Some minimum-energy toroidal equilibria

Equilibria with minimum energy are constructed from a variational principle in which the energy of a plasma is minimized subject to a recently proposed set of global invariants. The equilibrium equation is solved in axisymmetric, toroidal geometry. In order to compute toroidal equilibria the variational principle is exploited to obtain a reduced set of ordinary differential equations which are solved numerically. Tokamaklike and pinchlike solutions of minimum energy are found in toroidal geometry. Based on the ideal and resistive stability studies of the cylindrical limit of these solutions, it is argued that some of these equilibria should have robust stability to modes of low m and n number.