Macroscopic Stability Research on NSTX – Results and Theory Interaction S.A. Sabbagh 1, S.P....

Macroscopic Stability Research on NSTX – Macroscopic Stability Research on NSTX – Results and Theory InteractionResults and Theory InteractionS.A. Sabbagh1, S.P. Gerhardt2, R.E. Bell2, J.W. Berkery1, R.

Betti3, J.M. Bialek1, J. Breslau2, R. Buttery4, L. Delgado-Aparicio5, D.A. Gates2, B. Hu3, R. LaHaye4, J-K. Park2, J.E.

Menard2, H. Reimerdes1, K.C. Shaing5, K. Tritz6, and the NSTX Research Team

1Department of Applied Physics, Columbia University, New York, NY2Plasma Physics Laboratory, Princeton University, Princeton, NJ

3University of Rochester, Rochester, NY4General Atomics, San Diego, CA

5University of Wisconsin, Madison, WI 6Johns Hopkins University, Baltimore, MD

PPPL MHD Science Focus Group MeetingJanuary 6th, 2010

PPPL

College W&MColorado Sch MinesColumbia UComp-XGeneral AtomicsINELJohns Hopkins ULANLLLNLLodestarMITNova PhotonicsNew York UOld Dominion UORNLPPPLPSIPrinceton UPurdue USandia NLThink Tank, Inc.UC DavisUC IrvineUCLAUCSDU ColoradoU MarylandU RochesterU WashingtonU Wisconsin

Culham Sci CtrU St. Andrews

York UChubu UFukui U

Hiroshima UHyogo UKyoto U

Kyushu UKyushu Tokai U

NIFSNiigata UU Tokyo

JAEAHebrew UIoffe Inst

RRC Kurchatov InstTRINITI

KBSIKAIST

POSTECHASIPP

ENEA, FrascatiCEA, Cadarache

IPP, JülichIPP, Garching

ASCR, Czech RepU Quebec

NSTXNSTX Supported by

v1.0

NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 2January 6th, 2010

NSTX Macrostability Research is Addressing Topics Needed to Maintain Long-Pulse, High Performance ST

Motivation / Goals (e.g. from recent ReNeW process) Maintenance of high N with sufficient physics understanding allows

confident extrapolation to ST applications (Hybrid, CTF, DEMO) Sustain target N of ST applications with margin to reduce risk

Physics studied in NSTX to best ensure steady-state ST operation Locked mode behavior at low to moderate N < N

no-wall

Ability of plasma rotational stabilization to maintain high N

Possibility of multiple RWMs that can affect active control Physics of 3D fields to control plasma rotation profile (for greater

stability, confinement) NTM onset and marginal island width for stabilization Multiple scalable control systems to maintain <N>pulse

Successful connections being made to theory – continue/expand interaction…


NSTX Macrostability Research – Topics Covered in Talk

Error fields (n = 1 and n = 3)

Resistive wall modes

Non-resonant magnetic braking physics

NTM threshold physics

Improving <N>pulse with n = 1 and N feedback


n = 1 error field threshold for mode locking decreased as βN increased n = 1 rotating modes sometimes observed, study limited to static modes IPEC resonant field joins linear ne correlation from low-β to increased-β

Ideal plasma amplification of applied resonant field restores linear correlation of mode locking threshold with density

Lower-β locked later

(w/ larger RWM currents)

XP903:

J.-K. Park

Ide

al

Pla

sm

a A

mp

lifi

ca

tio

n

Higher-β locked earlier

(w/ smaller RWM currents)

vacuum

IPEC


Optimal n=3 Error Field Correction Determined vs. IP, BT

2009

2009

2009

“optimal” n = 3 error field correction attained by maximizing angular momentum, scanning Ip, Bt, elongation

n = 3 error field consistent with known equilibrium field coil distortion scales with equilibrium field coil current field phase and amplitude of correction is consistent with that expected from

coil distortion n = 3 error field correction routinely used to maximize plasma

performance in conjunction with n = 1 RWM feedback control NTV theoretical analysis performed by J-K Park for these cases

XP902: S. Gerhardt


ˆˆ2

3ˆˆ2

5**

deiil

iW

EeffbD

ETN

K

Resistive wall modes can terminate NSTX plasmas at intermediate plasma rotation levels without active control (no simple, scalar crit)

Kinetic modification to ideal MHD growth rate

Trapped and circulating ions, trapped electrons

Alfven dissipation at rational surfaces Stability depends on

Integrated profile: resonances in WK (e.g. ion precession drift)

Particle collisionalityTrapped ion component of WK (plasma integral)

Energy integral

Kb

Kw WW

WW

collisionality

profile (enters through ExB frequency)

