Magnetohydrodynamic Equilibrium and Stability of Spheromak Plasma in Flux Conserver

Abstract

The Green-function method is applied to the Grad-Shafranov equation for the plasma in a flux conserver with a rectangular cross section. The linear and the nonlinear MHD equilibrium configurations for various strengths of the toroidal magnetic field B_\varphi are determined by this method. The average beta value ⟨β⟩ and the safety factor are also evaluated. When B_\varphi is increased from zero, ⟨β⟩ decreases and vanishes at a force-free configuration. The safety factor takes a maximum value on the magnetic axis. A sufficient condition for stability to axisymmetric perturbations is derived by use of Edenstrasser’s condition. This sufficient condition holds for the flux conserver of any shape. As an example, the region, in which this sufficient condition is fulfilled, is shown graphically for the flux conserver with rectangular cross section.