On a 2-dimensional stationary free-boundary problem arising in the confinement of a plasma in a stellarator

Abstract

We obtain the existence of solutions of a two-dimensional free boundary problem modelling the magnetic confinement of a plasma in a Stellarator configuration. The nonlinear elliptic equation was obtained from the 3-D MHD system by Hender and Carreras using averaging arguments and a suitable system of coordinates. The final formulation as a free boundary problem involves the notion of relative rearrangement and has important differences with respect to the model for Tokamaks configurations. We use an iterative algorithm and some new properties on relative rearrangement in order to prove the existence of a solution giving rise to a free boundary.