Axially Symmetric Solutions to the Force-Free Magnetic Field Equations in Spherical and Cylindrical Coordinates

Phys. Rev. A Vol. 45, p. 7520 (1992) (PDF)

The force-free magnetic field condition is expressed in terms of a flux function; alpha is then also a function of the flux function, and with suitable restrictions the resulting equations can be separated and solved. The case of spherical coordinates yields four sets of solutions which are shown to be dependent and equivalent to a simple generalization of those given by Chandrasekhar [Proc. Natl. Acad Sci. USA Vol. 42, 1 (1956)]. Similarly, the case of cylindrical coordinates results in a generalization of the solution given by Furth, et al. [Rev. Sci. Instrum. Vol. 28, 949 (1957)].