A uniqueness result for a simple force-free magnetic field submitted to a topological constraint

Abstract

A proof is given of the following statement: if B is a smooth force-free magnetic field contained in a cylindrical domain of axis parallel to z and of star-shaped cross-section, and if B is topologically equivalent to the uniform field B₀=B₀z, then B=B₀. In addition to being a very first step in the general study of the uniqueness of a magnetostatic equilibrium subject to a topological constraint, this result has a direct relevance to the approach recently developed by Ng & Bhattacharjee (1998, Phys. Plasma, 5, 4028) to support Parker's theory of current sheets formation in the solar corona.