Two-Dimensional Analysis of Transport Phenomena in Tokamak Plasmas

1. 我们发展了托卡马克等离子体中新古典输运的二维公式。与传统的新古典输运分析通过通量-表面平均得到径向输运方程不同，我们推导出了保持极向角依赖的粒子和热通量。从多流体方程出发，分别用平行力平衡法计算极向输运通量，用环向力平衡法计算径向输运通量。将这些通量代入连续性方程，得到一个二维输运方程系统。采用傅里叶展开法在极向方向和有限差分法在径向方向对二维输运方程进行了数值求解。我们估计了输运通量的极向角依赖关系，并通过二维输运代码（TASK/T2）进行了定量分析。为了分析外围等离子体的行为，我们开发了一个二维有限元传输代码（TASK/TF）。基于通量坐标网格，采用全隐式方法研究了SOL等离子体的时间演化，并验证了稳定计算的正确性。本项目提供的四台计算机通过1Gbps以太网连接，使用MPI消息传递库修改二维码进行并行计算。提出了一种在计算机集群上直接求解带矩阵的新算法。

1. We have developed two-dimensional formulation of neoclassical transport in tokamak plasmas. In contrast to the conventional neoclassical transport analysis that leads to radial transport equations by means of flux-surface average, we have derived particle and heat fluxes keeping poloidal angle dependence. Starting from multi-fluid equation, we calculate poloidal transport flux from parallel force balance and radial one from toroidal force balance. Substituting these fluxes into continuity equations, we obtain a system of two-dimensional transport equations.2. The two-dimensional transport equation was solved numerically by Fourier expansion in poloidal direction and finite difference method in radial direction. We have estimated the poloidal angle dependence of the transport fluxes and carried out quantitative analysis by the two-dimensional transport code (TASK/T2).3. In order analyze the behavior of peripheral plasmas, we have developed a two-dimensional finite-element transport code (TASK/TF). Based on the flux coordinate mesh, time evolution of a SOL plasma was studied by full implicit method and stable computation was confirmed.4. The four computers provided by this project are connected through 1Gbps Ethernet and two-dimensional codes are modified for parallel computing with MPI message-passing library. A new algorithm to solve a band matrix directly on a computer cluster was also developed.