Waves in Plasmas - Columbia University
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Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 1 Waves in Plasmas Francesco Volpe Columbia University “Mirai” Summer School, 9-10 August 2012
Transcript of Waves in Plasmas - Columbia University
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 1
Waves in Plasmas
Francesco Volpe
Columbia University
“Mirai” Summer School, 9-10 August 2012
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 2
Itinerary to New York
1997-1998 Collective Thomson Scattering
measurement of Ti
1998 Liquid Metal Flow Simulations Univ. Trieste, Italy
1998-2002 Electron Bernstein Wave (EBW) Emission
and Current Drive (CD)
W7-AS Stellarator
(Garching, Germany)
2003-2006 EBW Emission and Heating MAST Spherical Tokamak
(Culham, UK)
Electron Cycl.CD Stabilization of
Neoclassical Tearing Modes
ITER Tokamak
2006-2008 Neoclassical Tearing Mode and Locked
Mode control
DIII-D Tokamak
(San Diego, USA)
2008 Electron Cyclotron Resonant Heating AUG Tokamak (Garching,
Germany)
2009 EBWs MST RFP (UW-Madison)
Collaboration on ECE and MHD DIII-D Tokamak
FTU Tokamak
(Frascati,
Italy)
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 3
Outline
Need for Heating
Ohmic Heating and Need for Auxiliary Heating
Neutral Beam Injection
Waves
Propagation
Absorption
Heating by Waves
Ion Cyclotron
Lower Hybrid
Electron Cyclotron
a-Particle Heating
Current Drive3rd
Part
2
nd
Part
1
stP
art
Motivated student
+ interesting topic
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 4
Motivation for Heating
Plasma forms at few eV,
but D-T nuclei fuse at 20-300keV
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 5
Ohmic Heating
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 6
Plasma Current confines Tokamak Plasma
and heats it by Joule Effect
Plasma = secondary of a transformer
Plasma stability requires:
2BR
Baq ar
Therefore:R
Bj
0
Bj
Iplasma
Bq
Ioh
F
R
a
Ohmic heating:2
oh jp
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 7
The hotter the plasma,
the more difficult to Ohmically heat it.
Dominant loss mechanism: bremsstrahlung loss power pb.
]keV,m,[Wm TnZ102.3p 33-e
2e
237b
Ohmic heating power:2
oh jp
]m,T,m [keV, R
B
Z
1
n
102T 3-
e
20
e
Ohmic heating alone: Te only a few keV
Need for additional heating power!
Plasma resisitivity:23
eT
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 8
Introduction to
Neutral Beam Injection
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 9
Energetic Neutral Particles penetrate Plasma
and release Energy
B-field
1. Injection of neutral fuel
atoms (H, D, T) at high
energies (Eb > 50 keV)
H,D,T
2. Ionization in the plasma
3. Beam particles
confined
4. Energy Release
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 10
Energy is released by
Collisions and Charge Exchange
HHHHfastfast Charge exchange:
Ion collision: eHHHH fa s tfa s t
Electron collision: e2HeHfastfast
Example:
beam intensity: /xexpI)x(I 0
Eb0= 70 keV220
tot m105 320m105n
m4.0n
1
tot
In large reactor plasmas: beam cannot reach core!
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 11
NB Injector = Accelerator + Neutralizer
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 12
Wave Propagation
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 13
Maxwell + Ohm Wave Equation
Maxwell‘s Equations for Plane Waves
and Generalized Ohm‘s law
kk Ekj ,, ,
0,2
2
, kk EKc
Ekk
tensordielectric : K
0
1
iK
BiEki
jEiHki 0
0 Eki
0 Bki
Dispersion relation 0),(1det NKNN
c
kN
where = conductivity tensor, combine in the wave equation
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 14
Linearized (small perturbations, )10 vvv
10 EEE
10 BBB
0
s
s,1ss1vnqj
011s
s1 BvE
m
qvi
)BvE(m
q
dt
vd
s
s
j (thus , thus Disp.Rel.) derived from
Lorenz force
and Fourier-transformed:
Solve for v1 and plug in
where s= e, i, …
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 15
Propagation in cold unmagnetized Plasma
simply depends on p
(HF, static ions)envj em
Eevi
E
m
neij
e
e
2
2
2
0
2
2
0
111
p
e
e
mi
nie
iK
012
2
2
22
E
cEkkEk
p
e0
e2
2e,p
m
ne
Plasma frequency:
Langmuir oscillations p
:Ek EM waves (2 sol.)2
2
2
222 1
pkcN
kx,ky
p
:E||k
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 16
Propagation in cold magnetized Plasma
also depends on c
zz
yyyx
xyxx
K00
0KK
0KK
K
s
2cs
2
2ps
yyxx 1KK
2ps
2
2ps
s
csyxxy iKK
s
2
2ps
zz 1K
Cyclotron frequency:s
0scs
m
Bq
y
x
z
B
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 17
Propagation in cold plasma magnetized along z
Wave equation:
where
only admits solution(s) if det(ij-N2dij+NiNj)=0 Dispersion Relation
Eigen-polarizations=(Eigen)modes = solutions of Eigen-value Problem for null eigen-value,
det(ij-N2dij+NiNj)=0.
