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: firstname.lastname@example.org
Accepted: 13 August 2004
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.
Key words: magnetohydrodynamics (MHD) / Sun: magnetic fields / Sun: corona
© ESO, 2005