of mesothermalcharacteristicsforaveragesolarwindconditions,adielectricairlessbodyperturbsthe flowing charged particles and forms a plasma wake at the trailing end of the obstacle in a manner that can be described by plasma expansion into a vacuum. The flux of electrons will be greater than ions in the vicinity of a plasma wake, as a consequence of the mobility in thermal electrons, whilephotoelectronsdominatethechargingprocessontheilluminatedsurface. Figure5.2depicts 75 of124 5.1DustTransportvsChargeState the overlay of the gravity field and electric field. The electric field is calculated by taking the gradientofthepotential,aftersolvingforPoisson’sequationfollowingthemethodologydescribed in Appendix B. As predicted by lunar studies, the electric field is strongest along the terminator region,inthetransitionbetweenthepositivedaysidepotentialtothenegativenightsidepotential. (a) p ,plasmapotential (b)n swi ,averagesolarwindions (c)n swe ,averagesolarwindelectrons (d)n phe ,illuminatedphotoelectrons Figure 5.1: Plasma contours around an asteroid under average solar wind plasma and uv-induced photoelectrons By inspection, the structure of the governing forces offers some insight to dynamics of dust transportanddustdistributioninthecircumasteroidalzone. Itisevidentthatthenetforcewillnot exhibit radial symmetry, notably at low altitudes where the electrostatic field is most substantial. Figure 5.3 shows a comparison of relative magnitudes of electrostatic forces, for all cases except neutral particles, as well as gravitational forces and solar pressure, along various radial directions from the surface. The red shaded region envelops the uncertainty in dust grain charging, while 76 of124 5.1DustTransportvsChargeState Figure5.2: Overlaycontourofthegravityfieldandelectricfieldaroundanasteroid an extreme charging of 1000 Q iso is well outside of this region. For low charge-mass ratio, solar radiation pressure dominates dust dynamics, while for large charge-mass ratio electrostatic forces dictate dust motion. Given the small size of the asteroid, gravitational attraction provides little influence on charged dust, however, for bodies greater than 1 km in size, gravity will contribute substantiallytodustdistribution. Figure5.3: Acclerationprofileonachargeddustasafunctionofaltitude 77 of124 5.1DustTransportvsChargeState 5.1.2 DustTransportandDistribution Dust density distribution contours are shown in Figure 5.4, while Figure 5.5 depicts sample dust trajectories. Inthedistributionplots,thequantityofdustdensitywasnormalizedbythetotalnum- berofsimulationparticleswithinthedomain. Thespatialdistributionofdustgrainsdoesnotreflect radial symmetry, as anticipated from inspection of the governing forces. By comparing the four distributioncontours,theneutralcaseandthedustysurfacecase,Q d ,aredominatedbysolarradi- ationpressure, acceleratingdustgrainsbeyondescapevelocity(Figure5.5aandFigure5.5b). For theisolatedchargingcase,Q iso ,electrostaticforcescompetewithradiationpressureasthegreater dustpopulationisboundedbythecircumasteroidalzone(Figure5.5c). Finally,forlarge∥Q d =m d ∥, electrostaticforcesdominatethemobilityofchargeddustasgrainsarelevitatedtogreateraltitude, migratingtowardstheupstreamregionwithoutescapingtheasteroid(Figure5.5d). Dustdensities atthesurfacereflectsimilartransportdynamicsasthegrainsareundisturbedonthewake-sidefor the neutral and Q d cases while the latter high charge states lead to greater accumulation on the day-side. The notion of dust pond formation observed on asteroids is supported in the simulation for a airless body that is not minimally charged, otherwise, solar radiation pressure tends to blow thedustgrainsoffthesurface. 78 of124 5.2DustTransportvs. GrainSize (a)neutraldust (b)Q d ,dustsurfacemodel (c)Q iso ,isolateddustmodel (d)1000Q iso Figure5.4: Dustdistributionaroundasmallasteroidforvariouschargestate 5.2 DustTransportvs. GrainSize 5.2.1 DustDistributionSimulation In this section, the effects of grain size on dust distribution are considered. All other parameters ofthesimulationweremaintainedforadustysurfacechargingmodelwhiletherangeofthegrain size varies for the following four cases: 2m, 20m, 200m and 2 mm. For comparison, lunar dust samples ranges from 46m to 110m and dust samples from Itokawa range from 30m to 180 m [88, 89]. Figure 5.6 shows the distribution for the various grain sizes. The differences in the dust densities between a 2 m grain and a 20 m grain are subtle. The distributions show that there fewer dust grains on the day-side surface and in the downstream “plume” for the 2 m 79 of124 5.2DustTransportvs. GrainSize (a)neutraldust (b)Q d ,dustsurfacemodel (c)Q iso ,isolateddustmodel (d)1000Q iso Figure5.5: Sampledusttrajectoriesaroundasmallasteroidforvariouschargestate grain. This suggests that the smaller grain is very efficiently removed from the surface by solar radiation pressure, escaping the gravitational well of the asteroid, as predicted by Lee [46]. In reality,smallerdustgrainsmaynotbesoeasilyremovedfromthesurfaceduetothecohesiveforces amongst the dusty surface. As the grains increased to 200 m, the majority of the dust appears to be gravitational bound to the asteroid. Fewer grains are swept away from the day-side as more of the population remains on the surface. The distribution also shows the emergence of a tenuous populationatlowaltitudesupstreamofthesphere. Forthe2mmgrainsize,solarradiationpressure appears to be insufficient at removing the majority of the dust from the surface. Surprisingly, there is thin population of grains at high altitudes directly upstream and downstream of the body. The mechanism for this enhanced group is unclear. For missions visiting a small asteroid with 80 of124 5.3DustTransportvs. Gravity (a)Dustdistributionfor2mgrainsize (b)Dustdistributionfor20mgrainsize (c)Dustdistributionfor200mgrainsize (d)Dustdistributionfor2mmgrainsize Figure5.6: Dustdistributionaroundasmallasteroidforvariousgrainsizes 2 mm sized grains, dawn/dusk sun-synchronous orbits are ideal for avoiding contamination and riskhazardstothespacecraft. 5.3 DustTransportvs. Gravity 5.3.1 DustDistributionSimulation In this section, the effects of gravity on the dust distribution is considered. Due to the limited computationalresourcesavailable,scalingupthesizeofobjectresultsinanexponentialgrowthof computationalnodesfortheIFE-PICplasma-asteroidmodel. Thisisaconsequenceoftheplasma scaling required to match the solar wind plasma densities and the photoelectrons densities, since 81 of124 5.3DustTransportvs. Gravity theDebyelengthof1.38mdeterminesplasmainteractionwiththesurface. Thesimulatedasteroid modelhasaradiusof10.2 D ,butiftheradiuswasincreasedbyafactorof10,thenthesimulation domain must also increase by a factor of 10 for each dimension, i.e. an increased domain size of 1000. The conjugate gradient solver implemented for the field solver scales by O(N 1:5 ) in computational time, where N is the number of nodes in the domain. Additionally, to maintain the resolution of the simulation, the number of macro particles scales linearly with the domain size. Without optimization or parallelization, a simulation wall time of3 days can easily scale up to 30,000days,conservatively. Eveninthemostoptimisticcaseinwhichthecodescaleslinearly,this wouldstillrequire3000daystocompletethesimulation. Instead,thisstudyconsideredscalingthe massdensityoftheasteroid,ratherthanthesizeoftheasteroidandtheninferringtheeffectgravity hasondustdistribution. g a (r) = r 3 r = GM r 3 r = G r 3 4 3 R 3 m r (5.1) The eq. (5.1) shows how the gravitational field scales with size and mass density for a uniform spherical object, wherer and r is the position vector and magnitude, respectively, from the center of mass, m is the mass density and R is the asteroid radius. For the gravity at the surface of the asteroid,randRareequivalent,sotheforceofgravityscaleslinearlywiththesizeoftheasteroid. The mass density also has a direct relation with the acceleration of gravity, thus, by scaling m , this implies the same scaling as with the asteroid size. Figure 5.7 shows the distribution around an asteroid with nominal mass density for 20 m-sized grains with the same range of charge state previously discussed. Figure 5.8, Figure 5.9, and Figure 5.10 illustrate the effects of dust distributionmassdensityscaledby10x,100xand1000x,respectively. Thisimpliesthesizeofthe asteroid to be 280 m, 2.8 km and 28 km, respectively. The effect of gravity on dust transport is intuitive, as the gravitational field strength increases, it becomes increasingly difficult for charged particlestolevitatefromthesurface. At100xand1000xgravity,thegravitationalfieldcompletely dominatesthedusttransportnearthesurface,withtheexceptionofthemostextremechargestate. 