Multipole tokamak equilibria

Abstract

Solutions are given for axisymmetric MHD-equilibria obtained by superposing the magnetic field of the plasma currents and the field of current-carrying conductors situated outside the plasma. These equilibria were numerically calculated by several different iteration methods for solving the non-linear free boundary problem. They can describe experiments in which the discharge time is long compared with the diffusion time of the magnetic field through the external conducting walls. Equilibria were obtained both for approximately circular plasma cross-sections and strongly elongated (elliptical) ones. Such calculations are of interest for constructing axisymmetric tokamak divertors, as well as for producing elongated crosssections, which have been postulated to be stable for higher values of plasma pressure. The results presented here are restricted to the case of zero plasma pressure and a particular current distribution in order to reduce the number of free parameters and allow more detailed discussion of the dependence of the equilibrium configurations on the arrangement of the external conductors and the currents.