Equilibrium Vacuum Magnetic Field of an Axisymmetric Torus with an Elliptical Plasma Cross-Section

Abstract

A method obtaining a vacuum magnetic field around a prescribed axisymmetric toroidal plasma equilibrium is described. The equilibrium vacuum field which fits the boundary conditions on the plasma-vacuum interface is obtained assuming a large aspect ratio. The equilibrium solution is given explicitly for an elliptical plasma cross section and the singularities of the resultant magnetic field are examined.