Complex phenomena in magnetized plasmas with an electron emission

Yevgeny RaitsesPrinceton 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

• EB 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 EB 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 mtorrRF-power: 50-60 WDC voltage/current: 0-100 V/0-3 AMagnetic field: up to 500 Gauss

Magnetically shieldedRF-plasma cathode

E

Coils Coils

B

Anode

Insulator

Axis

Plasma in E ×B region: weakly collisional, non-equilibrium, with magnetized electrons and non-magnetized ions

4/14

Neutral density ~ 1013 cm3

Plasma density ~ 0.5-3 1011 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 GaussElectron cross-field displacement during time loss (inelastic or wall collisions)

X ~ 2RLe (scat /2loss )0.5

Examples of E ×B devices

Sputtering magnetron discharge

Large Plasma Device (LaPD) at UCLA20-meter long, 1 meter diameter

Penning Gauge

ee

Diam ~ 1 -100 cm

B ~ 100 Gauss

Working gases: Xe, Kr

Pressure ~ 10-1 mtorr

Vd ~ 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 B2/2

e << L << i

Hall Thruster (HT) – fuel effective plasma propulsion device for space applications

E =-ve B

Neutral density ~ 1012-1013 cm3

Plasma density ~ 1011-1012 cm-3

Highly ionized flow: ion/n~ 80%

Electron temperature ~ 20-60 eV

Ion temperature ~ 1 eV

Ion kinetic energy ~ 102-103 eV

Collisionless, non-equilibrium plasma with magnetized electrons and non-magnetized ions

ea/h ~ 20 – 200

ei/h ~ 4103

ia/h ~ 10-100

Energy relaxation length in the inelastic range

*/h ~ 30 - 300

Parameters of HT plasma

Comparison of different E B plasma devicesDevice\Parameter R

cmL

cmT

eVB

GaussEmax

V/cmLAPD 50 1700 2-5 400 4-18Compact Auburn Torsatron 17 53 10 1000 5Blaamann 8 65 9 570 2-6Continuous Current Tokamak

40 150 150 3000 120

ALEXIS 10 170 5 100 2Reflex arc 2.5 300 5 4000 20Mistral 11.5 140 1.4 220

Maryland Centrifugal Experiment (MCX)

27 250 3 2000

CSDX 10 280 1.5-3 650 3-4

WVU Q-machine 4 300 0.2 1400 14State-of-the-art Hall thruster

2 2 20-60 100-300 700

PPPL Segmented Hall Thruster

2.5 2 100 115 1000

Cylindrical Hall thruster (CHT) – EB plasma in diverging magnetic field

Cathode-neutralizer

Electromagnets

N

N

Anode

Ceramic channel

S

S

Annular part

F = -B

F = -eEB

B

Cathode-neutralizer

Electromagnets

N

N

Anode

Ceramic channel

S

S

Annular part

F = -B

F = -eEB

B

• Similar to conventional HTs, the CHT operation is based on closed electron EB drift.

• Fundamentally differences from conventional HTs:

Electrons are confined in the magneto-electrostatic trap.

Ions are accelerated in a large volume-to-surface channelRelated concepts

DCF by MIT and HEMP by Thales, CHT by Osaka, etc.

Raitses and Fisch, Phys. Plasmas 8, 2579 (2001)

Unusual focusing of the plasma flow in diverging magnetic field of CHT

Cathode-neutralizer

Electromagnets

N

N

Anode

Ceramic channel

S

S

Annular part

F = -B

F = -eEB

B

Cathode-neutralizer

Electromagnets

N

N

Anode

Ceramic channel

S

S

Annular part

F = -B

F = -eEB

B

0

20

40

60

80

-90 -45 0 45 90

Angular position, deg

Ion

cu

rre

nt

de

ns

ity,

uA

/cm

^2

Self-sustained

Non-self-sustainedIkp=2.5 A

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 commonin industrial and laboratory plasmas: non-neutral plasmas, solar physics, magnetic mirrors, magnetic fusion devices, plasma centrifuges and, most recently, plasma thrusters

Cathode-neutralizer

Electromagnets

N

N

Anode

Ceramic channel

S

S

Annular part

F = -B

F = -eEB

B

Cathode-neutralizer

Electromagnets

N

N

Anode

Ceramic channel

S

S

Annular part

F = -B

F = -eEB

B

Rotating electron effects

1211

rr

B

12 E

const

rB

EBE

12

12

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

)ˆ(ˆ

2 br

e

m

en

bPE e

e

eS

Pressure gradient Centrifugal force effect on electrons

2BEec rmF

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

Fisch et al., PPCF, 53, 124038 (2011)

sinsinsinthe

BELe

ec

BE u

r

Ion focusing should benefit from supersonic electrons

Challenging requirements for the generation of supersonically rotating electrons in a steady state

