Variational moment method for computing magnetohydrodynamic equilibria

Abstract

A fast yet accurate method to compute magnetohydrodynamic equilibria is provided by the variational moment method, which is similar to the classical Rayleigh-Ritz-Galerkin approximation. The equilibrium solution sought is decomposed into a spectral representation. The partial differential equations describing the equilibrium are then recast into their equivalent variational form and systematically reduced to an optimum finite set of coupled ordinary differential equations. An appropriate spectral decomposition can make the series representing the solution converge rapidly and hence substantially reduces the amount of computational time involved. The moment method was developed first to compute fixed boundary inverse equilibria in axisymmetric toroidal geometry, and was demonstrated to be both efficient and accurate. The method since has been generalized to calculate free boundary axisymmetric equilibria, to include toroidal plasma rotation and pressure anisotropy, and to treat three-dimensional toroidal geometry. In all these formulations, the flux surfaces are assumed to be smooth and nested so that the solutions can be decomposed in Fourier series in inverse coordinates. These recent developments and the advantages and limitations of the moment method are reviewed. The use of alternate coordinates for decomposition is discussed.