1. The technical data in this document (or file) is controlled for export under the International Traffic in Arms Regulations (ITAR), 22 CFR 120-130. Violations of these laws may be subject to fines and penalties under the Arms Export Control Act, 22 U.S.C. 2778. May contain Georgia Tech proprietary information; Not for public dissemination. EFFECT OF ION-NEUTRAL COLLISIONS ON SHEATH POTENTIAL PROFILE 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 Lubos Brieda Particle in Cell Consulting LLC, Falls Church, VA 22046 33rd International Electric Propulsion Conference, The George Washington University, Washington, D.C., USA October 6 – 10, 2013

2. M OTIVATION 2 Hall-effect thruster [PPS-100ML] Wall power deposition  Performance Wall 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 retrieved 2013-09-30. The plasma-wall interface is critical in electric propulsion devices.

3. B ACKGROUND 3 Plasma Sheath: –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. B ACKGROUND 4 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 Presheath Transition Region Sheath ~ λ D ~ λ in

5. B ACKGROUND 5 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 Presheath Transition Region Sheath ~ λ D ~ λ in Collisions increase  presheath growth

6. B ACKGROUND 6 Theories for the sheath-presheath potential profile? Presheath with finite collisionality is difficult to solve analytically due to multiple length scales (sheath ~ λ D, presheath ~ λ in ) TheoryCollisions?Presheath? Child-Langmuir, 1913  Bohm, 1949  Sheridan, 1991  Riemann, 1997  Asymptotic matching, intermediate scale analysis

7. B ACKGROUND 7 Sheath theory is well-developed 1, 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) Experimental measurements are sparse 2 –Sheaths are thin, scale with electron Debye length, (often < 1 mm.) Thus, current objectives: 1.Experimentally characterize sheaths and presheaths in low n e, large-sheath environment. 2.Validate theoretical models for sheath scaling. 3.Validate particle-in-cell (PIC) simulation tool. 1.Allen, J. E., “The plasma–sheath boundary: Its history and Langmuir's definition of the sheath edge” Plasma Sources Sci. Technol. 18 (2009) 014004 2.Hershkowitz, N. “Sheaths: More complicated than you think” Physics of Plasmas 12, 055502 (2005.)

8. E XPERIMENTAL M ETHOD 8 To resolve sheaths, need large Debye length: Low n e Plasma Cell –Multidipole-type plasma device selected –Provides stable, spatially uniform, low-density plasma 90 cm 60 cm Heated filaments, biased below frame Cusp shaped field Permanent Magnets Aluminum Frame - - - + nene 10 10 – 10 6 cm -3 TeTe 0.5 – 10 eVλdλd 0.05 – 5 mm

9. E XPERIMENTAL M ETHOD 9 Vacuum Chamber – HPEPL VTF-2 Base pressure: 1.9 x 10 -9 Torr Gas Inlet Active Cryopumps (6) Plasma Cell CM Location (Capacitance Manometer) L = 9.2 m 4.9 m 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. p1–5 mTorr-Ar λ nn 0.5–0.1 m Kn0.01–0.1

10. E XPERIMENTAL M ETHOD 10 Place wall material sample in plasma, measure sheath Diagnostics: Emissive Probe  V p (x) Planar Langmuir Probe  T e, n e FFilaments MPermanent Magnets BMagnetic Field PLPPlanar Langmuir Probe EPEmissive Probe WWall material sample XMeasurement ordinate Key: F B M PLP EP W 60 cm __ X 90 cm

11. R ESULTS 11 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) p = 1 mTorrp = 5 mTorr λDλD 1.8 mm0.45 mm λ in 60 mm12 mm λ D / λ in 0.0300.037 Length scales of both sheath and presheath observable

12. R ESULTS 12 Emissive probe results: p = 1 mTorrp = 5 mTorr Sheath Potential8.3 V5.5 V Sheath Thickness1.9 cm1.2 cm

13. E XPERIMENTAL M ETHOD 13 Langmuir probe, determine bulk plasma parameters –Planar probe theory of Knapmiller et al. –Bi-Maxwellian bulk plasma indicated T e_hot = 3.8 eV T e_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. R ESULTS 14 Emissive probe (figure) and Langmuir probe (table): p = 1 mTorrp = 5 mTorr T e_cold 0.8 eV0.7 eV T e_hot 8.4 eV3.8 eV n e_cold 9.5 x 10 6 cm -3 1.9 x 10 8 cm -3 n e_hot 3.7 x 10 6 cm -3 5.6 x 10 7 cm -3 n e_total 1.3 x 10 7 cm -3 2.5 x 10 8 cm -3 Bulk Plasma Parameters:

15. R ESULTS 15 Potential profiles, normalized by V wall Increased collisionality  Growth of presheath

16. A NALYSIS 16 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 T e : 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. A NALYSIS 17 Floating wall potential, predicted vs. measured: p = 1 mTorrp = 5 mTorr Measured9.0 V6.5 V Harmonic Mean T e Prediction5.5 V3.8 V Hot T e Prediction45.3 V10.3 V Harmonic mean T e shows closer agreement, use that as boundary condition for sheath prediction

18. A NALYSIS 18 Comparison to Riemann 1997 fluid asymptotic matching model with predicted wall floating potential: 1 mTorr5 mTorr λDλD 1.8 mm0.44 mm λ in 60 mm12 mm TeTe 1.07 eV0.73 eV V sheath -5.5 eV-3.8 eV

19. A NALYSIS 19 Allowing parameters to vary, good fit can be achieved. R 2 > 0.98 1 mTorr5 mTorr λDλD 1.5 mm1.3 mm λ in 65 mm19 mm TeTe 0.8 eV0.7 eV V sheath -8.4 eV-5.5 eV

20. C ONCLUSIONS 20 1.Experimental measurements of sheaths and pre- sheaths obtained, presheath growth observed. 1.Potential profiles in qualitative agreement with asympotically-matched fluid theory. 2.Experiment agrees more closely to harmonic mean T e 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. 21 Thank you Questions? This work is supported by the Air Force Office of Scientific Research (AFOSR) through Grant FA9550-11-10160

22. E XPERIMENTAL M ETHOD 22 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. B ACKUP 23 Axial distance from magnet (in) Radial distance from magnet (in) Bulk plasma largely field- free (G) 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 0.0 0.2 0.4 0.6 0.8 1.0 1.2

24. C OLLABORATION 24 Measurement Theory Simulation Validate Verify Collaborative research strategy:

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