82 of124 5.3DustTransportvs. Gravity Theseresultsimplythatforasteroidsize ontheorderoften’sofkilometers, itisveryunlikelyfor a tenuous cloud of dust to surround the body as result of electrostatic levitation. Within the main asteroid belt, there are nearly ten thousand objects that fall into this size range. However, from lunar observations, dust grains can still be suspended at high altitudes. This study does not refute the presence of dust population around asteroids by other mechanisms such as seismic shaking, collisionswithotherbodies,orotherunexplainedphenomena. 83 of124 5.3DustTransportvs. Gravity (a)Q d (b)Q iso (c)1000Q iso Figure5.7: Distributionfornominalgravity (a)Q d (b)Q iso (c)1000Q iso Figure5.8: Distributionfor10xgravity 84 of124 5.3DustTransportvs. Gravity (a)Q d (b)Q iso (c)1000Q iso Figure5.9: Distributionfor100xgravity (a)Q d (b)Q iso (c)1000Q iso Figure5.10: Distributionfor1000xgravity 85 of124 5.4DustTransportvs. AsteroidShape 5.4 DustTransportvs. AsteroidShape Inthissection, theeffectofanasteroid’sshapeonthesurroundingdustdistributionisconsidered, alongwiththeeffectofabinaryasteroidsystem. Ingeneral,smallbodieshaveirregularshapesas thelocalgravityisnotsufficienttoaccretethemintospheres;hence,thedynamicsofdusttransport cannot simply be modeled using a sphere. Asteroids with a collisional history have likely been so disrupted that all that remains are multiple fragments of the parent body. This is the likely theory fortheformationofthebinaryasteroidsystemsobservedinspace. Suchasystemisdefinedbytwo asteroids orbiting their mutual barycenter. The dust distributions in this scenario were simulated todeterminetheireffectonthetransportofthedustparticles. 5.4.1 PlasmaEnvironmentSimulation For different asteroid shapes, the plasma flow field and surface charging will also change accord- ingly. Figure 5.11 shows the plasma potential contour for an irregularly-shaped asteroid, similar to that of a peanut. The center section of this body has a negative potential, due to the shadowed regionasaresultofitsorientationwithrespecttothedirectionoftheSun. Thedifferentialcharge of the surface leads to more regions of enhanced electric field, and thus, enhanced regions of dust transport. Figure 5.12 and Figure 5.13 depict the plasma potential contour for a binary system, both spherical in shape, for an orientation aligned with x-axis (aligned-binary) and one that is perpendicular with x-axis (transverse-binary), respectively. In the case of an aligned-binary, the negativelychargedregionsaresimilartothoseoftheirregularly-shapedasteroid,duetotheorien- tation of the binary system. For the transverse-binary case, the contours of potential have similar characteristicstothoseofanisolatedsphere,butwithsomeperturbedfieldbetweenthe2bodies. It shouldbenotedthatasteroidsystemhereispositionedveryclosetothedomainboundaryandthat the domain should have been expanded in the y-direction to minimize any field perturbation. The rate at which the binary objects in the system orbit each other will affect the kinetics of charged dustwithatimedependency. 86 of124 5.4DustTransportvs. AsteroidShape Figure5.11: Plasmapotentialcontourforanirregularly-shapedasteroid Figure5.12: Plasmapotentialcontourforanaligned-binaryasteroidsystem Figure5.13: Plasmapotentialcontourforatransverse-binaryasteroidsystem 87 of124 5.4DustTransportvs. AsteroidShape 5.4.2 DustDistributionSimulation Figure 5.14 presents the distribution of dust around an irregularly-shaped asteroid. There is an accumulationofdustgrainsinthenarrowmid-sectionoftheasteroid,asthisregioniswellshielded fromthesolarradiationpressure,especiallyfortheQ d model. Whencomparedwiththespherical caseinFigure5.4,theadditionalmassconfinesthepopulationofdusttoaloweraltitudewithfewer particlesescaping thecircumasteroidal zone. FortheQ iso model, the ring inthe aftsection with a more positively biased surface accumulates more dust than other regions of the irregular asteroid. Theenhancedelectricfieldhereattractedmoreofthedustparticlesratherthanallowingthemtobe levitated from the surface. The dust distribution shown in Figure 5.15 has more charged particles trapped at low altitudes than for the irregularly-shaped asteroid. Under the Q d condition, fewer dust grains are levitated from the surface of the downstream binary which may also effectively accumulate a population of dust that leaves the upstream binary. As with the irregularly-shaped case, a ring dust accumulation occurs at the more positively biased region of the downstream binary, while the negatively biased regions are sparsely populated. This must be attributed to enhanced levitation as this surface is well shielded from solar radiation pressure. The results for thetransverse-binaryasteroidinFigure5.16behavemuchlikethoseofanisolatedobjectforeach individual binary. In consideration of the changing orientation of the binary system, particles trapped between aligned-binary will later be lost as the system transitions into the transverse- binaryposition. Ifthedustgrainsmanageanextremechargestateof1000Q iso ,thelostoftrapped particlesbetweenbinarymaybeprevented. Spacecraftnavigationaroundmultiplebodiesislikely themostchallengingtocontrolandalsoposesagreaterriskofdustcontamination. 88 of124 5.4DustTransportvs. AsteroidShape (a)Q d (b)Q iso (c)1000Q iso Figure5.14: Dustdistributionaroundanirregularly-shapedasteroid 89 of124 5.4DustTransportvs. AsteroidShape (a)Q d (b)Q iso (c)1000Q iso Figure 5.15: Aligned-binary asteroid system dis- tribution (a)Q d (b)Q iso (c)1000Q iso Figure 5.16: Transverse-binary asteroid system distribution 90 of124 5.5SummaryandConclusion 5.5 SummaryandConclusion Numerical simulations for plasma-asteroid-dust dynamics were carried out to determine the dis- tribution of dust grains on a global scale in the circumasteroidal zone. This study considered the effectsofvariouschargestate,grainsize,gravityfieldandasteroidshape. Theresultsshowthatfor low charging state, solar radiation pressure is the dominating process for dust transport; however, extremechargingconditionsallowdustgrainstobeboundedtotheasteroidathigheraltitudes. As the size of the grain increased, the degree of dust levitation and transport diminished, such that millimeter-sizedparticleswereboundedtothesurface. Theinferredeffectsofincreasingthegrav- ity field strength showed that kilometer-sized asteroids and greater resulted in surface-bound dust astheelectrostaticforceandsolarradiationpressurecouldnotovercomethegravitationalpotential by levitation alone. Simulations for multiple bodies presented the most complex distributions and posedthegreatestchallengeforminimizingdustcontaminationduringrendezvousmissions. 91 of124 CHAPTER 6: CONCLUSIONS AND FUTURE RESEARCH Asteroids in space are airless, dusty objects immersed in the solar wind plasma and illuminated by solar radiation. The dust grains are susceptible to the competing effects from the gravitational force, theelectromagneticforceandsolarradiationpressure. Takentogether, theseeffectspresent a challenging problem in mitigating the risks of asteroid rendezvous missions. This dissertation experimentally investigated the parameters for dust and surface charging in order to constrain the first 3D model for plasma-asteroid-dust interaction and the dynamics of charged dust transport on aglobalscale. 6.1 ConclusionsandContributions Thisresearchsetouttoprovideanswersandinsighttothefollowingquestions: How does a dust grain charge in a dusty plasma environment compared to a single, isolated dustgrain? Howdoesanasteroidsurfacechargeinamesothermalplasma? Howdoestheinteractionbetweenplasmaanddustgrainsleadtodustlevitationandtransport aroundanasteroid? Whataretheparametersthatinfluencetheextentofdustlevitationandtransport? All of these questions were addressed in the context of the proceeding four chapters. The conclusionsreachedandresultingimplicationsaregiveninthissection. 92 of124 6.1ConclusionsandContributions 6.1.1 DustySurfaceChargingvs. IsolatedDustCharging In previous work, studies on dust charging only considered isolated dust grains. Chapter 3 pre- sented the first laboratory measurements of dusty surface charging by an expanding plasma in a localizedplasmawake. Theexperimentalresultsshoweddifferencesinchargingbetweenthedusty surfacemodelandtheisolateddustmodel,suchthatanisolateddustgraincanbechargedfromone tothreeordersofmagnitudehigherthanthedustysurface. Theresultsalsoshowthatindeep-wake charging, a dusty surface and a dielectric solid reach similar potentials, while in a shallow wake, theregolithsurfacepotentialcanbesignificantlymorepositivethanthatofasolidsurface. 