DIRECT VARIATIONAL SOLUTIONS TO THE GRAD-SCHLUTER-SHAFRANOV EQUATION

A direct variational method based on an energy principle is applied to obtain approximate magnetohydrodynamic equilibria for tokamak plasmas . The geometry of the nested magnetic flux surfaces is specified by a model that includes displacement, elongation and triangularity effects . The radial dependence in flux coordinates is described by a consiste nt set of trial functions which allows analytical calculation of the f lux-surface averaged internal energy density of the plasma. Approximat e solutions of the variational problem are obtained for arbitrary aspe ct-ratio tokamaks using a one-parameter optimization procedure.