Complex phenomena in magnetized plasmas with an electron

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

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

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

PPPL DC-RF E B discharge of Penning-type Coils Anode B Insulator Coils DC E×B fields applied in Magnetically shielded a 20 cm × 50 cm st. steel chamber RF-plasma cathode with ceramic side walls Plasma cathode: 2 MHz, 50 -200 W Ferromagnetic ICP E Axis 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

Plasma in E ×B region: weakly collisional, non-equilibrium, with magnetized electrons and non-magnetized ions Neutral density ~ 1013 cm 3 ea/L ~ 1 -2 Plasma density ~ 0. 5 -3 1011 cm-3 ei/L ~ 10 Electron temperature ~ 3 -5 e. V ee/L ~ 20 -50 Magnetic field: 5 -500 Gauss ia/L~ 0. 5 -3 Energy relaxation length in inelastic range > * */L ~ 2 For B = 35 Gauss ce/ coll ~ 150 -200 Electron cross-field displacement during time loss (inelastic or wall collisions) X ~ 2 RLe ( scat /2 loss )0. 5 4/14

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

Hall Thruster (HT) – fuel effective plasma propulsion device for space applications Diam ~ 1 -100 cm e e B ~ 100 Gauss Working gases: Xe, Kr Pressure ~ 10 -1 mtorr Vd ~ 0. 2 – 1 k. V Power ~ 0. 1 - 50 k. W Thrust ~ 10 -3 - 1 N E =-ve B e << L << i ü Unlike ion thruster, HT is not space-charge limited ü Thrust density is limited by B 2/2 Isp ~ 1000 -3000 sec Efficiency ~ 6 -70%

Parameters of HT plasma Neutral density ~ 1012 -1013 cm 3 ea/h ~ 20 – 200 Plasma density ~ 1011 -1012 cm-3 Highly ionized flow: ion/ n~ 80% ei/h ~ 4 103 ia/h ~ 10 -100 Electron temperature ~ 20 -60 e. V Ion temperature ~ 1 e. V Ion kinetic energy ~ 102 -103 e. V Energy relaxation length in the inelastic range */h ~ 30 - 300 Collisionless, non-equilibrium plasma with magnetized electrons and non-magnetized ions

Comparison of different E B plasma devices DeviceParameter R cm 50 17 8 40 LAPD Compact Auburn Torsatron Blaamann Continuous Current Tokamak ALEXIS 10 Reflex arc 2. 5 Mistral 11. 5 Maryland Centrifugal 27 Experiment (MCX) L cm 1700 53 65 150 T e. V 2 -5 10 9 150 B Gauss 400 1000 570 3000 Emax V/cm 4 -18 5 2 -6 120 170 300 140 250 5 5 1. 4 3 100 4000 220 2000 2 20 650 3 -4 CSDX 10 280 1. 5 -3 WVU Q-machine State-of-the-art Hall thruster 4 2 300 2 0. 2 1400 20 -60 100 -300 2. 5 2 PPPL Segmented Hall Thruster 100 115 14 700 1000

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 Raitses and Fisch, Phys. Plasmas 8, 2579 (2001) Related concepts DCF by MIT and HEMP by Thales, CHT by Osaka, etc.

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)

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

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

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

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

HT DeviceParameter to generate. Lsupersonically rotating. E/B/Veth is capable Emax R T B V electrons cm cm 50 1700 e. V 2 -5 Gauss 400 V/cm 4 -18 < 2 10 -2 Compact Auburn Torsatron Blaamann 17 53 10 1000 5 < 4 10 -3 8 65 9 570 2 -6 < 8 10 -3 Continuous Current Tokamak ALEXIS Reflex arc Mistral Maryland Centrifugal Experiment (MCX) 40 150 3000 120 8 10 -3 10 2. 5 11. 5 27 170 300 140 250 5 5 1. 4 3 100 4000 220 2000 2 20 CSDX 10 280 1. 5 -3 650 3 -4 < 1 10 -2 WVU Q-machine State-of-the-art Hall thruster 4 2 300 0. 2 1400 2 20 -60 100 -300 14 700 5 10 -2 < 1 LAPD PPPL Segmented (No SEE) Hall Thruster 2. 5 2 100 115 1000 2 10 -2 5 10 -3 4 10 -3 7 10 -2 1 -2

Electric field and thruster performance are affected by anomalous electron cross-field transport ü Thruster efficiency With all other parameters held constant, HTs efficiency reduces with increasing electron current across the magnetic field ü Classical collisional mechanism can not explain the discharge current measured for Hall thrusters: e-a~ 106 s-1 < eff ~ 107 s-1 ü 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

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)

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

SEE from dielectrics reaches 1 at lower energies (< 50 e. V) of primary electrons than for metals Pz 26 + Pz 26 - Teflon Boron Nitride PPPL SEE setup Note: for boron nitride, if primary electrons are Maxwellian (Te) 1 at Te = 18. 3 e. V Dunaevsky, Raitses, Fisch, Phys. Plasmas (2003)

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

SEE effect on plasma electrons: comparing experiment with predictions According to fluid theories, the maximum electron temperature should not be above 18. 3 e. V (for BN and Xenon) Fluid theory Temax 18. 3 e. V Large quantitative disagreement with fluid theory!

