Supported by Influence of kinetic effects on ballooning

Supported by Influence of kinetic effects on ballooning stability in NSTX –KO 1. 003 J. Manickam, C. Kessel and J. Menard Princeton Plasma Physics Laboratory Special thanks to R. Maingi, ORNL and S. Sabbagh, Columbia U. 45 th Annual Meeting of Division of Plasma Physics American Physical Society October 27 – 31, 2003 Albuquerque, New Mexico Columbia U Comp-X General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics NYU ORNL PPPL PSI SNL UC Davis UC Irvine UCLA UCSD U Maryland U New Mexico U Rochester U Washington U Wisconsin Culham Sci Ctr Hiroshima U HIST Kyushu Tokai U Niigata U Tsukuba U U Tokyo JAERI Ioffe Inst TRINITI KBSI KAIST ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching U Quebec

OUTLINE Motivation: b-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 KO 1. 003

Theory model – I finite-n corrections Solve ballooning equation for the growth-rate, g(q, qk) Dewar et al. Princeton Plasma Physics Report PPPL-1587 (1979) qk q . 2 ath n p r o tou grati n Co inte for BALMSC g=0 qk n 0 g=gmax -. 2 0. 5 Y(q)/ymax 0. 8 ncrit 0 0 g KO 1. 003

Theory model – I finite-n corrections Vary g and compute ncrit vs. g qk q . 2 100 BALMSC g=0 =0. 25 gmax =0. 75 gmax =gmax qk 0 -. 2 0. 5 Y(q)/ymax 0. 8 Single fluid Ideal MHD unstable n 0 0 g KO 1. 003

Theory model – II Ion diamagnetic drift stabilization Kinetic dispersion relation . 4* L Single fluid Ideal MHD unstable p Kinetically stabilized n 34 n Tang et al. Nuc. Fusion Vol. 22 (1982) Unstable band in n 0 0 g Lp = p/p’ Determines kinetic stabilization KO 1. 003

=9 p L • High-b 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 ~ 9 m • Observed values of Lp ~ 5 m m Kinetic considerations provide a bigger window of stability 5 m = Lp Optimized high-b case, bn=8, is stable when kinetics are included KO 1. 003

Ballooning mode analysis of NSTX • Survey of NSTX discharges with significant beta, bn>3, long flat-top, >150 ms, 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 KO 1. 003

There is a correlation of b-saturation with ballooning instability, when ncrit <20 bn vs. t Lpmax vs. t ncrit vs. g Note that kinetic effects do not provide complete stabilization KO 1. 003

In some cases b-saturation has no correlation with ballooning stability but may be due to confinement limits 108473 bn vs. t Lpmax vs. t ncrit vs. g KO 1. 003

In some cases b rises even when ballooning stability is violated – (108018 -ELMy) bn vs. t ncrit vs. t Lpmax vs. t ncrit vs. g kinetic effects do not provide complete stabilization KO 1. 003

There is no clear correlation of the giant ELM with ballooning stability bn vs. t Lpmax vs. t ncrit vs. g KO 1. 003

Discussion • We have established a procedure for studying ballooning modes, including kinetic effects • Ballooning stability at bn>8 is attainable with optimized profiles • Analysis of experimental data shows a qualitative correlation between b-saturation and ballooning instability with n-crit< 20 • Counter-examples of b 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 KO 1. 003