1. Complex phenomena in magnetized plasmas with an electron emission Yevgeny Raitses Princeton Plasma Physics Laboratory Michigan Institute for Plasma Science and Engineering Ann Arbor, December 5, 2012

2. Plasma Science & Technology Research at Princeton Plasma Physics Laboratory (PPPL) Heavy ion beam MRI

4. Outline E  B plasma devices: - Configurations - Electron rotating effects - Maximizing electric field applied in plasma Anomalous electron cross-field transport: - Secondary electron emission effects - Turbulent fluctuations and coherent structures - Suppression of anomalous electron transport Summary and concluding remarks

5. PPPL DC-RF E  B discharge of Penning-type DC E×B fields applied in a 20 cm × 50 cm st. steel chamber with ceramic side walls Plasma cathode: 2 MHz, 50-200 W Ferromagnetic ICP Operating parameters: Bkg. pressure: 0.1-1 mtorr RF-power: 50-60 W DC voltage/current: 0-100 V/0-3 A Magnetic field: up to 500 Gauss Magnetically shielded RF-plasma cathode E Coils B Anode Insulator Axis

6. Plasma in E ×B region: weakly collisional, non-equilibrium, with magnetized electrons and non-magnetized ions 4/14 Neutral density ~ 10 13 cm 3 Plasma density ~ 0.5-3  10 11 cm -3 Electron temperature ~ 3-5 eV Magnetic field: 5-500 Gauss ea /L ~ 1-2 ei /L ~ 10 ee /L ~ 20-50 ia /L~ 0.5-3 Energy relaxation length in inelastic range  >  * * /L ~ 2  ce / coll ~ 150-200 For B = 35 Gauss Electron cross-field displacement during time loss (inelastic or wall collisions) X ~ 2R Le ( scat /2 loss ) 0.5

7. Examples of E ×B devices Sputtering magnetron discharge Large Plasma Device (LaPD) at UCLA 20-meter long, 1 meter diameter Penning Gauge

8. e e Diam ~ 1 -100 cm B ~ 100 Gauss Working gases: Xe, Kr Pressure ~ 10 -1 mtorr V d ~ 0.2 – 1 kV Power ~ 0.1- 50 kW Thrust ~ 10 -3 - 1N Isp ~ 1000-3000 sec Efficiency ~ 6-70% Unlike ion thruster, HT is not space-charge limited Thrust density is limited by B 2 /2   e << L <<  i Hall Thruster (HT) – fuel effective plasma propulsion device for space applications E =-v e  B

9. Neutral density ~ 10 12 -10 13 cm 3 Plasma density ~ 10 11 -10 12 cm -3 Highly ionized flow:  ion /  n ~ 80% Electron temperature ~ 20-60 eV Ion temperature ~ 1 eV Ion kinetic energy ~ 10 2 -10 3 eV Collisionless, non-equilibrium plasma with magnetized electrons and non-magnetized ions ea /h ~ 20 – 200 ei /h ~ 4  10 3 ia /h ~ 10-100 Energy relaxation length in the inelastic range * /h ~ 30 - 300 Parameters of HT plasma

10. Comparison of different E  B plasma devices Device\Parameter R cm L cm T eV B Gauss E max V/cm LAPD5017002-5400 4-18 Compact Auburn Torsatron1753101000 5 Blaamann8659570 2-6 Continuous Current Tokamak 40150 3000 120 ALEXIS101705100 2 Reflex arc2.530054000 20 Mistral11.51401.4220 Maryland Centrifugal Experiment (MCX) 2725032000 CSDX102801.5-3650 3-4 WVU Q-machine43000.21400 14 State-of-the-art Hall thruster 2220-60100-300 700 PPPL Segmented Hall Thruster 2.52100115  1000

11. Cylindrical Hall thruster (CHT) – E  B plasma in diverging magnetic field Similar to conventional HTs, the CHT operation is based on closed electron E  B drift. Fundamentally differences from conventional HTs: Electrons are confined in the magneto-electrostatic trap. Ions are accelerated in a large volume-to-surface channel Related concepts DCF by MIT and HEMP by Thales, CHT by Osaka, etc. Raitses and Fisch, Phys. Plasmas 8, 2579 (2001)

12. Unusual focusing of the plasma flow in diverging magnetic field of CHT LIF measurements of ion velocity Ion current in plume Spektor et al., Phys. Plasmas 17, 093502 (2010) Raitses at al., Appl. Phys. Lett. 90, 221502 (2007)

