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Coordinate transformation and construction of finite element mesh in a diverted tokamak geometry
Contributions to Plasma Physics ( IF 1.3 ) Pub Date : 2020-01-28 , DOI: 10.1002/ctpp.201900145 Y. Nishimura, J.C. Lyu, F.L. Waelbroeck, L.J. Zheng, C.E. Michoski
Contributions to Plasma Physics ( IF 1.3 ) Pub Date : 2020-01-28 , DOI: 10.1002/ctpp.201900145 Y. Nishimura, J.C. Lyu, F.L. Waelbroeck, L.J. Zheng, C.E. Michoski
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:
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。
更新日期:2020-01-28
中文翻译:
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。