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

S A N D I E G O

DIII-DNATIONAL FUSION FACILITY

� 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

S A N D I E G O

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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DIII-DNATIONAL FUSION FACILITY

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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

S A N D I E G O

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

S A N D I E G O

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

S A N D I E G O

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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DIII-DNATIONAL FUSION FACILITY

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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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DIII-DNATIONAL FUSION FACILITY

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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

S A N D I E G O

DIII-DNATIONAL FUSION FACILITY

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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

S A N D I E G O

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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DIII-DNATIONAL FUSION FACILITY

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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

�

S A N D I E G O

DIII-DNATIONAL FUSION FACILITY

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New feedbackcoil

New feedbackcoil

Coil

o

x

PresentCoil

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DIII-DNATIONAL FUSION FACILITY

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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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