On the Magnetohydrodynamic Equilibrium Equations for an Axially Asymmetric Finite β Toroidal Plasma

Abstract

The well-known magnetohydrodynamic equilibrium equations are reduced to the equations of convenient forms for the purpose of an investigation for equilibria of axially asymmetric toroidal plasmas with diffuse boundaries by introducing two scalar functions corresponding to a stream function in an axially symmetric case. In the reductions, it is assumed that the toroidal effect is small; namely the quantities of the configurations are expanded in a ratio of the minor radius to the major radius in toroidal system. Mainly, configurations of bumpy type and helical type are considered. In the former case, the forms of the resultant solutions give us a picture of the bumpy type configuration which has helical character as the toroidal effect. The helical type configuration in the latter case has no longer completely helically symmetric structures because of its toroidal effect.