  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.
