关键词: 反场构型/
Grad-Shafranov方程/
分界面/
拉长比
English Abstract
Numerical solutions of Grad-Shafranov equation in a field-reversed configuration
Zhao Xiao-Ming,Sun Qi-Zhi,
Fang Dong-Fan,
Jia Yue-Song,
Liu Zheng-Fen,
Sun Cheng-Wei
1.Key Laboratory of Pulse Power, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621999, China
Fund Project:Project supported by the Research Program of Center for Fusion Energy Science and Technology, China Academy Engineering Physics (Grant No. J2014-0401-02) and the National Natural Science Foundation of China (Grant No. 11375163).Received Date:19 April 2016
Accepted Date:30 June 2016
Published Online:05 September 2016
Abstract: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 - z2a), in which a is the shaping parameter. When a=1, the separatrix shape is elliptical, and when a1, the separatrix shape is like a racetrack. The geometry character of the separatrix appears in the one-order equations (in one-order equations: (0)/(z) = (0)/(rs)(rs)/(z), where (0)/(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.
Keywords: field-reversed configuration/
Grad-Shafranov equation/
separatrix/
elongation
