S A N D I E G O
DIII-DNATIONAL FUSION FACILITY
OKABAYASHI Michio1, BIALEK James 2 , CHANCE Morrell1, CHU Ming3, FREDRICKSON Eric1,GAROFALO Andrea2, HATCHER Ronald1, JENSEN Torkil3, JOHNSON Larry1, LA HAYE Robert3, NAVRATIL Gerald 2, LAZARUS Edward4, SCOVILLE John Tim3, STRAIT Edward3, TURNBULL Alan,3
WALKER Michael, and the DIII-D Team
Joint Conference of the 12th International Toki Conference and The 3rd General Scientific Assembly of Asia Plasma and Fusion Association
on "Frontiers in Plasma Confinement and Related Engineering/Plasma Science"December 11-14, 2001, Ceratopia Toki, Toki, Gifu, Japan
1. Princeton Plasma Physics Laboratory
2. Columbia University, New York, New York
3. General Atomics, La Jolla, California4. Oak Ridge National Laboratory, Oak Ridge, Tennessee
RESISTIVE WALL MODE CONTROL ON THE DIII-D DEVICE
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3
q=3
q=4
ebp1 2 3 0.0 1.0
1.2
0.0
External kink bn limit b
�n = b/(Ip/aBt)
q=2
bn = 4
bn = 3
bn = 2
Performance
*
*
*
4.0
5.0
3.0
2.0
Ideal-Wall
No-Wall bn Limit
bn
N (Toroidal Number)
SUCCESSFUL RESISTIVE WALL MODE (RWM) CONTROL ISA PREREQUISITE FOR SUSTAINING IGNITION IN REACTOR ORIENTED DEVICES
- HIGH bn PROVIDES HIGH BOOTSTRAP CURRENT CONFIGURATION(Example: Fusion Ignition Reseach Experiment device)
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DIII-DNATIONAL FUSION FACILITY
Advanced Tokamak Regime with Reversed q(y)
AT Reversed q(y)35 sec burning(8.5T, 5.3MA)fbs = 65 - 75 %
Conventional q(y)18 sec burning(10T, 6.5MA)fbs = 15 - 20%
bt /(e(1+k�2)/2)
S A N D I E G O
DIII-DNATIONAL FUSION FACILITY
l Introduction- RWM characteristics - Two RWM control approaches
� Plasma rotation and magnetic feedback
l Recent RWM control experiments- Magnetic feedback compensates residual error field, increasing rotation and plasma pressure
l Achievement- Normalized Beta bn reached twice the no-wall limit, bn
no-wall
- bn is near the ideal-wall bn limit, bnideal-wall
l� Improvement of RWM physics
�l Modeling l Future plan l Summary
- Discovery of error field amplification (EFA)
OUTLINE
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DIII-DNATIONAL FUSION FACILITY
RESISTIVE WALL MODE - AN EXTERNAL KINK BRANCH WITH RESISTIVE WALL
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d Wp ( dWv gtw + dWv )
(gt w + 1)
gt w
(gt w + i NW� ) D+
= 0b •
+
Stablewith
Ideal-Wall
Unstablewith
Resistive-wall
Dissipation Stabilizing
IdealKink
ResistiveShell
Plasma Dissipation(Plasma Rotation)
Ideal Kink Branch
bn
Stable
0.0
dissipation branch
bnno-wall bn
ideal-wall
Shell Branch (ideal-wall)
dW Formulation
Stable Window
Wall Skin Time
f
Ideal kink RWM with rotation(NOVA-K code:PBXM)
(GATO: DIII-D)
q
1.0
2.0
3.0
4.0
0.0
1.0
0.0
Vf = 0
m=1
m=2m=3
q (y) q (y )m=1
m=21.0
2.0
3.0
4.0
0.0
m=3
0.0 1.0
1.0
0.0
q
Vf > Vfcrit
y
xr
y
RWM CHARACTERISTICS PREDICTED BY THEORY
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� Mode structure:- Retains mostly ideal MHD global mode structure
� Growth time:- ª wall skin time
� Toroidally quasi-stationary
� No magnetic islands
-> "Slowly evolving quasi-helical equilibrium"
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-2-1012340
SHIF
T[45
-195
](c
m) 1
234567
X-RA
Y(a
rb)
Relative displacement at half-radius
104108
0
5
10
15
1350 1400 1450 1500
dBr
(gau
ss)
TIME (ms)
Mode amplitude outside the wall
EXPERIMENT SHOWS THAT THE RW MODE STRUCTURE EXTENDS FROM PLASMA CORE TO OUTSIDE THE VACUUM VESSEL
� SXR at two toroidal locations separated by 150
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DIII-DNATIONAL FUSION FACILITY
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o
1.0 2.0
StableG= -5
G=-10
No Feedback
G= 0
8.0
0.0
-2.02.0
No Rotation
aWf = 0
aWf =-0.5
=-0.25
Stable
8.0
0.0
w
-2.0
TWO DISTINCT APPROACHES FOR RWM CONTROL HAVE BEEN PROPOSED
Use of Dissipation Magnetic Feedback(Plasma Rotation: by Bondeson)
Higher Gain
plasma dissipationparameter
HigherRotation
1.0
