Two-dimensional self-similar plasma equilibria

Abstract

Force-free plasma equilibria are expected to form in the solar corona, while in-situ spacecraft observations have shown that force-free equilibria are formed in the planetary magnetotails. In this paper, we develop fluid models of two-dimensional axially symmetric force-free equilibria and discuss similar slab equilibria. The group theory approach is used to find the symmetry groups and reduce the Grad-Shafranov equation with exponential and power law nonlinearities to ordinary differential equations for the self-similar (automodel) solutions that we analyze analytically and numerically. Force-free equilibria of the developed class have a magnetotail-type configuration with magnetic field lines stretched in the radial direction and represent nonlinear force-free equilibria, because rot B=α(r) B with α(r)≠const. Making use of the same symmetry groups, we generalize the developed force-free equilibria by including a finite plasma pressure gradient and compare different equilibria of the developed class. These models can be useful for describing the structure and stability of current sheets observed in planetary magnetotails and formed in the solar atmosphere.