Hefei, China/ August 2012 / Lecture 5 Valentin Igochine1
Physics and control of Resistive Wall Mode
Valentin Igochine
Max-Planck-Institut für Plasmaphysik, Euratom-Association, Garching, Germany
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine2
• Introduction•Motivation•Simple dispersion relation
• Physics of the RWM• Electromagnetic part • Kinetic part
• Control of RWM• Control methods• Triggering of RWMs
Outline
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine3
This scenario has to have higher βN compared to
conventional scenario to be attractive.
Advanced Tokamak Scenario
[C. M. Greenfield et. al. PoP 2004]
Stationary operations are possible
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine4
• Resistive wall mode is an external kink mode which interacts with the resistive wall.
• The mode will be stable in case of an perfectly conducting wall. Finite resistivity of the wall leads to mode growth.
Resistive Wall Mode (RWM)
[M.Okabayashi, NF, 2009]
[T. Luce, PoP, 2011]
RWM has global structure. This is important for “RWM ↔ plasma” interaction.
DIII-D
[I.T.Chapman, PPCF, 2009]
JET
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine5
Simplest RWM dispersion relation
10
bvac
p
idealMHD
dissipati
w vac
w
resistivewall
on
WnW
i DW
rotation frequency of the plasma perturbed energy in vacuum
growth rate
N
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine6
10
bvac
p
idealMHD
dissipati
w vac
w
resistivewall
on
WnW
i DW
rotation frequency of the plasma perturbed energy in vacuum
growth rate
Simplest RWM dispersion relation
N
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine7
10
bvac
p
idealMHD
dissipati
w vac
w
resistivewall
on
WnW
i DW
rotation frequency of the plasma perturbed energy in vacuum
growth rate
Simplest RWM dispersion relation
N
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine8
10
bvac
p
idealMHD
dissipati
w vac
w
resistivewall
on
WnW
i DW
Feedback stabilizes from no-wall limit
rotation frequency of the plasma perturbed energy in vacuum
growth rate
Simplest RWM dispersion relation
N
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine9
10
bvac
p
idealMHD
dissipati
w vac
w
resistivewall
on
WnW
i DW
Feedback stabilize from no-wall limit
rotation frequency of the plasma perturbed energy in vacuum
growth rate
Simplest RWM dispersion relation
N
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine10
10
bvac
p
idealMHD
dissipati
w vac
w
resistivewall
on
WnW
i DW
Feedback stabilizes from no-wall limit
Rotation stabilizes from ideal-wall limit
rotation frequency of the plasma perturbed energy in vacuum
growth rate
Simplest RWM dispersion relation
N
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine11
Resistive Wall Mode (RWM)
Stabilization is really important only in the advanced scenario.
RWM stabilization allows to gain this
region.
Conventional scenario(moderate improvements)
Advanced scenario(crucial improvements)
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine12
Physics of RWMs
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine13
RWM physics in tokamak
RWM physics in tokamaks
RWM interaction with externally produced magnetic fields
• resistive wall• error fields• control coils
RWM interaction with plasma
• plasma rotation
• fast particles
• thermal particles
+
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine14
RWM physics in tokamak
RWM physics in tokamaks
RWM interaction with externally produced magnetic fields
• resistive wall• error fields• control coils
Mode can be represented as a surface currents
Physics: electromagnetism
RWM interaction with plasma
• plasma rotation
• fast particles
Wave-particle interaction
Physics: kinetic description of the plasma-wave
interaction
+
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine15
RWM physics in tokamak
RWM physics in tokamaks
RWM interaction with externally produced magnetic fields
• resistive wall• error fields• control coils
Mode can be represented as a surface currents
Physics: electromagnetism
RWM interaction with plasma
• plasma rotation
• fast particles
• thermal particles
Wave-particle interaction
Physics: kinetic description of the plasma-wave
interaction
+
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine16
Interaction of RWM with external perturbations
Resistive wall (currents in the wall)
Inertial layer
Main plasma
Current layer (RWM)
Simple models
[R. Fitzpatrick, PoP, 2002; V.D.Pustovitov, Plasma Physics Reports, 2003;A.H.Boozer, PRL, 2001]
Real vessel
[F.Vilone, NF, 2010; E.Strumberger, PoP, 2008]
currents in the wall
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine17
RWM physics in tokamak
RWM physics in tokamaks
RWM interaction with externally produced magnetic fields
• resistive wall• error fields• control coils
Mode can be represented as a surface currents
Physics: electromagnetism
RWM interaction with plasma
• plasma rotation
• fast particles
Wave-particle interaction
Physics: kinetic description of the plasma-wave
interaction
+
Reversed Field Pinch:• small plasma rotation• no fast particles
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine18
What one can achieve in RFPs with external coils ?
