supported by aspect ratio considerations for resistive wall ...nstx s.a.sabbagh – iea workshop 59...

NSTX S.A.Sabbagh – IEA Workshop 59 – 02/15/05

S. A. Sabbagh1, A.C. Sontag1, R. E. Bell2, J. Bialek1, A. Garofalo1, D.A. Gates2,A. H. Glasser3, B.P. LeBlanc2, F.M. Levinton4, J.E. Menard2, H. Reimerdes1,W. Zhu1, M.G. Bell2, T.M. Biewer2, C.E. Bush5, J.D. Callen6, M.S. Chu7,C. Hegna6, S. M. Kaye2, L. L. Lao7, R. Maingi5, D. Mueller2, K.C. Shaing6,D. Stutman8, K. Tritz8, C. Zhang9

Aspect Ratio Considerations for Resistive Wall Mode Stabilization

Supported by

Columbia UComp-X

General AtomicsINEL

Johns Hopkins ULANLLLNL

LodestarMIT

Nova PhotonicsNYU

ORNLPPPL

PSISNL

UC DavisUC Irvine

UCLAUCSD

U MarylandU New Mexico

U RochesterU Washington

U WisconsinCulham Sci Ctr

Hiroshima UHIST

Kyushu Tokai UNiigata U

Tsukuba UU Tokyo

JAERIIoffe Inst

TRINITIKBSI

KAISTENEA, Frascati

CEA, CadaracheIPP, Jülich

IPP, GarchingU Quebec

IEA Workshop 59: Shape and Aspect Ratio Optimization for High Beta, Steady-State Tokamak

February 14 – 15, 2005General Atomics, San Diego, CA

1Department of Applied Physics, Columbia University, New York, NY, USA2Plasma Physics Laboratory, Princeton University, Princeton, NJ, USA

3Los Alamos National Laboratory, Los Alamos, NM, USA4Nova Photonics, Princeton, NJ, USA5Oak Ridge National Laboratory, Oak Ridge, TN, USA6University of Wisconsin, Madison, WI, USA7General Atomics, San Diego, CA, USA8Johns Hopkins University, Baltimore, MD, USA9Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China


Physics study of global MHD mode stabilization at low A provides understanding for all A, including ITER

• MotivationStudy / optimize high β stability of low A, spherical tokamakLow A, high q challenges theory and code benchmarkingCompare data from various A devices to test theory

• Key TopicsKink and RWM stabilization at low A; mode characteristicsToroidal rotation damping physicsCritical plasma rotation frequency for stabilization, Ωcrit

Resonant field amplification (RFA)Rotation effects on equilibrium at low A


Low A kink mode amenable to stabilization at high βN

θ/2π0.0 0.2 0.4 0.6 0.8 1.0

1

0

-1

δBψ

(arb

)

θ/2π(equal arc poloidal angle)

βN = 5.0114024

βN = 2.4104403

δBψ

(arb

) 1

0

-1

0 0 0 2 0 4 0 6 0 8 1 0

DIII-D 92544βN = 2.2

δBψ

(arb

) 2

0

-2

4

0.0 0.2 0.4 0.6 0.8 1.0

Higher A ~ 3.1 (DIII-D); βN = 2.2 (above βNno-wall)

Maximum amplitude on outboard side; relatively long poloidal wavelengthStrong wall coupling; effective wall stabilization

Lower A ~ 1.4 (NSTX)• βN = 2.4:

Minimum amplitude on outboard side; short poloidalwavelength inboard sideWeak wall coupling; ineffective wall stabilization

• βN = 5.0 (above βNno-wall)

Mode balloons out and can be effectively stabilized

R

Z θ

R0+ aR0- a

DCON

R0+ a R0+ aR0- a


Wall stabilization physics understanding is key to sustained plasma operation at maximum β

• High βt = 39%, βN = 6.8 reached

βN

li

βN/li = 12 68

4

10

wall stabilized

• Global MHD modes can lead to rotation damping, β collapse• Physics of sustained stabilization is applicable to ITER

• Operation with βN/βNno-wall > 1.3 at

highest βN for pulse >> τwall

βN

01234567

DCON

δW0

10

20

0.6 0.70.50.40.30.20.10.0t(s)

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

112402

wall stabilized

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 1.6

EFIT

core plasma rotation(x10 kHz)


Unstable n = 1-3 RWM observed

• n > 1 theoretically more prominent at low A

• Fitzpatrick-Aydemir (F-A) theory / experiment show

mode rotation can occur during growthgrowth rate, rotation frequency ~ 1/τwall

• << edge Ωφ > 1 kHz

RWM phase velocity follows plasma flown=1 phase velocity not constant due to error field

• Low frequency tearing modes absent

growth w/o mode rotation mode rotation during growth

βN

|δBp|(n=1)

(G)

(G)

(G)

|δBp|(n=2)

|δBp|(n=3)

φBp(n=1)(deg

)B

z(G) (f<40 kHz, odd-n)

n=2,3n=1 no-wall unstable

n=1-3 no-wall unstable

0.22 0.24 0.26 0.28t(s)

