NSTX The Resistive Wall Mode and Beta Limits in NSTX S. A. Sabbagh 1, J. Bialek 1, R. E. Bell 2, A. H. Glasser 3, B. LeBlanc 2, J.E. Menard 2, F. Paoletti.

NSTX

The Resistive Wall Mode and Beta Limits in NSTX

S. A. Sabbagh1, J. Bialek1, R. E. Bell2, A. H. Glasser3, B. LeBlanc2, J.E. Menard2, F. Paoletti1, M. Bell2, T. Biewer2, R. Fitzpatrick4, E. Fredrickson2,

A. M. Garofalo1, D.A. Gates2, S. M. Kaye2, L. L. Lao5, R. Maingi6, D. Mueller2, G. A. Navratil1, M. Ono2, Y.-K. M. Peng6, D. Stutman7, W. Zhu1,

and the NSTX Research Team

1Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA

2Plasma Physics Laboratory, Princeton University, Princeton, NJ, USA3Los Alamos National Laboratory, Los Alamos, NM, USA4University of Texas at Austin, Austin, TX, USA5General Atomics, San Diego, CA, USA6Oak Ridge National Laboratory, Oak Ridge, TN, USA7Johns Hopkins University, Baltimore, MD, USA

44th Annual Meeting of the APS Division of Plasma Physics

Orlando, Florida - November 11th, 2002

NSTX

NSTX is operating at sufficiently high beta to study passive wall stabilization

• Operation in wall-stabilized, high beta regime

• Resistive wall mode (RWM) and rotation damping

• Physical mechanisms for higher N and longer pulse

NSTX

NSTX is equipped to study passive stabilization

Machine

Aspect ratio ≥ 1.27

Elongation ≤ 2.5Triangularity ≤ 0.8Plasma Current ≤ 1.5 MAToroidal Field ≤ 0.6 TNBI ≤ 7 MW

Stabilizing plates

Analysis

EFIT – equilibrium reconstruction

DCON – ideal MHD stability

(control room analysis)VALEN – RWM growth rate

NSTX

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6li

N

Plasma operation now in wall-stabilized space

EFIT0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6li

N

2001 Data

N = 6 i

Wall stabilized

Nomin

al “n

o-wal

l lim

it”

2002 Data

EFIT

4 l i

6 l i

8 l i

10 l i

• Normalized beta, N = 6.5, with N/li = 9.5; N up to 35% over N no-wall

• Toroidal beta has reached 35% (t = 20<p> / B02 )

Design target

NSTX

Maximum N strongly depends on pressure peaking

0

1

2

3

4

5

6

7

8

1 2 3 4 5Fp

N

• Fp = p(0) / <p>

• P profile from EFIT using Pe, diamagnetic loop, magnetics

• Time-dependent calculations required to evaluate stability limits and mode structure

NSTX

Operational improvements yield higher, sustained N

• n=1 error field reduced by an order of magnitude in 2002

• H-mode pressure profile broadening raises N limit

• qmin > 1 maintained (EFIT qmin without MSE)

2001 (High error field) 2002 (Reduced error field)

t(s)

RWM

H-mode

qmin

Fp

N

Br

n=1(G)

0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.50

10

123

345

246

2

n = 1 no-wall unstable(DCON)

n = 1 unstable(with-wall) (no-wall)

n = 1 unstable106165

107636Locked modedetector

3.5 wall (VALEN)

NSTX

Rotation damping rate larger when N > N no-wall

• Rotation damping rate is ~ 6 times larger when N > N no-wall

ToroidalRotationF(kHz)

N

Br

n=1(G)

0

2.0

2

4

6

1.0

t(s)0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.5

2468

10

108197 107994

Locked modedetector

F (q = 2)F (R = 1.35m)

n = 1 no-wallunstable

RWM No RWM

n = 1,2 rotating modes

F (q = 2)F (R = 1.35m)

3.5 wall

(VALEN)

n = 1 rotating mode

NSTX

Two stages of rotation damping during RWM

• Initial stage: Global, non-resonant rotation damping

• Final stage: Local rotation damping at resonant surfaces appears as rotation slows

• Analogous to rotation dynamics in induced error field experiments E. Lazzaro, et al., Physics of Plasmas 9 (2002) 3906. (JET)

NSTX

-5

0

5

10

15

20

25

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

-20

-15

-10

-5

0

5

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5R(m)

-20

-15

-10

-5

0

5

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Rotation damping during RWM is rapid and global

• Field ripple damping by neoclassical toroidal viscosity ~ Br2Ti0.5

candidate for observed damping profile during RWM

R (m)

F

(kH

z)F

(k

Hz)

0.43 s

1079940.27 s0.29 s

0.31 s

0.33 s

0.35 s0.37 s

0.39 s

n = 1, 2 rotating modesF

(k

Hz)

F

(kH

z)

108197

0.29 s

0.31 s

0.33 s

0.31 s

0.33 s

RWM

R (m)

0.41 s

0.45 s

0.43 s

0.27 s0.29 s

0.31 s

0.33 s

0.35 s0.37 s

0.39 s0.41 s

0.45 s

0

5

10

15

20

25

30

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

NSTX

Core rotation damping decreases with increasing q

• Largest rotation damping (dF/dt = -600 kHz/s) at Bt < 0.4T, qmin < 2 Factor of 8 times larger than damping from n=2 island alone

