Self and mutual magnetic helicities in coronal magnetic configurations

¹ ESA Research and Scientific Support Department, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands e-mail: sregnier@rssd.esa.int
² Centre de Physique Théorique, École Polytechnique, 91128 Palaiseau, France
³ Montana State University, Physics Dept., 264 EPS Building, Bozeman, MT 59717, USA

Received: 24 May 2005
Accepted: 4 July 2005

Abstract

Together with the magnetic energy, the magnetic helicity is an important quantity used to describe the nature of a magnetic field configuration. In the following, we propose a new technique to evaluate various components of the total magnetic helicity in the corona for an equilibrium reconstructed magnetic field. The most meaningful value of helicity is the total relative magnetic helicity which describes the linkage of the field lines even if the volume of interest is not bounded by a magnetic surface. In addition if the magnetic field can be decomposed into the sum of a closed field and a reference field (following , Berger 1999 in Magnetic Helicity in Space and Laboratory Plasmas, ed. M. R. Brown, R. C. Canfield, & A. A. Pevtsov, 1), we can introduce three other helicity components: the self helicity of the closed field, the mutual helicity between the closed field and the reference field, and the vacuum helicity (self helicity of the reference field). To understand the meaning of those quantities, we derive them from the potential field (reference) and the force-free field computed with the same boundary conditions for three different cases: a single twisted flux tube derived from the extended Gold-Hoyle solutions, a simple magnetic configuration with three balanced sources and a constant distribution of the force-free parameter, and the AR 8210 magnetic field observed from 17:13 UT to 21:16 UT on May 1, 1998. We analyse the meaning of the self and mutual helicities: the self and mutual helicities correspond to the twist and writhe of confined flux bundles, and the crossing of field lines in the magnetic configuration respectively. The main result is that the magnetic configuration of AR 8210 is dominated by the mutual helicity and not by the self helicity (twist and writhe). Our results also show that although not gauge invariant the vacuum helicity is sensitive to the topological complexity of the reference field.