13. Plasma with azimuthal symmetric magnetic field and E×B rotating electrons is common in industrial and laboratory plasmas: non-neutral plasmas, solar physics, magnetic mirrors, magnetic fusion devices, plasma centrifuges and, most recently, plasma thrusters

14. Rotating electron effects Isorotation For magnetized electrons and non-magnetized ions, common assumption is that magnetic surfaces are equipotential surfaces leads to a force field that is perpendicular to the magnetic surfaces, a good assumption for non-rotating cold magnetized plasma

15. Ion focusing due to rotating electron effects Pressure gradientCentrifugal force effect on electrons Non-magnetized ions are not affected by the magnetic field, but the addition of the field E s results in focusing deflection of the original electric field E n Fisch et al., PPCF, 53, 124038 (2011) Ion focusing should benefit from supersonic electrons

16. Challenging requirements for the generation of supersonically rotating electrons in a steady state - Strong electric field and low magnetic field to get high E  B speed - Colder plasma Common approach: Control of E-field with biased electrodes

17. HT is capable to generate supersonically rotating electrons Device\Parameter R cm L cm T eV B Gauss E max V/cm V E/B /V eth LAPD5017002-5400 4-18 < 2  10 -2 Compact Auburn Torsatron 1753101000 5 < 4  10 -3 Blaamann8659570 2-6 < 8  10 -3 Continuous Current Tokamak 40150 3000 120  8  10 -3 ALEXIS101705100 2  2  10 -2 Reflex arc2.530054000 20  5  10 -3 Mistral11.51401.4220  4  10 -3 Maryland Centrifugal Experiment (MCX) 2725032000  7  10 -2 CSDX102801.5-3650 3-4 < 1  10 -2 WVU Q-machine43000.21400 14 5  10 -2 State-of-the-art Hall thruster 2220-60100-300 700 < 1 PPPL Segmented (No SEE) Hall Thruster 2.52100115  1000 1 - 2

18. Electric field and thruster performance are affected by anomalous electron cross-field transport Thruster efficiency With all other parameters held constant, HTs efficiency reduces with increasing electron current across the magnetic field Classical collisional mechanism can not explain the discharge current measured for Hall thrusters: e-a ~ 10 6 s -1 < eff ~ 10 7 s -1 Enhanced cross-field conductivity in HTs usually attributed to 1)SEE induced near-wall conductivity 2)Anomalous (Bohm-type) diffusion induced by high frequency azimuthal plasma oscillations 3)A new route for electron transport across magnetic field - low frequency rotating spoke oscillations

19. Effect of the channel wall material on the discharge characteristic Carbon segments drastically change V-I characteristics - Boron nitride - high SEE - Carbon velvet - zero SEE Raitses, Staack, Dunaevsky, Fisch, Phys. Plasmas (2006)

20. Wall material affects the maximum electron temperature in the thruster Raitses, Staack, Smirnov, Fisch Phys. Plasmas,2005 Electron temperature from emissive probe measurements PPPL Hall thruster setup

21. SEE from dielectrics reaches 1 at lower energies (< 50 eV) of primary electrons than for metals Teflon Boron Nitride Pz26 - Pz26 +  Note: for boron nitride, if primary electrons are Maxwellian  (T e )  1 at T e = 18.3 eV PPPL SEE setup Dunaevsky, Raitses, Fisch, Phys. Plasmas (2003)

22. SEE can significantly enhance electron flux from plasma to the wall  scs  T e  w (x) ee ii  see SEE turns sheath to space-charge limited regime [Hobbs and Wesson, 1967] When Fluid Approach

23. SEE effect on plasma electrons: comparing experiment with predictions Large quantitative disagreement with fluid theory! Fluid theory T e max  18.3 eV According to fluid theories, the maximum electron temperature should not be above 18.3 eV (for BN and Xenon)

24. Hall thruster plasma, 2D-EVDFIsotropic Maxwellian plasma, 2D-EVDF EVDF in HT is strongly anisotropic with beams of SEE electrons Loss cones and beams Sydorenko et al, Kaganovich et al., Phys. Plasmas (2005, 2006, 2007 2009), Ahedo, Phys. Plasmas (2005)

