Three-dimensional structures of magnetostatic atmospheres. I - Theory

This paper presents two families of magnetostatic equilibrium states for two atmospheres, one with a uniform gravity and the other with a gravity due to a point mass in spherical geometry. Taking the electric current to be everywhere perpendicular to the gravitational force, the fully three-dimensional problem is shown to be amenable to analytic treatment. The equilibrium equations are reducible to a single nonlinear scalar partial differential equation. The assumption on the electric-current orientation is less restrictive than those used to generate three-dimensional magnetostatic states in previous studies. Consequently, the new magnetostatic solutions reported here exhibit a rich variety of possible magnetic topologies. A subset of these solutions have magnetic topologies identical to those of the set of all potential magnetic fields. This subset of solutions are analyzed as illustrative examples, with an application to model the three-dimensional magnetic structure of cool plasma loops, often observed in the EUV corona. The prospect for modeling realistic structures in the solar atmosphere with observational inputs is pointed out. The discussion relates the theoretical development to the property of nonequilibrium discussed by Parker and others.