AN APPROXIMATE SELF-CONSISTENT THEORY OF THE MAGNETIC-FIELD OF FLUTEDPENUMBRAE

A self-consistent mathematical description of the magnetic field of fl uted sunspot penumbrae is presented. This description is based on an e xpansion of the nonlinear force-free magnetohydrostatic equations writ ten in cylindrical coordinates. The lowest order solutions are mathema tically equivalent to laminated force-free equilibria in Cartesian geo metry. The lowest order solutions have no toroidal component of the ma gnetic field and the magnetic pressure does not vary with azimuth but the solutions allow arbitrary variations of the magnetic field compone nts with azimuth. Explicit solutions are presented which have a realis tic radial profile of the magnetic field strength and reproduce the ba sic features of the observations.