Transcript slides - The Michigan Institute for Plasma Science and

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 cm3
ea/L ~ 1-2
Plasma density ~ 0.5-3  1011 cm-3
ei/L ~ 10
Electron temperature ~ 3-5 eV
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 ~ 2RLe (scat /2loss )0.5
4/14
Examples of E ×B devices
Large Plasma Device (LaPD) 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 kV
Power ~ 0.1- 50 kW
Thrust ~ 10-3 - 1N
E =-ve  B
e << L << i
 Unlike ion thruster, HT is not space-charge limited
 Thrust density is limited by B2/2
Isp ~ 1000-3000 sec
Efficiency ~ 6-70%
Parameters of HT plasma
Neutral density ~ 1012-1013 cm3
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 eV
Ion temperature ~ 1 eV
Ion kinetic energy ~ 102-103 eV
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
LAPD
R
cm
50
L
cm
1700
T
eV
2-5
B
Gauss
400
Emax
V/cm
4-18
Compact Auburn Torsatron
17
53
10
1000
5
Blaamann
8
65
9
570
2-6
Continuous Current
Tokamak
ALEXIS
40
150
150
3000
120
10
170
5
100
2
Reflex arc
2.5
300
5
4000
20
Mistral
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
14
State-of-the-art Hall
thruster
2
2
2.5
2
Device\Parameter
PPPL Segmented
Hall Thruster
20-60 100-300
100
115
700
1000
Cylindrical Hall thruster (CHT) – EB plasma in
diverging magnetic field
Ceramic channel
Electromagnets
S
N
B
• Fundamentally differences from
conventional HTs:
F = -B
F = -eE
B
S
N
Anode
Annular part
• Similar to conventional HTs, the
CHT operation is based on closed
electron EB drift.
Electrons are confined in the
magneto-electrostatic trap.
Ions are accelerated in a large
volume-to-surface channel
Cathodeneutralizer
Related 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
LIF measurements of ion velocity
Ceramic channel
Electromagnets
S
N
B
F = -B
F = -eE
B
Anode
Annular part
80
N
Cathodeneutralizer
Spektor et al., Phys. Plasmas 17, 093502 (2010)
Raitses at al., Appl. Phys. Lett. 90, 221502 (2007)
Ion current in plume
Self-sustained
Ion current density, uA/cm^2
S
Non-self-sustained
Ikp=2.5 A
60
40
20
0
-90
-45
0
45
Angular position, deg
90
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
Ceramic channel
Electromagnets
S
N
B
F = -B
F = -eE
B
S
N
Anode
Annular part
Cathodeneutralizer
Rotating electron effects
Isorotation
 1
 1  2  1
B      
r
r

 2  1
E 

 EB

E
2  1 


 const
rB  2  1 
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
Pe  bˆ me 2
ES 

 (r  bˆ )
ene
e
Pressure gradient Centrifugal force
effect on electrons
Fc  me r 2E B
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
  sin  
 u
 EB
sin   Le E B sin 
 ec
r the
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 Device\Parameter
is capable to generate
rotating
electrons
R
Lsupersonically
T
B
Emax
VE/B
/Veth
cm cm
50 1700
eV
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
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
 Thruster efficiency
TV jet
Ii


2 Pe
Ii  Ie
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 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
3
Carbon segmented
Discharge current, A
Boron nitride
2.5
2
1.5
- Boron nitride - high SEE
- Carbon velvet - zero SEE
1
0
200
400
600
Discharge voltage, V
800
Raitses, Staack, Dunaevsky, Fisch, Phys. Plasmas (2006)
Wall material affects the maximum
electron temperature in the thruster
PPPL Hall thruster setup
Maximum electron temperature, eV
Electron temperature from
emissive probe measurements
120
High SEE BN channel
Low SEE segmented
90
60
30
0
100
200
300
400
500
600
700
800
Discharge voltage, V
Raitses , Staack, Smirnov, Fisch Phys. Plasmas ,2005
SEE from dielectrics reaches 1 at lower energies
(< 50 eV) of primary electrons than for metals
2.0
Pz26 +
Pz26 -
1.5


1.0
Boron
Nitride
0.5
Teflon
PPPL SEE setup
0.0
0
20
40
60
80
100
Eprimary (eV)
Note: for boron nitride, if primary
electrons are Maxwellian
(Te) 1 at Te = 18.3 eV
Dunaevsky, Raitses, Fisch, Phys. Plasmas (2003)
SEE can significantly enhance electron flux
from plasma to the wall
Fluid Approach
w(x)
scs Te
 M ion
kTe 
w 
ln 1   
e 
 2πme




