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

Magnetic field lines near a given closed field line, 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 one half. The results are applied to a tokamak with a perturbation of the main field, the l equals 2 stellarator, the stability properties of equilibria with vanishing rotational transform, and the scaling of the equilibrium beta-value in configurations without net longitudinal current and with small rotational transform.