J. Manickam, C. Kessel and J. Menard

Princeton Plasma Physics LaboratorySpecial thanks to

R. Maingi, ORNL and S. Sabbagh, Columbia U.

45th Annual Meeting of Division of Plasma PhysicsAmerican Physical Society

October 27 – 31, 2003Albuquerque, New Mexico

Influence of kinetic effects on ballooning stability in NSTX –KO 1.003

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

KO1.003

OUTLINE

Motivation:-optimization requires stability to low-n kink-ballooning and high-n, ballooning modes. Kinetic considerations could stabilize the high-n ballooning modes and provide a larger window of stability

• Theory model– Finite-n corrections, kinetic effects

• Application to optimized high beta studies• Relevance of ballooning modes in NSTX

– Analysis of experimental data

• Discussion

KO1.003

Theory model – Ifinite-n corrections

Solve ballooning equation for the growth-rate, qk)Dewar et al. Princeton Plasma Physics Report PPPL-1587 (1979)

qmax

k

0.80.5

0

.2

-.2

n

BALMSC

k

ncrit

q

nncrit

range Unstable

max

Contour path

for integratio

n

kdqcritn

)( 2

KO1.003

Theory model – Ifinite-n corrections

qmax

k

0.80.5

0

.2

-.2

max

max

max

max

BALMSC

k

n

Single fluid Ideal MHDunstable

q

kdqcritn

)( 2

Vary and compute ncrit vs.

KO1.003

Theory model – IIIon diamagnetic drift stabilization

Lp = p/p’ Determines kinetic stabilization

**4.34)

)1(2

'(

4- 22

2

pi*2

pcrit

i

e

pi

Ln

T

Tcp

n

Kinetic dispersion relation

n

Single fluid Ideal MHDunstable n

Unstable band in n

Kineticallystabilized

34.4

*Lp

Tang et al. Nuc. Fusion Vol. 22 (1982)

KO1.003

Kinetic considerations provide a bigger window of stability

Optimized high- case,n=8, is stable when kinetics are included

L p =

9m

• High- kink optimized case,(with wall), is unstable to infinite-n ballooning

• Finite-n corrections predict ncrit = 50

• The mode would be stabilized by kinetic effects, unless, Lp ~ 9m

• Observed values of Lp ~ 5m L p=5m

KO1.003

Ballooning mode analysis of NSTX

• Survey of NSTX discharges with significant beta, n>3, long flat-top, >150ms, and a variety of ELM behaviours

– Double-null, frequent ELMs

– Lower single-null, sporadic or no ELMs

– Giant ELMs

• Multiple time slices, every 6 ms.

• EFIT equilibrium reconstruction including kinetic data

• No direct measurement of q

• No consideration of rotation

KO1.003

There is a correlation of saturation with ballooning instability, whenncrit <20

Note that kinetic effects do not provide complete

stabilization

n vs. t Lpmax vs. t

ncrit vs. t ncrit vs.

KO1.003

In some cases saturation has no correlation with ballooning stability but may be due to confinement limits

108473

n vs. t Lpmax vs. t

ncrit vs. t ncrit vs.

KO1.003

In some cases rises even when ballooning stability is violated – (108018-ELMy)

n vs. t Lpmax vs. t

ncrit vs. t ncrit vs. kinetic effects do not provide complete stabilization

KO1.003

There is no clear correlation of the giant ELM with ballooning stability

n vs. t Lpmax vs. t

ncrit vs. t

ncrit vs.

KO1.003

Discussion

• We have established a procedure for studying ballooning modes, including kinetic effects

• Ballooning stability at n>8 is attainable with optimized profiles• Analysis of experimental data shows a qualitative correlation

between -saturation and ballooning instability with n-crit< 20• Counter-examples of rising in the presence of ballooning

instability, have been observed• Uncertainty in the shear of the q-profile, is a major limitation in

this study • Additional issues that need consideration

– Role of rotation– Correlation with micro-stability and confinement