25.  (x) ii 22  1b 22  1p ii  1b  1p 1- primary 2- secondary SEE coefficients:  p  2p /  1p - SEE due to plasma electrons  b  2b /  1b - SEE due to beam electrons   1b /  2 - Penetration of the SEE beams Electron fluxes have several components, including counter-streaming SEE beams from opposite walls Total emission coefficient: Note,  p can be >  cr if  eff <  cr

26. PIC simulations predict: EVDF is decreasing f (v x ) Beam penetration is high,  0.9 f(v x ) unstable stable vxvx vxvx Conditions for the existence of self-sustained counter-streaming SEE electron beams Sydorenko et al., Phys. Plasmas 2007 1) Weak two-stream and plasma beam instabilities

27. Conditions for self-sustained counter- streaming SEE electron beams (Cont’d) 2) Sufficiently strong electric field - SEE electrons gain additional energy during the flight between the channel walls due to E  B motion - This energy must be high enough to induce strong SEE on opposite wall The maximum additional energy is scaled as For typical HT conditions: E = 100-200 V/cm, B ~ 100 Gauss  Bmax ~ 30-60 eV enough for strong SEE from any ceramic material

28. gives average velocity The displacement,, during the flight time H/u bx E B Near-wall conductivity SEE-induced cross-field current Wall collisionality - exchange of primary magnetized electrons by non-magnetized SEE electrons and current Kaganovich, Raitses, Sydorenko. Smolyakov, Phys. Plasmas (2007)

29. Two profiles for two regimes of SEE- induced electron cross-field current Classical sheath with SEE E = 200 V/cm Predicted profiles of the cross-field current density: Inverse sheath at a very strong SEE  > 1, E = 250 V/cm

30. Qualitative differences between the potential profile, relative to the wall, of a classical sheath (a), SCL sheath (b) and the new inverse sheath (c). Note that plasma electrons are still confined by the SCL sheath, but not confined by the inverse sheath. Results of particle-in-cell simulations of Hall thruster discharge: a comparison of results with classical (Sim. A), E = 200 V/cm, and inverse sheath (Sim. B) E = 250 V/cm. M. Campanell et al., Phys. Rev. Lett. 108, 255001 (2012) Disappearance of near-wall sheath at a very strong SEE  > 1

31. When plasma is bounded with non-emitting and zero-recycling (100% absorbing) walls Low back flux of contamination: Ion grazing incidence Redep. is trapped in velvet texture Low SEE because: Carbon has low SEE SEE electrons are trapped in inter-fiber micro cavities Carbon fibers bonded to carbon substrate Engineered materials to mitigate plasma-surface interaction effects, e.g. carbon velvet material Raitses, Staack, Dunaevsky, Fisch, Phys. Plasmas (2006)

32. Without SEE, the magnetized plasma can withstand much stronger electric field Probe path 0 -4.6 cm 2.5 cm High-SEENo-SEE With No-SEE walls, the electric field at high voltages,  1 kV/cm, approaches a fundamental limit for a quasineutral plasma: E ~ T e / D (T e ~ 100 eV, n e ~ 10 11 cm -3 )

33. Without SEE, the cross-field mobility reduces to almost classical collisional level Experimental cross-field mobility estimated using measured data and 1-D Ohm’s law at the placement of E max Possibly E  B shear effect? * For No-SEE, the shearing frequency, d(E z /B r )/dz, reaches 5-8 nsec -1 at 600 V Such a large shear may affect the dynamics of all instabilities, which were previously predicted for Hall thrusters at moderate voltages * Fernandez, Cappellli, et al., Phys. Plasmas 15, 2008

34. HT is capable to generate supersonically rotating electrons Device\Parameter R cm L cm T eV B Gauss E max V/cm V E/B /V eth LAPD5017002-5400 4-18 < 2  10 -2 Compact Auburn Torsatron 1753101000 5 < 4  10 -3 Blaamann8659570 2-6 < 8  10 -3 Continuous Current Tokamak 40150 3000 120  8  10 -3 ALEXIS101705100 2  2  10 -2 Reflex arc2.530054000 20  5  10 -3 Mistral11.51401.4220  4  10 -3 Maryland Centrifugal Experiment (MCX) 2725032000  7  10 -2 CSDX102801.5-3650 3-4 < 1  10 -2 WVU Q-machine43000.21400 14 5  10 -2 State-of-the-art Hall thruster 2220-60100-300 700 < 1 PPPL Segmented (No SEE) Hall Thruster 2.52100115  1000 1 - 2

