DIRECT VARIATIONAL SOLUTIONS OF THE TOKAMAK EQUILIBRIUM PROBLEM

A direct variational method based on an energy principle has been deve loped to calculate approximate solutions to the tokamak plasma equilib rium equation. The method uses a spectral representation of the magnet ic Bur surfaces in terms of Chebyshev polynomials. This representation allows analytic evaluation of the flux-surface average integrals, eli minating the poloidal angle dependence of the plasma internal energy. In this form the variational problem is reduced to the determination o f the spectral coefficients as functions of the radial coordinate. Glo bal approximate solutions are obtained by the introduction of trial fu nctions for the coefficients parametrized by a set of constants determ ined in such a way as to render the energy stationary. The method is i llustrated with applications to the START and MAST spherical tokamaks.