Two-Dimensional Analysis of Transport Phenomena in Tokamak Plasmas

1.建立了托卡马克等离子体中新经典输运的二维公式。与传统的新经典输运分析通过通量-表面平均法导出径向输运方程不同，我们得到了与极向角相关的粒子通量和热通量。从多流体方程出发，分别用平行力平衡和环向力平衡计算极向输运通量。将这些通量代入连续性方程，得到了二维输运方程组。采用极向傅立叶展开和径向有限差分方法对二维输运方程进行数值求解。利用二维输运程序(TASK/T2)估算了输运通量的极向角依赖关系，并进行了定量分析。为了分析外周等离子体的行为，我们开发了一个二维有限元输运程序(TASK/TF)。在通量坐标网格的基础上，采用全隐式方法研究了Sol等离子体的时间演化过程，得到了稳定的计算结果。该项目提供的四台计算机通过1Gbps以太网连接，并利用MPI消息传递库对二维码进行修改以进行并行计算。还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.