The SPIDER code — solution of direct and inverse problems for free boundary tokamak plasma equilibrium

The SPIDER code is an axisymmetric multipurpose plasma equilibrium solver for different formulations of the tokamak plasma equilibrium problems. This paper deals with solution of direct and inverse problems for free boundary plasma equilibrium. The first part of the paper concerns the direct axisymmetric free boundary plasma equilibrium problem, which is formulated for the poloidal magnetic flux function $\Psi$ and the unknown plasma domain $\Omega_p$ in terms of the Grad-Shafranov equation over an infinite domain. Computational algorithms for the cases of fixed rectangular grid and magnetic surface adaptive grid are described. The second part of the paper concerns the inverse free boundary plasma equilibrium problem of reconstruction of PFC currents as a module in the frame of the SPIDER code. Corresponding computational algorithm is described too. The results of simulations are presented. Derivation of the Grad-Shafranov equilibrium equation is given in the appendix.