3D modelling of the plasma environment of particle-emitting space probes - Modélisation 3D de l’environnement plasmique des sondes spatiales émettant des particules Versailles Saint-Quentin-En-Yvelines University PhD Thesis in Physics Presented by Benoît Thiébault Co-directed by Hervé de Feraudy and Alain Hilgers Paris, the 25 th November 2009

Outline Introduction Development of modelling methods and techniques Magnetospheric spacecraft sheath Double probe signal modelling Probe with a plasma engine Conclusions 2

Introduction Plasma interactions with satellites (1/5) Sheath structures – When a conductive surface is immersed in a plasma it captures particles and builds up a potential – The layer where the potential variation exists is called the electrostatic sheath (or sheath) – Its thickness is characterised by the Debye length, that depends on the plasma temperature and density – Particles within the sheath are repelled or attracted depending on their charge – The kinetic energy of a particle determines if it can reach the surface 3

Introduction Plasma interactions with satellites (2/5) Effect of sheaths on spaceborne objects – Disturbs the plasma around the object – Instruments within the sheath do not measure the characteristics of the environment plasma – Electromagnetic waves emitters/receivers should be designed for plasma conditions in the sheath Sheath modelling -One should model sheath geometry, potential distribution and other plasma characteristics distributions -This is not a new issue, but there is no theoretical standard solution because of the problem’s complexity -Sheath formation and stability governed by non linear processes: the space charge is determined by local deviation from neutrality ; the space charge results from potential distribution -Large variability of plasma encountered in space -Anisotropies create by wakes, shadowing, spacecraft shape -Surfaces and spacecraft can emit particles (photoemission, secondary emission, plasma thrusters) 4

Introduction Plasma interactions with satellites (3/5) Space plasmas – The ionosphere – The plasmasphere – The external magnetosphere – The magnetosheath – The lobes – The plasmasheet – The auroral regions 5

Introduction Plasma interactions with satellites (4/5) Variation of the Debye length (and hence sheath size) depending on the environment Comparison of the sheath size with the probes characteristic size Sheath-related problems are more likely in magnetosheath, lobes, auroral regions and plasmasheet 6

Introduction Plasma interactions with satellites (5/5) Interaction of plasmas with spaceborne objects – Electrostatic charging – Effects: Absolute charging Differential charging Deep charging Space charge – Impacts on measurements and security: ESD Surface contamination and erosion Influence on measurements 7

Introduction Plasma modelling (1/7) Assumptions and approximations – Focus on the sheath structure in the vicinity of the spacecraft => kinetic approach – Coulombian interactions (i.e. long-range) => particle-to-particle interactions << average effect of all particles within a finite sphere – Mean field effects most relevant => Vlasov equation – Long wavelength compared to sheath size => propagation effects are negligible => electric field dominated by Poisson equation – Equilibrium of charging processes reached => quasi-static assumption (no temporal derivatives) – Magnetic field neglected => this assumption is however not always valid 8

Introduction Plasma modelling (2/7) Field equation (Poisson) Force equation (Lorentz) Kinetic transport equation (Vlasov) – Means that the distribution function is constant along trajectories in phase space with 9

Introduction Plasma modelling (3/7) Current balance: – Ie: ambient electrons – Ii: ambient ions – Ibs: backscattered particles – Ise: secondary emission – Iph: photoemission – Ibeam: plasma generator – Ibulk: bulk currents 10

Introduction Plasma modelling (4/7) Analytical models for ambient currents – Orbit Motion Limiting (large sheath): orbit analysis. Energy and kinetic moments are constant – Sheath limiting (small sheath): all particles entering the sheath are collected 11 OMLSheath limiting

Introduction Plasma modelling (5/7) Analytical models for photoemission currents – Point emission: attracted particles return to the emitting surface depending on their energy – Planar emission: attracted particles return to the emitting surface depending on their energy and emission angle 12 Point sourcePlanar source

Introduction Plasma modelling (6/7) Turning point method – One tries to determine the regions in phase space of reconnected particles 13 Square angular moment