35. How azimuthal oscillations can cause cross-field transport? In principle, HT discharge is azimuthallyy symmetric If there are azimuthal oscillations of n e and  and they are correlated so that their time average over one period is nonzero, a wave-based azimuthal force appears: For Therefore, the F×B drift of that wave-based force could be responsible for collisionless cross-field transport

36. Hall Thruster Oscillations Oscillations in Hall thruster plasma

37. Imaging of HT operation Xenon operation of 12 cm diameter 2 kW PPPL Hall thruster Records 400,000 fps Unfiltered emission ~ 7.5 m away PPPL Hall Thruster Experiment (HTX) Phantom camera V7.3

38. High speed imaging of HT operation 12 cm diameter PPPL HT 300 V, 20 sccm Xenon 100 Gauss 700 W Steady-state operation

39. Rotating spoke Azimuthal non-uniformity of visible light emission and plasma density rotating in E  B direction (~ 10 kHz) observed using fast cameras and electrostatic probes for different types of HTs Low voltage operation (< 200 V), probes Janes and Lowder, Phys. of Fluids 9 (1966) Morozov, et al, Sov. Phys. Tech. Phys. 5 (1973) Meezan, Hargus, Cappelli, Phys. Rev E 63 (2001) Modern HTs, > 200 V, fast imaging and probes Parker, Raitses, Fisch, Appl. Phys. Lett., 97 (2010) McDonald and Gallimore, IEEE TPS, 11 (2011) Ellison, Raitses, Fisch, Phys. Plasmas 19 (2012) Griswold et al Phys. Plasmas 19, (2012) Theory and simulations of low frequency azimuthal oscillations Escobar and Ahedo, IEPC 2011 Matyash, Schneider et al., IEPC 2011 Vesselovszorov, IEPC 2011 Spoke is always ~ 10 times slower than local E  B speed !

40. A possible mechanism of cross-field transport through the spoke BrBr E 0z + - + + - - - - - + + + E 0z ×B EθEθ Eθ×BEθ×B Possible transport mechanism through the spoke:  Initial density perturbation  Only electrons undergo azimuthal drift motion  E θ generated across the perturbation  E θ ×B drift across the magnetic field, towards the anode Correlated density and azimuthal electric field fluctuations would explain enhanced electron transport

41. Cross-field transport through coherent plasma structures in magnetically controlled plasmas Serfanni et al, PPCF 49, 2007, Photo: Courtesy of S. Zweben Evolution of turbulent structures at the edge of the NSTX tokamak Non-diffusive transport - particles are not moving by a random walk (drift wave fluctuations), but rather form coherent structures (or blobs) that convect towards the walls UCLA LAPD Carter, Phys. Plasmas 13 (2006) MISTRAL, Aix-Marseille Univ. (E  B linear device) Jaeger, Pierre, Rebont, Phys. Plasmas 16 (2000) HIPIMS RU, Bohum

42. Cylindrical Hall thruster (CHT) Mirror-cusp magnetic field topology Similar to conventional HTs, the operation involves closed E  B electron drift Electrons are confined in the hybrid magneto-electrostatic trap Ions are accelerated in a large volume-to-surface area channel (potentially lower erosion) Raitses and Fisch, Phys. Plasmas 8, (2001) Cathode 100 W 2.6 cm CHT

43. Rotating spoke in CHT Cusp: Enhanced Radial Field Direction: ExB Frequency: 15-35 kHz Velocity: 1.2-2.8 km/s E/B: 10-30 km/sec E/B frequency 100-500 kHz Size: 1.0-1.6 cm

44. Does spoke conduct current ? Rotating spoke can not be observed in the discharge current traces Segmented anode (4 isolated segments) allows to see the rotating spoke Synchronized measurements with the fast camera reveal spoke-induced current More than 50% of the discharge current is conducted via the spoke Similar results were obtained for cylindrical and annular Hall thrusters Ellison, Raitses, Fisch, Phys. Plasmas 19 (2012)

45. Insight of spoke with probes Plasma density oscillations by planar tungsten probes Plasma potential oscillations by floating emissive probe Inside the channel: probe tips are flush with channel wall Outside the channel: probe tips are at radial position of channel wall Stationary probe arrays Slow movable probe 3 azimuthal probes, 90 degrees apart, per axial location 2 azimuthal probes, 30 degrees apart, on a movable positioner outside the channel 23 mm 13 mm backmiddlefront

