Spectral method for obtaining three-dimensional magnetohydrodynamic equilibria

A description is given of a new code, MOMCON (spectral moments with constraints), that obtains three-dimensional ideal magnetohydrodynamic (MHD) equilibria in a fixed toroidal domain using a Fourier expansion for the inverse coordinates (R,Z) representing nested magnetic surfaces. A set of nonlinear coupled ordinary differential equations for the spectral coefficients of (R,Z) is solved using an accelerated steepest descent method. A stream function lambda is introduced to improve the mode convergence properties of the Fourier series for R and Z. Constraint equations relating the m greater than or equal to 2 moments of R and Z are solved to define a unique poloidal angle