Introduction Plasma modelling (7/7) Type of numerical models – Vlasov codes (e.g. Turning point-based) – Fluid methods – PIC methods (e.g. PicUp3D, SPIS) – Hybrid methods (e.g. SPIS) 14

Introduction Contribution and adopted approach Clarify the domains of validity of analytical Langmuir probes approximations by comparison with turning point method Validation of 3D kinetics codes by comparison with the turning point method and cross-comparison 1D modelling of photoemission can provide a good qualitative estimate and reach an order of magnitude for key parameters Used to model with light means the Cluster magnetospheric spacecraft sheath Application of Langmuir probe models to double probe experiment. One can deduce an estimation of the plasma temperature from double probe measurements 3D model of ion-emitting spacecraft to evaluate the impact of the ion flow on spacecraft potential and explain observed potential fluctuations correlated with solar panels orientation 15

Outline Introduction Development of modelling methods and techniques Magnetospheric spacecraft sheath Double probe signal modelling Probe with a plasma engine Conclusions 16

Modelling methods and techniques Limiting models applicability (1/4) Application to Cluster magnetospheric spacecraft and its probes 17 Cluster spacecraft geometry Currents to take into account On spacecraft body -Ie,s: ambient electrons -Ii,s: ambient ions -Iph,s: photoemission -Ibias: biased current On probes -Ie,p: ambient electrons -Ii,p: ambient ions -Iph,p: photoemission

Modelling methods and techniques Limiting models applicability (2/4) Impact parameter values versus probe potential for Cluster magnetospheric spacecraft and its probes, for several plasma densities Densities from top to bottom (in part/cc): 1000, 100, 10, 1, 0.1 Impact parameter OML / Impact parameter >> 1 => SL SpacecraftProbe 18

Modelling methods and techniques Limiting models applicability (3/4) Ambient currents models – Probe or spacecraft potential versus plasma density for an equilibrium Maxwellian plasma, for three different models: OML, SL and turning point method SpacecraftProbe 19

Modelling methods and techniques Limiting models applicability (4/4) Photoelectrons currents models: – Spacecraft of probe potential versus plasma density for OML, SL and turning point methods Spacecraft or probes (does not depend on radius) 20

Modelling methods and techniques Turning point method adaptation (1/2) 21 Convergence algorithm adaptation – Riemann integration instead of energy quadrature for an improved numerical stability Code validation by comparison with Laframboise model and PicUp3D Potential versus radial distance without photoemission Potential versus radial distance with photoemission

Modelling methods and techniques Turning point method adaptation (2/2) Photoemission modelling in 1D and comparison with 3D modelling: potential versus radial distance for photoelectrons- emitting probe 22

Modelling methods and techniques PIC model PicUp3D: R&D prototype SPIS: industrial code 23

Outline Introduction Development of modelling methods and techniques Magnetospheric spacecraft sheath Double probe signal modelling Probe with a plasma engine Conclusions 24

Magnetospheric spacecraft sheath Photoemission related issues The electrostatic potential is not necessarily a monotonic function of the distance from the spacecraft When the background plasma density is low and the Debye length large enough, the sheath behaviour may be dominated by the photoelectrons Impact on Langmuir probes measurements 25

Magnetospheric spacecraft sheath Applications (1/2) Revisited estimation of Geotail potential barriers 26 Potential barrier versus spacecraft potential Barrier position versus spacecraft potential

Magnetospheric spacecraft sheath Applications (2/2) Application to Cluster spacecraft Influence of the temperature Lower temperature => smaller barrier 27 Potential barrier versus spacecraft potential Barrier position versus spacecraft potential

Magnetospheric spacecraft sheath Remaining issues Spherical symmetry hypothesis neglects the influence of the long wire booms Plasma emitter not modelled Wake effect neglected 28

Magnetospheric spacecraft sheath Conclusion Non monotonic potential distribution in the sheath Negative potentials can develop A good order of magnitude of the sheath characteristics is obtained with the improved turning point model, in the direction perpendicular to the illumination In the distant magnetosphere, the barrier potential can vary from below tenth of one Volt to a few Volts. When active devices are used to control the spacecraft potential, a compromise is to be found in order to: – minimise the size of the barriers – reduce the spacecraft potential to a low value compatible with the instruments requirements 29

