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Field line integration for MHD equilibria near a closed magnetic field line

Magnetic field lines near a given closed field line which is taken as a magnetic axis are calculated analytically. Existence properties are obtained for equilibria whose rotational transform on a magnetic axis is an integer multiple of ½. The results are applied to a tokamak with a perturbation of the main field, the ℓ = 2 stellarator, the stability properties of equilibria with vanishing rotational transform, and the scaling of the equilibrium β-value in configurations without net longitudinal current and with small rotational transform.