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 Mo deling and Integrated Simulation of Burning Plasmas and 21 COE 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
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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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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
1. Motivations2. Basic Equations3. 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
ezee
zes
ze
z
z
nDAbnbt
n
Anba
Adt
d
a
dbA
t
DAbbt
22*
22*2
22
*
222*22
)(
)( )(
)( )( )(
⊥⊥
⊥⊥⊥
⊥⊥⊥⊥⊥
∇+∇∇⋅−∇⋅φ∇×−=∂∂
∇∇μ−∇⋅⎟⎠
⎞⎜⎝
⎛ρ+∇⎟
⎠
⎞⎜⎝
⎛+φ∇⋅−=∂∂
φ∇∇+∇∇⋅−φ∇∇⋅φ∇×−=φ∇∂∂
∇⋅φ∇×+∂∂
=
×∇+=
) (
*
btdt
d
bAbb z
Safety factor profile :
Equilibrium density profile:
Key Parameters:
Assumption : Single Helicity
12
0 0 ) 1( 4 1 )(
−
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛−−= arqqrq
,85.00=q 125.2)( =aq
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −ε−=n
nlrrnrn 0
0 tanh 1 )(
,0.1)5.0( =aq
de / a, ρs / a, εn
m / n = 1
r0/a = 0.5, ln/a = 0.16
(a) Linear Calculations
3. Results of Cylindrical Model
de/a = 0.0005315, ρs/a = 0.002891, 1/0 = 417μsec
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)