Outline Introduction Development of modelling methods and techniques Magnetospheric spacecraft sheath Double probe signal modelling Probe with a plasma engine Conclusions 30

Double probe signal modelling Modelling principle and issues Cluster is equipped with an electric field and waves instrument (EFW) and a relaxation sounder (WHISPER) that measure the plasma density up to 80 part/cc It has been shown that there is a relationship between the density and the potential This relationship does not depend on temperature There should be a method to determine the plasma density from Langmuir probes potential measurements 31

Double probe signal modelling Langmuir probes modelling (1/2) 32 Langmuir probes modelling using OML and turning point methods – Spacecraft and probe behave quite differently for positive potentials

Double probe signal modelling Langmuir probes modelling (2/2) Probe potential versus plasma density: comparison with data 33

Double probe signal modelling Remaining issues Temperature assumed to be constant along the spacecraft orbit Effect of photoemission has been neglected 34

Double probe signal modelling Conclusion In dense plasma situations, typically inside the plasmasphere, one can obtain accurate densities measurement from the floating potential of the probes. When the plasma temperature is unknown, in plasma densities below 100 cm -3, the method can lead to 50% uncertainties, and to a factor of 2 or even 3 for densities between 100 and 1000 cm -3 35

Outline Introduction Development of modelling methods and techniques Magnetospheric spacecraft sheath Double probe signal modelling Probe with a plasma engine Conclusions 36

Probe with a Plasma Engine Thrusters modelling SMART-1 mission – First ESA mission to use electric propulsion as main propulsion system (PPS1350 de SNECMA). – 14 months journey to the moon, only 80 kg of propellant Equipped with Electric Propulsion Diagnostic Package (EPDP) to monitor impact of electric propulsion on spacecraft

Probe with a Plasma Engine Measurements (1/4) OML and turning point modelling compared to measurements

Probe with a Plasma Engine Potential fluctuations (2/4) Influence of solar panel orientation on potential and phenomenology

Probe with a Plasma Engine Modelling and measurements (3/4) SPIS simulation results Solar panels facing the CEX plasmaSolar panels facing the wake

SPIS simulation results Probe with a Plasma Engine Modelling and measurements (4/4)

Outline Introduction Development of modelling methods and techniques Magnetospheric spacecraft sheath Double probe signal modelling Probe with a plasma engine Conclusions 42

Conclusions (1/3) Objective: to characterize and model the impact of plasma interactions with space systems to improve satellites security and durability and to better interpret measurements Domains of validity of theoretical models were verified and the models were applied successfully on real world situations Two types of modelling approaches: – Analytical models (less costly, but coarse approximations) – PIC simulations (can reproduce complexity, but very costly) Budget constraints are critical and the simplest methods are often preferred – It is important to appreciate the domains of applicability of modelling approaches – This has been studied by comparison with more complex codes 43

Conclusions (2/3) A complete study of a spacecraft requires full 3D modelling – Validation of 3D kinetic codes has been performed – 1D solution can provide a good qualitative description and the correct order of magnitude of some key parameters This property has been used to describe the sheath of the Cluster magnetospheric spacecraft with relatively light computer resources Domains of validity of Langmuir probes theory identified – Langmuir probes theory has been applied to double probe experiment – We have been able to deduce a plasma temperature estimate from measurements of two plasma probes working in density mode if they have different biased currents 3D modelling of a thruster-equipped system to explain the possible impact of the ion flux on potential fluctuations 44

Conclusions (3/3) Remaining questions – Questionable hypothesis of spherical symmetry (and influence of wire booms) – Transition effects (eclipse to sunlight) have been neglected – Fluctuation and stability of potential barriers should be investigated – Trapped particles in potential wells have been neglected. How they are generated and their stability should be studied – Secondary particles distribution function could be improved, as well as its influence on barrier position and depth 45

Acknowledgements Thank you Hervé de Feraudy and Alain Hilgers Julien Forest Members of the jury Versailles Saint-Quentin-En-Yvelines university My friends and family My wife 46