0
0
02
||
2
||
2
||
2
||
z
y
x
zz
yyyx
xyxx
E
E
E
NNN
NN
NNN
s cs
ps
yyxx 22
2
1
22
2
ps
ps
s
csyxxy i
s
ps
zz 2
2
1
notation:
N||=Nx
N
=Nz
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 18
Special case 1: perpendicular to B (Nz=0)
UH
k
L
Alfvèn-Wave
0
O-Mode
X-Mode
Lower Hybrid Wave
Upper Hybrid Wavepe
R
LH
ci
ECRH
LH
ICRH
3 frequency regions
for plasma heating:
ce
y
x
z
B
eXtr
aord
ina
ry (
X)
mo
de
N
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 19
Resonances and Cutoffs
N 0 „cutoff“
reflection
tunnelling
vph = / k >c!
N „resonance“ vgr= / k 0
wave „gets stuck“
wave energy
Dissipation,
Mode conversion
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 20
Special case 2: propagation along B (Nx=0)
Electron
Cyclotron Wave
ECR
ICR
Ion-
Cyclotron-Wave
Whistler-Wave
Alfvèn-Wave
L-Wave
R-Wave
k
ce
ci
02 solutions: xyxxz iN 2
2,1
of polarization: iE
E
y
x
y
x
z
B
N
RL
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 21
Band gaps depend on direction
of propagation and polarization
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 22
Interferometry
Because, in unmagnetized
plasma, or ⊥B but O-mode,
In conclusion,
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 23
Polarimetry
Note: polarization rotation is Df/2
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 24
Case 3: arbitrary oblique propagation:
Appleton-Hartree dispersion relation
After algebra,
where and
B
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 25
Upper hybrid oscillations
In unmagnetized plasma or along B,
⊥B, where restoring Lorentz force is maximum,
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 26
Waves refracted, reflected, scattered, etc.
by the Plasma extract info on ne, B, Te,i etc.
N2 < 0N=1
ne=ne, crit
dzE
transmitterreceiver
B0
Cutoff of
ordinary waveTransmission ne
Reflectometry ne, B
Interferometry ne
Scattering Te, Ti
Absorption ne
Emission Te, ne
pe ne
c B
vth,I,e Te,i
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 27
In warm plasma,
Lorenz force replaced by Vlasov Equation
Cold plasma theory breaks down where
1vk
2
c
th
1vk
n2
th||
c
or
Larmor radius for perpendicular wavelength
close to wave-particle resonance
(within few Doppler widths)
Linearized Vlasov equation:
0v011v01x1t fBvEm
qfBv
m
qfvf
Complicated form of Kij involving Bessel Functions
New set of (electrostatic) waves
Lorenz force (single particle): 011s
s1 BvE
m
qvi
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 28
Summary for the 1st Part
• Importance of heating
• In general, plasma heating is species-selective and
anisotropic
• Ohmic heating suffers from unfavourable Te-dependence of
resistivity and from disruption limit on max current density j
• Accelerator + Neutralizer = Neutral Beam Injector
• Maxwell, Ohm, Lorenz (and, in warm plasma, Vlasov)
Dispersion relation Wave propagation, plethora of
modes, resonances and cutoffs
• Derived Dispersion Relation for cold unmagnetized plasma;
discussed results in presence of B
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 29
Outline
Need for Heating
Ohmic Heating and Need for Auxiliary Heating
Neutral Beam Injection
Waves
Propagation
Absorption
Heating by Waves
Ion Cyclotron
Lower Hybrid
Electron Cyclotron
a-Particle Heating
Current Drive3rd
Part
2
nd
Part
1
stP
art
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 30
Wave Absorption
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 31
Landau Damping
(Electrostatic) waves, k || E
At t=0E
z
At t=T/4
vpht
vt
Ez
Strong wave-particle
interaction if: vpht=vt
vkvk
Group of resonant particles: collk
v
On average: slower particles are accelerated
faster particles are decelerated f(v)
vph
0v
f
phv
Net loss of wave energy
No collisions necessary!
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 32
Cyclotron Damping
Electromagnetic wave E k
vph = / k||
Ex
Ey
z
left-handed polarized wave
tip of electric field vector
Resonance condition: (3,...) 2, 1,l wherelvk s||||
g
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 33
2nd and higher Harmonics damped if wave-field
non-uniform on length-scale of Larmor radius
t=0 t=T/2 t=T
BB B
v
v
v
s2
E
gradient of electric field
0
r
El
l
T=period of the wave
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 34
EM wave heating: waves are damped where
resonance is fulfilled localized heating!
