Singular perturbation theory applied to magnetohydrostatic equilibria: Proof of convergence

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Abstract
Magnetohydrostatic equilibria with two relevant length scales are considered. Their ratio Ε 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 α, β (3‐D case) are shown that can be expanded into convergent power series in Ε. This ensures further the existence of weakly 2‐D and 3‐D equilibria within a bounded domain.