6.1.2 AsteroidSurfaceCharging Previously, the studies of surface charging have focused on planar geometries. Chapter 2 pre- sented an investigation of a simulated plasma-asteroid charging from a global perspective. The experimental results compared the current balance and surface potential of a conducting sphere andadielectricsphereimmersedinadriftingmesothermalplasma. Theplasmaparametersaround the sphere were measured to determine the net flux of ions and electrons to the surface. Mea- sured surface potentials for the conductor and insulator were in good agreement with analyti- cal calculations, according to probe theory. Numerical plasma simulations used input parame- ters matching the characteristics of laboratory plasma source and the material properties of the spheres. The plasma-asteroid model solved Poisson’s equation self-consistently utilizing realistic ion-to-electron mass ratio and plasma temperature to determine the floating potential and the flux of incident charged species. The validation of the laboratory experiment gives us confidence in extrapolatingthedynamicsofplasma-asteroidinteractioninspace. 93 of124 6.2ProposedFutureResearch 6.1.3 Dynamics of Plasma-Asteroid-Dust Interactions vs Dust Transport andDistribution Previous groups have studied the dynamics of charged dust grains in a plasma environment, but only in specific, localized conditions. The dust transport model presented in Chapter 5 is the first model to examine the dust dynamics in an asteroid environment on a global scale. Parame- ters determined from the dusty surface charging experiment and the asteroid charging experiment offered constraints to impose on the numerical model. Charged dust grains were subjected to competing effects of asteroid gravitational force, electrostatic force and solar radiation pressure. The effects of charge state, grain size, gravity field and asteroid shape on dust distribution were examined. Solarradiationpressureisthedominatingfactorfortransportunderalowcharingstate around small asteroids, while extreme charging conditions make the electrostatic force the domi- nating factor. Dust dynamics are sensitive to the individual grain size; as the size of the particle is increased, the forces acting on the grain are attenuated and it becomes bounded to the surface. A study of the gravity strength implied that the gravitational field becomes the dominating factor for asteroids in the kilometer range or greater, where electrostatic levitation cannot induce dust transport. Lastly,theasteroidshapecontributestodusttransportinmostcomplexaspects,making dust distribution more difficult to predict. Rendezvous missions to multiple body systems require thegreatercautionminimizethehazardsofdustcontamination. 6.2 ProposedFutureResearch Follow-uptasksforplasma-dust-interactionsareoutlinedinthissection. 6.2.1 PlasmaDiagnosticsDevelopment Fordetailedmeasurementswithsmallobjects,currentprobeslacktheresolutiontorefinethekinet- ics of plasma species in a laboratory setting. The development of smaller probes will enhance the 94 of124 6.2ProposedFutureResearch viewingofplasmaparameters,particularlyfornear-surfacemeasurements. Alternatively,utilizing alargerplasmasourcewillallowforalargertestvolume,alargertargetsurface,andtheabilityto charge multiple objects simultaneously. It will also be beneficial to compare the accuracy of the probeswithmeasurementsusingdifferentfacilitiesandplasmadiagnostics. 6.2.2 ParallelizationofPlasmaModel The simulation model for plasma-asteroid interaction is a sequential code. As a result, even a modest scaling of the simulation domain leads to lengthy computational times. An increased per- formanceinthemodelwillallowforreasonablesimulationtimesforlargerdomains. Themajority of the computation in the code is spent on the field solver. Parallelization of the field solver will offerthegreatestgainsinperformance. 6.2.3 CEXandFacilityEffects The 4 cm argon electron bombardment ion source is well-characterized in the vacuum chamber, but it has a very low propellant ionization efficiency (< 5%). The presence of a dense neutral backgroundisnotrepresentativeoftheplasmaenvironmentbeyondtheEarth’supperatmosphere. A more efficient plasma source can better simulate the in-situ space environment in addition to determiningtheimpactofCEXionsandfacilityeffectsonplasma-surfaceinteractions. 6.2.4 DustDistributionfromImpactEjectra Anotherstudyworthinvestigatingisthedistributionofdustfromcraterimpact,eitherbymicrom- eteorite or by an artificial impactor. The velocity distribution of crater ejecta has been well- characterized,andtheimplementationofthisdistributionintothedusttransportmodelwillprovide anewperspectiveforthecompetingforcescontributingtodustdynamicsaroundanasteroid. 95 of124 6.2ProposedFutureResearch 6.2.5 Time-VariantPlasmaChargingModel Development of a self-consistent time-variant charging model is an active area of research for dusty plasmas. As particles traverse through different plasma environments, the charge state will respondaccordingtothenewcurrentbalanceflux. 6.2.6 ImplementCohesiveForceintoDustTransportModel On a dusty surface, the strongest force acting on dust grain is the inter-grain cohesive force. Any electrostaticlevitationmustfirstovercomethecohesionfromtheneighboringparticles. 96 of124 APPENDIX A: LABORATORY EXPERIMENTAL SETUP AND PLASMA DIAGNOSTICS Few laboratory studies have addressed “dusty surface” charging under mesothermal plasma flow conditions similar to those at the lunar terminator. In order to experimentally simulate and inves- tigate the near-surface plasma field and the charging of a dusty surface, this chapter presents the details of the vacuum facility, the mesothermal plasma source, and the plasma diagnostics we utilizedtosimulateourchargingenvironment. A.1 VacuumFacility FigureA.1: Stainlesssteelvacuumchamber Experiments were conducted under a simulated space environment within a cylindrical, stainless steelvacuumchamber(showninFigureA.1)measuring0.915mindiameterand1.22minlength, thatispumpedbyanAlcatelmechanicalroughingpumpandaCVI-TM500cryogenicpumpwitha pumpingspeedof10,500L/sfornitrogengasand8,500L/sforargongas. Thechamberreachesa 97 of124 A.2ElectronBombardmentGriddedIonSource floorpressureof1x10 6 Torrwithnogasflow,apressureof7x10 6 Torrataflowrateof20sccm of N 2 gas, and a pressure of 3x10 6 Torr at a flow rate of 2.5 sccm of Ar gas. The chamber is equippedwithone8"Conflatport,sixISO-200ports,andelevenKF-40ports. A.2 ElectronBombardmentGriddedIonSource (a)4-cmplasmasource (b)Sourceelectricalconfiguration FigureA.2: Plasmasourceandelectricalconfiguration A 4-cm diameter gridded electron-bombardment ion source is used to generate a mesothermal plasma beam to simulate average solar wind conditions. Figure A.2 depicts the source schematic. To generate the plasma, N 2 or Ar gas flows through the feed line into the ionization chamber. The tungsten filament inside the source is heated until it goes into thermionic emission. A ring ofmagnetsconfinesthethermalelectronswhiletheneutralgasmoleculesareionizedviaelectron bombardment. The ionization chamber is biased to a high potential (500-1100 V), leading to ions withenergyequalto500-1100eV.Electronsarecollectedattheanodecup(biased50Vabovethe ionization chamber) and ions are accelerated by gridded ion optics. The grounded enclosure acts asaFaradaycagetoprotectsensitivehardwarefromthehighvoltageandpreventpotentialdistur- bances. Ahotfilamentneutralizeremitselectronsatthesourceexittomaintainquasi-neutralityto 98 of124 A.3PlasmaDiagnostics the accelerated beam, preventing electrical arcs due to charge imbalance. With a typical electron temperatureof2eV,theelectronsarethefaster,moremobilespeciesduetothedifferenceinmass. Theplasmabeamemittedbythesourcewascharacterizedindetailin[82]. A.3 PlasmaDiagnostics (a)Probetraversingsystem (b)SuiteofProbes FigureA.3: Plasmadiagnosticsontraversingsystem. Thesuiteofprobesin(b)arefastenedtothe label“ProbeSuite”in(a). A suite of plasma diagnostics is implemented to measure both the plasma environment and the target surface potential. The diagnostic sensors are fastened to a 3-D traversing system that pre- cisely maneuvers the probes in the vacuum chamber in order to obtain 3-D spatial distributions of plasma parameters, shown in Figure A.3a. The traversing system moves with a stepper motor for each axis that is controlled through LabVIEW manually or by a path file input to command a specific path design. The plasma environment is measured using a Langmuir probe, LP (electron number density n e and temperature T e ), two Faraday probes, Axial FP and Radial FP (ion num- ber densityn i ), an emissive probe, EP (field potential ), and a retarding potential analyzer, RPA (ion beam energy E b ) [82]. With the exception of the Radial FP and the EP, the probes must be 99 