MAGNETOSTATIC STRUCTURES OF THE SOLAR CORONA .1. A MODEL-BASED ON THECAUCHY BOUNDARY-VALUE PROBLEM

A model is presented for the static equilibrium of a magnetized, polyt ropic atmosphere stratified by uniform gravity and invariant in a Cart esian direction. The profiles of plasma pressure and magnetic shear as functions of the magnetic stream function, which render the governing equation linear, lead to unphysical features if these profiles are ap plied to the infinite half-space bounded below by a plane. These undes irable features are shown to be removed when these special profiles ar e localized to a region bounded by a magnetic flux surface, outside of which is an atmosphere in plane-parallel hydrostatic equilibrium with a potential magnetic field. Two families of solutions are constructed by direct solution of the Cauchy boundary value problem for the Lapla ce equation, one with continuous and the other with discontinuous pres sures across this magnetic boundary. Illustrative solutions are analyz ed, with applications to long-lived density enhancements and depletion s in the solar corona. In particular, the hydromagnetic stability of p ressure discontinuities is studied as an example of a general result d ue to Hu (1988). It is pointed out that the stability of the sharp int erface between the prominence cavity and the high-density coronal helm et may be understood in terms of competing effects arising from densit y stratification and magnetic curvature. The model presented lays the mathematical groundwork for the other papers of the series.