SINGULAR PERTURBATION-THEORY APPLIED TO MAGNETOHYDROSTATIC EQUILIBRIA - PROOF OF CONVERGENCE

Magnetohydrostatic equilibria with two relevant length scales are considered. Their ratio epsilon is assumed to be small. Regular solutions in the sense of singular perturbation theory are discussed and the magnetic flux function A (2-D case) and Euler potentials alpha, beta (3-D case) are shown that can be expanded into convergent power series in epsilon. This ensures further the existence of weakly 2-D and 3-D equilibria within a bounded domain.