Generalized magnetohydrostatic equilibria

Abstract

This note shows the existence of a generalized class of magnetohydrostatic elliptic equilibria of a perfectly conducting fluid in systems with cylindrical topology for which the surfaces of constant pressure have an elliptic transverse cross section with the eccentricity given by an arbitrary function of the axial distance. Further, it is shown that a change in the parameters characterizing the solution leads to a generalized class of hyperbolic equilibria for which the surfaces of constant pressure have a hyperbolic transverse cross section with the eccentricity given by an arbitrary function of the axial distance. Whereas the first class of equilibria is of interest in a plasma-confinement system, the second class of equilibria is of interest in a magnetic-field-line reconnection system.