-20-10

010200

100200300

01020300

102030400

2040600246

0.18 0.20 0.22 0.24 0.26 0.28t(s)

-20-10

010200

100200300

0

10

200

1020300

1020300246

114147 114452

moderotation

mode growth


• Visible light emission is toroidally asymmetric during RWM

• DCON theory computation displays mode uses experimental equilibrium reconstructionincludes n = 1 – 3 mode spectrumuses relative amplitude / phase of n spectrum measured by RWM sensors

Camera shows scale/asymmetry of theoretical RWMRWM with ∆Bp = 92 G

Before RWM activity

114147t = 0.250s

114147t = 0.268s

Theoretical ∆Bψ (x10) with n=1-3 (DCON)

114147 114147

(interior view)(exterior view)


Plasma rotation damping described by NTV theory

• Evolution detail differs for other modesno momentum transfer across rational surfacesno rigid rotor plasma core (internal 1/1 mode)

t=0.265576

t=0.275576

113924

1.0 1.2 1.4 1.6R(m)

Ωφ/2

π(k

Hz) 2520

1015

5

T d(N

m-2

)

0.40.30.20.10.0

-0.1-0.2

0

t = 0.276s

TNTV

t=0.225729t=0.235729t=0.255729

40

30

20

10114452

Ωφ/2

π(k

Hz) t(s)

0.2260.2360.256

theory

• Neoclassical toroidal viscosity (NTV)

• Rapid, global damping observed during RWMEdge rotation ~ 2kHz maintainedLow frequency tearing modes absent

full rotation evolution

1.0 1.2 1.4 1.6R(m)

0.8

t(s)0.2660.276

initial rotation evolution

measured-ρR2(dΩφ/dt)

axis edge


NTV Torque depends on aspect ratio, n, q

Neoclassical toroidal viscosity (NTV) theory (K.C. Shaing et al., Phys. Fluids 29 (1986) 521)

( )21 2 2

2mode

, 0

1.3651.182 1.365

i

mni r

NTVm nt

p B n qT Rv B m nqφ

φ

π δε≠

= Ω − Ω + −

∑

dominant m:

( )21 2

2 2mode

i

i rNTV

t

p BT R n qv Bφ

φ

π δε

= Ω − Ω

• n, q (profile) variation can be considered in a single machine

• ε = 1/A variation can be made between machinesmeasured rotation profile

measured Ti0.5 profile


q1 2 3 4 5

ωφ/ω

A

0.5

0.4

0.3

0.2

0.1

0.0

stabilized1/(4q2)not stabilized

Experimental Ωcrit follows Bondeson-Chu theory

• Experimental Ωcritstabilized profiles: β >βN

no-wall (DCON)profiles not stabilized cannot maintain β > βN

no-wall

regions separated by ωφ/ωA =1/(4q2)

• Drift Kinetic TheoryTrapped particle effects significantly weaken stabilizing ion Landau damping Toroidal inertia enhancement more yields Ωcrit = ωA/(4q2)

• Neoclassical effect: Is there an ε0.5 scaling?

ωφ/ωA(q,t) profiles

Phys. Plasmas 8 (1996) 3013


ωφ/ω

AΩcrit follows F-A theory with neoclassical viscosity

q95

2 4 6 8 10

0.06

0.05

0.04

0.03

0.02

0.01

0.00

stabilized1/(4q2)not stabilized

ωφ/ωA in F-A inertial layer (edge) • Experimental Ωcritstabilized points:β >βN

no-wall (DCON)points not stabilized cannot maintain β > βN

no-wall

regions separated by ωφ/ωA =1/(4q2)

• F-A TheoryStandard F-A theory yields Ωcrit ~ 1/q neoclassical viscosity includes toroidalinertia enhancement• Ωcrit ~ ε/q2 or ε0.25/q2

depending on RWM dissipation strength

(K. Shaing, PoP 2004)


DIII-D/NSTX RWM experiment to investigate q, A effects

• RWM physics in similar shape• q and A dependence of

Ωcrit : A scaling ~ factor 1.2 – 2.2Toroidal rotation dampingResonant field amplification

NSTX 108420 @ 415ms

DIII-Dcenterline

NSTXcenterline

DIII-D (LaHaye, et al.)

