Analytic Three-Dimensional Solutions of the Magnetohydrostatic Equations with Twisted Field Lines

Two types of exact solutions of the MHD equilibrium equations are presented. The equilibria exhibit neither continuous nor mirror symmetry. The configurations are infinitely extended along a straight axis with surfaces of constant pressure closed around the axis. The cross sections are elliptic for equilibria of the first type. For the second type they are elliptic only close to the axis. Field and current lines turn around the axis and extend from minus to plus infinity in the axial direction. In these limits the configurations become singular. The rotational transform and the local shear are discussed. copyright 1996 The American Physical Society