Modeling Surface Charging with DRACO Electric Propulsion Simulation Package

1. Modeling Surface Charging with DRACO Electric Propulsion Simulation Package Alexander Barrie, Randy Spicer, Joseph Wang Department of Aerospace & Ocean Engineering Virginia Polytechnic Institute & State University

2. Outline • Introduction • DRACO Overview • DRACO Surface Charging Module • Initial Results • Plume Impingement on Composite Sphere • Spacecraft Charging in Solar Wind Plasma • Ion Thruster Plume Interaction with Solar Array • Conclusion

3. Introduction • There has been significant progress in EP plume modeling and simulation • Particle-in-cell has become standard modeling algorithm • Numerous PIC based EP plume models have been developed • Due to computational constraints, PIC simulations of EP plumes are mostly applied to simplified spacecraft models • A new EP simulation package, DRACO, is being developed as a first principle based design tool for realistic spacecraft • Objective of this work: develop a surface interaction and charging module for DRACO

4. Coliseum • Surface • Simulation mesh • Material specs • Plasma Simulation: • RAY (sputtering / deposition) • PRESCRIBED_PLUME • AQUILA (Hybrid PIC-DSMC) • DRACO (Full/Hybrid PIC-MCC) • Results • Plume properties • Surface erosion/deposit • Particle Sources • Exp profile: LIF, j • HPHall, CHETC • Sputter Model • Lab measurements • Model, f(E,q) • Collisions • Cross-sections, literature • Limited data 1 Gibbons, M.R., Kirtley, D.E., VanGilder, D.E., Fife, J.M., AIAA-2003-4872. 2 Santi, M., Cheng, S., Celik, M., Martinez-Sanchez, M., and Peraire, J., AIAA-2003-4873. 3 Brieda, L., Pierru, J., Kafafy, R., and Wang, J., AIAA-2004-3633. POC: lubos.brieda@edwards.af.mil

5. DRACO • A set of multi-purpose 3-D electrostatic PIC codes developed at VT and AFRL • QN-PIC: • Quasi-neutral plasma with Boltzmann electrons • FD-PIC: • Full particle/hybrid PIC • Standard finite-difference field solver • IFE-PIC • Full particle/hybrid PIC • Hybrid finite element/finite difference formulation • Immersed finite element field solver • Mesh-Object Intersection (VOLCAR) • Interface between PIC and CAD defined spacecraft model

6. DRACO Mesh • To maintain the computational speed of PIC, DRACO uses a Cartesian-Tetrahedral mesh • Intersection of spacecraft surface on mesh determined by the VOLCAR module • Particle impingement location on spacecraft surface determined by the Particle-Surface Intersection module

7. Surface Charging Module • Surface charging is an important interaction aspect for spacecraft using electric propulsion • In most EP plume models, spacecraft is typically modeled as a conductor • Plume interactions with more complex surfaces (e.g.. cover glass of solar cell, conductor with dielectric coating, etc) have not been studied in detail • Surface Charging Module: to calculate differential charging on a composite surface Surface Potential, s Internal Potential, q Driving Potential, d Ground Potential, g Model for solar array element }i

8. Surface Potential • For a conducting surface: charges collected will be distributed such that surface potential is uniform • For a dielectric surface: local surface potential is determined by local charge deposition • Surface potential is calculated based on internal potential, surface charge, and capacitance of the surface element

9. Charge Propagation • When an ion/electron hits the surface, its charge is first stored and then moved through the material based on conductivity and the local electric field q E

10. Charge Propagation • Charge flow from surface to interior: • Surface current: • Based on the interior electric field between neighboring elements

11. Current Collection • Current collection is simulated using full particle • Both ions and electrons are treated as macro-particles • To speed up this process, ions are run first with fluid electrons until a steady state is reached. Electrons are then introduced and a full PIC is run for the charging calculations.

12. Current Collection Test case: comparison of the I-V curve for a spherical Langmuir probe in a stationary plasma (Te=10eV)

13. Plume Impingement on Composite Spheres Purpose: investigate surface charging induced by the impingement of ion thruster plume. The sphere consists of an interior sphere with a thin coating. Three different compositions are considered

14. Simulation Setup

15. Results Dielectric surface: charge remains where it impacts and results in large differential charging on surface Conduction through surface, with internal charge sink: differential charging reduced by small surface conductivity if leakage charge can be removed internally. Conductive interior: a conductive interior results in a uniform potential distribution on the surface.

16. Spacecraft in Solar Wind Plasma Purpose: investigate surface charging of a combination of structures of different materials • Spacecraft model: • A combination of a sphere and a thin plate with an interior driving potential gradient • The main body and panel are electrically connected to allow charge transfer between the two components • Ambient plasma: similar to solar wind at 1 AU. • Photoelectron emission NOT included.

17. Simulation Setup

18. Results Initial Setup Conductive Conductive w/o gradient

19. Results Dielectric Conductive Sphere Conductive Sphere Dielectric Coverglass Semi-Conductive Coverglass

20. Spacecraft in SW • A conductive body with no gradient will reach a uniform (floating) potential. • An applied gradient will lower the ground voltage substantially, so to allow a net current of 0V. • In a dielectric material, each element will act independently, canceling out the applied gradient. The surface will reach a relatively uniform potential similar to that of the conductive case. • Adding a small amount of conductivity to the gradient surface will allow the ground voltage to be affected, and the gradient will persist into the surface, but at a lesser range (by 12V in this case) since some charge will still reside in the surface in a similar fashion to the dielectric case since it takes time to conduct to the ground.

21. Ion Thruster Plume Interactions with Solar Array Purpose: investigate surface charging of the solar cell cover glass in the charge exchange plasma environment • Spacecraft: • Similar to the DAWN spacecraft • Main body assumed to be conductive • Solar panel assumed to be covered by a cover glass • Ion thruster plume: • 3 NSTAR ion thruster • Due to computational constraints, plume simulation and charging simulation are carried out separately. • Charging simulation is performed only for a section of the solar panel.

22. Plume Environment(Wang et al., 2006) The plume environment is obtained using hybrid IFE-PIC. Simulation domain is 9mX9mX15m with a resolution of 5cm. Plume simulation is run on parallel computer Using ~31million elements and ~125 million particles

23. Charging Simulation The domain represented in the charging case was 72cm away from the panel in all directions. The gradient applied to the section is 0-60V. Coverglass conductivity: 1e-5 S/m Surface thickness: 5mm

24. Charging Result The potential gradient of the solar cell is reduced (by 18V) by the presence of charge in the cover glass. A potential gradient in the transverse direction also develops due to non uniform plasma densities from the plume.

25. Summary and Conclusions • A charging module has been developed and integrated to the DRACO code • The charging module has the capability to resolve differential charging for complex surfaces (dielectric, conductive, and semiconductive materials). • Initial simulations are carried out to study differential charging induced by plume impingement, spacecraft charging under the solar wind environment, and solar array cover glass charging under the ion thruster plume environment. • Future study will investigate surface charging of an entire spacecraft in the plume environment