46. Spoke is everywhere along the channel, but the coherent rotation is only near the anode An azimuthal mode does exist in all three regions. Mode is strongest in the back, although also “noisy” and extends over a large frequency range Density fluctuations: S(kθ,ω) k θ >0 corresponds to E×B direction Anode regionChannel middleCathode region Parker, Raitses, Fisch, Appl. Phys. Lett., 97 (2010)

47. - Potential and density fluctuations - Cross-field current estimation The density oscillates in-phase with the spoke current The potential is ~45  out of phase The azimuthal electric field The current to the anode: where  d =E/B The drift current is ~¼ the discharge current, explaining a large fraction of the electron cross-field current to the anode Ellison, Raitses, Fisch, Phys. Plasmas 19 (2012)

48. Do we know how to explain the spoke instability in Hall thrusters? 3-D Full PIC with MC collisions relate the spoke to neutral depletion Matyash, Schneider et al., IEPC 2011 A linear stability analysis of the ionization region in HT An extension of Morozov’s linear analysis for collisionless instability Spoke appears when the ionization and E-field make it possible to have positive gradients of plasma density and ion velocity Escobar and Ahedo, IEPC 2011

49. Potential explanation was given 20 years ago Modified Simon-Hoh instability (MSHI) - electrostatic instability in a plasma with magnetized electrons and unmagnetized ions due to finite ion Larmor radius effect on azimuthal velocity difference between electrons and ions Y. Sakawa, C. Josh, P. K. Kaw, F. F. Chen, V. K. Jain, Phys. Fluids B 5, 1993 F. C. Hoh, Phys. Fluids 6, 1963  n eo  E r0 > 0 Simon-Hoh instability (SHI) for Penning discharge Conditions for SHI  n eo  0

50. Can MSHI be excited in CHT plasma ? From the dispersion relation for MSHI, the instability is excited when Y. Sakawa et al Phys. Fluids B 5, 1993 From probe measurements of plasma properties and spoke in near- anode region of the Xenon CHT thruster: B r  900 Gauss, E z  10-20 V/cm, k   1 cm -1, b  30 Azimuthal ion velocity at the location of instability Not far from our observations

51. Can spoke be suppressed and controlled? Resistors attached between each anode segment and the thruster power supply The feedback resistors, Rf, are either 1 , 100 , 200 , or 300  Spoke increases the current through the segment leading to the increase the voltage drop across the resistor attached the segment. This results in the reduction of the voltage between the segment voltage and the cathode.

52. Spoke suppression with the feedback control Feedback offFeedback on The suppression of the spoke leads to a reduction in the total discharge current due to the anomalous current that is carried by the spoke.

53. Summary E  B electron rotation can be used to focus the ion flow in a weakly collisional plasma with magnetized electrons and non-magnetized ions Ion focusing is due to centrifugal force on electrons To maximize ion focusing supersonically rotating electrons are needed To achieve supersonic rotation of electrons, plasma needs to withstand a strong electric field Off all steady-state E  B plasma devices, Hall thruster can produce the strongest electric field Electric field in Hall thrusters is limited by anomalous electron cross- field transport: wall conductivity and spoke instability Need better understanding of spoke and near-wall conductivity: needed 3D PIC simulations, theory of instabilities, experiments Reduction of anomalous transport by minimizing SEE effects and suppression of spoke instability was demonstrated

54. Acknowledgement Nathaniel J. Fisch and Igor Kaganovich (PPPL) Alex Khrabrov, Michael Campanell, Lee Ellision and Martin Griswald (PPPL) Konstantin Matyash and Ralf Schneider (University of Greifswald, Germany) Thiery Pierre (Aix-Marseille University, France) Andrei Smolyakov (University of Saskatchewan, Canada) Stephane Mazouffre (CNRS-ICARE, France) Amnon Fruchtman (Holon Institute of Technology, Israel)

55. Can MSHI be excited in CHT plasma ? For excitation of MSHI From dispersion relation for MSHI Y. Sakawa et al Phys. Fluids B 5, 1993 For Xenon CHT near the anode and spoke: B r  900 Gauss, E z  10 V/cm, k   1 cm -1 Azimuthal component of ion velocity Smirnov, Raitses, Fisch, Phys. Plasmas 14, 2007`