Surface currents on models of force-free solar magnetic flux tubes

A model of a cylindrically symmetric, force-free magnetic field consisting of a sequence of concentric layers with piecewise-constant a is used to construct models of the surface currents on isolated, force-free magnetic flux tubes. Two boundary conditions are considered: a current-neutralized flux tube (Bq = 0, B, + 0 a t r > r,), and an isolated current-carrying flux tube (Bq f 0, B, = 0 a t r > r,). A single-a model that is current-neutralized is a reverse-field pinch, and is unacceptable as a model for a solar flux tube. Examples of two-a models for a current-neutralized flux tube are presented. The models of the surface currents satisfying either boundary condition are shown to simplify considerably when the surface layer is thin. A model consisting of several layers, with piecewise-constant a, may be used to find an approximate solution for a force-free flux tube with an arbitrarily specified current profile.