Analytical examples of reversal current, zero core current, and surface current, toroidal magnetostatic equilibria with nested flux surfaces

Abstract

We present exact analytical examples of three types of axisymmetric toroidal magnetostatic equilibria with nested flux surfaces: (1) current reversal equilibria, for which the net toroidal current switches from a negative to a positive value when moving away from the magnetic axis; these equilibria have a non-monotonic pressure profile, in accordance with Hammett et al.’s theorem stating that the pressure on the current reversal surface has to exceed the volume-averaged pressure within that surface; (2) zero core current equilibria, in which the toroidal current density vanishes inside some flux surface; and (3) surface current equilibria, constituted of an arbitrary number of nested layers inside which the plasma pressure is constant and the magnetic field force-free, with two adjacent layers being separated by a current sheet. All these configurations are obtained by shaping in an adequate way the arbitrary function which intervenes in the class of generalized isodynamic equilibria first constructed by Palumbo and recovered later on by Bishop and Taylor. A derivation of these equilibria by a method slightly different from Palumbo’s is given in an Appendix.