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

用三维福克-普朗克码分析输运现象

• 批准号: 03808001
• 负责人: FUKUYAMA Atsushi
• 金额: $ 1.28万
• 依托单位: Okayama University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1991
• 资助国家: 日本
• 起止时间: 1991 至 1992
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-03808001/
• 关键词: Plasma; Transport Phenomena; Fokker-Planck Equation; Coulomb Collision; Neoclassical Transport; Turbulent Transport; ク-ロン衝突

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.

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，发展了漂移-动力学方程，导出了耦合的三维Fokker-Planck方程。三维Fokker-Planck数值程序已经扩展到包括由于库仑碰撞和电磁涨落引起的空间扩散。从漂移轨道的分析出发，解析地计算了库仑碰撞或波粒相互作用引起的速度修正引起的特征半径的变化。由碰撞项导出了Fokker-Planck方程中的速度扩散项、空间扩散项和交叉项。无碰撞漂移轨道的周期性使我们能够对分布函数进行傅立叶展开。首次考虑了极向角对分布的影响.采用反弹平均三维福克-普朗克程序研究了射频波的加热和电流驱动。考虑到快电子的空间扩散，得到了驱动电流的径向分布和电流驱动效率.通过采用全隐式方法，三维Fokker-Planck程序的数值稳定性得到了显著改善。与交替方向隐式法相比，射频电流驱动法的输入功率上限大大提高。