of124 A.3PlasmaDiagnostics oriented parallel to the x-axis, facing the plasma flow. Since electrons are thermal, they can reach the EP from any direction. Consequently, the EP can be oriented in any direction, provided the probe body does not interfere with the plasma flow. A data acquisition system was used to send and collect signals of each probe, which were then recorded by the computer and written to a text fileforpost-processing. Forlow-resolutionfieldmeasurementswhereruntimesareshort,itisoftenconvenienttofasten the entire probe suite to the stage of the traversing system, particularly when there are no other objects in the scan region. However, the weight of the probes causes the stepper motors to miss steps, leading to choppy movements and position errors. In addition, all the wires leading to the probesuitecanbecomerathercumbersometomanage. In experimental configurations with charging targets such as those discussed in this disserta- tion, a single probe is mounted on a lighter supporting rod for quicker and more accurate scans. Experiencehaveprovedthataligningmultipleprobesforprecisemaneuveringismoretroublethan it’s worth; measurements with a single probe was more efficient and reliable, despite the need to break vacuum to set-up the next probe between runs. Both the plasma source and the cryopump require a cool down period after operating for a duration of one hour to avoid overloading the equipment. For a small scanning field, it is possible to collect data with multiple probes, but high resolutionscansaretypicallylimitedtooneprobeperrun. A.3.1 LangmuirProbe A Langmuir probe is one of the most extensively used diagnostics in plasma physics, with exten- sive literature characterization since the 1960’s [90]. In it’s simplest form, a Langmuir probe is a bare wire immersed in a plasma. Probe theory is utilized to obtain the current-voltage (I-V) characteristicsastheappliedbiasvoltageoftheprobeissweptfromanegativetoapositivepoten- tial. The measured I-V curve can then be used to determine the electron temperature, T e , and numberdensity,n e . ThecharacteristiclengthofthecylindricalLangmuirprobeusedinthisstudy 100 of124 A.3PlasmaDiagnostics FigureA.4: Langmuirprobeandelectricalschematic was 6.35 mm and the probe radius was 0.5 mm. The Langmuir probe was biased from -40 V to +60 V, and the voltage drop across a resistor was recorded over the voltage sweep, as shown in Figure A.4. The generated I-V curve is shown in Figure A.5a. By taking the natural log of this curve,T e ineViscalculatedfromtheslopeofthe“T e line”byeq.(A.1),asshowninFigureA.5b. Then, n e is calculated from eq. (A.2), where I e;sat is the electron saturation current and A probe is the probe collecting surface area. The plasma potential, p , can also be taken from the Langmuir probe; however in a flowing plasma, such as an ion beam, this measurement can be perturbed, necessitatingtheuseofanemissiveprobeforbetteraccuracy. T e = 1 slope(T e line) (A.1) n e = I e;sat eA probe √ 2m e kT e (A.2) A.3.2 EmissiveProbe An emissive probe, shown in Figure A.6, was used to measure the plasma potential, p . It con- sists of an exposed electrode and is electrically heated to the point of strong thermionic electron emission. Usingtheinflection-pointmethod,theplasmapotentialcanbedeterminedbysweeping theemittingprobe’sbiasfromlargenegativetolargepositivevoltagesandmeasuringthecollected 101 of124 A.3PlasmaDiagnostics FigureA.5: ExampleLangmuirprobeI-Vcurve FigureA.6: Emissiveprobeandelectricalschematic current at each bias voltage, similar to the method used for Langmuir probe. By using a polyno- mialfittotheI-Vcurve,thepointofinflectionissolvednumericallyandthecorrespondingvoltage equates to the local plasma potential, as depicted in Figure A.7. The inflection point method has been shown to provide an accurate measurement of the plasma potential [91]. In the absence of a significant magnetic field or large density gradient, space charge effects are negligible and can be ignored. Sheath potentials can be measured utilizing this method. The emissive probe used in this experimental investigation had a probe radius of curvature of 2 mm with a tungsten filament diameterof0.3mm. 102 of124 A.3PlasmaDiagnostics -40 -30 -20 -10 0 10 20 30 40 V (V) -4 -3 -2 -1 0 1 2 3 4 5 I (A) 10 -4 EP data point 1 FigureA.7: ExampleemissiveprobeI-Vcurvewithinflection-pointmethod FigureA.8: Faradayprobeandelectricalschematic A.3.3 FaradayProbe A Faraday probe (FP) determines ion current density by measuring the ion current flux onto a fixed-areacollector. Thedesignisastainlesssteel,nudeFaradayprobe,whichisdirectlyexposed to plasma flow. The stainless steel collecting surface directly faces the oncoming beam, allowing forcollectionofaxiallyflowingions. Theguardringisconcentricwiththecollectingsurface,with agapof1.0mmbetweenthetwo. Thepurposeoftheguardringistocreateauniformsheathover the collecting surface by minimizing edge effects. The gap is chosen to be sufficiently small with 103 of124 A.3PlasmaDiagnostics respecttotheDebyelengthtoensureoverlapofthecollectorandguardringsheathstoensureaflat, uniform sheath over the collector [92]. The collecting surface outer diameter is 5.0 mm, and the guardringouterdiameteris8.0mm. Boththecollectingsurfaceandguardringaredesignedtobe biased to an identical negative potential, -20 V below the facility ground, as shown in Figure A.8, to prevent electrons from reaching the surface. Measured ion current at any point in the field is recordedbymeasuringthevoltagedropacrossaresistor,andthevalueisdividedbythecollecting surface area to yield ion current density, J i . The conservation of of energy, is given by eq. (A.4), where o istheionacceleratingvoltageand p istheplasmapotentialmeasuredwiththeemissive probe. This equation is solved for each value of p to get a set ofv i . For a given ion mass, m i , a setofvaluesoftheiondensity,n i ,canbecomputedusingeq.(A.5). then i couldbedeterminedwitheq.(A.5),foragivenionmass,m i . J i =en i v i (A.3) 1 2 m i v 2 i =e( o p ) (A.4) n i = J i e √ m i 2e( o p ) (A.5) For the axial FP measurements in the main beam, the calculated values of n i yield densities that are inconsistent with the n e measured by the Langmuir probe, with the ions being an order of magnitude greater. Under typical plasma source conditions, the core of the emitted beam is consideredtobequasi-neutralanddeparturefromabalanceofchargedspeciesisdifficulttomain- tain without neutralizing arcs from elsewhere in the vacuum chamber. Such arcs are not observed duringexperiments,whichconfirmsthereisnotadearthofelectronsinourplasma. Alternatively, excesselectronsareeasilymitigatedthroughthegroundedwallofthevacuumchamber. Underthe 104 of124 A.3PlasmaDiagnostics assumptionofquasi-neutrality,onlytheelectrondensitiesarepresentedforplasmasourcecharac- terization, while ion beam currents and thrust are determined from Faraday probe measurements and not ion densities [93]. For the propulsion community, ion density is not an important param- eter to characterize; however, for surface charging studies, accurate ion density measurement is a crucial parameter for current collection. To rectify the inconsistency, ion density is calculated by solving Poisson’s equation, given in eq. (B.4), using n e and p measured by the Langmuir probe and emissive probe, respectively. A radial profile of the plasma potential is shown in Figure A.9, along with a data curve fit. The measured and calculated plasma densities are plotted on Fig- ure A.10. Within the ion beam (radial position 0 to 4.5 cm), the calculated n i is approximately 10% of the density derived from the Faraday probe. Outside the plume of the plasma beam, ion densityandelectrondensityconverges. Forchargingresultsinthemainbeam,currentbalancecal- culationsutilizedthereducediondensityvalue(10%)tosimplifypost-processingofexperimental data. Figure A.9: Radial (i.e., the -y-axis) profile of plasma beam potential, p . Main beam is between 0to4.5cm. 105 of124 A.3PlasmaDiagnostics FigureA.10: Radialprofilesofplasmadensities. Mainbeamisbetween0to4.5cm. A.3.4 RetardingPotentialAnalyzer Aretardingpotentialanalyzer(RPA)isanelectrostaticplasmadiagnosticinstrumentusedtomea- sure the ion energy distribution. An RPA consists of a current collector that is typically shielded fromtheupstreamplasmabyaseriesofbiasedgrids. Theinstrumentonlyallowsionswithenergy- to-chargeratioshigherthantheretardingpotentialtoreachthecollector(soitdoesnotdistinguish betweensinglyandmultiply-chargedions). FigureA.11: RPAandelectricalschametic Athree-gridRPAdesignwasfabricated,asillustratedinFigureA.11. Thefirstgridisfloating to reduce plasma perturbations, the second grid is biased to -40 V to repel electrons, the third 106 of124 A.3PlasmaDiagnostics grid is swept through the maximum expected ion retarding voltage, and the back plate is biased negatively to ensure ion collection. The mesh opening dimension is chosen to be less than the sheaththicknessoverthe electronrepellinggrid, toensurethat electronswillnot passthroughthe grid uninfluenced by the grid bias. The grid spacing is chosen to be less than the sheath thickness over the ion retarding grid to mitigate space charge effects. The mesh grids and collector are stainlesssteel. Ceramicinsulatorsisolategridsfromeachotherandthecollector. FigureA.12: RPAmainbeamionenergydistribution dI dV =A c en i √ 2e m i V rpa f(V rpa ) (A.6) Toobtaintheionenergydistribution,thecollectorcurrentisfirstplottedagainsttheionretard- ingvoltage,asshowninFigureA.12a. Thederivative dI dV isthentaken,whichyieldstheionenergy distributionpereq.