An Improved 3D MHD Equilibrium Formulation

Three fully three-dimensional finite element formulations of magnetohydrodynamic (MHD) plasma equilibrium are presented. The first one is based on the curl of the equilibrium equation, but it fails since it does not take account of the component of the current density parallel to the magnetic flux density and does not include the pressure as a variable. Two new formulations are introduced which remedy these shortcomings. One of them turns out to be too ill-conditioned to be used. Finally, a novel approach based on a current vector potential to represent the current density is shown to be stable and is validated by showing that it converges to the solution obtained by a previously authenticated 2D method for an axisymmetric problem.