[T. Bolzonella, V. Igochine, et.al., PRL, 2008;V. Igochine, T. Bolzonella, et.al., PPCF, 2009][P. R. Brunsell et.al. , PRL, 2004]
Feedback Stabilization of Multiple Resistive Wall Modes
Decoupling and active rotation of a particular RWM
EXTRAP T2R RFX
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine19
RWM physics in tokamak
RWM physics in tokamaks
RWM interaction with externally produced magnetic fields
• resistive wall• error fields• control coils
Mode can be represented as a surface currents
Physics: electromagnetism
RWM interaction with plasma
• plasma rotation
• fast particles
• thermal particles
Wave-particle interaction
Physics: kinetic description of the plasma-wave
interaction
+
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine20
RWM interaction with plasma
[M. Okabayashi et. al. PPCF 2002]
RWM is unstable if rotation drops below critical value
Plasma rotation try to decouple RWM from the wall and plays stabilizing role
How strong the rotation stabilization?What is the critical rotation which is necessary to stabilize RWM?Is only the plasma rotation important?
The answers depend on the type of interaction between RWM and plasma rotation which is considered by the model and/or accuracy of the model for such interaction
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine21
Implementation of the rotation effects in linear MHD
Linearized MHD equations with influence of rotation
is the (non-uniform) rotation frequency of the plasma at equilibrium
is the toroidal mode numbern
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine22
Implementation of the rotation effects in linear MHD
is the (non-uniform) rotation frequency of the plasma at equilibrium
is the toroidal mode number
momentumequation
Linearized MHD equations with influence of rotation
n
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine23
Implementation of the rotation effects in linear MHD
Dissipation, viscous stress tensor
One has to make approximations for
kinetic description of the dissipation
Linearized MHD equations with influence of rotationmomentum
equation
is the (non-uniform) rotation frequency of the plasma at equilibrium
is the toroidal mode numbern
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine24
Simplest variant of the viscous stress tensor
Fluid approximation of the Landau damping:
‘sound wave damping’[Hammet G W and Perkins F W 1990 Phys. Rev. Lett]
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine25
Simplest variant of the viscous stress tensor
Fluid approximation of the Landau damping:
free parameter between 0.1 and 1.5
‘sound wave damping’[Hammet G W and Perkins F W 1990 Phys. Rev. Lett]
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine26
Simplest variant of the viscous stress tensor
Fluid approximation of the Landau damping:
‘sound wave damping’[Hammet G W and Perkins F W 1990 Phys. Rev. Lett]
free parameter between 0.1 and 1.5
‘kinetic damping’model uses kinetic energy principle with[Bondeson A and Chu M S 1996 Phys. Plasmas]
* 0, 0D No free parameters
magnetic drift frequency
diamagnetic frequency
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine27
Comparison of the critical rotation with experiments
[LaHaye, NF, 2004]
no-wall ideal-wall
sound wave dampingoverestimate
„kinetic damping“ modelunderestimate
N
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine28
Comparison of the critical rotation with experiments
[LaHaye, NF, 2004]
no-wall ideal-wall
sound wave dampingoverestimate
„kinetic damping“ modelunderestimate
…but rotation is sufficiently strong in these experiments due to NBI
N
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine29
Experiments with balanced NBI input in DIII-D
[Reimerdes, PPCF, 2007]
[Strait, PoP, 2007]
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine30
Experiments with balanced NBI input in DIII-D
[Reimerdes, PPCF, 2007]
[Strait, PoP, 2007]No stabilization is possible here
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine31
Comparison with almost zero rotation case in NSTX
[S.A. Sabbagh, IAEA, 2010, PD/P6-2]
Stabilization is achieved for almost zero rotation
(not possible in ”kinetic model”)
Thus, an important part is missing in the model!
