1. 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 Influence of kinetic effects on ballooning stability in NSTX –KO 1.003 Supported by 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

2. 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

3. KO1.003 Theory model – I finite-n corrections Solve ballooning equation for the growth-rate,  q  k ) Dewar et al. Princeton Plasma Physics Report PPPL-1587 (1979)  q  max kk 0.80.5 0.2 -.2   n   BALMSC kk n crit q   max Contour path for integration

4. KO1.003 Theory model – I finite-n corrections  q  max kk 0.80.5 0.2 -.2   max  max  max  max BALMSC kk  n    Single fluid Ideal MHD unstable q Vary  and compute n crit vs. 

5. KO1.003 Theory model – II Ion diamagnetic drift stabilization L p = p/p’ Determines kinetic stabilization Kinetic dispersion relation  n  Single fluid Ideal MHD unstable n   Unstable band in n Kinetically stabilized 34.4*L p Tang et al. Nuc. Fusion Vol. 22 (1982)

6. 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 n crit = 50 The mode would be stabilized by kinetic effects, unless, L p ~ 9m Observed values of L p ~ 5m L p =5m

7. 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

8. KO1.003 There is a correlation of  saturation with ballooning instability, when  n crit <20 Note that kinetic effects do not provide complete stabilization  n vs. t L p max vs. t n crit vs. t n crit vs. 

9. KO1.003 In some cases  saturation has no correlation with ballooning stability but may be due to confinement limits 108473  n vs. t L p max vs. t n crit vs. t n crit vs. 

10. KO1.003 In some cases  rises even when ballooning stability is violated – (108018-ELMy)  n vs. t L p max vs. t n crit vs. t n crit vs.  kinetic effects do not provide complete stabilization

11. KO1.003 There is no clear correlation of the giant ELM with ballooning stability  n vs. t L p max vs. t n crit vs. t n crit vs. 

12. 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