1. 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 25th November 2009

2. Outline Introduction Development of modelling methods and techniques
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

3. 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

4. Introduction Plasma interactions with satellites (2/5)
The main physical quantities to specify are:
The spacecraft surface potential
The potential distribution around the spacecraft
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

5. 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

6. 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
Lets look at what happens away from the surface
One usually consider that the plasma is neutral, this is not necessary the case on spatial scales of what is called the Debye length
Currents arriving at the surface are governed by the sheath geometry, which is governed by plasma charateristics

7. 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

8. 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

9. Introduction Plasma modelling (2/5)
Type of numerical models
Fluid methods
Hybrid methods (e.g. SPIS)
Kinetic method (e.g. PicUp3D, SPIS)
Kinetic 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)
Particle In Cell
PicUp3D (precursor) and SPIS used at ESA

10. Introduction Plasma modelling (3/5)
Objective: determine regions in phase space of particles reconnected to their source (infinity for ambient particle, S/C surface for photoelectrons).
Energy conservation: ET=EC+EP=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
Reconnected particle:
Turning point:

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

12. 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
OML
Sheath limiting

13. 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.

14. 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

15. Modelling methods and techniques Turning point method adaptation
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
T=1eV
n=100cc
Tph=2.5eV
Jph=50μA/m2
T=1eV
n=55cc
Potential versus radial distance
without photoemission
Potential versus radial distance
with photoemission

16. 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

17. 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
Spacecraft
Probe

18. 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
T=1eV
n=100cc
Tph=2.5eV
Jph=50μA/m2

19. 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

20. 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

21. 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.
Potential barrier versus spacecraft potential
Barrier position versus spacecraft potential

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

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

24. 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

25. 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

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

27. 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 [Perdersen 2001]
There should be a method to determine the plasma density from Langmuir probes potential measurements

28. Double probe signal modelling Langmuir probes modelling (1/3)
Langmuir probes modelling using OML and turning point methods
Spacecraft and probe behave quite differently for positive potentials

29. 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)

30. 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/m2 [Perdersen et al., 2001] => T between 0.9 and 1 eV
Jph = 49 μA/m2 [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

31. 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

32. 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

33. Spacecraft with a plasma engine 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

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

35. 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

36. 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

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

38. 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 (1012 to 1013 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

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

40. 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.

41. 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

42. 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

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

44. Backup slides

45. Earth magnetosphere

46. 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 << 1 => OML / Impact parameter >> 1 => SL
Spacecraft
Probe

47. 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)