NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

REACHING THE IDEAL WALL LIMIT IN DIII-D

A.M. Garofalo1

in collaboration withJ. Bialek1, M.S. Chu2, J. Jayakumar3, T.H. Jensen2,

L.C. Johnson4, R.J. La Haye2, G.A. Navratil1,M. Okabayashi4, H. Reimerdes1, J.T. Scoville2,

E.J. Strait2, and A.D. Turnbull2

1 Columbia University2 General Atomics

3 Lawrence Livermore National Laboratory4 Princeton Plasma Physics Laboratory

ColumbiaUniversity

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

Has DIII-D observed the ideal-wall limit (at β >> βno-wall)?

What are the observed characteristics that prove this?

How did DIII-D achieve these results?

Can RWM stabilization be sustained near the ideal-wall limit?

How do we extrapolate these results to a reactor?

SOME KEY QUESTIONS

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

1.0

0 500 1000 1500 2000Time (ms)

2100

3.0

2.0

0.0

βN

2.4*li

No-wall limit

Rotation Period ~1 ms < τwall

80

40

δBp (

G)

0

300

200

Toro

idal

Angl

e

100

2111.0 2111.5Time (ms)

2112.0 2112.5

τg ~ 200 µs

3

6

0

9

12

1800 1900 2000 22000

40

80

Time (ms)

0.02*fA

fP at q~2

n=5

n=4

n=3

Freq

uenc

y (k

Hz)

Plasma rotation (kHz)

IDEAL n=1 KINK OBSERVED AT TWICE THE NO-WALL βN LIMIT

Rapid growth rate and rotation suggest little or no effect from resistive wall Very reproducible disruption

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

Ideal MHD calculations find the equilibrium <10% away from βNideal wall

Growth rate is consistent with ideal-wall stability limit Ideal MHD mode driven slowly (τh >> τMHD) through stability limit: τg = τMHD

2/3 τh1/3 ⇒ τMHD = 4µs (J. Callen, et al., Phys. Plasmas, 1999)

Resistive wall mode destabilized at ideal-wall stability limit

Ideal-Wall Dimension/DIII-D vessel

βN=3.23

n=1 ideal MHD stability (GATO)

— γ2/ωA2

Gro

wth

Rat

e (s

-1)

IdealWall Limit

1

100

104

Ideal Kink

ResistiveWall Mode

βN - βNno-wall

βNideal-wall

- βNno-wall

1.00.80.60.40.20

VALEN 3-D No Feedback, no rotation

5000

00.95 1.0 1.05 1.1 1.15

Idea

l wal

l at p

ositi

on o

f DIII

-D v

esse

l

(d)

0.001

0.002

0.003

0.004

0.005

Scaled-uppressure data

βN=3.14

βN=3.05Experimental pressure data(t=2040 ms)

CALCULATIONS INDICATE INSTABILITY OCCURS AT IDEAL-WALL β LIMIT

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

CerFit: Ti vs rho shot: 106535 time: 2040.0000

0

2

4

6

8

10

CerFit: Toroidal Rotation shot: 106535 time: 2040.0000

-0.5

0

0.5

1.0

1.5

2.0

~8 kHz

IDEAL n=5 KINK LOCALIZED NEAR THE FOOT OF AN INTERNAL TRANSPORT BARRIER

Ti (keV)

Toroidal rotation (105 rad/s)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Ion temperature and rotation data show n=5 mode is NOT an edge mode

Normalized ρ

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

Spline fitting of profile data is normally carried out using smallest number of knots Stability of n=1 kink is not affected by

small scale features of internal profiles

Presence of an ITB justifies additional knotsfor the core profiles

New equilibrium reconstruction is marginally stable to n=5 mode,localized near the ITB

OBSERVATION OF n=5 KINK PROVIDES USEFUL HINTS TOWARDS NUMERICAL RECONSTRUCTION OF EQUILIBRIUM

Thomson Data, shot: 106535, time: 2040.0000

0.0 0.2 0.4 0.6 0.8 1.0 1.20

2

4

6

8

10

12

= Core

= Tangential

Normalized ρ

ne (1019 m-3)

0.0 0.2 0.4 0.6 0.8 1.0

Normalized ψ

-0.08

-0.12

-0.04

0.0

0.08

0.04

0.12Reξψ

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D λ1.41 2.00 2.45 2.83

—50

0

50

100

150

—150

—100

2025

2042

2008

19751992

1958

1858190818751925 1892

1942

2025

∆φ (ο)

(a)

—40

—50

—30

—10

0 4 8 10

—20

0

dfp/dt (kHz/s) at q=3

B23/1 /fp (G

2/kHz)

(b)

Induction motor model of the plasma rotationpredicts a linear relationship between the rotation decay rate and the RESULTING error field

