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.

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Presentation transcript:

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/ Yamaguchi University † University of California at Los Angeles ‡ Kyushu University *Japan Atomic Energy Research Institute

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

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

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.

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.

2. Basic Equations

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

(a) Linear Calculations 3. Results of Cylindrical Model

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

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

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

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

Mode Structure in r-  A B

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

Linear Mode Pattern Movie of Vortex Generation

Magnetic Field Structure

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 ).

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

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

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

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

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

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.