An approximate self-consistent theory of the magnetic field of fluted penumbrae

A self-consistent mathematical description of the magnetic field of fluted sunspot penumbrae is presented. This description is based on an expansion of the nonlinear force-free magnetohydrostatic equations written in cylindrical coordinates. The lowest order solutions are mathematically equivalent to laminated force-free equilibria in Cartesian geometry. The lowest order solutions have no toroidal component of the magnetic field and the magnetic pressure does not vary with azimuth but the solutions allow arbitrary variations of the magnetic field components with azimuth. Explicit solutions are presented which have a realistic radial profile of the magnetic field strength and reproduce the basic features of the observations.