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

This paper is a study of a family of nonlinear force-free magnetic fields, in Cartesian geometry and invariant in a given direction, as simple models of the magnetic fields in the solar corona. Posed as a problem in the infinite half-space bounded below by the photosphere taken as a rigid plane, the solution is constructed with the field-aligned currents confined within a cylindrical plasma surface outside of which the magnetic field is potential. An infinity of solutions are shown to be tractable by the method of images of potential theory. Among the results 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 continuous 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 the force-free solutions are also carried out to demonstrate (i) the formation of a magnetic cusp point in a bipolar magnetic field in equilibrium with an isotropic pressure, and (ii) the possibility of a Kuperus-Raadu type prominence embedded in a horizontal, helical magnetic flux rope. The prominence model presented offers a simple physical explanation of the magnetograph observations of the past three decades showing a general increase of the prominence magnetic-field intensity with height.