Resonant
Layer
m
qBc
Rc
Antenna
iso-B lines Excitation: external or
at plasma edge
Wave: propagating /
evanescent
Propagation can be
complicated codes:
Ray tracing
Beam tracing
Full wave
Resonant particles acquire
energy at expense of wave,
then thermalize with the others
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 35
Frequencies with good absorption
1vk sith|| generally
sl Then good absorption where
Electrons: 28 GHz / B[T] Electron Cyclotron Resonance Heating ECRH
Hydrogen: 15 MHz / B [T] Ion Cyclotron Resonance Heating* ICRH
Cyclotron Resonance
Landau Resonance
eth|| vk cmkeVTGHz3.1 ||e Lower Hybrid Heating LH
* Landau Resonance and Magnetic Pumping also contribute to ICRH
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 36
Ion Cyclotron
Resonance Heating
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 37
Ion Cyclotron Resonance Heating
Dispersion relation has two solutions:
fast wave E B0 n > 2 x 1019m-3
slow wave E || B0 n < 1 x 1019m-3
Problem:
near =ci wave is right-handed,
but ions resonate with (absorb from) left-handed polarization!
Solution:
Inject a minority species.
Wave right-handed at majority resonance, =cM
but damped at minority resonance, =cm
Majority heating also possible, by Doppler broadening:
E+=0 at =cM, but finite at =cMkvth,i
cmcm 1010050 , ||
Preferrable, but needs
tunnel of cutoff region
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 38
ICRH - Wave Propagation
ASDEX UpgradeF. Meo, P. Bonoli
Re(Ey)
Multiple current straps
Alcator C-Mod
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 39
ICRF Technology - Generator
4 amplifier chain
final stage:
tetrode with
2MW / 10 sec
tunable between
30 and 110 MHz
efficiency 60%
tetrode
final stage
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 40
ICRH - Wave Power Transport
50W Coaxial transmission lines
20cm diam., low loss
Matching network
antenna resistance 50W
dependent on plasma
Matching
network
generator antenna
ASDEX-UpgradeTrans-
mission
line
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 41
ICRH - Wave excitation
Fast wave
k
B0
Ehf
BhfBant
Slow wave
k
B0
Ehf
Bhf
Iant
Strap
antenna
Faraday
screen
W7-AS Antenna
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 42
Lower Hybrid
Heating & Current Drive
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 43
2 solutions of dispersion relation: slow wave (exhibits lower hybrid res.)
fast wave
ne>1017m-3 at antenna, to enter plasma
k|| > kc to reach center.
Lower Hybrid Heating
k|| too low, power stays
near plasma edge
eLHi cm1 ,cm102||
sw
fw
k
radius
k||sufficiently high,
slow wave travels into plasma,
absorption at LH or before
k
Lower
Hybrid
resonance
radius
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 44
LH - Wave Propagation
For k|| > kcrit vgr, vph independent of k||.
all launched power flows into same direction.
antenna structure
Depends on
ne and B.
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 45
Klystron and Grill
Beam
dump
cathode
anode
-wave
input
-wave
output
3.7 GHz
500 kW
3 sec
klystron waveguide grill
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 46
LH - Wave Excitation
Fast wave
k
B0
Ehf
Bhf
Slow wave
k
B0
Ehf
BhfMultiple
wave
guides
Ewg
ASDEX
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 47
Summary for the 2nd Part
• Electrons can “surf” electrostatic waves (Landau Damping)
• Or gyrate in phase with circular e.m.waves (Cyclotron
Damping), and so gain energy
• Processes are resonant well-localized
• Two examples:
– Ion cyclotron, strap antenna
– Lower hybrid, microwaves, grill
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 48
Outline
Need for Heating
Ohmic Heating and Need for Auxiliary Heating
Neutral Beam Injection
Waves
Propagation
Absorption
Heating by Waves
Ion Cyclotron
Lower Hybrid
Electron Cyclotron
a-Particle Heating
Current Drive3rd
Part
2
nd
Part
1
stP
art
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 49
Electron Cyclotron
Resonance Heating
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 50
Electron Cyclotron Resonance Heating
Dispersion relation has two solutions for perpendicular propagation:
ordinary (O)-mode E || B0
extraordinary (X)-mode EB0
No low density cut-off, but high density cutoff.
Ions can be assumed stationary, but relativistic electron mass has to
be included.
mm2
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 51
ECRH - O1 mode heating
2p
222 ck
DispersionReflection at cut-off region
Density gradient leads
to diffraction away from
plasma center.
ne O-mode
cutoff
B
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 52
ECRH - X1 mode heating
Resonance inaccessible from
low field side because no
propagation between cutoff and
upper hybrid resonance.