(A.6)[92],whereA c istheRPAcollectorareaandV rpa istheionretardingvolt- age. FigureA.12bdisplaystheresultingionenergydistributionforthemainbeamions. Themost probableionenergy(voltageatthepeakofthedistribution)closelymatchestheinputbeamvoltage o =1100V. 107 of124 A.3PlasmaDiagnostics FigureA.13: Treknon-contactingESVMprobe A.3.5 Non-contactingElectrostaticVoltmeter AcommercialTrek323-L-CEnon-contactingelectrostaticvoltmeter(ESVM)andamodel6000B- 8 side-view probe with a voltage range of100 V, an accuracy of50 mV, and a response time of 300 ms were used to measure surface potentials. This non-contacting electrostatic voltmeter (ESVM) is a vibrating capacitive probe that determines surface potentials with a current nulling method. A capacitor is created between the sample surface with potentialϕ s , and the probe head, with potential V. The probe head contains an electrode, which vibrates with frequency, !, and amplitude,d 1 . This forms a time-dependent gap,d = d 0 +d 1 sin(!t), whered 1 <d 0 between the samplesurfaceandelectrode,andwhentheelectrodepotentialisequaltoϕ s ,currentstopsflowing totheelectrode. Thisestablishesthesurfacepotentialmeasurementwithgoodaccuracy,provided thattheprobespacing-to-surfaceis1to3mm. Thenon-contactingprobeensuresthesurfaceisnot disturbedwhenperformingitsmeasurement. FigureA.13illustratestheprobe-surfacecapacitance andpresentsasideviewoftheprobeaboveasamplesurface. 108 of124 APPENDIX B: PLASMA-ASTEROID INTERACTION MODEL Theasteroidsurfaceisdirectlyexposedtoavarietyofspaceplasmaenvironmentsandischargedby plasmaimpingementandsolarradiation. Athree-dimensional,non-homogeneousimmersedfinite element, fully kinetic particle-in-cell (IFE-PIC) model developed by Han et al [94] is employed to simulate of plasma flow past an asteroid. For a collisionless plasma, the electromagnetic force governsthetrajectoryofachargedparticlebyNewton’ssecondlaw: F =m dv dt =q(E+vB) (B.1) v = dx dt (B.2) whereq isthechargecarriedbytheparticle,misthemassoftheparticle,xisthepositionvector, v is the velocity vector, andB is the external magnetic field (note: in some plasma-asteroid inter- actions,externalBmaybeneglected). TheelectricfieldEiscalculatedfromtheelectricpotential by E =∇ (B.3) whereisdeterminedbysolvingPoisson’sequation: ∇E =∇(∇) =∇ 2 = c ϵ (B.4) for a corresponding permittivity of the medium ϵ, space charge density c . Space charge density is defined as the net sum of the charged species, i.e. c = q[n i n e n ph ]. The PIC simulation self-consistently solves for plasma dynamics and field quantities by iterating the following steps (FigureB.1): 109 of124 Charge Weighting: The charges carried by simulation particles are “scattered” and depositedontomeshnodesforspacechargedensity c ; FieldSolving: ThePoisson’sequationissolvedforEand; Force Weighting: The electric field is interpolated from mesh nodes and “gathered” to updateparticlevelocityv; Particle Move: The equation of motion is integrated to update each simulation particle positionx. FigureB.1: PICloopiteration 110 of124 The non-homogeneous IFE formulation provides the capability to treat asteroid surface as an “interface” between medium 1 (asteroid body) and medium 2 (plasma) rather than a bound- ary. Across the interface, the surface floating potential and E in their respective media are self- consistentlycalculatedbylocalchargedepositionwhiletheelectricfieldissubjecttothefluxjump condition(FigureB.2)[95]: [ ϵ @ @n ] = (ϵ 2 E 2 ϵ 1 E 1 )n = s (B.5) where the integration is taken at interface ;n is the surface unit normal vector, s is the surface charge density, ϵ 2 is the permittivity of free space, and ϵ 1 corresponds to a relative permittivity (or the dielectric constant) for asteroid surface regolith. The permittivity of a dielectric is defined as the product of the permittivity of free space, ϵ o , and the dimensionless dielectric constant, ϵ rd , which has a estimated value of 4 for asteroid regolith, compatible with the published value for carbonaceouschondrites[80,96,97]. TheIFEfieldsolverenablesaccuratesolutionoftheEfield forcomplexsurfaceterrainfeatureswithoutsacrificingPICsimulationperformance[98]. FigureB.2: Fluxjumpacrosstheinterfacecausedbysurfacecharging 111 of124 B.1PlasmaSpecies TableB.1: Averagesolarwindplasmaandphotoelectron(at90 o SEA)parameterat1AU Species Numberdensity Driftvelocity Thermalvelocity Temp Debyelength n[cm 3 ] v d [km/s] v t [km/s] T [eV] D [m] S.W.Electron 8.7 468 1450 12 8.73 S.W.Ions 8.7 468 31 10 7.97 Photoelectron 64 N/A 622 2.2 1.38 B.1 PlasmaSpecies The IFE-PIC plasma-asteroid model considers three plasma species: 1) solar wind ions, 2) solar wind electrons, and 3) photoelectrons. Typical average solar wind plasma parameters at 1 AU from the Sun are summarized in Table B.1. This plasma flow is mesothermal as characterized by v ti ≪ v sw ≪ v te , where v sw is the solar wind drifting velocity v d . To maintain the correct the mesothermal velocity ratio, the simulations use the real proton-to-electron mass ratio. All species areconsideredtobeinequilibriumwithaMaxwellianvelocitydistribution. Photoelectronnumber densityatthesurfacevariesasafunctionofsolarelevationangle(SEA),,givenby n ph = 2J ph ev t;ph sin() ≃ 64sin() cm 3 (B.6) foryieldsundersimilarconditionasthelunarsurface[59]. Inthisstudy,solarwindflowandsolar UV radiation are both assumed to be parallel along the x-direction. All plasma species assume a Maxwellianvelocitydistribution. B.2 SimulationDomainandBoundaryConditions ThedomainsizeforIFE-PICmodelis120x30x30PICcells,whichis120x1.38mby30x1.38m by 30x1.38 m in physical units. For an axially symmetric configuration shown in Figure B.3, a quarter-sphere asteroid is centered at 30 cells downstream from X min . A potential field bound- ary condition with Zero-Neumann ( @ @n =0) is applied at X max , Y min , and Z min domain planes. 112 of124 B.3ExampleSimulationResults PotentialreferenceplaneswhicharedefinedatX min ,Y max ,andZ max ,wouldinsteadhaveaZero- Dirichlet (=0) condition. For simulation particles, a reflecting boundary condition is applied atY min , andZ min symmetry plane while open boundary condition is applied atX max plane. Par- ticles representing solar wind electrons and ions are pre-loaded into the simulation domain and injected at X min , Y max and Z max , drifting in the positive x-direction. Illuminated surface yields photoelectron emission. The net current collection at the surface determines the surface potential oftheasteroid. FigureB.3: Simulationsetupforplasmainteractionsforanilluminatedasteroid B.3 ExampleSimulationResults The PIC simulation was performed on a Linux workstation in the Laboratory for Astronautical PlasmaDynamics. Therunstookatotalwallclocktimeof75hrs( ^ t = 1000),reachingsteadystate with a clock time≃ 30 hrs ( ^ t = 400). The simulation domain had≃ 12.5 million macro-particles representing average solar wind plasma and photoelectrons at steady state. The following sample resultillustratesasteadystateconditionatsimulationtime ^ t = 600. Althoughthemodelsimulates an axially symmetric quarter-sphere to represent the airless body, for viewing convenience, the 113 of124 B.3ExampleSimulationResults plots are mirrored across the y = 0 plane, providing a hemispherical view of the plasma-asteroid interaction. B.3.1 PlasmaEnvironmentandFieldProperties FigureB.4aandB.4bshowthedensitycontoursofsolarwindionsandelectrons,respectively. The results clearly show the local plasma wake downstream caused by the asteroid as an obstacle in a mesothermal plasma. Figure B.4c is the density contour for the photoelectron species induced by UV illumination. As expected, photoelectron emissions dominated the plasma density in the region near the surface on the dayside, which is evident in Figure B.4c, while the space charge in the overall domain are predominately quasi-neutral, net total number density of zero, as shown in FigureB.4d. FigureB.5depictstheelectricpotentialcontourintheIFE-PICsimulationdomainaswellasa closerviewofthesurfacechargingdeterminedbychargedeposition. Differentialchargingbetween thesunlitsurfaceandtheshadowedsurfaceisclearlyshownandcompatiblewithlunarobservation near the terminator. Lastly, Figure B.6 highlights the electric field vector near the asteroid terrain, wherethe vectorarrowfollowspositivetest chargeconvectionwhile themagnitude field vectoris portrayedbythefieldcolormap. Insummary,thesimulationresultsoftheIFE-PICplasma-asteroidinteractionmodelforanair- less spherical dielectric body, immersed in solar wind plasma and photoelectrons, in the absence of an external B, are compatible with observations by former lunar missions. The density con- tours and field properties indicate that complex interactions are at play between ambient plasma environmentandasteroidsurfacetopography. Therefore,thecapabilitytoresolvesurfacepotential from charge deposition offers a significant tool to analyze and gain detailed knowledge regarding futurespaceexplorationmissions. 