Mathematics – Logic
Scientific paper
May 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005agusmsp33a..04r&link_type=abstract
American Geophysical Union, Spring Meeting 2005, abstract #SP33A-04
Mathematics
Logic
7509 Corona, 7513 Coronal Mass Ejections, 7519 Flares, 7524 Magnetic Fields
Scientific paper
Together with the magnetic energy, the magnetic helicity is an important quantity used to describe the nature of a magnetic field configuration. The most meaningful value of helicity is the relative magnetic helicity (relative to a reference field) 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), we can introduce three other helicity values: 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 nonlinear force-free field computed with the same boundary conditions for three different cases: (i) a single twisted flux tube derived from the extended Gold-Hoyle solutions, (ii) a simple magnetic configuration with three balanced sources and a constant distribution of the force-free parameter, and (iii) the AR 8210 magnetic field observed at 19:40 UT on May 1, 1998. The self and mutual helicities corresponds to the twist and writhe of confined flux bundles, and the crossing of field lines in the magnetic configuration respectively. The vacuum helicity is interpreted as a measure of the topological complexity of the field.
Canfield Richard C.
Regnier Stéphane
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