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

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

Conditions for the existence of self-sustained counter-streaming SEE electron beams 1) Weak two-stream and plasma beam instabilities PIC simulations predict: unstable • EVDF is decreasing f (vx) f(vx) • Beam penetration is high, 0. 9 vx stable f(vx) vx Sydorenko et al. , Phys. Plasmas 2007

Conditions for self-sustained counterstreaming 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 e. V enough for strong SEE from any ceramic material

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

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

Disappearance of near-wall sheath at a very strong SEE > 1 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)

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

Without SEE, the magnetized plasma can withstand much stronger electric field High-SEE 2. 5 cm No-SEE Probe path -4. 6 cm 0 With No-SEE walls, the electric field at high voltages, 1 k. V/cm, approaches a fundamental limit for a quasineutral plasma: 11 -3

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 Emax Possibly E B shear effect? * For No-SEE, the shearing frequency, d(Ez/Br)/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

HT DeviceParameter to generate. Lsupersonically rotating. E/B/Veth is capable Emax R T B V electrons cm cm 50 1700 e. V 2 -5 Gauss 400 V/cm 4 -18 < 2 10 -2 Compact Auburn Torsatron Blaamann 17 53 10 1000 5 < 4 10 -3 8 65 9 570 2 -6 < 8 10 -3 Continuous Current Tokamak ALEXIS Reflex arc Mistral Maryland Centrifugal Experiment (MCX) 40 150 3000 120 8 10 -3 10 2. 5 11. 5 27 170 300 140 250 5 5 1. 4 3 100 4000 220 2000 2 20 CSDX 10 280 1. 5 -3 650 3 -4 < 1 10 -2 WVU Q-machine State-of-the-art Hall thruster 4 2 300 0. 2 1400 2 20 -60 100 -300 14 700 5 10 -2 < 1 LAPD PPPL Segmented (No SEE) Hall Thruster 2. 5 2 100 115 1000 2 10 -2 5 10 -3 4 10 -3 7 10 -2 1 -2

How azimuthal oscillations can cause cross-field transport? • In principle, HT discharge is azimuthallyy symmetric • If there azimuthal oscillations of ne and they are and 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

Hall Thruster Oscillations in Hall thruster plasma

Imaging of HT operation PPPL Hall Thruster Experiment (HTX) Xenon operation of 12 cm diameter 2 k. W PPPL Hall thruster Phantom camera V 7. 3 • Records 400, 000 fps • Unfiltered emission • ~ 7. 5 m away

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

Rotating spoke Azimuthal non-uniformity of visible light emission and plasma density rotating in E B direction (~ 10 k. Hz) 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) Mc. Donald 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 Spoke is always ~ 10 times slower than local E B speed ! Escobar and Ahedo, IEPC 2011 Matyash , Schneider et al. , IEPC 2011 Vesselovszorov, IEPC 2011

A possible mechanism of cross-field transport through the spoke E 0 z×B - -+ + - +- + + - Eθ Eθ×B Br Possible transport mechanism through the spoke: ØInitial density perturbation ØOnly electrons undergo azimuthal drift motion ØEθ generated across the perturbation ØEθ×B drift across the magnetic field, towards the anode Correlated density and azimuthal electric field fluctuations would explain enhanced electron transport

Cross-field transport through coherent plasma structures in magnetically controlled plasmas 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 Evolution of turbulent structures at the edge of the NSTX tokamak UCLA LAPD Serfanni et al, PPCF 49, 2007, Photo: Courtesy of S. Zweben MISTRAL, Aix-Marseille Univ. (E B linear device) Carter, Phys. Plasmas 13 (2006) Jaeger, Pierre, Rebont, Phys. Plasmas 16 (2000) HIPIMS RU, Bohum

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) 100 W 2. 6 cm CHT Raitses and Fisch, Phys. Plasmas 8, (2001) Cathode

Rotating spoke in CHT Cusp: Enhanced Radial Field Direction: Frequency: Velocity: E/B frequency Size: Ex. B 15 -35 k. Hz 1. 2 -2. 8 km/s 10 -30 km/sec 100 -500 k. Hz 1. 0 -1. 6 cm

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)

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 3 azimuthal probes, 90 degrees apart, per axial location back middle 2 azimuthal probes, 30 degrees apart, on a movable positioner outside the channel front 13 mm Slow movable probe Stationary probe arrays 23 mm

Spoke is everywhere along the channel, but the coherent rotation is only near the anode Density fluctuations: S(kθ, ω) kθ>0 corresponds to E×B direction Anode region Channel middle Cathode region • 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 Parker, Raitses, Fisch, Appl. Phys. Lett. , 97 (2010)

- 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)

Do we know how to explain the spoke instability in Hall thrusters? • 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 • 3 -D Full PIC with MC collisions relate the spoke to neutral depletion Matyash , Schneider et al. , IEPC 2011

Potential explanation was given 20 years ago Simon-Hoh instability (SHI) for Penning discharge Conditions for SHI neo 0 neo Er 0 > 0 F. C. Hoh, Phys. Fluids 6, 1963 • 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

Can MSHI be excited in CHT plasma ? From the dispersion relation for MSHI, the instability is excited when Azimuthal ion velocity at the location of instability 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: Br 900 Gauss, Ez 10 -20 V/cm, k 1 cm-1, b 30 Not far from our observations

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.

Spoke suppression with the feedback control Feedback off Feedback 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.

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 crossfield transport: wall conductivity and spoke instability • Need better understanding of spoke and near-wall conductivity: needed 3 D PIC simulations, theory of instabilities, experiments • Reduction of anomalous transport by minimizing SEE effects and suppression of spoke instability was demonstrated

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)

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