Analysis of Transport Phenomena by a Three-Dimensional Fokker-Planck Code

为了用速度分布函数描述托卡马克等离子体中的输运现象，建立了一个漂移动力学公式来推导耦合的三维福克-普朗克方程。将三维福克-普朗克数值编码扩展到包括库仑碰撞和电磁波动引起的空间扩散。从漂移轨道的分析出发，解析计算了由于库仑碰撞或波粒相互作用引起的速度修正所引起的特征半径的变化。Fokker-Planck方程中的速度扩散项、空间扩散项和交叉项由碰撞项导出。无碰撞漂移轨道的周期性使我们能够对分布函数进行傅里叶展开。本文首次纳入了分布的极向角依赖性。利用反射平均三维福克-普朗克代码研究了射频波的加热和电流驱动。考虑了快电子的空间扩散，得到了驱动电流的径向分布和电流驱动效率。采用全隐式方法，极大地提高了三维福克-普朗克码的数值稳定性。射频电流驱动的输入功率上限比可选的定向隐式方法要大得多。

In order to describe the transport phenomena in a tokamak plasma in terms of the velocity distribution function, a drift-kinetic formulation has been developed to derive coupled three-dimensional Fokker-Planck equations. The three-dimensional Fokker-Planck numerical code has been extended to include the spatial diffusion due to Coulomb collisions and electromagnetic fluctuations.1. From the analysis of the drift orbit, the change of characteristic radius due to the velocity modification through Coulomb collision or wave-particle interaction has been analytically calculated. The velocity diffusion term, the spatial diffusion term and the cross terms in the Fokker-Planck equation are derived from the collision term. The periodicity of the collisionless drift orbit enables us to Fourier-expand the distribution function. Poloidal angle dependence of the distribution has been included for the first time.2. The bounce-averaged three-dimensional Fokker-Planck code has been employed to study the heating and current drive by the RF waves. Taking account of the spatial diffusion of the fast electrons, the radial profile of the driven current as well as the current drive efficiency have been obtained.3. By employing the full implicit method, the numerical stability of the three-dimensional Fokker-Planck code has been drastically improved. The upper-limit of the input power in the RF current drive is much enlarged compared with the alternative directional implicit method.