Vacuum solution for Solov'ev's equilibrium configuration in tokamaks

Nuclear Fushion

article

Tao Xu¹  Richard Fitzpatrick¹ 

[1] Department of Physics, Institute for Fusion Studies, University of Texas at Austin;Institute of Fusion and Plasma Research, College of Electrical and Electronic Engineering, Huazhong University of Science and Technology

关键词: plasma equilibrium;    Grad–Shafranov equation;    homogeneous solution;   

DOI  :  10.1088/1741-4326/ab1ce3

来源: Institute of Physics Publishing Ltd.

【 摘 要 】

In this work, we construct a tokamak plasma equilibrium generated by a combination of currents flowing within the plasma and in distant external magnetic field coils. The plasma toroidal current density takes the simple form inside the plasma (whererandzare cylindrical coordinates, anda ,b , andRare constants), and is zero in the surrounding vacuum. The Grad–Shafranov equation possesses a well-known exact analytic solution within the plasma due to Solov'ev. We use a Green's function method to compute the poloidal magnetic flux generated by plasma currents, together with a parameterized homogeneous solution to the Grad–Shafranov equation (that is well-behaved at smallrandz ), to construct the vacuum solution. The vacuum solution is matched to the analytic solution on the last closed magnetic flux surface (LCFS) to determine the parameters in the homogeneous solution. This procedure is performed for both up–down-symmetric double-null and up–down-asymmetric single-null equilibria. We find that any magnetic X-points on the LCFS are distorted due to the fact that one quadrant is filled by a current-carrying plasma, whereas the other three are filled by a vacuum in which no current flows. In particular, the vacuum quadrant opposite the plasma-filled quadrant expands at the expense of the other three quadrants.

【 授权许可】

Unknown