RESISTIVE WALL MODE CONTROLON THE DIII-D DEVICEOKABAYASHI 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,3 and the DIII-D Team1.

Princeton Plasma Physics Laboratory

2.

Columbia University, New York, New York

3.
4.

General Atomics, La Jolla, California
Oak Ridge National Laboratory, Oak Ridge, Tennessee

Joint Conference of the 12th International Toki Conference andThe 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

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

SUCCESSFUL RESISTIVE WALL MODE (RWM) CONTROL IS
A PREREQUISITE FOR SUSTAINING IGNITION IN REACTOR ORIENTED DEVICES- HIGH bn PROVIDES HIGH BOOTSTRAP CURRENT CONFIGURATION(Example: Fusion Ignition Reseach Experiment device)
Performance

External kink bn limitb n = b/(Ip/aBt)
5.0

Advanced Tokamak Regime with Reversed q(y)Ideal-Wallbn

*
q=2
1.2

bn = 4bt /(e(1+k2)/2)

4.0

bn = 3bn = 2No-Wall bn Limit

3.0

2.0

AT Reversed q(y) *q=335 sec burning(8.5T, 5.3MA)
fbs = 65 - 75 %123
N (Toroidal Number)

0.0

0.0

*
q=4

Conventional q(y)18 sec burning(10T, 6.5MA)
fbs = 15 - 20%

ebp

1.0

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

OUTLINE●Introduction- RWM characteristics- Two RWM control approaches
Plasma rotation and magnetic feedback●

Recent RWM control experiments- Magnetic feedback compensates residual error field, increasing
rotation and plasma pressure●Achievement- Normalized Beta bn reached twice the no-wall limit, bnno-wall- bn is near the ideal-wall bn limit, bnideal-wall●Improvement of RWM physics- Discovery of error field amplification (EFA)●●●Modeling
Future plan
Summary

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

RESISTIVE WALL MODE
- AN EXTERNAL KINK BRANCH WITH RESISTIVE WALL
dW Formulation
IdealKinkResistiveShell

Plasma Dissipation(Plasma Rotation)•d Wp+( dWbv gtw + dWv )(gt w + 1)+(gt w + i NWf) D=0

Wall Skin Time

Ideal Kink Branch

0.0

Shell Branch (ideal-wall)
Stable Window

gt w
Stabledissipation branchbnStablewith
Ideal-Wall
no-wallbn

Unstablewith
Resistive-wall

Dissipation Stabilizing

ideal-wallbn

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

RWM CHARACTERISTICS PREDICTED BY THEORY
Mode structure:- Retains mostly ideal MHD
global mode structure
Growth time:- ª wall skin time

1.0xr

0.0

4.0

Vf > Vfcrit

3.0

3.0

m=1

m=1q (y)y(NOVA-K code:PBXM)

4.0 1.0

Vf= 0

m=2

Toroidally quasi-stationary

RWM with rotation

Ideal kink

2.0
m=3q (y)

q

2.0 q
m=3

m=2

1.0
0.0

1.0
0.0

0.0
0.0

y

1.0

No magnetic islands-> "Slowly evolving quasi-helicalequilibrium"(GATO: DIII-D)

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

EXPERIMENT SHOWS THAT THE RW MODE STRUCTURE EXTENDSFROM PLASMA CORE TO OUTSIDE THE VACUUM VESSELSHIFT[45-195](cm)

X-RAY(arb)SXR at two toroidal locations separated by 150 o765432
104 Relative displacement at half-radius
3210-1-2dB r (gauss)

15

DIII-D

104108Mode amplitude outside the wall

10
50
1350

1400
TIME (ms)

1450

1500

NATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

TWO DISTINCT APPROACHES FOR RWM
CONTROL HAVE BEEN PROPOSEDUse of Dissipation(Plasma Rotation: by Bondeson)

Magnetic Feedback
Required power level is modest

Critical rotation velocity for stabilitya few % of Alfven velocity
8.0gtw

8.0
plasma dissipationaWf = 0parameter

No Rotation

0.0
Stable-2.0

1.0
no-walllimit

No Feedback
HigherRotation=-0.25aWf =-0.5gtw

Higher Gain
G= 0

0.0-2.0
1.0
2.0
bn - bno-wall )ideal-wall(1 +no-wallideal-walllimit- bnbnG= -5(1 +G=-10bn-bideal-wallnStablebno-walln)no-wallbn