H. Reimerdes, et al, D3DMP# 2005-04-58


Resonant Field Amplification increases at high βN

• Plasma response to applied field from initial RWM stabilization coil pair

AC and pulsed n = 1 field• RFA increase consistent with DIII-D• Stable RWM damping rate of 300s-1

measured in NSTX, similar to DIII-D

βN

βNno-wall

(n = 1)

0

0.2

0.4

0.6

4.0 4.5 5.0 5.5 6.0

plas

ma

∆Bp

/ app

lied

Bp

DIII-DNSTX

plas

ma

∆Br/ a

pplie

d B r

phas

e sh

ift (d

eg)

βN/ βNno-wall


Peak pressure shifts significantly off axis: low A, high Vφ

Pki

netic

(kP

a)P

dyna

mic

(kP

a)

10

20

30

0

2

3

4

5

6

Poloidal flux and pressure

-2

-1

1

2

0Z(m

)

0.5 2.01.0 1.5R(m)

2.01.5R(m)

0 1.0 2.00.5 1.5R(m)

ψ isotherm constraint

(mWb/rad*10)

-6

-4

-2

2

0

magnetic axis

0.0

114444t=0.257s

1

0 1.00.5

magnetic axis

0

0.96 1.081.00 1.04R(m)

-0.2

0.2

0.0

Pitch angle (rad) vs. R

MSE data

peak pressure

(1/2ρVφ2 )


1.000.800.600 .400 .200 .0010 -1

10 0

10 1

10 2

10 3

10 4

10 5

norm

Growth

rate

[

1/s

]

0.20.0 0.4 0.6 0.8 1.0

NSTX control modeling predicts 68% stable margin above βNno-wall with initial external coil system

• Control coil / sensor design with realistic geometry

• Internal control coil design computed to reach Cβ = 94%

VALEN model – external coil design(cutaway view)

Gro

wth

rate

(s-1

)

10-1

100

101

102

103

104

105

Passive

With-wall limit(βN wall)

1.0 2.5

Active feedback coil

Internal control coils

Cβ ≡ (βN – βNNo-wall)/(βNwall – βNNo-wall)

Activegain (V/G)

Sensors(Equilibria used have βNno-wall = 5.1; βNwall = 6.9)


ITER active coil modification can significantly raise stable βN

VALEN dual-wall vessel / blanket model(full view)

Active feedback coil modification(coils in ports)

Gro

wth

rate

(s-1

)

10-1

100

101

102

103

104

105

106

βN2.0 3.0 4.0 5.0

(no blankets)

107

Activegain

(V/Wb) 108

(blankets)

Passive

• Original external coil design for ITER stabilizes up to βN = 2.7

• Proposed improvement raises maximum stable βN to near 5 (!)


Kink/RWM stabilization research at low aspect ratio illuminates key physics for general high β operation

• Plasma with βt = 39%, βN = 6.8, βN/li = 11 reached; βN/βNno-wall > 1.3

• Unstable n = 1-3 RWMs measured (n > 1 prominent at low A)

• Critical rotation frequency ~ ωA/q2 strongly influenced by toroidal inertia enhancement (prominent at low A)

• Rapid, global plasma rotation damping mechanism associated with neoclassical toroidal viscosity (stronger at low A, high q)

• Resonant field amplification of stable RWM increases with increasing βN(similar to higher A)

• Plasma rotation at low A can significantly alter core pressure gradients

• Full RWM stabilization coil and MSE diagnostic will be used to study and suppress RFA, actively stabilize RWM, sustain high beta in 2005

Will allow thorough comparison with higher aspect ratio DIII-D plasmas


Supporting slides follow


Theory provides framework for wall stabilization study

• TheoryIdeal MHD stability – DCON (Glasser)• arbitrary 2-D geometry

RWM passive/active stability – VALEN• 3-D geometry

Drift kinetic theory (Bondeson – Chu)• cylindrical; toroidal expansion

RWM dynamics (Fitzpatrick – Aydemir)• cylindrical

( ) ( ) ( )( )[ ] ( )( ) ( )( )2**

211ˆ11ˆˆˆˆ mdmdSmdsii −=++−−+Ω−+Ω− γγνγ φφ

plasma inertia dissipation mode strength wall response wall/edge couplingS* ~ 1/τwall

Ωφ

0.0 0.5 1.0 1.5-1.0

-0.5

0.0

0.5

1.0

mod

e st

reng

th s

ideal wall limit

no-wall limitν*=

Fitzpatrick-Aydemir (F-A)stability curves

plasma rotation

Phys. Plasmas 9 (2002) 3459

stable

wall stabilized

stable


Chord 3

Chord 4

Chord 5

Bay G array (0 deg)Bay J array (90 deg)

Inte

nsity

(arb

)

• Experiment / theory show RWM not edge localized

Supported by measured ∆Te

114024, t=0.273sβN = 5

0.27 0.28 0.29

8

4

0

6

4

0

6

4

0

t(s)

Inte

nsity

(arb

)In

tens

ity (a

rb)

0.0 0.5 1.0 1.5 2.0R(m)

2

1

0

-1

-2

Z(m

)

35 4

RWM growth

2

1

00.0 0.2 0.4 0.6 0.8 1.0

DCON n = 1 modedecomposition

ψn

(arb

)

m=34 56

USXR separated by 90 degrees

ψn = 0.13

ψn = 0.4

Soft X-ray emission shows toroidal asymmetry during RWM

2

2

6

2

ψn = 0.24

m=2

ψn:0.13 0.24

m=1

0.4

supported by aspect ratio considerations for resistive wall ...nstx s.a.sabbagh – iea workshop 59...

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