Effect of Ion-Neutral Collisions on Sheath Potential Profile

1. Effect of Ion-Neutral Collisions on Sheath Potential Profile 33rd International Electric Propulsion Conference, The George Washington University, Washington, D.C., USA October 6 – 10, 2013 Samuel J. Langendorf, Mitchell L.R. Walker High-Power Electric Propulsion Laboratory, Georgia Institute of Technology, Atlanta, GA 30332 USA Laura P. Rose, Michael Keidar Micropropulsion and Nanotechnology Laboratory, George Washington University, Washington, D.C. 20052 USA LubosBrieda Particle in Cell Consulting LLC, Falls Church, VA 22046

2. Motivation Hall-effect thruster [PPS-100ML] Wall power deposition  PerformanceWall material erosion  Lifetime Dudeck, M., et al. "Plasma Propulsion for Geostationary Satellites and Interplanetary Spacecraft." Romanian Journal of Physics 56 (2011): 3-14. Gridded Ion Engine [NSTAR] Wall (grid) ion optics  Performance Wall (grid) erosion  Lifetime GRC – Deep Space 1 Mission <http://www.grc.nasa.gov/WWW/ion/past/90s/ds1.htm> retrieved 2013-09-30. • The plasma-wall interface is critical in electric propulsion devices.

3. Background • PlasmaSheath: • Non-neutral region that forms near walls interacting with plasma to control fluxes of + and – charge in order to satisfy the wall boundary condition. • These charged-particle fluxes facilitate power deposition to the wall and resultant phenomena (erosion, SEE.) - + + + - - - + - + + - - + + - + + + Plasma Sheath

4. Background • Sheath and Presheath: • Multiple regions corresponding to different physical length scales • Near-wall sheath region: non-neutral, scales with Debye length • Quasi-neutral presheath: scales with ion-neutral mean free path ~ λD ~ λin Presheath Sheath Transition Region

5. Background • Sheath and Presheath: • Multiple regions corresponding to different physical length scales • Near-wall sheath region: non-neutral, scales with Debye length • Quasi-neutral presheath: scales with ion-neutral mean free path ~ λD ~ λin Presheath Sheath Transition Region Collisions increase  presheath growth

6. Background • Theories for the sheath-presheath potential profile? • Presheath with finite collisionality is difficult to solve analytically due to multiple length scales (sheath ~ λD , presheath ~ λin ) • Asymptotic matching, intermediate scale analysis

7. Background • Sheaththeory is well-developed1, however: • Sheaths with multiple complications (collisions, secondary electron emission (SEE), magnetic fields, flowing plasma, non-Maxwellian plasma, warm ions) are still difficult to model. … (EP devices) • Experimentalmeasurements are sparse2 • Sheaths are thin, scale with electron Debye length, (often < 1 mm.) • Thus, current objectives: Experimentally characterize sheaths and presheaths in low ne, large-sheath environment. Validate theoretical models for sheath scaling. Validate particle-in-cell (PIC) simulation tool. Allen, J. E., “The plasma–sheath boundary: Its history and Langmuir's definition of the sheath edge” Plasma Sources Sci. Technol. 18 (2009) 014004 Hershkowitz, N. “Sheaths: More complicated than you think” Physics of Plasmas 12, 055502 (2005.)

8. Experimental Method • To resolve sheaths, need large Debye length: • Low nePlasma Cell • Multidipole-type plasma device selected • Provides stable, spatially uniform, low-density plasma - - - + Cusp shaped field Heated filaments, biased below frame 60 cm Permanent Magnets Aluminum Frame 90 cm

9. Experimental Method • Vacuum Chamber – HPEPL VTF-2 • Base pressure: 1.9 x 10-9Torr L = 9.2 m Active Cryopumps (6) Plasma Cell Gas Inlet 4.9 m CM Location (Capacitance Manometer) • Need local pressure measurement? • Transitional flow regime, expect minimal • pressure difference between Plasma Cell and CM. • First order COMSOL transitional flow model indicates • 0.001 to 0.01 mTorr pressure difference.