Hu and Betti, Phys. Rev. Lett 93 (2004) 105002.

precession drift bounce

Modification of Ideal Stability by Kinetic theory (MISK code) investigated to explain experimental RWM stabilization


0.00 0.01 0.02 0.03 0.04Re(WK)

0.00

0.01

0.02

0.03

Im(

WK)

φ/φexpφ/φexpφ/φexpφ/φexpφ/φexpφ/φexpφ/φexpφ/φexpφ/φexpφ/φexpw

0.0

-0.2

-0.4

-0.60.20.40.60.81.01.2

80

60

40

20

0

[kH

z]

1.00.80.60.40.20.0

/a

/exp

= 0.2

exp

/exp

= 2.0

Kinetic modifications show decrease in RWM stability at relatively high V

Marginally stable experimental plasma reconstruction, rotation profile

exp

Variation of away from marginal profile increases stability

Unstable region at low Role of energetic particles now

under investigation (Berkery, et al.)

Theoretical variation of

Marginally stable

experimentalprofile

121083

RWM stability vs. V (contours of w)

/a

/exp

2.0

1.0

0.2

/

2 (

kHz)

Im(

WK)

Re(WK)

/exp

w

experiment

2.0

1.0

0.2

unstable

/exp

J.W. Berkery

NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 9January 6th, 2010 9

Channel of “Weak Rotation” for RWM passive stabilization observed in MISK calculations for NSTX; altered by plasma collisionality

Stabilization from precession drift resonance at low rotation and bounce resonance at high rotation

Stability dependence on collisionality key for ST fusion burn devices

w contours vs. ν and NSTX 121083

unstable

Marginal stability

experiment

J.W. Berkery (APS DPP 2009 invited talk; PRL accepted)


High N shots exhibit low frequency mode activity in magnetic and kinetic diagnostics

0

20

40

nano

amps

0

40

80

nano

amps

0

100

nano

amps

0

100

200

nano

amps

0

200

400

nano

amps

0100

200

300

nano

amps

0

200

400

nano

amps

0.4 0.6 0.8 1.0 1.2seconds

0

400

800

nano

amps

133775Shots:

133775

0.80.4 0.6 1.0 1.2t(s)

Multi-energy SXR data shows ~ 30 Hz mode activity

02

03

04

05

06

08

10

14

edge

core

0

4

8

-

0

200

ampe

res

0

4

8

km/s

ec

0.5

1.5

Tesl

a

0.0010

0.0030

0.0050

Tesl

a

0 0.2 0.4 0.6 0.8 1.0 1.2seconds

-40

0

40

nano

amps

133775Shots:

N

2

4

8

133775

0.80.4 0.6 1.0 1.2t(s)

0.20.0

IRWM-6 (kA)

0.2

0

048 /ch-18

(kHz)

Bpun=1(G)

BNn=1(G)

Ip = 0.8 MA

ME

-SX

Rlo

w-2

3050

10

0.5

1.5

Soft X-ray measurements show low frequency mode activity is global

Mode activity in RWM frequency range coincident in magnetics, SXR

n = 1 RWM feedback on

0

40

040

0100

0

200

0200

0200

0

400

0400

(arb

)

XP935: S.A. Sabbagh

When unstable, growing n = 1 RWM appears to be independent of ~30 Hz activity


RWM multimode response theoretically expected to be significant at high N based on ideal MHD theory

Boozer multimode criterion for n = 1 met at high N

|W| smallest for 2nd n = 1 eigenfunction Ratio of |W| for 3rd vs. 1st least stable mode sometimes also > 1

N

(PoP 10 (2003) 1458.)

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2

-20-10

01020

0.0 0.2 0.4 0.6 0.8 1.0 1.2

133775

mode 3

mode 1

mode 2

t(s)

W(arb)

no-wall stability DCON

0.2 0.80.4 0.60.0 1.0 1.2

-20

-10

0

10

0

2

4

6

0.0 0.2 0.4 0.6 0.8 1.0 1.2

|W|ratio

0

2

4

mode 1/mode 3

mode 1/mode 2

n = 1multimode

period

t = 0.655s

mode 1

mode 2

2.01.00.0 R(m)

1.0

-1.0

Z(m

)

2.0

0.0

-2.0

DCON BN

mode 3

(deg) 1800

BN(a

rb)

mode 1

mode 2

mode 3

133775

XP935: S.A. Sabbagh


Multi-mode VALEN code (RWM control) testing successfully on high N NSTX plasmas

mmVALEN to be used to examine response of 2nd mode to n = 1 feedback, error field and compare to experiment

