Magnetohydrodynamic Equilibrium with Prolate Spheroidal Plasma-Vacuum Interface

Abstract

The Grad-Shafranov equation for a prolate spheroidal plasma is solved by using the prolate spheroidal coordinates. The magnetic field in the vacuum region surrounding the plasma is determined by use of the Maxwell equation and the pressure-balance condition on the plasma-vacuum interface. The result obtained in this letter is an exact solution to the magnetohydrodynamic equilibrium equation. The magnetic-field configuration of the spheroidal plasma is found to be considerably different from that of the spherical plasma.