Two-dimensional force-free magnetic fields described by some nonlinear equations

A force-free magnetic field arises as a special case in the magnetostatic equation in plasmas when only the magnetic energy density is relevant while all other energy densities are negligible and so only the magnetic pressure is considered. In this article, we find the exact solutions of two-dimensional force-free magnetic fields described by Liouville, sine, double sine, sinh-Poisson, and power force-free magnetic equations. We use the generalized tanh method. In all those cases, the ratio of the current density and the magnetic field is not constant as it happens, e.g., in the solar atmosphere. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3520065]