A High Order Solver for the Grad-Shafranov Free Boundary Problem

Abstract: In magnetic confinement fusion devices, the equilibrium

configuration of a plasma is determined by the balance between the

hydrostatic pressure in the fluid and the magnetic forces generated by

an array of external coils and the plasma itself. The equilibrium con-

figuration is determined by the solution to a nonlinear elliptic partial

differential equation. However, since the location of the plasma is not

known a priori, the domain of definition of the PDE must be determined as a problem unknown 

leading to a free boundary problem. In this talk

we will discuss some recent advances in and interior/exterior iterative

solution strategy. Computationally, this involves the coupling of a hy-

bridizable discontinuous Galerkin solver for the solution of the problem

inside the assumed plasma domain and a boundary integral equation

solver for the solution of the exterior problem, and a minimization

step. This is joint work with Antoine Cerfon (NYU), Manuel Solano

˜(University of ConcepciA³n, Chile) and Evan Toler (NYU/Argonne).