114 of124 B.3ExampleSimulationResults (a)Averagesolarwindions (b)Averagesolarwindelectrons (c)Illuminatedphotoelectron (d)Totalspacecharge Figure B.4: Density contours of average solar wind plasma, uv-induced photoelectron, and total spacechargedensity (a)Potentialfieldcontour (b)Closeupviewofsurfacecharging FigureB.5: Potentialcontouraroundasteroidcalculatedbynon-homogeneousIFEsolver 115 of124 B.3ExampleSimulationResults FigureB.6: ElectricvectorfieldcalculatedbyIFE-PICplasma-asteroidinteraction 116 of124 BIBLIOGRAPHY Bibliography [1] S. S. Board et al., Vision and Voyages for Planetary Science in the Decade 2013-2022. NationalAcademiesPress,2012. [2] I.Crawford,“Asteroidsintheserviceofhumanity,”Asteroids: ProspectiveEnergyandMate- rialResources,editedbyV.Badescu,Springer,2013,p.vii-x,vol.1,p.7,2013. [3] E. Asphaug, “Growth and evolution of asteroids,” Annual Review of Earth and Planetary Sciences,vol.37,no.1,pp.413–448,2009. [4] M. Elvis, “Let’s mine asteroids - for science and profit,” Nature, vol. 485, no. 7400, p. 549, 2012. [5] P.Michel,“Formationandphysicalpropertiesofasteroids,”Elements,vol.10,no.1,pp.19– 24,2014. [6] A. Morbidelli, W. Bottke, D. Nesvorn` y, and H. Levison, “Asteroids were born big,” Icarus, vol.204,no.2,pp.558–573,2009. [7] W.Bottke et al.,“Thefossilizedsizedistributionofthemainasteroidbelt,” Icarus,vol.175, no.1,pp.111–140,2005. [8] P. Pravec, A. W. Harris, and B. D. Warner, “Nea rotations and binaries,” in Near Earth Objects, our Celestial Neighbors: Opportunity and Risk, vol. 2 of Proceedings of the Inter- nationalAstronomicalUnion,pp.167–176,August2007. [9] K. Walsh, A. Morbidelli, S. Raymond, D. O’Brien, and A. Mandell, “A low mass for mars fromjupitersearlygas-drivenmigration,”Nature,vol.475,no.7355,pp.206–209,2011. [10] A. Rivkin, E. Howell, L. Lebofsky, B. Clark, and D. Britt, “The nature of m-class asteroids from3-mobservations,”Icarus,vol.145,no.2,pp.351–368,2000. [11] J. Richardson, H. Melosh, R. Greenberg, and D. O’Brien, “The global effects of impact- induced seismic activity on fractured asteroid surface morphology,” Icarus, vol. 179, no. 2, pp.325–349,2005. 117 of124 BIBLIOGRAPHY [12] H. Miyamoto et al., “Regolithmigration and sorting on asteroid itokawa,” Science, vol.316, no.5827,pp.1011–1014,2007. [13] M. Barucci, A. Doressoundiram, M. Fulchignoni, M. Florczak, M. Lazzarin, C. Angeli, and D. Lazzaro, “Search for aqueously altered materials on asteroids,” Icarus, vol. 132, no. 2, pp.388–396,1998. [14] A. Rivkin and J. Emery, “Detection of ice and organics on an asteroidal surface,” Nature, vol.464,no.7293,pp.1322–1323,2010. [15] S. Abe et al., “Mass and local topography measurements of itokawa by hayabusa,” Science, vol.312,no.5778,pp.1344–1347,2006. [16] S. Lowry et al., “The internal structure of asteroid (25143) itokawa as revealed by detection ofyorpspin-up,”Astronomy&Astrophysics,vol.562,p.A48,2014. [17] D. Britt, D. Yeomans, K. Housen, and G. Consolmagno, “Asteroid density, porosity, and structure,”inAsteroidsIII(W.Bottke,A.Cellino,P.Paolicchi,andR.Binzel,eds.),pp.485– 500,UniversityofArizonaPress,Tucson,2002. [18] R.Russell,“Surveyofspacecrafttrajectorydesigninstronglyperturbedenvironments,”Jour- nalofGuidance,Control,andDynamics,vol.35,no.3,pp.705–720,2012. [19] D. Scheeres, “Close proximity dynamics and control about asteroids,” in American Control Conference(ACC),2014,pp.1584–1598,2014. [20] R. Werner and D. Scheeres, “Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 castalia,” Celestial MechanicsandDynamicalAstronomy,vol.65,no.3,pp.313–344,1997. [21] S. Casotto and S. Musotto, “Methods for computing the potential of an irregular, homo- geneous, solid body and its gradient,” in Astrodynamics Specialist Conference, Guidance, Navigation,andControlandCo-locatedConferences,AmericanInstituteofAeronauticsand Astronautics,Aug.2000. [22] Y. Takahashi and D. Scheeres, “Small body surface gravity fields via spherical harmonic expansions,” Celestial Mechanics and Dynamical Astronomy, vol. 119, pp. 169–206, June 2014. [23] R.Park,R.Werner,andS.Bhaskaran,“Estimatingsmall-bodygravityfieldfromshapemodel and navigation data,” Journal of Guidance, Control, and Dynamics, vol. 33, no. 1, pp. 212– 221,2010. [24] Y. Ren and J. Shan, “On tethered sample and mooring systems near irregular asteroids,” AdvancesinSpaceResearch,vol.54,no.8,pp.1608–1618,2014. 118 of124 BIBLIOGRAPHY [25] J.Halekas,Y.Saito,G.Delory,andW.Farrell,“Newviewsofthelunarplasmaenvironment,” PlanetaryandSpaceScience,vol.59,no.14,pp.1681–1694,2011. [26] D.Mitchell,J.Halekas,R.Lin,S.Frey,L.Hood,M.Acuña,andA.Binder,“Globalmapping of lunar crustal magnetic fields by lunar prospector,” Icarus, vol. 194, no. 2, pp. 401–409, 2008. [27] J. Halekas, G. Delory, R. Lin, T. Stubbs, and W. Farrell, “Lunar prospector observations of the electrostatic potential of the lunar surface and its response to incident currents,” Journal ofGeophysicalResearch,vol.113,no.A09102,2008. [28] R. Ebert, D. McComas, H. Elliott, R. Forsyth, and J. Gosling, “Bulk properties of the slow and fast solar wind and interplanetary coronal mass ejections measured by ulysses: Three polar orbits of observations,” Journal of Geophysical Research: Space Physics, vol. 114, no.A1,p.A01109,2009. [29] T. Stubbs, J. Halekas, W. Farrell, and R. Vondrak, “Lunar surface charging: A global per- spectiveusinglunarprospectordata,”inDustinPlanetarySystems,2007. [30] D. Reasoner and W. Burke, “Characteristics of the lunar photoelectron layer in the geomag- netictail,”JournalofGeophysicalResearch,vol.77,no.34,pp.6671–6687,1972. [31] R.Manka,“Plasmaandpotentialatthelunarsurface,”PhotonandParticleInteractionswith SurfacesinSpace,pp.347–361,1973. [32] J. Freeman and M. Ibrahim, “Lunar electric fields, surface potential and associated plasma sheaths,”Earth,Moon,andPlanets,vol.14,no.1,pp.103–114,1975. [33] J. Halekas, R. Lin, and D. Mitchell, “Large negative lunar surface potentials in sunlight and shadow,”GeophysicalResearchLetters,vol.32,no.L09102,2005. [34] J.Halekas,G.Delory,D.Brain,R.Lin,M.Fillingim,C.Lee,R.Mewaldt,T.Stubbs,W.Far- rell,andM.Hudson,“Extremelunarsurfacechargingduringsolarenergeticparticleevents,” GeophysicalResearchLetters,vol.34,no.L02111,2007. [35] J.S.Halekas,G.T.Delory,R.P.Lin,T.J.Stubbs,andW.M.Farrell,“Lunarsurfacecharging duringsolarenergeticparticleevents: Measurementandprediction,”JournalofGeophysical Research: SpacePhysics,vol.114,no.A5,2009. A05110. [36] O. Berg, “A lunar terminator configuration,” Earth and Planetary Science Letters, vol. 39, no.3,pp.377–381,1978. [37] N. Borisov and U. Mall, “Charging and motion of dust grains near the terminator of the moon,”PlanetaryandSpaceScience,vol.54,no.6,pp.572–580,2006. 