1. Analytic modelling of Rosetta spacecraft potential measurements based on SPIS simulations Master thesis by: Christian Hånberg Swedish Institute of Space Physics (IRF)

2. Background IRF Langmuir probe on the Rosetta Spacecraft – Meets comet Churyomov-Gerasimenko in 2014 – Plasmas will be dense at the fully developed comet, but are solar-wind-like in early phase – Plasma density in tenuous plasmas best measured from the s/c potential

3. The Rosetta spacecraft & Langmuir probes Measured probe-to-spacecraft potential used for estimating s/c potential, also influenced by s/c-plasma interactions Main perturbation sources: S/c turning around solar panel axis (turns out to be smallest effect) Wake forming in the solar wind Photoelectron cloud (turns out to be biggest effect)

4. Project scope Use and extend previous SPIS simulations performed by Alexander Sjögren Parametric study: dependence on n e, T e, T i, bulk speed, photoemission Derive quasi-empirical model compensating for angular dependent disturbances – Main result: model for potential at each probe position as function of True s/c potential Plasma parameters Probe position around s/c – Data comparison not within scope of present project

5. Model & Solar aspect angle Solar panels point to sun Solar wind parallel to sunlight  Wake & photoelectron cloud fixed wrt solar panels  S/c turning angle around solar panel axis (solar aspect angle) is the only position variable for the probes Rosetta model for SPIS Includes the booms for the Langmuir probes

6. Meshing Different sized tetraeders – Reducing simulation times Total number of 165 000

7. Wake &Photoelectrons SPIS simulations for typical solar wind parameters. Note scale 10x higher at right. Solar wind flow

8. Simulation results Parameters: n = 5cm -3 V s = 10V T e = 12eV T i = 5eV T ph = 2eV V s = 5V v i = 400km/s r = 1AU Wake effects Photoelectron effects

9. Plasma density proxy Spacecraft potential (V s ) Potential between probe and spacecraft (V ps ) Potential at probe position (V p ) V ps = V p – V s V ps easy to measure at high time resolution Good V s and density proxy if perturbations in V p are under control Strategy: (1)Derive a model for the perturbations from the simulations (2)Parametrize the model by comparing simulations for varying plasma parameters

10. Defining an angular dependent model Based on simulations a natural model is: V p (Ф) = U a + U w (Ф) + U f (Ф) V p = Voltage at probe position U a = Potential field from spacecraft U w = Potential drop in wake U f = Potential drop due to photoelectrons Ф = solar aspect angle

11. Fitting to simulations Linear least-square-fitting Wake and photoelectron influence modelled with gaussians Parameter values for the two probes

12. Parameters and fitting results

13. Shielding model Quasi-empirical: reasonable expressions fitted to SPIS results with few free parameters Plasma inverse shielding length Inverse shielding length due to photoelectrons Total inverse shielding length (one free param)

14. Parametrized models Potential drop due to photoelectrons Potential drop due to wake Potential field from spacecraft

15. Sample results Plasma and photoelectron parameters vary between the simulations Probe 1 Probe 2 Solid  Simulated Dotted  Fitted Dashed  Modelled

16. Sample results (shifted) Plasma and photoelectron parameters vary between the simulations Probe 1 Probe 2 Solid  Simulated Dotted  Fitted Dashed  Modelled

17. Conclusions & future work Developed model gives – Good fits to simulation data for wake and photoelectrons – Estimations to wake and photoelectron influence on probe voltage in SW Random errors below the 0.1 V level Refine empirical model for influence from potential field from spacecraft Compare model with real data from Rosetta