Three-dimensional Structures of Magnetostatic Atmospheres. III. A General Formulation

This paper presents a mathematical description of the three-dimensional structures of static, magnetized atmospheres in terms of the electric-current flux surfaces. In the first paper of this series, a class of three-dimensional magnetostatic states was presented. These states are characterized by electric currents flowing perpendicular to gravity which was taken to be either uniform in space or spherically symmetric about a point mass. A limitation of these solutions is that the magnetic field in general cannot have a net twist. The new formulation generalizes these solutions in two significant ways, namely, to allow for other general potential body forces than the special gravitational forces assumed in the first paper and to include the presence of a net magnetic twist. This theoretical development opens up opportunities in modeling realistic solar magnetic fields as well as other astrophysical magnetic fields. The obliquely rotating magnetosphere and self-gravitating magnetized plasma clouds are two astrophysical examples for which the governing equations are derived. The complete analytic solution to a specific problem is presented, which illustrates the anchoring of a fully three-dimensional force-free magnetic field in the solar atmosphere to the base of the atmosphere through a non-force-free boundary layer where the magnetic field interacts strongly with the plasma. This and a rich variety of other three-dimensional magnetic fields will be studied in the subsequent papers of this series.