X2 accessible from LFS
i.e. second harmonic heating
ne
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 53
ECRH Sources: Gyrotrons
B field
superconducting
coils
Window
Diamond
annular
electron beam
resonator
collector
Up to 1 MW cw (>30min)
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 54
Mirrors correct wavefront and polarization and
match sources to Transmission Lines
spherical
load
1 MW, 1 s
(CNR Milano)
Matching Optics Unit
gyrotron
to HE11 line
short pulse
load
to
long
pulse
load
polarizer 1
polarizer 2
phase
correcting
mirrors
Design
IPF Stuttgart
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 55
Power is transmitted by mirrors or waveguides
and launched by steerable mirrors
ECRH launching mirrors in sector 5
launcher mirrors:
Cr / Cu / Au - coated graphite
Localized, adjustable Heating & CD
suppresses MHD instabilities such as
Neoclassical Tearing Modes (NTMs)
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 56
a-Particle Heating
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 57
a-Particle Heating
D-T fusion reaction:
confinedlong lysufficient if
plasma heats
4
plasma leaves
)MeV 5.3(He)MeV 1.14( nTD
Heating power density: Evnn2.0 TD
where iTv
peaked heating profile
a-particles need to be well confined through
large plasma currents in tokamaks
optimized stellarator fields
Loss mechanisms: field ripples
MHD events
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 58
Evidence for a-particle heating
D, T experiments only done on JET and TFTR
JET NBI heating30 MW
16 MW (max)
0 2 sec
Ti030 keV
Te0
a-particle heating
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 59
Analogy: coal oven - fusion oven
Activation
energyEnergy gain
Energy
Reaction time
Ignition
Heating Sustain
reaction
pn
np
n
Sustain
reaction
Heat
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 60
Current Drive
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 61
Non-inductive current drive
Asymmetric velocity distribution can be a side effect of plasma heating.ions
electrons dv vfvnqj ||||s
ss
Needed for : Steady-state tokamak
current profile control in tokamaks
MHD-mode stabilisation.
(bootstrap current compensation in stellarators)
Efficiency: Theory: coll||coll
2lleell
||||eth
.v
1
2vmn
vne
p
j
Experiment: th
320e
exWP
AImRm10n
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 62
Current drive with EM waves
the|||| vkv +
- small change of electron momentum
3||coll v
v
1 2v
OH
IC (EC)
LH
the|||| vkv + change of electron momentum / wave energy
+ many electrons
- large fraction of trapped electrons
- 2/3ecoll T
Parallel momentum injection: required total electron momentum smkg102 4
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 63
Fisch-Boozer: Heating electrons of v||>0 or <0
makes them less resistive net current
Electron velocity distribution
Trapped cone
Resonant electrons:
- nce / g - k║v║=0
k║≠0 (oblique launch)
Preferential heating of
electrons with v║>0
become less collisional
less resistive net
current
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 64
Current drive efficiencies
Efficiency
LHCD 0.35 – 0.4
ICCD 0.1 x Te [ 10 keV]
ECCD <0.1 x Te [ 10 keV]
NICD .2 x Te [ 10 keV]
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 65
Outlook to ITER
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 66
ECRH in ITER will use 24 gyrotrons, connected to
3-4 Upper Launchers and 1 Equatorial Launchers
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 67
ECRH/ECCD in ITER will serve several purposes
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 68
Summary Heating
Heating scheme Advantages Disadvantages
Ohmic efficient Cannot reach ignitionNot in stellarators
NBI reliable close to torusnegative ions necessary
LH Efficient current drive Antenna close to plasmaOff-axis
ECRH Reliableflexible
Electron heating(density limit)
ICRH Ion-heatingCentral heating
Antenna close to plasmaAntenna coupling
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 69
Auto-evaluation Quiz
1. What makes auxiliary Heating necessary?
2. What’s the only frequency relevant to propagation in the
simplest plasma you can think of (cold, unmagnetized,
unbounded, no impurities, etc.etc.)?
3. What’s, in your opinion, the main advantage of wave
heating?
4. What’s the common principle shared by all CD methods?
5. Can you imagine a distribution function f(v) that delivers
energy to the wave by the Landau mechanism?
Answers in next slide
Mirai Summer School, Japan, August 9, 2012 F. Volpe – „Waves in Plasmas“ 70
Answers to the Quiz
1. Because Te-3/2
2. pe
3. Localized and adjustable
4. Asymmetry: asymmetric resistivity (Fisch-Boozer),
asymmetric trapping (Ohkawa), uncompensated
ion and electron flows (NBCD)
5. Bump-on-tail