NSTX
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine32
Possible variants of modeling
Self-consistent modeling(MARS,…)
Linear MHD + approximation for damping term
• (+) rotation influence on the mode eigenfunction
• (-) damping model is an approximation
Perturbative approach(Hagis,…)
Fixed linear MHD eigenfunctions as an input for a kinetic code
• (-) rotation does not influence on the mode eigenfunctions
• (+) damping is correctly described in kinetic code
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine33
Possible variants of modeling
Self-consistent modeling(MARS,…)
Linear MHD + approximation for damping term
• (+) rotation influence on the mode eigenfunction
• (-) damping model is an approximation
Perturbative approach(Hagis,…)
Fixed linear MHD eigenfunctions as an input for a kinetic code
• (-) rotation does not influence on the mode eigenfunctions
• (+) damping is correctly described in kinetic code
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine34
Perturbative approach. Influence of the resonancesδ
WK
Average dAverage b
[I.T.Chapman,
PPCF, 2009]
Transit Frequency Rvtht /~Bounce Frequency
Precession Drift Frequency
RvRr thb //~ Rvr thLd //~
d b tst
ab
leu
nsta
ble
Change in mode energy has a term which contains several different resonances
(denominator of equation tends to zero, get a large contribution to δWK)
JET
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine35
Perturbative approach. Influence of the resonancesδ
WK
Average dAverage b
[I.T.Chapman,
PPCF, 2009]
Transit Frequency Rvtht /~Bounce Frequency
Precession Drift Frequency
RvRr thb //~ Rvr thLd //~
d b tst
ab
leu
nsta
ble
Different resonances are important! & Low frequencies are important!
Change in mode energy has a term which contains several different resonances
(denominator of equation tends to zero, get a large contribution to δWK)
JET
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine36
New model for rotation influence on the MHD modes (MARS-K)
• full toroidal geometry in which the kinetic integrals are evaluated • * 0, 0D
Kinetic effects are inside the pressure
[Liu, PoP, 2008, Liu, IAEA, 2010]
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine37
• full toroidal geometry in which the kinetic integrals are evaluated • …but still some strong assumptions are made: neglects the perturbed electrostatic potential, zero banana width for trapped particles, no FLR corrections to the particle orbits. There is no guaranty that all important effects are inside.
* 0, 0D
Kinetic effects are inside the pressure
[Liu, PoP, 2008, Liu, IAEA, 2010]
New model for rotation influence on the MHD modes (MARS-K)
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine38
Application of both models for ITER
RWM is stable at low plasma rotation up to without feedback due to mode resonance with the precession drifts of trapped particles.
0.4C
[Liu, NF,2009, IAEA, 2010]
perturbative self-consistent
idealwall
idealwall
nowall
nowall
rotationrotation
Stable at low rotation
black dots are stable
RWM
NN
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine39
Application of both models for ITER
RWM is stable at low plasma rotation up to without feedback due to mode resonance with the precession drifts of trapped particles.… but some important factors are missing (for example alpha particles are not taken into account).
0.4C
[Liu, NF,2009, IAEA, 2010]
perturbative self-consistent
idealwall
idealwall
nowall
nowall
rotationrotation
Stable at low rotation
black dots are stable
RWM
N N
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine40
Influence of α-particles on RWM in ITER (perturbative)
[Liu, NF, 2010]
Thermal particles only
Thermal particles and α-particles
Stabilization at higher rotation from
α-particles
ideal wall
no-wall
rotationideal wall
no-wall
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine41
Control of RWMs
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine42
Control by external magnetic coils
DIII-D: two coil sets 6 C-coils, 12 I-coils usually connected in quartets.
Controller
Power Amplifiers
Information about the mode
Control algorithm
Decided amplitudes for external currents
Control currents
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine43
Feedback logic (inside the controller)
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine44
Looking more closely at feedback control system components
Sensors and mode identification
Control logic: intelligent shell-like or including plasma response? …
Power supply
Coil geometry, number and position
Basic control logic
There are multiple possibilities in each of the points and one has to find optimum solution.
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine45
How important low n control close to the pressure limit?
NSTX
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine4646
Why the RFPs are important for RWM study?
RFX-mod “quantum” for active control: =7.5°; =90°.Area covered=0.52%
RFX-mod control system is routinely working on discharges with 30-40 MW Ohmic input power, where effective control is essential.
RFX-mod control system is made by 192 active saddle coils, each independently fed. 100% coverage of the plasma surface.
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine4747
Active system reconfiguration
NB: it is a software reconfiguration, active on selected harmonics only!
This will allow to understand how much coils we need for RWM stabilization.
The main idea is to test on the same plasma and on the same device different active control configurations.
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine48
Resistive Wall Mode (RWM)
[T. Luce, PoP, 2011] Installation of the high field side coils is much more easy then in the other places.
And these coils are much more effective due to the ballooning mode structure!
Number of the coils is restricted by:
-Tokamak design
- Required currents for active control
Restricted number of coils could lead to the sideband and excitation of other modes (multiple modes control is
necessary)
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine49
JT-60SA RWM stability simulations
RWM growth rates versus achievable-N calculated by VALEN. No-wall, ideal wall N-limits and feedback with different proportional gains cases are shown. High gain is required for higher N
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine50
E. Olofsson et al, RFX-mod programme workshop, 2011
E. Olofsson et al, “Closed loop direct parametric identification of magnetohydrodynamic normal modes spectra in EXTRAP T2R reversed-field pinch,” Proceedings of the 3rd IEEE Multi-conference on Systems and Control (MSC) July 2009
From intelligent shell (SISO) to real time DFT and to dithering.
