Numerical solution of a nonlocal problem arising in plasma physics

In this paper, we present a numerical method to approximate the equilibrium of a plasma magnetically confined in a stellarator device. We consider a two-dimensional nonlocal free-boundary problem which involves both relative and decreasing rearrangements. We use a finite-element discretization to the differential operator and an iterative algorithm in the nonlinear terms. An approximation scheme for the computation of the rearrangement has been implemented and tested. Finally we give numerical results for an helical system.