Analytic solutions of ∇ × B=λB having separatrices for geometries with one ignorable coordinate

Analytic solutions of ∇×B=λB are presented for PS-1 and CTX types of spheromaks, and for the proposed Wisconsin reversed-field pinch. Inherent in the spheromak solutions is a separatrix that separates a region of closed magnetic field lines from a surrounding region of open ones. Such a structure enhances the plausibility of maintaining steady-state spheromak operation by driving a steady current along the open field lines.