RWM growth time vs. betaN 133775 - mmVALEN

0.000

0.005

0.010

0.015

0.020

0.025

5.0 5.5 6.0 6.5 7.0

NM

od

e g

row

th t

ime

(s)

N

Growth rate vs. # of modes – mmVALEN

133775

t = 0.655s

116 DCON modes

76 DCON modes

Typical growth

times (experiment)

J. Bialek


100 110 120 130 140 150r (cm)

-20

0

20

40

60

80

nq

E [kH

z], i/

[kH

z],1

/2

ti [

kH

z]

0123456

0

200

400

600

800

05

10152025

0

5

10

15

20

0.5 0.55 0.60 0.65 0.70 0.75 0.80 0.85sec

02468

10

Stronger braking with constant n = 3 applied field as E reduced – accessing superbanana plateau NTV regime

XP933: S.A. Sabbagh

133367

t = 0.815 s

i = 1

nqE

i/(kH

z)

Torque not 1/(non-resonant) NTV in “1/ regime” (|nqE| < i/ and *i < 1) Stronger braking expected when E ~ 0 (superbanana plateau) (K.C. Shaing et al., PPFC 51

(2009)) – theoretical analysis continues (Sabbagh)

E ~ 0

/

2 (

kHz)

20

15

10

5

0

1.0 1.1 1.2 1.3 1.4 1.5R(m)

t(s)

0.795

0.805

0.815

N

4

Ic (kA)

2

/ch-5 (kHz)

/ch-12 (kHz)

/ch-18 (kHz)

core

mid

outer

6

0

0.4

0.020

100

20

10

0

8

400.5 0.6 0.7 0.8

Faster braking with Constant N, applied n = 3 field No mode activity

t (s) 40

0

Broad, near zero

WITHOUT rational surface locking

n = 3 braking

80


Consistent pre-2009 DIII–D/NSTX results on m/n = 2/1 NTM marginal island width for stability; good restabilization data sets in 2009

Wmarg/0.5i ratio ~ 2 in tokamaks

AUG, DIII-D, JET data for 3/2 mode

First results show Wmarg/0.5i also ~ 2 for NSTX (2/1 mode) (!)

NSTX XP914: R. LaHaye

Pre-2009 2009 data

Status: DIII-D Used gas puff to stay in H-mode 5 good 2/1 (and 2 good 3/1) cases

Status: NSTX Achieved a reproducible onset condition

using modest Li evaporation 8 good cases (2009)


Required (missing) bootstrap drive for NTM onset better correlated with rotation shear than rotation magnitude

Rotation variation via n = 1 or 3 applied field

Operational space fully spanned up to locked mode limits

No measureable trend vs. rotation

Weak positive correlation with normalized rotation shear

Lowest/highest thresholds at low/high rotation shear

2d fit vs rotation & rotation shear offers little improvement

Consistent with prior results (S.P. Gerhardt, et al., 2008)

0L

qj

BS

,Sau

ter/B

0

Lqj

BS

,Sau

ter/B

(dF/dr) ALS

F2/1 Hz

XP915: R. Buttery


Successful N feedback at varied plasma rotation levels

Prelude to control Reduced by

n = 3 braking does not defeat FB control

Increased PNBI needed at lower

Steady N established over long pulse independent of

over a large range

0

2

4

6

-

0

2.0

4.0

6.0

MW

-600

-200

200

600

ampe

res

0

4

8

12

km/s

ec

0

10

20

km/s

ec

0 0.2 0.4 0.6 0.8 1.0 1.2Seconds

-10

0

10

Gau

ss

135468135513

Shots:

135468135513

0.80.4 0.6 1.0 1.2t(s)

0.20.0

N

24

6

I RW

M-6 (

kA) 0.6

0

246

-0.6

PN

BI (

MW

)

/ c

h-1

8

(kH

z)

/ c

h-5

(kH

z)

48

10

20

10

n = 3 error correctingphasing

n = 3 brakingphasing

n = 1 feedback

XP934: S.A. SabbaghS.A. Sabbagh, S. Gerhardt, D. Mastrovito, D. Gates

0


NSTX Macrostability Research – Interaction with Theory

Error fields (n = 1 and n = 3) IPEC used successful to support experiment; continue IPEC development,

including interface of ideal plasma response to other analyses (Park, Boozer) Resistive wall modes

MISK development continues (CU, U. Rochester, PPPL), present focus on energetic particle description, comparison to experiment (Berkery, et al.)