Close loop system identification (reversed field pinch)
(plasma)
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine51
E. Olofsson et al, Plasma Physics and Controlled Fusion (53), (084003)
Cylindrical stability vs. Dithering in reversed field pinch
Modeled picture Experimental picture
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine52
Difference between current driven and pressure driven RWMs
Interaction of RWM with plasma is different for current driven and pressure driven RWMs.One has to investigate pressure driven cases. RFPs expertise is not applicable here.
Current driven kink-peeling Current driven kink Pressure driven kink
0.1N 0.14N 3.55N
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine53
Triggers for RWM at low plasma rotation
[M.Okabayashi et.al, NF, 2009][G. Matsunaga et.al., PRL, 2009Okabayashi et.al., PoP, 2011]
ELMs
It is important that RWM could be triggered by core (off axis fishbones) and edge (ELMs) modes. This also shows global structure of RWM.
Integrated control of different MHD modes is required to stabilize RWM.
Energetic Particle Driven Wall Mode (EWM)
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine54
Review papers
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine55
Conclusions
RWMs may limit our operations close to the pressure limit.
RWM stability is affected by interactions with resistive wall, external fields, fast particles and plasma rotation.
Stabilization at low rotations (comparable and less to what is expected for ITER) is achieved, but self consistent modeling is still a problem.
Recent modeling shows that RWMs could be stable in ITER without external feedback well above the no wall limit (kinetic effects at low plasma rotation)
Other modes are able to trigger RWMs at low plasma rotation.
For RWM control we need further optimization of: sensors, actuators, control stratages and identification tools.
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine56
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine57
Open issues and discussion
Present and coming devices:- sensor optimization: field component, number, position, sampling frequency
- actuator optimization: mode rigidity
- controller optimization: test different control strategies, noise effect removal
- develop advanced identification tools (dithering, ...)
- prove stabilization of multiple unstable RWMs (long pulses needed)
Future devices: ITER- compatibility of RWM active control with other control needs (e.g. ELM mitigation) still to be fully assessed
Future devices: DEMO class- Are active coils compatible with a DEMO/reactor environment?
- Can we imagine other RWM control strategies for burning plasmas
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine58
Resistive Wall Mode (RWM)
[DIII-D review 2002]
Mode is always unstable
Mode is always stable
Mode stabilization is necessary
Stabilization gives approximately factor 1.5-2 in βN , which is about factor 3-4 for fusion power.
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine59
Early suggestions for active control
C.G. Gimblett, PPCF, 31 2183 (1989)
Intelligent shell
A network of active coils which cover the surface of the resistive wall compensates for the dissipated flux on the resistive wall according to the measurements of an associated network of sensors.
Rotating secondary wall
A rotating secondary wall can stabilize a thin shell mode (today a RWM). The rotation rate required is determined largely by the inverse time constant of the least conducting wall.
C.M. Bishop, PPCF, 31 1179 (1989)
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine60
Two essential components in feedback (modeling point of view)
Plasma dynamics (Plant, P) Controller (K)
Liu, Phys. Plasmas, 7 3684 (2000)
Basic control logic
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine6161
Different configurations explored
48 () x 4 (): 100%
48 () x 1 (): 25%
16 () x 1 (): 8.3%
3 () x 4 (): 6.25%
8 () x 1 (): 4.2%
12 () x 1 (): 6.25%
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine62
Present facilities for RWM control studies
DIII-D: two coil sets 6 C-coils, 12 I-coils usually connected in quartets.
See also the MAST system (RFA studies).
New HBT-EP (Columbia University, New York) setup: 6x20 control coils for modularity tests, 20 adjustable wall segments.
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine63
Facilities for RWM control studies
JET Error Field Correction Coils (RFA studies).
See also MAST system.
New AUG Active in-vessel coils to be coupled with a new conducting wall for MHD stabilization experiments
Hefei, China/ August 2012 / Lecture 5 Valentin Igochine64
Resonant Field Approximation (RFA)
A.M. Garofalo et al., Phys. Of plasmas 9 1997 (2002)A.M. Garofalo et al., Phys. Of plasmas 9 1997 (2002) H. Reimerdes et al., PRL 93 135002 (2006)H. Reimerdes et al., PRL 93 135002 (2006)
Top Related