反场构型等离子体中Grad-Shafranov方程的数值解

Numerical solutions of Grad-Shafranov equation in a field-reversed configuration

基于反场构型(field-reversed configuration)渐近理论,编写了反场构型等离子体中二维Grad-Shafranov方程的数值模拟代码,研究了不同拉长形状的反场构型剖面.通过模拟,得到了磁面坐标系中反场构型等离子体压强及梯度分布,同时求解了大拉长比、不同分界面(separatrix)类型的磁通量分布.研究结果表明,等离子体压强梯度随着磁通量呈线性增长,在分界面处发生突变;分界面处的等离子体压强越高,分界面内部的压强会更高,即具有更高的等离子体β值,反映了反场构型较好的约束效果.

The solution of Grad-Shafranov equation in field-reversed configuration（FRC） is a basic problem.The solution of Grad-Shafranov equation can help to understand most of physical processes in FRC plasma,such as magnetohydrodynamic（MHD） instabilities and plasma transport.In the present paper,based on the FRC asymptotic theory by Barnes D C,the code for solving the two-dimensional Grad-Shafranov equation in FRC is developed.By using the code,the equilibriums of FRC with different elongations and separatrix radii are investigated in the present paper.The one-dimensional numerical results show that the plasma density gradient increases linearly with magnetic flux increasing in the FRC center,while,it steepens due to the high magnetic field distribution at the separatrix.The results also show that the plasma density in the closed field region increases with the density at the separatrix increasing,which implies that FRC embodies the strong confinement ability.It is a key problem to choose equations determining the shape of the separatrix in a two-dimensional numerical investigation.In the present paper,the shape equation is described as rs=rs max（1- z^2a）,in which a is the shaping parameter.When a=1,the separatrix shape is elliptical,and when a〉 1,the separatrix shape is like a racetrack.The geometry character of the separatrix appears in the one-order equations（in one-order equations： ψ0/ z=（ ψ0/ rs）（ rs/ z）,where ψ0/ rs is determined by lead equations and rs/ z is given by separatrix equation）.The two-dimensional numerical results show that O-point moves outward as the sparatrix radius increases.The curvature radius of magnetic flux surface increases with the separatrix radius increasing.The O-point of magnetic flux surface is just at the curvature center.Thus O-point moves outward as the sparatrix radius increases.