Multi-mode RWM analysis with new mmVALEN code (Bialek, Boozer), comparison to experiment (Sabbagh)

Non-resonant magnetic braking physics Continued development of MHD models (CU, PPPL, UW), working from Shaing

model (Sabbagh), Park/Boozer model (Park), etc. (e.g. Cole, et al.) Work aimed for comparison to particle codes (GTC-Neo (Wang), FORTEC-3D

(Satake)) should continue NTM threshold physics

Mostly empirical, or simple MRE assumptions to date, largest gap in theory support here (linear – computation of ’ (PEST 3), non-linear codes ?)

Improving <N>pulse with n = 1 and N feedback, general RMPs Multi-faceted, including beta, rotation control (Gerhardt, Koleman), RWM

control optimization (Hopkins, et al.), ideal, RWM, NTM, ELM stability theory


Backup Slides


NSTX Macrostability Research in 2009 is Addressing Topics Furthering Steady Operation of High Performance Plasmas

Ideal plasma amplification of applied n = 1 resonant field (IPEC) joins linear density scaling of mode locking threshold from low to moderate-β

Optimal n=3 error field correction determined vs. IP, BT

RWM instability, observed at intermediate plasma rotation, correlates with kinetic stability theory; role of energetic particles under study

Low frequency ~ O(1/wall) mode activity at high N being investigated as potential driven RWM

Theory shows multi-mode RWM response may be important at high N; multi-mode VALEN code now passing initial tests

Strong non-resonant braking observed NTV braking observed from all i/nqE(R) variations made; apparent transitions in NTV at low

Expanded NTM onset experiments continue to find best correlation between NTM onset drive and flow shear

Successful NBI power limitation via new N feedback control system; initial success in regulation of N at varied plasma rotation levels


0

0.4

0.8

ampe

res

2

4

6

-

-600

-200

200

ampe

res

0

4

8

km/se

c

0

10

20

30

km/se

c

2

6

Tesl

a

0.0010

0.0030

0.0050

Tesl

a

0 0.2 0.4 0.6 0.8Seconds

0.0002

0.0006

0.0010

Tesl

a

133467Shots:

When unstable, observed growing n = 1 RWM appears to be independent of the driven, ~30 Hz activity

Unstable RWM is locked; driven mode co-rotating at low frequency Unstable RWM grows (magnetics); low frequency mode appears steady in SXR

2

4

6

-

2

6

Tesl

a

0

20

40

nano

amps

0

40

nano

amps

0

40

80

nano

amps

0

100

200

nano

amps

0

100

200

nano

amps

0

200

nano

amps

0.6 0.65 0.70 0.75 0.80 0.85seconds

200

600

1000na

noam

ps

133467Shots:

02

03

04

06

08

10

14

high-f mode

core133467

edge

N4

0.40.8

IRWM-6 (kA)

0.2

2

10

84

/ch-18 (kHz)

Bpun=1(G)

BNn=1(G)

3050

10

200

IP (MA)

/ch-5 (kHz)

6

2

-0.2-0.6

6

2

6

100

BRun=1(G)

133467

0.20.0 0.4t(s)

0.8t(s)

0.6 0.650.6 0.7 0.80.75 0.85

N46

2BN

n=1(G)26

ME

-SX

Rlo

w

unstable RWMn = 3 braking

unstable RWM


Multi-mode VALEN code (RWM control) testing successfully on ITER Scenario 4 cases (reversed shear)

At highest N, n =1 and 2 are unstable

N

Number of modes (VALEN)

Gro

wth

rat

e (1

/s)

Growth time vs. betaN - ITER Scen 4

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

2 2.5 3 3.5 4

Mo

de

gro

wth

tim

e (s

)

single-mode

matched to N

wall

multi-mode

VALEN

(converged)

DCON W shows several modes with high response Three n = 1 modes at high N

Two n = 2 modes at high N

n = 1

J. Bialek


Illustration of Bn() on plasma surface from mmVALEN for ITER Scenario 4, N = 3.92

n = 1 eigenfunctions shown

multi mode response (incl. wall), total Bn

Bn from wall, plasma

Bn from wall alone

toroidal

toroidal

po

loid

alpo

loid

al

outboard

inboard

inboardoutboard

inboard

inboard

J. Bialek


Illustration of Bn() on plasma surface from mmVALEN for NSTX shot 133775 (t=0.655s)

single mode response, total Bn

multi mode response, total Bn

Bn from wall, multi mode response

Bn from wall, multi mode response

toroidal

toroidal

toroidal

po

loid

al

po

loid

alp

olo

idal

J. Bialek

outboard

inboard

inboard

outboard

inboard

inboard

outboard

inboard

inboard

Macroscopic Stability Research on NSTX – Results and Theory Interaction S.A. Sabbagh 1, S.P....

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Transcript of Macroscopic Stability Research on NSTX – Results and Theory Interaction S.A. Sabbagh 1, S.P....