Direct variational solutions of the tokamak equilibrium problem

A direct variational method based on an energy principle has been developed to calculate approximate solutions to the tokamak plasma equilibrium equation. The method uses a spectral representation of the magnetic flux surfaces in terms of Chebyshev polynomials. This representation allows analytic evaluation of the flux-surface average integrals, eliminating the poloidal angle dependence of the plasma internal energy. In this form the variational problem is reduced to the determination of the spectral coefficients as functions of the radial coordinate. Global approximate solutions are obtained by the introduction of trial functions for the coefficients parametrized by a set of constants determined in such a way as to render the energy stationary. The method is illustrated with applications to the START and MAST spherical tokamaks.