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 Doctoral school M2RM2 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 – Plasma interactions with satellites – Plasma modelling Development of modelling methods and techniques Magnetospheric spacecraft sheath Double probe signal modelling Spacecraft with a plasma engine Conclusions 2

Introduction Plasma interactions with satellites (1/5) Physical processes -A material surface immersed in a plasma collects particles -Charged particle collection may result in net electrical current through surfaces and build-up of electrostatic potential until an equilibrium state is reached Examples of effects on spacecraft – Electrostatic charging (+100 V / V) – Electrostatic discharges – Surface contamination and erosion – Influence on measurements It is necessary to predict these phenomena in order to assess effects on spacecraft 3

Introduction Plasma interactions with satellites (2/5) 4 The main physical quantities to specify are: – The potential distribution around the spacecraft – The spacecraft surface potential – The currents to the surface – The collection and emission of particles at the surface Assumptions and approximations – Focus on the potential distribution in the vicinity of the spacecraft => kinetic approach – Coulombian interactions (i.e. long-range) => Mean field effects most relevant => Vlasov equation – Long wavelength compared to characteristic sizes => propagation effects are negligible => electric field described by Poisson equation – Equilibrium of charging processes reached => quasi-static assumption (temporal derivatives neglected) – Magnetic field neglected => this assumption is however not always valid

Introduction Plasma interactions with satellites (3/5) The collection and emission of particles at the surface: – Ie: ambient electrons – Ii: ambient ions – Ibs: backscattered particles – Ise: secondary emission – Iph: photoemission – Ibeam: plasma generator – Ibulk: bulk currents 5

Introduction Plasma interactions with satellites (4/5) Potential distribution modelling : the electrostatic sheath – The plasma 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 -One should model sheath geometry that depends on plasma conditions and on anisotropies create by wakes, shadowing, spacecraft shape, particle emissions, etc. -Sheath formation and stability are governed by non linear processes -This is not a new issue, but there is no theoretical standard solution because of the problem’s complexity 6

Introduction Plasma interactions with satellites (5/5) Plasma characteristics and order of magnitudes -The plasma environment varies a lot depending on orbit and solar activity. -Surfaces and spacecraft can emit particles (photoemission, secondary emission, plasma thrusters), influencing the plasma characteristics 7

Introduction Plasma modelling (1/5) Field equation (Poisson) Force equation (Lorentz) Kinetic transport equation (Vlasov) – Means that the distribution function is constant along trajectories in phase space with 8

Introduction Plasma modelling (2/5) 9 Type of numerical models – Vlasov codes – Fluid methods – PIC methods (e.g. PicUp3D, SPIS) – Hybrid methods (e.g. SPIS) Numerical models capture most of the complexity They are however time consuming Still require several approximations leading to uncertainties not always easy to quantify Therefore, analytical models are often preferred (when applicable)

Introduction Plasma modelling (3/5) 10 Objective: determine regions in phase space of particles reconnected to their source (infinity for ambient particle, S/C surface for photoelectrons). Energy conservation: E T =E C +E P =constant Kinetic energy is always positive: Angular momentum is defined by: There is a function g that determines whether or not a particle is reconnected to its source o Reconnected particle: o Turning point:

Introduction Plasma modelling (4/5) 11 Square angular momentum

Introduction Plasma modelling (5/5) Limiting models for ambient currents – OML: Orbit Motion Limiting (large sheath): orbit analysis. Energy and angular momentum are constant – SL: Sheath limiting (small sheath): all particles entering the sheath are collected 12 OMLSheath limiting

Introduction Work approach Overall objective: Specify when and how analytical models can be used for quantitative assessment of spacecraft plasma interactions. Approach -Development of an algorithm for computing exact solutions for spherically symmetric problems using the turning point method. -Clarify the domains of validity of analytical Langmuir probes approximations by comparison with turning point method -Show that 1D modelling of photoemission can provide a good qualitative estimate and reach an order of magnitude for key parameters -Characterise the sheath properties using analytical models for Cluster S/C -Application of Langmuir probe models to double probe experiment. Estimation of the plasma temperature from double probe measurements -3D model of ion-emitting spacecraft. Impact of the ion flow on spacecraft potential. Correlation of potential variation with solar panels orientation. 13

Outline Introduction Development of modelling methods and techniques – Turning point method adaptation – Limiting models applicability – Application of 1D model to photoemission modelling Magnetospheric spacecraft sheath Double probe signal modelling Spacecraft with a plasma engine Conclusions 14

Modelling methods and techniques Turning point method adaptation 15 Convergence algorithm adaptation – Riemann integration instead of energy quadrature for an improved numerical stability, especially for large Debye length Code validation by comparison with Laframboise [1966] model and 3D PIC Codes Potential versus radial distance without photoemission Potential versus radial distance with photoemission T=1eV n=55cc T=1eV n=100cc T ph =2.5eV J ph =50μA/m 2

Modelling methods and techniques Limiting models applicability (1/2) The objective is to determine the domains of validity of limiting models Requires to determine whether the sheath is thick or thin with respect to probe dimensions Depends on plasma density and temperature Depends on probe size Example with typical probe size and plasma environment: – Spacecraft body equivalent to 1.41 m radius sphere – 4 probes (4 cm radius spheres) mounted at the end of 40 m long thin wire booms 16

Modelling methods and techniques Limiting models applicability (2/2) 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 17

