resistive wall mode control in diii-d · 2006. 11. 16. · 1000 15 3 4 114340 114336 2 no-wall...
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Resistive Wall Mode Control in DIII-D
by
Andrea M. Garofalo1
for
G.L. Jackson2, R.J. La Haye2, M. Okabayashi3, H. Reimerdes1,
E.J. Strait2, R.J. Groebner2, Y. In4, M.J. Lanctot1, G.A. Navratil1,
W.M. Solomon3, H. Takahashi3, and the DIII-D Team
1Columbia University, New York, New York2General Atomics, San Diego, California3Princeton Plasma Physics Laboratory, Princeton, New Jersey4FAR-TECH, Inc., San Diego, California
presented at the
Workshop on Active Control of MHD Stability:
Active MHD control in ITER
Princeton Plasma Physics Laboratory, Princeton, New Jersey
November 6 - 8, 2006
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D
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βN = 4βT/(ε/(1+κ2)/2)
βN = 3
βN = 2
Ideal-wallβ-limit
No-wallβ-limit
Tokamak Steady-State Efficiency
Toka
mak
Fus
ion
Perf
orm
ance
• ITER Steady-State scenario (#4) requires
Resistive Wall Mode stabilization
– Target: N ~ 3, above the no-wall
stability limit Nno-wall
~ 2.5
• Sufficient plasma rotation could
stabilize RWM up to ideal-wall N limit
ITER #4
VALEN RWM feedback modeling: ITER with blanket (ports covered)
Resistive Wall Mode Stabilization is Needed for Steady
State Tokamak Operation at High Fusion Performance
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6 External coils
βN = 4βT/(ε/(1+κ2)/2)
βN = 3
βN = 2
Ideal-wallβ-limit
No-wallβ-limit
Tokamak Steady-State Efficiency
Toka
mak
Fus
ion
Perf
orm
ance
• ITER Steady-State scenario (#4) requires
Resistive Wall Mode stabilization
– Target: N ~ 3, above the no-wall
stability limit Nno-wall
~ 2.5
• Sufficient plasma rotation could
stabilize RWM up to ideal-wall N limit
• Present ITER design of external error
field correction coils is predicted to
allow RWM feedback stabilization if
plasma rotation is not sufficient
ITER #4
VALEN RWM feedback modeling: ITER with blanket (ports covered)
Resistive Wall Mode Stabilization is Needed for Steady
State Tokamak Operation at High Fusion Performance
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• ITER Steady-State scenario (#4) requires
Resistive Wall Mode stabilization
– Target: N ~ 3, above the no-wall
stability limit Nno-wall
~ 2.5
• Sufficient plasma rotation could
stabilize RWM up to ideal-wall N limit
• Present ITER design of external error
field correction coils is predicted to
allow RWM feedback stabilization if
plasma rotation is not sufficient
• Improved design for RWM stabilization
could allow studies of scenarios
approaching advanced tokamak
reactor concepts, i.e. N > 4
ARIES-RS
A-SSTR
ITER #4
VALEN RWM feedback modeling: ITER with blanket (ports covered)
Resistive Wall Mode Stabilization is Needed for Steady
State Tokamak Operation at High Fusion Performance
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RWM Stabilization by Rotation Allows Demonstration
of High Performance Tokamak Regimes
• High , N, high bootstrap current fraction, high energy confinementsustained simultaneously for 2 s in DIII-D
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RWM Stabilization by Rotation Allows Demonstration
of High Performance Tokamak Regimes
• High , N, high bootstrap current fraction, high energy confinementsustained simultaneously for 2 s in DIII-D
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RWM Stabilization by Rotation Allows Demonstration
of High Performance Tokamak Regimes
• High , N, high bootstrap current fraction, high energy confinementsustained simultaneously for 2 s in DIII-D
• Multiple control tools needed, including
– Simultaneous ramping of plasma current and toroidal field
– Simultaneous feedback control of error fields and RWM
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Plasma Rotation Control is Needed to ExploreRegime of High Beta and Low Rotation
• Plasma rotation is sufficient to stabilize RWMs in most DIII-D scenarioswith all co-injected neutral beams (same direction as Ip)
– Unidirectional NB heating in high beta plasmas applies strong torque
– Difficult to test RWM feedback control under realistic reactorconditions
C-coilI-coil Vessel
Poloidal Field Sensor
• Resonant and non-resonantmagnetic braking toreduce the rotation havedisadvantages
– Feedback system tendsto respond to appliedresonant braking field
– Fine control is difficult:rotation tends to lock
– Once locked, brakingfield may excite islandsin the plasma
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Magnetic Braking Using n=1 External or Intrinsic FieldsYields RWM Rotation Thresholds ~O(1%) of A (q=2 or 3)
• DIII-D using only uni-directional NBI:– Magnetic braking is applied by removing the empirical correction of the
intrinsic n=1 error field– Critical rotation frequency crit at q = 2
surface ranges from 0.7 to 2.5% oflocal A
2003-05 data2006
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1000
15
3
4 114340 114336
2
No-Wall Limit (approx.)