Varying the assumed amplitude and phase of the REFERENCE, INTRINSIC error field yields a contour plot of χ2 with a very shallow minimum for a 3/1 field

PLASMA ROTATION DECAY RATES DO NOT CORRELATE WITH ANY m/n=3/1 INTRINSIC ERROR FIELD

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

—30

—20

—10

0

10

1.0 1.2 1.4 1.6

2000

3000 28002600

1800

2400

1600

22002000

1400

1800

2400 1600

2200

2600

14001200

1000600 800

(a)

λ

∆φ (ο)

Best fit to model suggests relevant intrinsic error field is m/n=2/1, with B2/1 ~ 7 gauss (Garofalo, La Haye, and Scoville, Nucl. Fusion, 2002)

Varying the assumed amplitude and phase of the REFERENCE, INTRINSIC error field yields a contour plot of χ2 with a very deep minimum for a 2/1 field

PLASMA ROTATION DECAY RATES CORRELATE WITH A ~7 gauss m/n=2/1 INTRINSIC ERROR FIELD

0.0 0.5 1.0—70

—50

—30

—10(b)

dfp/dt (kHz/s) at q=2

B22/1 /fp (G

2/kHz)

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

RESISTIVE WALL MODE STABILIZED BY ROTATION IS WEAKLY DAMPED - HAS STRONG RESPONSE TO RESONANT PERTURBATIONS

15500.0

1.0

2.0

3.00

1

2

30

1

2

34

1650Time (ms)

1750

No wall beta limit

Error field component on 2/1 surface(gauss)

n = 1 δBr at wall (gauss)(plasma response only)

βN RWM is nearly stationary n = 1 mode ⇒ can resonate with n = 1 INTRINSIC error field

RWM is closer to marginal stability at higherβN ⇒ resonant response increases as βN increases above the no-wall limit

"Error field amplification" clearly demonstratedusing external n=1 field pulses

(A. Garofalo, et al., Phys. Plasmas, 2002)

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

RWM feedback finds same error field correction obtained by rotation optimization Dominant error field is m/n=2/1 field

Sustained plasma rotation allows βN >> 4li in negative central shear plasma with 85% noninductive current (65% bootstrap current), and βT > 4%

Large (2,1) tearing mode limits duration of high performance phase

βN

1200 1400 1600 1800 2000 2200 2400Time (ms)

1000

frot (kHz) at q = 2

4l i ~ No-Wall Limit

6l i 106795

543210

20

10

0

2/1 Tearing Mode

PHYSICS OF RWM AND PLASMA ROTATION TRANSLATES WELLTO ADVANCED TOKAMAK PLASMAS

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

OBSERVED SCALING OF CRITICAL PLASMA ROTATION FOR ONSET OF RESISTIVE WALL MODE IS CONSISTENT WITH MHD THEORY

B

B

B

B

BBB

B

BB

HHHH

H

H

H

Hidden variable is βN / βN

f = 2.78τAcorr = —0.79σ = –1.3 kHz

B

H

—2.10 T

—1.05 T

15

10

5

00 0.25

ALFVEN Time (Microsec) at q=2

0.50 0.75

— σ

+σ

Criti

cal F

requ

ency

(kHz

) at q

=2

—1.14–0.17

. . . βN / 2.4li = 0.9 ~ 1.9

no-wall

Consistent with inverse of ALFVEN TIME: ΩcτA ~2% (Bondeson and Ward, 1994)

MARS (Bondeson , Liu, Chu) calculations for ITER predict plasma rotation would be marginal for RWM stabilization

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

12-coil internal set available forexperiments 2003

Off-midplane coils allow better matching to poloidal spectrum of error field or RWM

Feedback stabilization is calculated to open high beta wall-stabilized regime toplasma without rotation

Gro

wth

Rat

e (s

-1)

IdealWall Limit

1

100

104

Ideal Kink

ResistiveWall Mode

βN - βNno-wall

βNideal-wall

- βNno-wall

1.00.80.60.40.20

12-coil set (internal)

No Feedback6-coil set (C-coil)

(VALEN 3-D)

RWM STABILIZATION UP TO THE IDEAL-WALL LIMIT PREDICTED WITH NEW INTERNAL CONTROL COILS, WITHOUT PLASMA ROTATION

NATIONAL FUSION FACILITYS A N D I E G O

DIII-D

SUMMARY

Ideal-wall βN limit observed at βN = 2xβNno-wall in DIII-D

Sustained operation at βN just below the ideal-wall limit is possible by correction of

intrinsic m/n=2/1 error field

Projected plasma rotation in ITER may not be sufficient for RWM stabilization

New internal control coils and poloidal field sensors in DIII-D should allow

RWM stabilization near the ideal-wall βN limit in absence of plasma rotation