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

J. J. Aly

doi:10.1051/0004-6361:20041547

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Volume 429 / No 1 (January I 2005)

A&A, 429 1 (2005) 15-18

Abstract

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Issue		A&A Volume 429, Number 1, January I 2005


Page(s)		15 - 18
Section		Astrophysical processes
DOI		https://doi.org/10.1051/0004-6361:20041547
Published online		13 December 2004

A&A 429, 15-18 (2005)

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

J. J. Aly

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 $\vec{B}$ is a smooth force-free magnetic field contained in a cylindrical domain of axis parallel to $\vec{{\hat z}}$ and of star-shaped cross-section, and if $\vec{B}$ is topologically equivalent to the uniform field $\vec{B}_{0}=B_{0}\vec{{\hat z}}$ , then $\vec{B}=\vec{B}_{0}$ . 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

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