1. Kinetic MHD Simulation in Tokamaks H. Naitou, J.-N. Leboeuf †, H. Nagahara, T. Kobayashi, M. Yagi ‡, T. Matsumoto*, S. Tokuda* Joint Meeting of US-Japan JIFT Workshop on Theory-Based Modeling and Integrated Simulation of Burning Plasmas and 21COE Workshop on Plasma Theory ------Kyodai-Kaikan, Kyoto, 2003/12/15-17 ------ Yamaguchi University † University of California at Los Angeles ‡ Kyushu University *Japan Atomic Energy Research Institute

2. Key Words Sawtooth Crash m=1/n=1 Internal Kink Mode Kinetic MHD Model Collisionless Magnetic Reconnection Diamagnetic Effects Sheared Poloidal Flow of m=1 Kelvin-Helmholtz (K-H) Instability Vortex Generation

3. Outline 1.Motivations 2.Basic Equations 3.Results of Cylindrical Code (a) Linear Calculations (b) Nonlinear Calculations 4.Toroidal Code (Kinetic-FAR) 5.Summary

4. 1. Motivation There is no complete theory to explain the sawteeth phenomena in tokamaks without inconsistency. Resistive MHD model is not appropriate. Kinetic MHD model can elucidate (a) fast sawtooth crash. (b) nonlinear acceleration of the growth rate. (c) diamagnetic stabilization.

5. Gyrokinetic particle simulation and gyro- reduced-MHD (GRM) simulation have revealed the fast full reconnection followed by the second phase of axis q-value less than unity. Linear and nonlinear studies by GRM code. ……… Summarized in this presentation. The vortex generation by K-H instability can be a critical issue for the complete understandings of the sawtooth crash.

6. 2. Basic Equations

7. Safety factor profile : Equilibrium density profile: Key Parameters: Assumption : Single Helicity d e / a,  s / a,  n m / n = 1 r 0 /a = 0.5, l n /a = 0.16

8. (a) Linear Calculations 3. Results of Cylindrical Model

9. d e /a = 0.0005315,  s /a = 0.002891, 1/  0 = 417  sec Electron Diamagnetic Stabilization of Kinetic Internal Kink Mode

10. Mode Structure in r-   * e /  0 = 1.48 (theoretically unstable)

11. Mode Structure in r-   * e /  0 = 1.98 (theoretically close to marginal point)

12. Electron and Ion Diamagnetic Effects d e /a = 0.0005315,  s /a = 0.002891, T i /T e = 1.0, 1/  0 = 340  sec

13. Mode Structure in r-  A B

14. (b) Nonlinear Calculations d e = 0.01,  s = 0.03 Linear Growth Rate

16. Linear Mode Pattern Movie of Vortex Generation

17. Magnetic Field Structure

19. 4. Toroidal Code (Kinetic-FAR) Kinetic terms are included. Can treat realistic equilibrium with shaping, finite beta, and curvature. Can directly compare resistive MHD with kinetic MHD. Two approaches based on resistive FAR (R-FAR) code and turbulent FAR (K-FAR) code. Made cylindrical by keeping only m=0 and n=0 component in Grad-Shafranov toroidal equilibrium and switching off toroidal terms ( e.g. curvature ).

20. Comparison between GRM and K-FAR cylindrical model d e = 0.01,  s = 0.03

21. Comparison Between GRM and T-FAR GRM   r  T-FAR   r   z )

22. Comparison Between R-FAR and T-FAR K-FAR   r  T-FAR   r   z )

23. RSTEQ Toroidal Equilibrium  =9.8x10 -3  =a/R=1/3

24. Comparison between Toroidal and Cylindrical Cases d e = 0.01,  s = 0.03 Preliminary

25. 5. Summary We believe that vortex generation due to K-H instability has critical effects on the nonlinear developments of kinetic internal kink modes. Comparison with K-H theory is underway. ------------ growth rate, threshold, etc. Effects of vortex generation may be important for the complete understandings of sawtooth crash phenomena. Kinetic modifications of FAR code are underway to tackle these issues.