10. Experimental Method • Place wall material sample in plasma, measure sheath • Diagnostics: • Emissive Probe  Vp(x) • Planar Langmuir Probe  Te, ne Key: 90 cm B W 60 cm PLP EP F __ M X

11. Results • Cases at 1 and 5 mTorr • Argon gas • HP grade BN wall • Ion mean free path < device length (60 cm) • Debye length ~ emissive probe spatial resolution (0.5 mm) Length scales of both sheath and presheath observable

12. Results • Emissive probe results:

13. Experimental Method • Langmuir probe, determine bulk plasma parameters • Planar probe theory of Knapmiller et al. • Bi-Maxwellian bulk plasma indicated Te_hot = 3.8 eV Te_cold = 0.7 eV Knappmiller, S., Robertson, S., Sternovsky, Z., “Method to find the electron distribution function from cylindrical probe data,” Physical Review E, 73(6), 066402, 2006.

14. Results • Emissive probe (figure) and Langmuir probe (table): Bulk Plasma Parameters:

15. Results • Potential profiles, normalized by Vwall Increased collisionality  Growth of presheath

16. Analysis • Need to predict floating wall potential • For Maxwellian argon plasma, fluid result: • For a bi-Maxwellian plasma, the Bohm speed shown to be that of a Maxwellian plasma with weighted harmonic mean Te: Emphasizes cold electron temperature • Alternatively, from solution of Tonks-Langmuir problem with a bi-Maxwellian plasma: Emphasizes hot electron temperature Song, S. B., Chang, C. S., & Choi, D. I., “Effect of two-temperature electron distribution on the Bohm sheath criterion,” Physical Review E, Vol. 55, No. 1, 1213, 1997. Godyak, V. A., Meytlis, V. P., Strauss, H. R., “Tonks-Langmuir Problem for a Bi-Maxwellian Plasma,” IEEE Transactions on Plasma Science, Vol. 23, No. 4, 1995.

17. Analysis • Floating wall potential, predicted vs. measured: • Harmonic mean Te shows closer agreement, use that as boundary condition for sheath prediction

18. Analysis • Comparison to Riemann 1997 fluid asymptotic matching model with predicted wall floating potential:

19. Analysis • Allowing parameters to vary, good fit can be achieved. • R2 > 0.98

20. Conclusions • Experimental measurements of sheaths and pre-sheaths obtained, presheath growth observed. • Potential profiles in qualitative agreement with asympotically-matched fluid theory. • Experiment agrees more closely to harmonic mean Te method for predicting floating potential in bi-Maxwellian plasma. Future Work: • Resolve the transition region with higher spatial resolution, compare fluid and kinetic model scalings. • Validate results against PIC simulation. • Investigate effect of magnetic field.

21. Thank you Questions? This work is supported by the Air Force Office of Scientific Research (AFOSR) through Grant FA9550-11-10160

22. Experimental Method • Emissive probe: determine plasma potential in the sheath • Sweep at multiple low emission levels • Identify inflection point (e.g., left figure) • Extrapolate to zero emission  plasma potential (e.g., right figure) Smith, J. R., Hershkowitz, N., and Coakley, P., “Inflection point method of interpreting emissive probe characteristics,” Rev. Sci. Instrum. 50 (2), Feb. 1979.

23. Backup Gaussmeter 200 180 160 140 120 100 80 60 40 20 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 Bulk plasma largely field-free Axial distance from magnet (in) (G) Radial distance from magnet (in) 0.0 0.2 0.4 0.6 0.8 1.0 1.2

24. Collaboration Collaborative research strategy: Validate Measurement Simulation Verify Validate Theory

25. Background What kind of sheaths to investigate? • Ion-neutral collisions  presheath growth • Studies in HET’s have shown presheath-like potential structures permeating the full width of the discharge channel. ϕ Presheath effects not confined to near-wall sheath region!