Ideal-WallLimit
FeedbackStabilizedwith LowRotation
No-Feedback
βN /li
1
frot (kHz) at ρ = 0.6
3
150 δBp (Gauss)
50
9
1200 1400 1600 0.0
30
25
20
15
10
5
0
Rotation Frequency (kHz)
0.2ρ
0.4
114340 1500 ms
114336 1390 ms
0.6 0.8 1.0Time (ms)
Feedback
2
5
q(r)
1
0
3
4
Resonant Braking Provides Demonstration ofTransient Feedback Stabilization at Low Rotation
• I-coil feedback sustains beta (for ~30 w) indischarge with near-zero rotation at all n=1rational surfaces
• Comparison case without feedback is unstableeven with lower beta and faster rotation
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• Braking effect saturates asbraking field is increased
• Saturated rotation agrees withneoclassical toroidal viscositymodel
– K.C. Shaing, S.P. Hirshmanand J.D. Callen, Phys.Fluids 29, 521 (1986)
Non-Resonant n=3 Braking Did Not Give Access to
the Low-rotation Regime
• n=3 magnetic braking can create large drag torque
• RWM remains stable when correction of n=1 error field is optimal (DEFC)
dL /dt = TNB
L /M
k( D ) In=32
2/ 3 Ti /(Zi eB R)D ~
Crit
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• Small n=1 errorfield introducedaccidentally (oneC-coil pair)
• RWM onsetobserved forsufficiently largen=3 and n=1 errorfield
Non-Resonant n=3 Braking Can Give Access to
Unstable RWM, If n=1 Error Correction Is Non-optimal
• C-coil used for n=1 error field correction (red=optimal)
• I-coil used for n=3 magnetic braking
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Balanced injection provides effective rotation
control without magnetic perturbations
• Magnetic braking experiments suggestedthat RWM stabilization requires mid-radiusplasma rotation ~O(1%) of the Alfven
frequency, A
– This level of rotation may not be realizedin ITER
• Recent experiments using balanced NBI inDIII-D (and JT-60U) show that the plasmarotation needed for RWM stabilization is muchslower than previously thought
– ~O(0.1%) of A
– Such a low rotation should be achievablein ITER
• Even with sufficient rotation, active feedbackmay still be needed, but the systemrequirements could be reduced
Top view of
DIII-D
210° neutral
beamline was
rotated 39°
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Much Slower Rotation Before RWM Onset is Observed by
Reducing the Injected Torque With Minimized Error Fields
– Plasma rotation is reduceduniformly for <0.9
– crit at q = 2 is ~7x slower thanmeasured with magnetic braking
• DIII-D using a varying mix of co and counter NBI:
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Weak -Dependence is Observed for Rotation
Thresholds Measured With Minimized Error Fields
Magnetic braking 2003-052006
• RWM onset ( ) observed when V at q=2 is ~10-20 km/s, or ~0.3% oflocal VA
BalancedNBI
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Independent, Simultaneous Discovery of Low RWM
Rotation Thresholds in DIII-D and JT-60U
0
0.2
0.4
0.6
0.8
1
-60 -40 -20 0 20
C
Vt(km/s) at q=2
N
no-wall
x
xx
xx
x
N
ideal-wall
JT-60U DIII-D
[Takechi, IAEA FEC 2006]
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Profiles at RWM Onset Suggest Rotation in theOuter Region of the Plasma Is Important
• Central rotation seems uncorrelated with RWM onset
• Negative mode rotation at
onset suggests strong
interaction near plasma
edgeCo-rotation
Counter-rotation
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MHD Spectroscopic Measurements With Varying
Plasma Rotation Shows Importance of Edge Rotation
• Natural rotation frequencyof stable RWM, RWM,
obtained from
measurements of plasma
response at single
frequency
• Plasma rotation variedwith nearly constant N
• RWM crosses zero when
rotation between q=3 and
q=4 crosses zero
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0.81.01.2
0
1
2
0
10
20
2.6 2.8 3.0 3.2 3.4 3.6
n=1 δBp (G)
Vφ at q=2 (km/s)
βN/2.5li
IC-coil (kA)
Time (s)
-10
10
30
Sensitivity to Error Fields Confirms
N Is Above No-Wall Limit
• Ideal MHD stability calculations
(DCON code and GATO code)predict N
no wall (2.5±0.1)li
• Sensitivity to field asymmetries brackets
