Non-force-free solar magnetic fields in magnetohydrostatic equilibrium

Abstract

The objective of the paper is to examine a class of non-force-free fields analytically. Specifically, magnetic fields in magnetohydrostatic equilibrium with a plasma in a gravitational field are treated in an approximation of two independent variables but three vector components. Spherical coordinates are emphasized, although the formal results for cylindrical and Cartesian coordinates are presented in the appendices. Formal solutions for the magnetic-field components are obtained in terms of the plasma variables, and field line equations are derived. A final equation governing the plasma variables is then obtained. Procedures are developed for analyzing this equation and obtaining sets of self-consistent particular solutions to the governing equations; a number of such sets of solutions are presented. As an example, one solution set is examined, illustrating the application of the results to the analysis of solar observational data.