When   0, w  5.27 Te (for Xenon)
i
e
see
 
cr
scs
When  Te   cr  1  w  Te
SEE turns sheath to space-charge
limited regime
[Hobbs and Wesson, 1967]
Maximum electron temperature, eV
SEE effect on plasma electrons: comparing
experiment with predictions
120
According to fluid theories, the
maximum electron temperature
should not be above 18.3 eV
(for BN and Xenon)
High SEE BN channel
Low SEE segmented
90
60
Fluid theory Temax  18.3 eV
30
0
100
200
300
400
500
600
700
800
Discharge voltage, V
Large quantitative disagreement with fluid theory!
EVDF in HT is strongly anisotropic with
beams of SEE electrons
Hall thruster plasma, 2D-EVDF
Isotropic Maxwellian plasma, 2D-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
1p
1b
2
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
(x)
2
i
1p
1b
Total
emission
coefficient:

eff
p

1 (  p   b )
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
unstable

f (v )  0
2
v
f(vx)
PIC simulations predict:
• EVDF is decreasing f (vx)
• Beam penetration is high, 0.9
vx
stable
f(vx)

f (v )  0
2
v
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
 B max  2eE Le
For typical HT conditions: E = 100-200 V/cm, B ~ 100 Gauss
 Bmax ~ 30-60 eV enough for strong SEE from any ceramic material
Near-wall conductivity SEE-induced
cross-field current
Wall collisionality - exchange of primary magnetized
electrons by non-magnetized SEE electrons
The displacement , c  v / c , v  ud 
Ez
Bx
during the flight time H/ubx
gives average velocity
1
uz ~ ud ubx / Hc
B
T E
m p
J bz 
ne ex 2z
H 1  b
M Bx
x/H
and current
E
0
-4
-2
z/c
0
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 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 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 Device\Parameter
is capable to generate
rotating
electrons
R
Lsupersonically
T
B
Emax
VE/B
/Veth
cm cm
50 1700
eV
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
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
0  euz ne Br  me e ne u

uz  e

u ce
• 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:
F  en 'e E ' ,
• For F  me ve neu :
Jz  
0  F  ene uz Br  me e ne u
F  Br
B2
• Therefore, the F×B drift of that wave-based force could be
responsible for collisionless cross-field transport
Hall
Thruster
Oscillations
Oscillations
in Hall
thruster plasma
Imaging of HT operation
PPPL Hall Thruster Experiment
(HTX)
Xenon operation of 12 cm diameter
2 kW PPPL Hall thruster
Phantom camera V7.3
• 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 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
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
E0z×B
E0z
- -+ +
- +- + +
- +
-
Eθ
Eθ×B
Br
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
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)
Ceramic channel
Electromagnets
S
• Mirror-cusp magnetic field topology
• Similar to conventional HTs, the
operation involves closed EB
electron drift
N
• Electrons are confined in the hybrid
magneto-electrostatic trap
B
F = -B
F = -eE
B
S
• Ions are accelerated in a large
volume-to-surface area channel
(potentially lower erosion)
N
Anode
Annular part
Cathodeneutralizer
Raitses and Fisch, Phys. Plasmas 8, (2001)
100 W 2.6 cm CHT
Cathode
Rotating spoke in CHT
Cusp: Enhanced Radial Field
Direction:
Frequency:
Velocity:
E/B:
E/B frequency
Size:
ExB
15-35 kHz
1.2-2.8 km/s
10-30 km/sec
100-500 kHz
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
Slow
movable
probe
13 mm
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 ( B / n)  0
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
1
Conditions for SHI
neo 0
neo Er0 > 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
ion  E z 0 / Br 0 ,  de  E z 0 / Br 0
Azimuthal ion velocity at the location of instability

ion
2
Ez 0
RLion

, b
 1
2
2 L0
Br 0 2b
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
f  kion / 2 ~ 10 - 20 kHz
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 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 ?
From dispersion relation for MSHI
Y. Sakawa et al Phys. Fluids B 5, 1993
R  k , I 
ion
cs2 k2 ( EB  ion )
 de
For excitation of MSHI
ion  E z 0 / Br 0 ,  de  E z 0 / Br 0
Azimuthal component of ion velocity
ion
2
Ez 0
RLion

, b
 1
2
2 L0
Br 0 2b
For Xenon CHT near the anode and spoke:
Br 900 Gauss, Ez  10 V/cm, k  1 cm-1
b  30, f  kion / 2 ~ 10 kHz
Smirnov, Raitses, Fisch, Phys. Plasmas 14, 2007`