Modelling methods and techniques Application of 1D models to photoemission modelling Photoemission modelling in 1D and comparison with 3D modelling: potential versus radial distance for photoelectrons- emitting probe 18 T=1eV n=100cc T ph =2.5eV J ph =50μA/m 2

Outline Introduction Development of modelling methods and techniques Magnetospheric spacecraft sheath – Photoemission-related issues – Applications – Remaining issues – Conclusion Double probe signal modelling Spacecraft with a plasma engine Conclusions 19

Magnetospheric spacecraft sheath Photoemission-related issues The electrostatic potential is not always 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 Zhao et al. [1996] predicted the potential barrier position and depth for the Geotail spacecraft Our results show that the barrier position is much more variable 20

Magnetospheric spacecraft sheath Applications (1/2) Revisited estimation of Geotail potential barriers, using analytical modelling of the sheath (Turning point method), compared to Zhao et al. results, based on an empirical potential profile. 21 Barrier position versus spacecraft potential Potential barrier versus spacecraft potential

Magnetospheric spacecraft sheath Applications (2/2) 22 Potential barrier versus spacecraft potential Barrier position versus spacecraft potential Probes position Application to Cluster spacecraft

Magnetospheric spacecraft sheath Remaining issues Spherical symmetry hypothesis neglects the influence of the long wire booms Plasma emitter not modelled Wake effect neglected 23

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 24

Outline Introduction Development of modelling methods and techniques Magnetospheric spacecraft sheath Double probe signal modelling – Modelling principle and issues – Langmuir probes modelling – Conclusion Spacecraft with a plasma engine Conclusions 25

Double probe signal modelling Modelling principle and issues (1/2) Application to Cluster magnetospheric spacecraft and its probes 26 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

Double probe signal modelling Modelling principle and issues (2/2) 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 27

Double probe signal modelling Langmuir probes modelling (1/3) 28 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 (2/3) Probe potential versus plasma density: comparison with data (potential is a direct measurement, density deduced from plasma frequency) 29

Double probe signal modelling Langmuir probes modelling (3/3) Photoemission parameters used to fit with data depending on total photoelectron current density – Jph = 56 μA/m 2 [Perdersen et al., 2001] => T between 0.9 and 1 eV – Jph = 49 μA/m 2 [Eriksson, 2005] => T between 0.6 and 0.7 eV Remaining issues: – Temperature assumed to be constant along the spacecraft orbit – Effects of wire booms potential on photoelectrons propagation: we neglect recollection of photoelectrons between S/C elements 30

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 31

Outline Introduction Development of modelling methods and techniques Magnetospheric spacecraft sheath Double probe signal modelling Spacecraft with a plasma engine – SMART-1 mission – Modelling and measurements – Conclusion Conclusions 32

Spacecraft with a plasma engine SMART-1 mission 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

Spacecraft with a plasma engine Modelling and measurements (1/4) OML and turning point modelling compared to measurements

Spacecraft with a plasma engine Modelling and measurements (2/4) Influence of solar panel orientation on potential and phenomenology η is the effective density depletion in the wake over the solar panel

Spacecraft with a plasma engine Modelling and measurements (3/4) Analytical model for computing spacecraft floating potential – Current balance (OML): – Where: are currents collected by solar panel electrodes at are currents collected by spacecraft at – Results based on the importance of the “wake” No wake Empty wake

SPIS simulation results Spacecraft with a plasma engine Modelling and measurements (4/4)

Spacecraft with a plasma engine Conclusion The main cause of the variations of the spacecraft potential is the variation of the current balance collected at the level of the solar panels electrodes with their orientation Solar panels facing the plasma flow: – The density is high (10 12 to m -3 ) and the electrodes collect a large number of electrons – The electrodes potential and the one of the satellite become very negative Solar panels facing the wake: – Solar panel potential is much higher than the plasma potential – The spacecraft potential is floating at a value that is less negative This is in agreement with the observations

Outline Introduction Development of modelling methods and techniques Magnetospheric spacecraft sheath Double probe signal modelling Spacecraft with a plasma engine Conclusions 39

Conclusions (1/3) Interactions with the plasma affect spacecraft instruments and equipments In order to improve satellites security and durability and to better interpret measurements, it is necessary to predict these phenomena There are two families of modelling approaches: – Analytical models (less costly, but coarse approximations) – PIC simulations (can reproduce complexity, but very costly) Budget constraints are critical for most space projects and the simplest methods are often preferred Our objective was to specify when and how these analytical models can be used for quantitative assessment of spacecraft plasma interactions. 40

Conclusions (2/3) An algorithm for computing exact solutions for spherically symmetric problems using the turning point method has been developed and tested Domains of validity of theoretical models were verified thanks to this algorithm We have shown that 1D modelling of photoemission can provide a good qualitative estimate and reach an order of magnitude for key parameters These analytical models were applied successfully on real world situations: -We characterised Cluster sheath properties using relatively light computer resources -We have been able to deduce a plasma temperature estimate from measurements of two plasma probes working in density mode -We used both analytical and 3D models to explain the possible impact of the solar panels orientation on the spacecraft potential variations 41

Conclusions (3/3) Remaining questions – Questionable hypothesis of spherical symmetry (and influence of wire booms) – Transition effects (e.g. eclipse to sunlight) have been neglected – Magnetic field effects have been neglected and could have some influence on the results – 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 42

Acknowledgements Thank you Members of the jury Hervé de Feraudy and Alain Hilgers Julien Forest My friends and family My wife 43

Backup slides 44

Earth magnetosphere 45

Modelling methods and techniques Limiting models applicability 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 46