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.
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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.
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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