2.0

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

PLASMA ROTATION DELAYS RWM ONSET(km/s)(gauss)A decrease in rotation with bn > bnno-wall, leading to rapid RWM growth
Small amplitude RWM near threshold may cause rotational drag3bn2
Estimated ideal MHD limit
101510 n=1 dBr at wall
50150 Plasma Toroidal Rotationr ~ 0.6
1005001100
1200
1300
Time (ms)97798 97802

1400

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

RWM MAGNETIC CONTROL HARDWARE ON DIII-D
Vacuum VesselInternal dBr
Saddle Loops
12(6 pairs))

External dBr
Saddle Loops
6 (3pairs)

InternaldBpProbes
4 locations

Error Field Correction
andFeedback

6 coils (3 pairs) + 3 Power Supplies

Feedback Logic
Smart Shellcontrolsensors

Total leakage flux

dBr Saddle Loop

Mode-only flux

dBp Probe(Virtual Ideal Shell)

Mode control

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

INTERNAL LOOPS ARE MORE EFFECTIVE THAN EXTERNAL LOOPS● Comparison of dBr loops with smart shell logic-Experiment agrees with theoretical predictions
Ip ramp is used to maintain no-wall bn limit roughly constant in time

3.0

Internal dBr
Estimatedno-wall bn limit

bnNo Feedback
0.0
15

External dBr

External dBr

W/2p

Internal dBr(kHz)
No Feedback

0.0
2.0Ip
(MA)
0.0q
1300

95q

= 4.5
140095= 4.0Time (ms)

1500

1600

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

dBp "MODE CONTROL" IS FAR SUPERIOR TO dBr "SMART SHELL LOGIC"
Plasma rotation was well maintained over a longer duration in spiteof lowering edge-q●106196/106187/106193

3Mode Control dBp sensor(Internal)

bn1

Smart ShelldBr sensor(Internal)

No FeedbackEstimatedno-wall bn limit

20.0

10.0
W /2 p(khz)
0.0
3.0Ip(MA)0.0
1300

DIII-Dq95

q 95 = 3.3= 4.0

1400

1500

1600

Time (ms)

NATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

HIGH bn DURATION WAS EXTENDED BY > 500 ms
bn reached twice the bnno-wall, close to bn ideal-wall (GATO-code)
MHD at collapse is ideal kink like behavior(With dBp sensor and modest Ip ramp operation)
Bp (G)

3.0

Feedback Onbn106530/106535

Estimated no-wall bn limit
Toroidal Angle

W/2p (kHz)10g ~300ms

400

no feedback
0.0106535

80

300
200
100
2111.00.0
4.0

2111.5 2112.0
Time (ms)2112. 5

Coil Current n=1 Amplitude (kA)
Rotation Period ~1 ms <

0.0
50.0

10.0

• Ideal MHD LikeBehavior

Coil Current n=1 Toridal Phase (deg.)

1200

DIII-DTime (ms)2200

NATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

FEEDBACK COMPENSATES RESIDUAL ERROR FIELD-Preprogramming coil currents without feedback, matched to currents withfeedback, produce similar bn and rotation
106532/106534

Optimized Preprogram only

3.0

With Feedbackbn

Estimated no-wall bn limit
0.0
10.0
W/2p(kHz)
0.0
5.0
Coil Amplitude(kA)With Feedback

0.0
50.0
Coil Tor. Phase(degrees)
10.0

Optimized Preprogram only
1200

Time (ms)2200

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

ERROR FIELD AMPLIFICATION (EFA) INCREASED AT b n > bn no-wall(gauss)(A)• Helical resonance to non axi-symmetric magnetic field
432
10
4000
3000
2000
10000
3.0
2.0105432 105439 105444bN
Approximate no-wall beta limit- First predicted by A. Boozer
Phy. Rev. Lett. 86, 1176 (2001)
Error Field Correction Current
n=1 Br at Wall (plasma response only)

1.0Time (ms)1600
Amplitude

0.25

1750

Observed Plasma Response Toroidal Phase Shift
0.0

Amplitude

0.0

Increasing error field(degrees)

0.6

DIII-D

1.0

bn/bnno-wall

1.6

- 180

bn/bnno-wall

NATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

TWO PROCESSES: ROTATIONAL STABILIZATION
AND MAGNETIC FEEDBACK HAVE BEEN UNIFIED IN A
SYNERGISTIC MANNER, OPENING A PATH TO IDEAL-WALL bn LIMIT
Maintain
PlasmaRotation

