Cylindrical linear force-free magnetic fields with toroidal flux surfaces

Abstract

A linear force-free field solution is presented in cylindrical coordinates, formulated in terms of trigonometric and Bessel functions. A numerical exploration has revealed that this solution describes magnetic field lines that meander in Cartesian space, as well as field lines that lie on toroidal flux surfaces. These tori are in (or close to) the plane perpendicular to the cylindrical axis. Nested tori, as well as tori with shells that have finite thickness, were found. The parameter space of the solution shows that the tori exist within a bounded range of values.