NSTX WZ – XP524 - NSTX Results Review ‘05

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XP524: Physics and Control of Toroidal Rotation Damping in NSTX

W. Zhu1, S.A. Sabbagh1, A.C. Sontag1, J. Bialek1, R.E. Bell2, J.E. Menard2, D.A. Gates2, C.C. Hegna3, B.P. LeBlanc2, K.C. Shaing3,

D. Battaglia3, and the NSTX Research Team

1Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY2Plasma Physics Laboratory, Princeton University, Princeton, NJ3University of Wisconsin, Madison, WI

v1.0

NSTX Results ReviewDecember 12th, 2005

Princeton Plasma Physics Laboratory

NSTX WZ – XP524 - NSTX Results Review ‘05

Produce low rotation (ITER relevant) target plasmas

Good control by current timing / magnitude

Study physics of plasma rotation damping due to applied field / RWM

n=1 and n=3 fields used

6 ex-vessel non-axisymmetric field coils

6

4

2

0

3

2

1

0

N

IR

WM(kA

)

0.4

0.3

0.2

0.1

0.00.4

0.3

0.2

0.1

0.0

V/

VA

V/

VA

Core region

Edge region

116924116930116931

0.0 0.2 0.4 0.6 0.8

Time (s)

n=3 DC field pulse

R=1.08m

R=1.30m

Non-axisymmetric fields used to study plasma rotation damping

NSTX WZ – XP524 - NSTX Results Review ‘05

Attention placed on studying non-resonant rotation damping physics

Non-resonant Global profile

control by pulsing the applied field

Resonant Local JxB

torque can explain damping by tearing modes

Outward momentum transfer across rational surface

Leads to rigid rotor core

0.9 1.0 1.1 1.2 1.3 1.4 1.5R (m)

40

30

20

10

040

30

20

10

0

Ft

(kH

z)F

t (k

Hz)

Spin-down

Spin-up !

116937

Time (s)0.345s0.355s0.365s0.375s0.385s

Time (s)0.405s0.415s0.425s0.435s

0.9 1.0 1.1 1.2 1.3 1.4 1.5R (m)

40

30

20

10

0F

t (k

Hz)

10

0

-10

-20

-30

Ft (kH

z)

116190

Time (s)0.345s0.355s0.365s

Time (s)0.345-0.355s0.355-0.365s

n = 1 tearing mode

resonant dampingnon-resonant damping

q = 2

NSTX WZ – XP524 - NSTX Results Review ‘05

Neoclassical toroidal viscosity (NTV) theory tested as non-resonant damping mechanism

2NTVJ BR T T

t

Torque balance:

ii22

3 tv Rq

C1 1.365ps

221 212 0

2, 0 1

1

i

nmps r mi

NTV NTVn mt t ps

n bpT R q T

v B m nq

KC

(Set = 0 here - tearing modes avoided.)

Damping caused bykinked field

K.C. Shaing, Phys. Fluids 29 (1986) 521.; E. Lazzaro Phys. Plasmas 9 (2002) 3906.

measured

computed

Ti1/2 profiles collisionalityfactor

NSTX WZ – XP524 - NSTX Results Review ‘05

NTV theory applied to different periods in discharge

Plasma N at or below no-wall limit

Resonant Field Amplification (RFA)

6

4

2

01612

840

NB

p (G

)

3

2

1

0

IRW

M (kA)

Unstable RWM

NB

p (G

)

IRW

M (kA)

2.52.01.51.00.50.0

Applied field

Plasma N above no-wall limit

Applied field is amplified by stable RWM

Applied field RFA1 2

0.30 0.35 0.40 0.45 0.50 0.55

Time (s)

n = 3 applied field n = 1 applied field543210

5040302010

00.35 0.40 0.450.30

Time (s)

NSTX WZ – XP524 - NSTX Results Review ‘05

0

1000

2000

3000

1 1.1 1.2 1.3 1.4 1.5

Radius (m)

n2b

r2 (

G2)

Applied field alone yields moderate, global rotation damping

n = 3 DC field (800A)

Damping reduced at large R due to reduction in Ti

n=1-15 field components included

Resonant denominator in NTV theory might be overemphasized

Function of collisionality

Time0.375s0.395s

Time0.375-0.395s

116935

1.0 1.1 1.2 1.3 1.4 1.5Radius (m)

40

30

20

10

00.4

0.3

0.2

0.1

0.0

Ft (

kHz)

T (

N m

-2)

Vacuum Field n2br2

(VALEN)n=3

n=9

n=15

measured

TNTV

K = 8

NSTX WZ – XP524 - NSTX Results Review ‘05

0

100

200

300

1 1.1 1.2 1.3 1.4 1.5

Radius (m)

n2 b

r2 (G

2 )

RFA enhances, broadens rotation damping

n = 1 DC field (800A)

n=5 torque larger than n=1 torque (n2b2 scaling)

n=1-15 components included

Broadening damping profile

Time0.355s0.365s0.375s

1.0 1.1 1.2 1.3 1.4 1.5Radius (m)

40

30

20

10

00.4

0.3

0.2

0.1

0.0

Ft (

kHz)

T (

N m

-2)

Time0.355-0.365s0.365-0.375s

116939

n=1

n=5

n=11

n=7

Vacuum Field n2br2

(VALEN)

measured

TNTV

K = 8

NSTX WZ – XP524 - NSTX Results Review ‘05

RWM eigenfuction can explain broader damping

DCON n = 1 (m = -12 to 26) RWM calculated eigenfunction

No-wall boundary condition Need to evaluate with-wall

boundary condition; inclusion of measured n = 2 component

Time0.365-0.375s0.375-0.385s

Time0.355s0.365s0.375s0.385s0.395s0.405s

40

30

20

10

0

Ft (

kHz)

RWM mode decomposition

0.0 0.2 0.4 0.6 0.8 1.0

|n|

Bn

(arb

)

1.0

0.5

0.0

-0.5

m = 1m = 2 3 4 5 6

116939

116939 t = 0.39s

T (

N m

-2)

measured

TNTV

NSTX WZ – XP524 - NSTX Results Review ‘05

Control of plasma rotation profile allows study of rotation damping physics

Applied n=1,3 DC and AC fields used to alter plasma rotation profile in a controlled fashion

Plasma rotation recovers if applied field reduced before RWM critical rotation profile reached

Rotation damping profile from applied n = 1,3 fields and RFA follows neoclassical toroidal viscosity (NTV) theory

NTV theory tested, including n scaling, reduced damping at low Ti, global/non-resonant mechanism

Continued work to resolve magnitude (multiplicative factor, K) At APS ‘05, K ~ 8 - 10; trapped particle effects may reduce to 2 – 3

(K.C. Shaing) Lazzaro, et al. estimate trapped particles increase NTV by (646/q2)

NSTX WZ – XP524 - NSTX Results Review ‘05

Full calculation of NTV theory giving quantitative agreement with experiment

• Since APS ’05 Computation in Hamada

coordinates

• Cylindrical approximations eliminated

Fourier decomposition of mod(B) Full NTV plateau regime

computation

• Multiplicative factor K ~ 3.4

• Need to re-run analysis for shots taken in XP 524

Added full trapped particle computation (Shaing, PoP 2003) to NTV

• Computed and compared to XP for the first time

• Multiplicative factor K ~ 0.5

Hamada coordinate grid

0.0

0.5

1.0

1.5

-0.5

-1.0

-1.5

Z(m)

R(m)0.60.2 1.0 1.4

116939t = 0.39s