� Critical rotation velocity for stability a few % of Alfven velocity
� Required power level is modest
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DIII-DNATIONAL FUSION FACILITY
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no-walllimit
ideal-walllimit no-wallbn
no-wallbbn - ideal-wallbn -
(1 + ) no-wallbn
no-wallbnbn - ideal-wallbn -
(1 + )
gtwgt
1100 1200 14001300Time (ms)
(gau
ss)
0
15010050
1510
05
(km
/s)
n=1 dBr at wall
Plasma Toroidal Rotationr ~ 0.6
210
3bn
97798 97802
Estimated ideal MHD limit
PLASMA ROTATION DELAYS RWM ONSET
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� A decrease in rotation with bn > bn , leading to rapid RWM growth� Small amplitude RWM near threshold may cause rotational drag
no-wall
Feedback
RWM MAGNETIC CONTROL HARDWARE ON DIII-D
Logic control sensors
Smart Shell Total leakage flux dBr Saddle Loop(Virtual Ideal Shell)
Mode control Mode-only flux dBp Probe
6 coils (3 pairs) + 3 Power Supplies
Vacuum VesselExternal dBr
Saddle LoopsInternal dBrSaddle Loops
InternaldBp
Probes
6 (3p airs)12( 6 pairs))
4 locations
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DIII-DNATIONAL FUSION FACILITY
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Error Field Correction and Feedback
(kHz)
Ip(MA)
15
0.0
W�/2p
2.0
0.0
b�n
3.0
0.0
Estimated no-wall b�n limit
Internal d�Br
Internal d�Br
External d�Br
External d�Br
No Feedback
1400Time (ms)
1300 1500
q = 4.0q = 4.5
1600
No Feedback
- Ip ramp is used to maintain no-wall b�n limit roughly constant in time
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DIII-DNATIONAL FUSION FACILITY
� l Comparison of d�Br loops with smart shell logic
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- Experiment agrees with theoretical predictions
INTERNAL LOOPS ARE MORE EFFECTIVE THAN EXTERNAL LOOPS
95 95
20.0
10.0
3
1
1600
3.0
1400Time (ms)
bn
(khz)
Mode Control
Smart ShelldBr sensor(Internal)
Estimatedno-wall bn limit
dBp sensor
No Feedback
1300 1500
Ip(MA)
0.0
0.0
q = 3.3q = 4.0
(Internal)
106196/106187/106193
� l
Plasma rotation was well maintained over a longer duration in spite
of lowering edge-q
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DIII-DNATIONAL FUSION FACILITY
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W� /2 p
dBp "MODE CONTROL" IS FAR SUPERIOR TO dBr "SMART SHELL LOGIC"
9595
0.0
10
3.0
0.0
Estimated no-wall bn limit
no feedback
Feedback On
Coil Current n=1 Amplitude (kA)
Coil Current n=1 Toridal Phase (deg.)50.00.0
4.0
1200 2200Time (ms)10.0
bn
�W/2p (kHz)
HIGH bn DURATION WAS EXTENDED BY > 500 ms
80106535
40
Bp
(G)
0
300
200
Toro
idal
Angl
e
100
2111.0 2111.5
Rotation Period ~1 ms <
Time (ms)2112.0 2112.5
g ~300ms
• Ideal MHD Like Behavior
(With d�Bp sensor and modest Ip ramp operation)106530/106535
� bn reached twice the bnno-wall, close to bn ideal-wall (GATO-code)� MHD at collapse is ideal kink like behavior
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0.0
10.0
3.0
0.0
bnEstimated no-wall b�n limit
With Feedback
Optimized Preprogram only
Coil Amplitude(kA)
Coil Tor. Phase(degrees)
50.00.0
5.0
1200 2200Time (ms)10.0
FEEDBACK COMPENSATES RESIDUAL ERROR FIELD
�W/2p (kHz)
106532/106534
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� - Preprogramming coil currents without feedback, matched to currents with feedback, produce similar bn and rotation
With Feedback
Optimized Preprogram only
Observed Plasma Response
bn/bnno-wallbn/bnno-wall0.6 1.0 1.6
0.25
0.0 - 180
Toroidal Phase ShiftAmplitude
Amplitude (degrees)
0.0
�
ERROR FIELD AMPLIFICATION (EFA) INCREASED ATbn > bn no-wall
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• Helical resonance to non axi-symmetric magnetic field
105432 105439 105444 N
n=1 Br at Wall (plasma response only)
0
(A)
01234
1000200030004000
1.0
2.03.0
(gau
ss)
Time (ms)
Error Field Correction Current
Approximate no-wall beta limit
Increasing error field
b
1600 1750
- First predicted by A. Boozer Phy. Rev. Lett. 86, 1176 (2001)