119 of124 BIBLIOGRAPHY [38] W. Farrell, T. Stubbs, R. Vondrak, G. Delory, and J. Halekas, “Complex electric fields near the lunar terminator: The near-surface wake and accelerated dust,” Geophysical Research Letters,vol.34,no.L14201,2007. [39] W. Farrell, T. Stubbs, J. Halekas, R. Killen, G. Delory, M. Collier, and R. Vondrak, “Antic- ipated electrical environment within permanently shadowed lunar craters,” Journal of Geo- physicalResearch: Planets,vol.115,no.E3,p.E03004,2010. [40] J. Wang, X. He, and Y. Cao, “Modeling electrostatic levitation of dust particles on lunar surface,”PlasmaScience,IEEETransactionson,vol.36,no.5,pp.2459–2466,2008. [41] A. Poppe, M. Piquette, A. Likhanskii, and M. Horányi, “The effect of surface topography on the lunar photoelectron sheath and electrostatic dust transport,” Icarus, vol. 221, no. 1, pp.135–146,2012. [42] M. Zimmerman, W. Farrell, T. Stubbs, J. Halekas, and T. Jackson, “Solar wind access to lunarpolarcraters: Feedbackbetweensurfacechargingandplasmaexpansion,”Geophysical ResearchLetters,vol.38,no.19,2011. [43] J. Burns, P. Lamy, and S. Soter, “Radiation forces on small particles in the solar system,” Icarus,vol.40,no.1,pp.1–48,1979. [44] D.HamiltonandJ.Burns,“Orbitalstabilityzonesaboutasteroids: Ii.thedestabilizingeffects ofeccentricorbitsandofsolarradiation,”Icarus,vol.96,no.1,pp.43–64,1992. [45] J. Burns and D. Hamilton, “Debris about asteroids: Where and how much?,” in Asteroids, Comets,Meteors1991,vol.1,pp.101–108,1992. [46] P.Lee,“Dustlevitationonasteroids,”Icarus,vol.124,no.1,pp.181–194,1996. [47] M. Horányi, J. Szalay, S. Kempf, J. Schmidt, E. Grün, R. Srama, and Z. Sternovsky, “A permanent, asymmetric dust cloud around the moon,” Nature, vol. 522, no. 7556, pp. 324– 326,2015. [48] J. Gaier, “The effects of lunar dust on eva systems during the apollo missions,” NASA Tech Rpt.TM-2005-213610,2005. [49] T. Stubbs, R. Vondrak, and W. Farrell, “Impact of dust on lunar exploration,” Dust in Plane- tarySystems,vol.643,pp.239–243,2007. [50] E. Mazets et al., “Dust in comet p/halley from vega observations,” in Exploration of Halleys Comet,pp.699–706,Springer,1988. [51] R.Lorenz,“Solararraydegradationbydustimpactsduringcometaryencounters,”Journalof spacecraftandrockets,vol.35,no.4,pp.579–582,1998. 120 of124 BIBLIOGRAPHY [52] B. Walch, M. Horányi, and S. Robertson, “Charging of dust grains in plasma with energetic electrons,”Physicalreviewletters,vol.75,no.5,p.838,1995. [53] P.ShuklaandB.Eliasson,“Colloquium: Fundamentalsofdust-plasmainteractions,”Reviews ofModernPhysics,vol.81,no.1,p.25,2009. [54] S. Lai, Fundamentals of Spacecraft Charging: Spacecraft Interactions with Space Plasmas. PrincetonUniversityPress,2012. [55] E.Sternglass,“Theoryofsecondaryelectronemissionbyhigh-speedions,”PhysicalReview, vol.108,no.1,p.1,1957. [56] K. Kanaya and H. Kawakatsu, “Secondary electron emission due to primary and backscat- teredelectrons,”JournalofPhysicsD:AppliedPhysics,vol.5,no.9,p.1727,1972. [57] H. Garrett, “The charging of spacecraft surfaces,” Reviews of Geophysics, vol. 19, no. 4, pp.577–616,1981. [58] E.Whipple,“Potentialsofsurfacesinspace,”ReportsonProgressinPhysics,vol.44,no.11, p.1197,1981. [59] R. F. Willis, M. Anderegg, B. Feuerbacher, and B. Fitton, “Photoemission and secondary electronemissionfromlunarsurfacematerial,”inPhotonandParticleInteractionswithSur- faces in Space (R. J. L. Grard, ed.), vol. 37 of Astrophysics and Space Science Library, pp.389–401,SpringerNetherlands,1973. [60] J.Goree,“Chargingofparticlesinaplasma,”PlasmaSourcesScienceandTechnology,vol.3, no.3,p.400,1994. [61] A. Zobnin, A. Nefedov, V. SinelShchikov, and V. Fortov, “On the charge of dust particles in a low-pressure gas discharge plasma,” Journal of Experimental and Theoretical Physics, vol.91,no.3,pp.483–487,2000. [62] M.Lampe,“Limitsofvalidityfororbital-motion-limitedtheoryforasmallfloatingcollector,” Journalofplasmaphysics,vol.65,no.3,pp.171–180,2001. [63] M.Horányi, “Chargeddustdynamics in thesolar system,” Annual Review of Astronomy and Astrophysics,vol.34,no.1,pp.383–418,1996. [64] D. Mendis, “Progress in the study of dusty plasmas,” Plasma Sources Science and Technol- ogy,vol.11,no.3A,p.A219,2002. [65] A. Barkan, N. D’Angelo, and R. Merlino, “Charging of dust grains in a plasma,” Physical ReviewLetters,vol.73,no.23,pp.3093–3096,1994. [66] R. Merlino and J. Goree, “Dusty plasmas in the laboratory, industry, and space,” Physics Today,vol.57,no.7,pp.32–39,2004. 121 of124 BIBLIOGRAPHY [67] P. Shukla, “Nonlinear effects in dusty plasmas,” in Proceedings of the First Capri Workshop onDustyPlasmas,vol.29,pp.38–39,1989. [68] N.Rao,P.Shukla,andM.Yu,“Dust-acousticwavesindustyplasmas,” Planetary and space science,vol.38,no.4,pp.543–546,1990. [69] A. Barkan, R. Merlino, and N. D’angelo, “Laboratory observation of the dust-acoustic wave mode,”PhysicsofPlasmas,vol.2,no.10,pp.3563–3565,1995. [70] D.Samsonovetal.,“Kineticmeasurementsofshockwavepropagationinathree-dimensional complex(dusty)plasma,”PhysicalReviewE,vol.67,no.3,p.036404,2003. [71] C. Ticos, A. Dyson, P. Smith, and P. Shukla, “Pressure triggered collective oscillations of a dust crystal in a capacitive rf plasma,” Plasma Phys. Control. Fusion, vol. 46, no. 12B, pp.B293–B300,2004. [72] X. Wang, M. Horányi, and S. Robertson, “Dust transport near electron beam impact and shadowboundaries,”PlanetaryandSpaceScience,vol.59,no.14,pp.1791–1794,2011. [73] D.Ferguson,“Newfrontiersinspacecraftcharging,”PlasmaScience,IEEETransactionson, vol.40,no.2,pp.139–143,2012. [74] H. Senshu, H. Kimura, T. Yamamoto, K. Wada, M. Kobayashi, N. Namiki, and T. Mat- sui, “Photoelectric dust levitation around airless bodies revised using realistic photoelectron velocitydistributions,”PlanetaryandSpaceScience,vol.116,pp.18–29,2015. [75] J.Colwell,A.Gulbis,M.Horányi,andS.Robertson,“Dusttransportinphotoelectronlayers andtheformationofdustpondsoneros,”Icarus,vol.175,no.1,pp.159–169,2005. [76] C. Hartzell and D. Scheeres, “Dynamics of levitating dust particles near asteroids and the moon,”JournalofGeophysicalResearch: Planets,vol.118,no.1,pp.116–125,2013. [77] Y. Yamauchi and R. Shimizu, “Secondary electron emission from aluminum by argon and oxygenionbombardmentbelow3kev,”JapaneseJournalofAppliedPhysics,vol.22,no.4A, p.L227,1983. [78] P.Auerkari,Mechanicalandphysicalpropertiesofengineeringaluminaceramics. Technical ResearchCentreofFinlandEspoo,1996. [79] D. Hasselkamp, “Kinetic electron emission from solid surfaces under ion bombardment,” in ParticleinducedelectronemissionII,pp.1–95,Springer,1992. [80] O.CallaandI.Rathore,“Studyofcomplexdielectricpropertiesoflunarsimulantsandcom- parisonwithapollosamplesatmicrowavefrequencies,”AdvancesinSpaceResearch,vol.50, no.12,pp.1607–1614,2012. 122 of124 BIBLIOGRAPHY [81] J.Lim,S.Yun,andJ.Lee,“Electricalpropertiesofaluminumsilicatefilmsgrownbyplasma enhanced atomic layer deposition,” Electrochemical and solid-state letters, vol. 9, no. 1, pp.F8–F11,2006. [82] J. Polansky, J. Wang, and N. Ding, “Experimental investigation on plasma plume potential,” PlasmaScience,IEEETransactionson,vol.41,pp.3438–3447,Dec.2013. [83] J. Wang, D. Han, and Y. Hu, “Kinetic simulations of plasma plume potential in a vacuum chamber,”PlasmaScience,IEEETransactionson,vol.43,no.9,pp.3047–3053,2015. [84] A. Gurevich, L. Pitaevskii, and V. Smirnova, “Ionospheric aerodynamics,” Space Science Reviews,vol.9,no.6,pp.805–871,1969. [85] J. Wang and D. Hastings, “Ionospheric plasma flow over large high voltage space platforms. ii: Theformationandstructureofplasmawake,”PhysicsofFluidsB:PlasmaPhysics,vol.4, no.6,pp.1615–1629,1992. [86] N. Ding, J. Wang, and J. Polansky, “Measurement of dust charging on a lunar regolith simu- lantsurface,”PlasmaScience,IEEETransactionson,vol.41,pp.3498–3504,Dec.2013. [87] J. Conway and N. Sloane, Sphere packings, lattices and groups, vol. 290. Springer Science &BusinessMedia,2013. [88] W. Carrier III, “Particle size distribution of lunar soil,” Journal of Geotechnical and Geoen- vironmentalEngineering,vol.129,no.10,pp.956–959,2003. [89] T. Nakamura et al., “Itokawa dust particles: a direct link between s-type asteroids and ordi- narychondrites,”Science,vol.333,no.6046,pp.1113–1116,2011. [90] N.Hershkowitz,PlasmaDiagnostics: DischargeParametersandChemistry,vol.1,ch.How Langmuirprobeswork,pp.113–183. AcademicPress,Inc.,1989. [91] J. Smith, N. Hershkowitz, and P. Coakley, “Inflection-point method of interpreting emissive probecharacteristics,”ReviewofScientificInstruments,vol.50,no.2,pp.210–218,1979. [92] Y.Azziz,ExperimentalandtheoreticalcharacterizationofaHallthrusterplume. PhDthesis, MassachusettsInstituteofTechnology,2007. [93] M. Walker, R. Hofer, and A. Gallimore, “The effects of nude faraday probe design and vac- uumfacilitybackpressureonthemeasuredioncurrentdensityprofileofhallthrusterplumes,” in38thAIAA/ASME/SAE/ASEEJointPropulsionConference&Exhibit,p.4253,2002. [94] D.Han,P.Wang,X.He,T.Lin,andJ.Wang,“A3dimmersedfiniteelementmethodwithnon- homogeneous interface flux jump for applications in particle-in-cell simulations of plasma- lunarsurfaceinteractions.”Unpublished. [95] J.D.Jackson,Classicalelectrodynamics. JohnWiley&Sons,3rded.,1999. 123 of124 BIBLIOGRAPHY [96] S. Sarma, T. Subba Rao, and M. Mautner, “Electrical properties of murchison carbonaceous chondritemeteorite,”BalkanPhysicsLetters,vol.12,no.1,pp.31–37,2004. [97] F. Vilas, “Spectral characteristics of hayabusa 2 near-earth asteroid targets 162173 1999 ju3 and2001qc34,”TheAstronomicalJournal,vol.135,no.4,pp.1101–1105,2008. [98] D. Han and J. Wang, “Numerical simulations of surface charging at the lunar terminator,” in 53rdAIAAAerospaceSciencesMeeting,AIAASciTech,AIAA2015-1394,2015. 124 of124