• When qmin ~ 2 damping rate is reduced and F is maintained longer

• Consistent with theory linking rotation damping to low order rational surfaces

0

5

10

15

20

25

30

35

0 0.1 0.2 0.3 0.4 0.5 0.6t (s)

rota

tion

freq

uenc

y (k

Hz)

108195 Bt=0.34T108197 Bt=0.39T108189 Bt=0.44T108420 Bt=0.44T

qmin

1.41.71.92.1

1.4 1.7 1.92.1qmin

EFIT qmin without MSE

Ip = 0.8 MA

NSTX

Plasma stabilized above no-wall N limit for 18 wall

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

N

108420

Ip = 0.8 MA

-15

-10

-5

0

5

0.0 0.2 0.4 0.6 0.8t (s)

W(arb)

DCON

n = 1 with-wall

n = 1 no-wall

VALEN mode growth time = 15 ms

VALEN mode growth time = 0.03 – 0.05 ms

• Plasma approaches with-wall N limit VALEN growth rate

becoming Alfvénic

• F(0) increases as N >> N no-wall

• Passive stabilizer loses effectiveness at maximum N

Neutrons collapse with N - suggests internal mode

• TRANSP indicates higher Fp

Computed N limits conservative

30 kHz

F(0)

5MW NBI

N > no-wall limit

qmin > 2

NSTX

Research on passive stabilization and high N rotation damping physics has begun

• Passive stabilization above ideal no-wall N limit by up to 35% Improvement in plasmas with highest N up to 6.5; N/li = 9.5

• The N limit increases with decreasing pressure profile peaking

• Rotation damping at N > N no-wall has two stages Global, non-resonant damping Local, resonant field damping during final stage

• Rotation damping rate substantially decreases as q increases

• Passive stabilization becomes less effective at highest N

• Active feedback design shows sustained N/N wall = 94% possible See Bialek, et al., GP1.107 Tuesday

For more RWM detail, see NSTX poster session (Tuesday)

NSTX

Other presentations on NSTX beta limits, RWM, and mode stabilization

• High toroidal beta plasmas Gates, et al., BI1.001 Monday

• High poloidal beta plasmas Menard, et al., CO1.002 Monday

• Resistive wall modes Zhu, et al., GP1.106 Tuesday

(Sabbagh for) Paoletti, et al., GP1.105 Tuesday

• RWM active feedback design Bialek, et al., GP1.107 Tuesday

PresentationSubject

NSTX

Active stabilization might sustain 94% of with-wall limit

• System with ex-vessel control coils can reach 72% of N wall

• System with control coils among passive plates can only reach 50% of N wall

VALEN model of NSTX(cutaway view)

7.57.06.56.05.55.010- 1

100

101

102

103

104

105

figure B3 active feedback in NSTXData from "NSTX.04.2002"

beta normal

grow

thrate

(1/s

)G

row

th r

ate

(s-1)

N

5.510-1

5.0 6.0 6.5 7.0 7.5

100

101

102

103

104

105

Passive

With-wall limit(N wall)

0.1 1.0

figure B1''10/09/02 16:27:06 EST artemis executable: xvps6

VALEN model figure B1''

X

Y

Z Modeled active feedback coils

In-vessel control coils

Activegain (V/G)

Bialek, et al., GP1.107 Tuesday

NSTX

Te perturbation measured during RWM

• No low frequency (< 80 kHz) rotating modes observed during measured Te

• Te displacement precedes n=2 rotating mode

t = 0.293 s

t = 0.310 s

0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.5

1.0

1.5

Te

(keV

)

R (m)

109030

Thomson scattering (LeBlanc)0.26 0.30 0.34

Fre

quen

cy (

kHz)

20

0

40

60

80

100

t(s)

1 2 3 4mode number

t = 0.293 s t = 0.31 s

N246

0.0 0.1 0.2 0.3 0.4

2

1

0

t(s)

Br

n=1(G)

Locked modedetector

N > no wall limit

NSTX

N limit now insensitive to plasma proximity to wall

• At high N ~ 5, external modes are well-coupled to passive stabilizing plates, independent of gap Confirmed by ideal

MHD stability calculations

• Higher error field (2001 data) may have also lowered limit for smaller outer gap

See W. Zhu, et al., GP1.106 Tuesday

2002 data (H-mode)2001 data (L-mode)0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 2.5 5.0 7.5 10.0plasma outer gap (cm)

N a

t fa

st c

olla

pse

NSTX

Rotation damping strongest where mode amplitude largest

• Field ripple damping by neoclassical parallel viscosity ~ Br2Ti0.5

possible candidate for observed damping profile

q=2 q=3 ........

0.28

0.20

0.12

0.04

0.00

Aco

sine

0.0 0.5 1.0r/a

m=1

m=3

m=2

0.08

0.16

0.24

Naxis edge

Mode decompositionToroidal rotation evolution

106165

axis edge

t = 0.15 s

t = 0.17 s

t = 0.19 s

(a

rb)

t = 0.192 s

R (cm)100 120 140 160

F

(kH

z)

25

20

15

10

5

0

NSTX

Mode intensifies in divertor region at highest N

N = 5.1

VALEN / DCON computed n = 1 external mode currents

N = 7.1

• Increased p drive more significant in producing higher growth rate