Nno wall between 2.3li and 2.5li,
consistent with stability calculations
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MHD Spectroscopic Measurements With Varying N
Explain Sharp Threshold of Sensitivity to Error Fields
• Natural rotation frequencyof stable RWM, RWM,
obtained from
measurements of plasma
response at single
frequency
– N varied with nearly
constant high plasma
rotation
• RWM ~0 when N Nno-wall
• No momentum exchange
between mode and static
non-axisymmetric field
when natural rotation
frequency of RWM is zero
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Ideal MHD With Kinetic Damping Model of Dissipation
Is Consistent With New Low Threshold Rotation
• Marginal stability predicted
with 70% of experimental
rotation profile for balanced
NBI plasmas
– Kinetic damping model
[Bondeson and Chu]
implemented in MARS-F
MARS-F
Magnetic braking 2003-052006
BalancedNBI
• Sound wave damping model needs at least 300% of experimental
rotation profile for marginal stability
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MARS-F With Kinetic Damping Model SuggestsImportance of Plasma Rotation Near the Edge
• Experimental rotation profile is scaled tofind marginal stability– RWM growth rate RWM and mode
rotation frequency RWM are normalizedto growth rate without rotation
• RWM rotates in direction of plasma edge
RWM rotation rate
RWM growth rate
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High Rotation Threshold Measured With Magnetic Braking
Is Consistent With Torque-balance Equilibrium Bifurcation
• Increasing static resonant error
field (n=m/q) leads to bifurcation in
torque-balance equilibrium of
plasma
– Rotation must jump from a high
value to essentially locked
• “Induction motor” model of error
field-driven reconnection
[Fitzpatrick]:
– Plasma rotation at critical point,
Vcrit~1/2 of unperturbed rotation, V0
• Lower neutral beam torque gives
lower V0, therefore a lower Vcrit at
entrance to “forbidden band of
rotation”
Magnetic braking thresholds
Uni-directional NBI
After beamline re-orientation
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"Forbidden Band" of Rotation Results in a Higher
Effective Rotation Threshold for RWM Onset
TNB - L/τL
dL/dt
LL0
• With no error field, torque balance requires NB torque = viscous torque
Stable torquebalance
equilibrium
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-TEM
TNB - L/τL
dL/dt
LL0
"Forbidden Band" of Rotation Results in a Higher
Effective Rotation Threshold for RWM Onset
• With uncorrected error field, resonant field amplification by stable RWM leadsto large electromagnetic torque
Stable torquebalance
equilibrium
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-TEM
TNB - L/τL
dL/dt
LL0
"Forbidden Band" of Rotation Results in a Higher
Effective Rotation Threshold for RWM Onset
• With uncorrected error field, resonant field amplification by stable RWM leadsto large electromagnetic torque increasing with beta above no-wall limit
Stable torquebalance
equilibrium
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-TEM
TNB - L/τL
dL/dt
LL0~L0/2
"Forbidden Band" of Rotation Results in a Higher
Effective Rotation Threshold for RWM Onset
• With uncorrected error field, resonant field amplification by stable RWM leadsto large electromagnetic torque increasing with beta above no-wall limit
Torquebalance
equilibrium
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"Forbidden Band" of Rotation Results in a Higher
Effective Rotation Threshold for RWM Onset
• With uncorrected error field, resonant field amplification by stable RWM leadsto large electromagnetic torque increasing with beta above no-wall limit
• As perturbation amplitude increases, torquebalance jumps to low-rotation branch
-TEM
TNB - L/τL
dL/dt
LL0~L0/2
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"Forbidden Band" of Rotation Results in a Higher
Effective Rotation Threshold for RWM Onset
• With uncorrected error field, resonant field amplification by stable RWM leadsto large electromagnetic torque increasing with beta above no-wall limit
