用二维含时Fokker-Planck方程分析Tokamak中α粒子的输运

ANALYSIS OF THE α PARTICLE TRANSPORT IN TOKAMAKS BY THE TWO-DIMENSIONAL TIME-DEPENDENT FOKKER-PLANCK EQUATION

按分布函数的定义不同,描述高能带电粒子在等离子体中输运的 Fokker-Planck 方程有不同的形式。从数值计算的观点出发对两种不同形式的 Fokker-Planck 方程作了比较和评价,并指出Fokker-Planck 碰撞项可解释为速度空间的对流扩散项。在此基础上用有限差分方法求解二维(速度一维,几何一维)含时 Fokker-Planck 方程,编制了计算程序 CAPT,并将其应用于α粒子的输运研究。最后计算了典型的 Tokamak D-T 聚变堆参数下α粒子的损失,并给出了堆内α粒子的分布及损失α粒子的速度分布。

For different definitions of the distribution function,there are different forms of Fokker- Planck equation to describe the energetic charged particles transport in plasma.The different forms of Fokker-Planck eqation have been compared and evaluated from the viewpoint of numerical calculation,and it is indicated that the Fokker-Planck collision term can be interpreted as the convection diffusion term in the velocity space.Based upon this,a code,CAPT,has been made to solve the two-dimensional(space and velocity)time-dependent Fokker-Planck equation by difference method,and it is applied to study the alpha particles transport problem.The loss of alpha particles has been calculated for a typical Tokamak D- T fusion reactor,and the core alpha particles distribution and the lost alpha particles velocity distribution have also been shown.