Professor Anthony Yeates anthony.yeates@durham.ac.uk
Professor
Unique topological characterization of braided magnetic fields
Yeates, A.R.; Hornig, G.
Authors
G. Hornig
Abstract
We introduce a topological flux function to quantify the topology of magnetic braids: non-zero, line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a cross-section of the magnetic field, and measures the average poloidal magnetic flux around any given field line, or the average pairwise crossing number between a given field line and all others. Moreover, its integral over the cross-section yields the relative magnetic helicity. Using the fact that the flux function is also an action in the Hamiltonian formulation of the field line equations, we prove that it uniquely characterizes the field line mapping and hence the magnetic topology.
Citation
Yeates, A., & Hornig, G. (2013). Unique topological characterization of braided magnetic fields. Physics of Plasmas, 20(1), Article 012102. https://doi.org/10.1063/1.4773903
Journal Article Type | Article |
---|---|
Publication Date | Jan 1, 2013 |
Deposit Date | Jan 7, 2013 |
Publicly Available Date | Jan 10, 2013 |
Journal | Physics of Plasmas |
Print ISSN | 1070-664X |
Electronic ISSN | 1089-7674 |
Publisher | American Institute of Physics |
Peer Reviewed | Peer Reviewed |
Volume | 20 |
Issue | 1 |
Article Number | 012102 |
DOI | https://doi.org/10.1063/1.4773903 |
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Copyright Statement
© 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Yeates, A.R. and Hornig, G. (2013) 'Unique topological characterization of braided magnetic fields.', Physics of plasmas., 20 (1). 012102 and may be found at http://dx.doi.org/10.1063/1.4773903
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