• As perturbation amplitude increases, torquebalance jumps to low-rotation branch
-TEM
TNB - L/τL
Forbidden band of rotation
dL/dt
LL0~L0/2
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-TEM
TNB - L/τL
Forbidden band of rotation
dL/dt
LL0~L0/2
"Forbidden Band" of Rotation Results in a Higher
Effective Rotation Threshold for RWM Onset
• With uncorrected error field, resonant field amplification by stable RWM leadsto large electromagnetic torque increasing with beta above no-wall limit
RWM stabilizationthreshold
• As perturbation amplitude increases, torquebalance jumps to low-rotation branch
• With large non-axisymmetric field, bifurcationof rotation occurs above RWM threshold
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-TEM
TNB - L/τL
Forbidden band of rotation
dL/dt
LL0~L0/2
"Forbidden Band" of Rotation Results in a Higher
Effective Rotation Threshold for RWM Onset
• With uncorrected error field, resonant field amplification by stable RWM leadsto large electromagnetic torque increasing with beta above no-wall limit
1100 1200 14001300Time (ms)
0
150
100
50
15
10
0
5
# of Neutral Beam Sources
2
1
0
3
βN
97798 97802
8
0
4
n=1 δBr at wall (Gauss)
Plasma Toroidal Rotation (km/s)ρ ~ 0.6
V0V0/2V0 V0/2
RWM stabilizationthreshold
• As perturbation amplitude increases, torquebalance jumps to low-rotation branch
• With large non-axisymmetric field, bifurcationof rotation occurs above RWM threshold
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Recent Model by Fitzpatrick Includes RWM Dispersion
Relation With Neoclassical Poloidal Viscosity
• “True” critical
rotation for RWM is
seen only when
resonant error field
is small
• Resonant surface
is just outside
plasma
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Offset Rotation, Not Bifurcation, Observed With
Non-resonant n=3 Braking and ~Balanced Injection
• In=3 > 3 kA has
little effect on
plasma rotation
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With Optimal Error Field Correction, RWM Stabilization at
Very Slow Plasma Rotation Sustained for >300 Wall Times
End of counter NBI
• Plasma rotation at q=2~0.35% A just above crit
is sufficient to sustain N
above no-wall limit
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In High Performance Plasmas (Rapid Rotation)
Active RWM Feedback Is Required• In DIII-D, high rotation is maintained with large, slow-varying n=1
currents in external coils for error field correction• Smaller, faster-varying n=1 currents in internal coils respond to transient
events (e.g. large ELMs), maintain RWM stabilization
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• First attempts of RWM feedback not yet conclusive
RWM Feedback at Slow Rotation More Difficult
Than Anticipated
• Onset of 2/1 tearing mode
frequently observed near
RWM onset
– High susceptibility to
tearing in the vicinity of
an ideal MHD stability
limit
– High susceptibility to
penetration of resonant
non-axisymmetric fields
(RWM at amplitude
below detection) at
very slow rotation
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RWM Stabilized With Near-balanced
Neutral Beam Injection
• The plasma rotation needed for RWM stabilization is much slowerthan previously thought –> ~0.3% at q=2
– Achieved with neutral beam line re-orientation in DIII-D:
• Balanced neutral beam injection -> lower injected torqueand plasma rotation with minimized non-axisymmetric fields
– Such a slow rotation should be achievable in ITER
• Resonant magnetic braking experiments overestimate the criticalrotation
– Induction motor model of error field driven reconnection canexplain observation of higher apparent thresholds
– Non-resonant braking cannot slow rotation below RWM lowthreshold, consistent with NTV theory
• Ideal MHD with dissipation (MARS-F with kinetic model) isconsistent with experimental observations
– Edge plasma rotation may be crucial
• Even with sufficient rotation, active RWM feedback is still needed
– System requirements for ITER could be reduced