Finite element methods to calculate ideal magnetohydrodynamic flow equilibria in Tokamaks

Abstract

The MHD equations which describe a stationary equilibrium in axisymmetric geometry lead to a quasilinear partial differential equation for the flux Ψ, one nonlinear and three linear algebraic equations for the mass density ρ, the poloidal current J and the two tangential velocity components υ t and υ P, respectively. These equations are solved numerically by a continuation method, by a Picard iteration and finite element approaches using conforming and nonconforming (hybrid) finite elements. The nodal points are redistributed iteratively such that they fall on initially prescribed constant flux surfaces. For different coordinate systems the different finite element approaches are applied to a static case and compared. The influence of flow is shown by applying our fixed boundary code CLIO to a particular plasma configuration (PDX Tokamak).