- Strong electric field and low magnetic field to get high EB speed

- Colder plasma

Common approach: Control of E-field with biased electrodes

HT is capable to generate supersonically rotating electrons Device\Parameter R cm

Lcm

TeV

B Gauss

Emax

V/cm

VE/B/Veth

LAPD 50 1700 2-5 400 4-18 < 210-2

Compact Auburn Torsatron

17 53 10 1000 5 < 410-3

Blaamann 8 65 9 570 2-6 < 810-3

Continuous Current Tokamak

40 150 150 3000 120 810-3

ALEXIS 10 170 5 100 2 210-2

Reflex arc 2.5 300 5 4000 20 510-3

Mistral 11.5 140 1.4 220 410-3

Maryland Centrifugal Experiment (MCX)

27 250 3 2000 710-2

CSDX 10 280 1.5-3 650 3-4 < 110-2

WVU Q-machine 4 300 0.2 1400 14 510-2

State-of-the-art Hall thruster

2 2 20-60 100-300 700 < 1

PPPL Segmented (No SEE) Hall Thruster

2.5 2 100 115 1000 1 - 2

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~ 106 s-1 < eff ~ 107 s-1

Enhanced cross-field conductivity in HTs usually attributed to1) 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

ei

i

e

jet

II

I

P

TV

2

1

1.5

2

2.5

3

0 200 400 600 800Discharge voltage, V

Dis

ch

arg

e c

urr

en

t, A

Carbon segmented

Boron nitride

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

0

30

60

90

120

100 200 300 400 500 600 700 800

Discharge voltage, V

Ma

xim

um

ele

ctr

on

te

mp

era

ture

, e

V

High SEE BN channel

Low SEE segmented

Raitses , Staack, Smirnov, Fisch Phys. Plasmas ,2005

Electron temperature from emissive probe measurements

PPPL Hall thruster setup

SEE from dielectrics reaches 1 at lower energies (< 50 eV) of primary electrons than for metals

0 20 40 60 80 1000.0

0.5

1.0

1.5

2.0

Eprimary

(eV)

Teflon

Boron Nitride

Pz26 -

Pz26 +

Note: for boron nitride, if primary electrons are Maxwellian(Te) 1 at Te = 18.3 eV

PPPL SEE setup

Dunaevsky, Raitses, Fisch, Phys. Plasmas (2003)

SEE can significantly enhance electron flux from plasma to the wall

e

ionew πm

M

e

kT

21ln

scs Te

w(x)

e

i

see

ecrcr

e TT scsw 1

SEE turns sheath to space-charge limited regime [Hobbs and Wesson, 1967]

When

Xenon)(for 275 ,0 w eT. When

Fluid Approach

SEE effect on plasma electrons: comparing experiment with predictions

Large quantitative disagreement with fluid theory!

0

30

60

90

120

100 200 300 400 500 600 700 800

Discharge voltage, V

Ma

xim

um

ele

ctr

on

te

mp

era

ture

, e

V

High SEE BN channel

Low SEE segmented

Fluid theory Temax 18.3 eV

According to fluid theories, the maximum electron temperature should not be above 18.3 eV (for BN and Xenon)

Hall thruster plasma, 2D-EVDF Isotropic 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)

(x)i

2

1b2

1p

i

1b

1p

1- primary2- 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

)( bp

peff

1

Total emission coefficient:

Note, p can be > cr if eff < cr

PIC simulations predict:

• EVDF is decreasing f (vx)

• Beam penetration is high, 0.9

0)(2

vfv

f(vx)

f(vx)

unstable

stable

vx

vx

0)(2

vfv

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

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 EB 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

LeB eE 2max

gives average velocity

/c cv zd

x

Ev u

B

21p ex z

bz eb x

T EmJ n

H M B

The displacement , , during the flight time H/ubx

~ /z d bx cu u u H

0

1

-4 -2 0

z/c

x/H

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)

Two profiles for two regimes of SEE-induced electron cross-field current

Classical sheath with SEEE = 200 V/cm

Predicted profiles of the cross-field current density:

Inverse sheath at a very strong SEE > 1, E = 250 V/cm

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

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 trappedin 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)

Without SEE, the magnetized plasma can withstand much stronger electric field

Probe path

0-4.6 cm

2.5 cm

High-SEE No-SEE

With No-SEE walls, the electric field at high voltages, 1 kV/cm, approaches a fundamental limit for a quasineutral plasma:

E ~ Te/D (Te ~ 100 eV, ne ~ 1011 cm-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 EB 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 is capable to generate supersonically rotating electrons Device\Parameter R cm

Lcm

TeV

B Gauss

Emax

V/cm

VE/B/Veth

LAPD 50 1700 2-5 400 4-18 < 210-2

Compact Auburn Torsatron

17 53 10 1000 5 < 410-3

Blaamann 8 65 9 570 2-6 < 810-3

Continuous Current Tokamak

40 150 150 3000 120 810-3

ALEXIS 10 170 5 100 2 210-2

Reflex arc 2.5 300 5 4000 20 510-3

Mistral 11.5 140 1.4 220 410-3

Maryland Centrifugal Experiment (MCX)

27 250 3 2000 710-2

CSDX 10 280 1.5-3 650 3-4 < 110-2

WVU Q-machine 4 300 0.2 1400 14 510-2

State-of-the-art Hall thruster

2 2 20-60 100-300 700 < 1

PPPL Segmented (No SEE) Hall Thruster

2.5 2 100 115 1000 1 - 2

How azimuthal oscillations can cause cross-field transport?• In principle, HT discharge is azimuthallyy symmetric

• If there are azimuthal oscillations of ne 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

0 ezz e r e e e

ce

ueu n B m n u

u

' ' , 0e e z r e e eF en E F en u B m n u

2 :

B

BFJunvmF r

zeee

Hall Thruster OscillationsOscillations in Hall thruster plasma

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

High speed imaging of HT operation

12 cm diameter PPPL HT300 V, 20 sccm Xenon

100 Gauss700 W

Steady-state operation

Rotating spoke

Azimuthal non-uniformity of visible light emission and plasma density rotating in EB direction (~ 10 kHz) observed using fast cameras and electrostatic probes for different types of HTs

Low voltage operation (< 200 V), probesJanes 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 probesParker, 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 oscillationsEscobar and Ahedo, IEPC 2011Matyash , Schneider et al., IEPC 2011Vesselovszorov, IEPC 2011

Spoke is always ~ 10 times slower than local EB speed !

A possible mechanism of cross-field transport through the spoke

Br

E0z+- ++--

--- +

++

E0z×B

Eθ

Eθ×B

Possible transport mechanism through the spoke:

Initial density perturbation

Only electrons undergo azimuthal drift motion

Eθ generated across the perturbation

Eθ×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

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. (EB linear device)

Jaeger, Pierre, Rebont, Phys. Plasmas 16 (2000)

HIPIMSRU, Bohum

Cylindrical Hall thruster (CHT)

• Mirror-cusp magnetic field topology• Similar to conventional HTs, the operation involves closed EB 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-neutralizer

Electromagnets

N

N

Anode

Ceramic channel

S

S

Annular part

F = -B

F = -eEB

B

Cathode-neutralizer

Electromagnets

N

N

Anode

Ceramic channel

S

S

Annular part

F = -B

F = -eEB

B

Cathode

100 W 2.6 cm CHT

Rotating spoke in CHT

Cusp: Enhanced Radial Field

Direction: ExBFrequency: 15-35 kHzVelocity: 1.2-2.8 km/sE/B: 10-30 km/secE/B frequency 100-500 kHzSize: 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

Stationary probe arrays

Slowmovableprobe

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

back middle front

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)kθ>0 corresponds to E×B direction

Anode region Channel middle Cathode region

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?

•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

0)/( nB

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

neo Er0 > 0

1Simon-Hoh instability (SHI) for Penning discharge

Conditions for SHI

neo 0

Can MSHI be excited in CHT plasma ?

, / 00 rzion BE / 00 rz

ed BE

12

,2 2

0

2

0

0 L

Rb

bB

E Lion

r

zion

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:

Br 900 Gauss, Ez 10-20 V/cm, k 1 cm-1, b 30

Azimuthal ion velocity at the location of instability

kHzkf ion 20-01~2/ 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• EB 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 EB 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

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 ?

ed

ionBEs

Iion

R

kck

)(

,22

For excitation of MSHI

, / 00 rzion BE / 00 rz

ed BE

12

,2 2

0

2

0

0 L

Rb

bB

E Lion

r

zion

From dispersion relation for MSHIY. Sakawa et al Phys. Fluids B 5, 1993

For Xenon CHT near the anode and spoke: Br 900 Gauss, Ez 10 V/cm, k 1 cm-1

Azimuthal component of ion velocity

kHzkfb ion 01~2/ ,30 Smirnov, Raitses, Fisch, Phys. Plasmas 14, 2007`