A coordinate transformation technique between straight magnetic field line coordinate system (Ψ, θ) and Cartesian coordinate system (R, Z) is presented employing a Solov'ev solution of the Grad‐Shafranov equation. Employing the equilibrium solution, the poloidal magnetic flux Ψ(R, Z) of a diverted tokamak, magnetic field line equation is solved computationally to find curves of constant poloidal angle θ, which provides us with explicit relations R = R(Ψ, θ) and Z = Z(Ψ, θ). Correspondingly, conversion from one coordinate to the other along particle trajectories in the vicinity of separatrix is demonstrated. Based on the magnetic structure, a finite element mesh is generated in a diverted tokamak geometry to solve Poisson's equation.

中文翻译：

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转向托卡马克几何中有限元网格的坐标变换和构造

提出了一种利用Grad-Shafranov方程的Solov'ev解在直磁场线坐标系（Ψ，θ）和笛卡尔坐标系（R，Z）之间进行坐标转换的技术。利用平衡解，通过计算求解转向的托卡马克磁场线方程的极向磁通量Ψ（R，Z），以找到恒定极向角θ的曲线，从而为我们提供了显式关系R  =  R（Ψ，θ）和ž  =  ž（Ψ，θ）。相应地，说明了在分离线附近沿粒子轨迹从一个坐标向另一坐标的转换。基于磁性结构，以转向的托卡马克几何形状生成有限元网格，以求解泊松方程。