Reducing
Residual Error Field

RWM / EFA

Magnetic Feedback
Sensor

8.0

Unified Themeno FB
no Rotation

gtw

Increasing Rotation

G=0
G=-50.0-2.0

DIII-D

Increasing Gain

1.0
no-walllimit

G=-10 Stablebno-walln)(1 +no-wallideal-wall- bnbnbn

2.0
ideal-walllimit

NATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

LUMPED PARAMETER FORMULATION- Explicit Presentation of Boundary Condition

lplw

dW approach
PlasmaDissipationa(gtw +iWf) + dWp +Mpclcwallcoil

Resistive Wall(dWv b gtw + dWv)/(gtw + 1) = 0
plasmasurface

Lumped formulation
Ideal MHD[(bo - 2/f) + a ( / t + (W f ) / f )] y(a)= (a/m) dy /dr|r=af = m - nq
yj = Mjk Ik
Plasma surface

Mwp / t(Ip) + Lw / t (lw) +Mwc / t (lc) + Rw lw = 0
Wall surface

Slow time limit:

2L eff I p + Mpw I w + Mpc I c = 0 :L eff =

(bn - 1 + iaW +kW )(bn + 1 + iaW+kW 2), bn = 2/f -1•EFA Amplitude • 1/ L eff
L eff : equivalent to "magnetic decay index" of vertical instability ( Ip <-> dZp)

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

EFA RESPONSE TO PULSED FIELD IS QUALITATIVELYCONSISTENT WITH MODEL ESTIMATE
Amplitude

Observed Plasma Response to0.25

0.0

Mode
toroidalphase
shift(degrees)Modeamplitude

0.0

0.6

1.0

bn/ b nno-wall

Amplitude

1.6-1800.6

1.0

bn/ b nno-wall

1.6

Estimate with Lumped Parameter Model0.250.0

Toroidal phase shift

Modetoroidalphaseshift(degrees)

Modeamplitude(arb)

0.0

Toroidal phase

0.6

1.0
bn/ b nno-wall

1.6-1800.6

1.0

bn/ b nno-wall

1.6

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

EXPERIMENTS SUPPORT "RIGID DISPLACEMENT" MODE STRUCTURE• Simplify model development of RWM like Lumped parameter formulation and VALEN code
Three Toroidal Arrays of Saddle Loops
Provide Poloidal Mode Structure
Upper Array1(Without feedback)

03353

300200100

Toroidal Array0Midplane Array

3002001000Lower Array

300
200
10001450

16001700
Time (ms)Mode Structure Relative to Midplane
Without Feedback (103353)
With Feedback (103355)
1.0
0.5
0.0-0.5
-1.0

= +50

1.0
0.5
0.0
-0.5
-1.0

=0

1.0
0.5
0.0
-0.5
-1.0

= - 500100
200
Relative Toroidal Angle

300

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

PROPOSED IMPROVEMENT OF RWM FEEDBACK ON DIII-D
Additional six upper- and six lower- coils and internal Bp sensors increaseachievable b very close to ideal-wall b limit (VALEN CODE / no rotation)
NoFeedback(no FB)

Present coil Present coilandandExternal Br Internal Br

Present coilandinternal Bp

New coils
andinternal Bp

New feedback
coil

and
10 4og(sec-1)
InternaldBp

10 2

10 0x

PresentCoil Coil0.0

no wall
limit

0.2

0.4

0.6

bn-

bideal-wallnbno-wallnbno-wall
n

0.8

1.0

ideal wallb limitNew feedback
coil

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy

SUMMARY
RWM control●Two schemes, rotational stabilization and magnetic feedback, previously
considered distinct, now function as a unified process in a synergistic manner●Feedback process tracks and compensates the residual error field, maintains
the rotation, and achieves high bn●A key to this success is the use of Bp sensors inside the vessel and mode control logic●High bn condition is also achievable with optimized error field correction without feedback

High bn achievement●Achievement of twice the no-wall bn limit close to ideal-wall bn limit
consistent with experimental MHD observation

Understanding of RWM physics● Greatly improved by the discovery of Error Field Amplification
Future plans●New coils will be installed for achieving high bn over wide parameter ranges

DIII-DNATIONAL FUSION FACILITYSAN DIEGO

294-01/jy