Magnetohydrodynamic Equilibrium and Stability of Spheromak with Spheroidal Plasma-Vacuum Interface

摘要

The analytic solutions to the Grad-Shafranov equation are obtained for a prolate and an oblate spheroidal plasma by using Hill's vortex model. Effects of a toroidal magnetic field B sub ph1 on the magnetohydrodynamic (MHD) equilibrium configurations are investigated by using these analytic solutions. When B sub ph1 is larger than that of the force free configuration, the spheroidal plasmas in a vacuum magnetic field are shown to be unable in the MHD equilibrium. The several physical quantities on the equilibrium configuration are evaluated. The spheromak plasma is proved to be unstable if the derivative of p with respect to psi is not = 0 and the second derivative of V w.r.t. psi is = or 0 on the magnetic axis. Here p is the pressure and V(psi) the volume surrounded by a magnetic surface of psi = const. The equilibrium configurations of the spheroidal plasmas by using Hill's vortex model are shown to satisfy the above conditions, i.e., to be unstable.