Abstract (if available)

Abstract Asteroids are the remnants of the formation of the solar system and they constitute a wealth of information relating to evolution of the solar system. The origin of the solar system questions can only be fully addressed in the context of an ambitious program of space exploration to the asteroids. Asteroids in space are airless, dusty objects immersed in the solar wind plasma and illuminated by solar radiation. The dust grains are susceptible to the competing effects from the gravitational force, the electromagnetic force and solar radiation pressure that culminate to a challenging problem in mitigating the risks of asteroid rendezvous missions. ❧ This dissertation experimentally investigated the charging properties of dust grains in a plasma in order to develop the first 3D model for plasma-asteroid-dust interaction and the dynamics of charged dust transport on a global scale. Laboratory measurements of a simulated plasma-asteroid surface provided the charging model and the charging parameters of conducting objects, dielectric objects and dust grains immersed in a mesothermal plasma flow. A plasma-asteroid-dust transport numerical model incorporated the results of the particle-in-cell plasma-asteroid charging simulation with a finite-element gravitational field model and a solar radiation pressure model to determine the dust distribution around small asteroids under various scenarios. ❧ The effects of dust particles are important concerns for spacecraft functionality and survivability, but there are still large uncertainties in the current knowledge of dust transport on planetary surfaces. The following statements summarize the principal finding of this dissertation: First, solar radiation pressure dominates the transport of the particles under a low charging state, while the electrostatic force becomes the dominant factor for more extreme charging conditions. Second, the dust dynamics are sensitive to the sizes of the individual grains such that as the grain size is increased, the forces acting upon it are effectively attenuated and the grain becomes more tightly bound to the surface on which it is located. Thirdly, and intuitively, a relatively strong gravitational field acts to confine more of the dust to lower altitudes. Lastly, the asteroid shape contributes to dust transport in more complex ways, making it more difficult to predict the dust distribution. Implications of the study may advance the current understanding of the asteroid environment and improve functionality of future spacecraft design for asteroid rendezvous missions.

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Creator Yu, William (author)

Core Title Numerical and experimental investigations of dust-plasma-asteroid interactions

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Astronautical Engineering

Publication Date 08/02/2018

Defense Date 03/20/2018

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

Tag asteroids,complex plasma,dust grain,dusty plasma,electrostatic force,gravitational field,gravity,numerical simulations,OAI-PMH Harvest,particle-in-cell,plasma,solar radiation pressure,space,surface charging,vacuum experiments

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Wang, Joseph (committee chair), Gruntman, Michael (committee member), Rhodes, Edward (committee member)

Creator Email w.yu@usc.edu,willyu28@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-46088

Unique identifier UC11671849

Identifier etd-YuWilliam-6606.pdf (filename),usctheses-c89-46088 (legacy record id)

Legacy Identifier etd-YuWilliam-6606.pdf

Dmrecord 46088

Document Type Dissertation

Format application/pdf (imt)

Rights Yu, William

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