Coordinate transformation and construction of finite element mesh in a diverted tokamak geometry

A coordinate transformation technique between straight magnetic field line coordinate system (psi, theta) 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 psi(R, Z) of a diverted tokamak, magnetic field line equation is solved computationally to find curves of constant poloidal angle theta, which provides us with explicit relations R = R(psi, theta) and Z = Z(psi, theta). 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.