FORCE-FREE MAGNETIC-FIELDS WITH SINGULAR CURRENT-DENSITY SURFACES

This paper is a study of a family of nonlinear force-free magnetic fie lds, in Cartesian geometry and invariant in a given direction, as simp le models of the magnetic fields in the solar corona. Posed as a probl em in the infinite half-space bounded below by the photosphere taken a s a rigid plane, the solution is constructed with the field-aligned cu rrents confined within a cylindrical plasma surface outside of which t he magnetic field is potential. An infinity of solutions are shown to be tractable by the method of images of potential theory. Among the re sults presented is the demonstration of a magnetic flux surface in the plasma interior, which is ideally stable, where the electric current density becomes an integrable infinity, created quasi-statically by co ntinuous boundary displacement of the magnetic footpoints. This result is discussed in connection with Parker's theory of coronal heating by the dissipation of electric current sheets. Simple modifications of t he force-free solutions are also carried out to demonstrate (i) the fo rmation of a magnetic cusp point in a bipolar magnetic field in equili brium with an isotropic pressure, and (ii) the possibility of a Kuperu s-Raadu type prominence embedded in a horizontal, helical magnetic flu x rope. The prominence model presented offers a simple physical explan ation of the magnetograph observations of the past three decades showi ng a general increase of the prominence magnetic-field intensity with height.