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

CEA/DSM/DAPNIA, Service d'Astrophysique (CNRS FRE 2591), CE Saclay, 91191 Gif-sur-Yvette Cedex, France e-mail: jjaly@discovery.saclay.cea.fr

Received: 29 June 2004
Accepted: 13 August 2004

Abstract

A proof is given of the following statement: if is a smooth force-free magnetic field contained in a cylindrical domain of axis parallel to  and of star-shaped cross-section, and if  is topologically equivalent to the uniform field , then . 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.