-2.0
8.0
0.0
1.0 2.0no-wall
limitideal-wall
limit
Unified Theme
G=-5
no FBno Rotation
G=0
Stable
TWO PROCESSES: ROTATIONAL STABILIZATION AND MAGNETIC FEEDBACK HAVE BEEN UNIFIED IN A
SYNERGISTIC MANNER, OPENING A PATH TO IDEAL-WALL bn LIMIT
RWM / EFA
Sensor
Maintain PlasmaRotation
Magnetic Feedback
ReducingResidual Error Field
Increasing Rotationgtw
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DIII-DNATIONAL FUSION FACILITY
no-wallbn
no-wallbnbn - ideal-wallbn -
(1 + )
G=-10Increasing Gain
(bn - 1 + i aW + kW2
(bn + 1 + i aW+kW 2)
LUMPED PARAMETER FORMULATION
/ t(Ip) + Lw / t (lw) +
wc / t (lc) + R lw = 0f = m - nq
Slow time limit:Leff Ip + Mpw Iw + Mpc Ic = 0 :
plasma wall coil
EFA Amplitude • 1/ Leff
Leff =
[(bo - 2/f) + a ( / / t + (�W ) / f )] y(a)= (a/m) dy /dr|r=a
Plasma
a(gtw+iW� f) + dWp (dWv b gtw + dWv)/(gtw + 1) = 0+
Resistive Wall
Mpc
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DIII-DNATIONAL FUSION FACILITY
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Plasma surfaceWall surface
- Explicit Presentation of Boundary Conditionlp lw lc
surface
dW approach
Lumped formulation
yj = Mjk Ik
M w
•
Mwp
)
f
Dissipation
Ideal MHD
Leff : equivalent to "magnetic decay index" of vertical instability ( Ip <-> dZp)
bn = 2/f -1,
Observed Plasma Response to
0.6 1.0
bn/ n
1.6
Modeamplitude
0.25
0.0
Modetoroidal phase shift(degrees)
-180
Toroidal phase
0.6 1.0 1.6
Amplitude
Estimate with Lumped Parameter Model
0.0
EFA RESPONSE TO PULSED FIELD IS QUALITATIVELY CONSISTENT WITH MODEL ESTIMATE
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no-wall
0.6 1.0 1.6
Modeamplitude (arb)
0.25
0.0
Modetoroidal phase shift
(degrees)
-180
Toroidal phase shift
0.6 1.0 1.6
Amplitude0.0
b
bn/ nno-wall
b
bn/ nno-wall
b
bn/ nno-wall
b
EXPERIMENTS SUPPORT "RIGID DISPLACEMENT" MODE STRUCTURE
• Simplify model development of RWM like Lumped parameter formulation and VALEN codeThree Toroidal Arrays of Saddle Loops
Provide Poloidal Mode Structure (Without feedback)
Mode Structure Relative to MidplaneWithout Feedback (103353)
= +50 1.00.5
-0.5-1.0
0.0
1.00.5
-0.5-1.0
0.0
1.00.5
-0.5-1.0
017001600Time (ms)
1450
300
200
100
0
300
200
100
0
300
200
100
0
Lower Array
Midplane Array
Upper Array1 03353
100 200 300Relative Toroidal Angle
0.0
= - 50
=0
With Feedback (103355)To
roid
alAr
ray
�
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DIII-DNATIONAL FUSION FACILITY
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New feedbackcoil
New feedbackcoil
Coil
o
x
PresentCoil
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PROPOSED IMPROVEMENT OF RWM FEEDBACK ON DIII-D�
six upper- and six lower- coils and internal Bp sensors increase
achievable b very close to ideal-wall b limit (VALEN CODE / no rotation)
ideal wallb limit
no wall limit
NoFeedback(no FB)
Present coiland
internal Bp
Present coil andInternal Br
and
New coilsand
internal Bp
1.00.80.60.40.20 .010 0
10 2
10 4
Present coil andExternal Br
g(sec-1)
InternaldBp
no-wallbn
no-wallbnbn - ideal-wallbn -
Additional
l Two schemes, rotational stabilization and magnetic feedback, previously considered distinct, now function as a unified process in a synergistic manner
l Feedback process tracks and compensates the residual error field, maintains the rotation, and achieves high bn
l� A key to this success is the use of Bp sensors inside the vessel and mode control logic
l� High bn condition is also achievable with optimized error field correction
without feedback
RWM control
SUMMARY
S A N D I E G O
DIII-DNATIONAL FUSION FACILITY
l� Achievement of twice the no-wall bn limit close to ideal-wall bn limit
l Greatly improved by the discovery of Error Field Amplification
High bn achievement
Understanding of RWM physics
l New coils will be installed for achieving high b over wide parameter ranges
Future plans
n
consistent with experimental MHD observation
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