Yeates, A.R. and Hornig, G. (2013) 'Unique topological characterization of braided magnetic fields.', Physics of plasmas., 20 (1). 012102.
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.
| Item Type: | Article |
|---|---|
| Full text: | (VoR) Version of Record Download PDF (877Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | http://dx.doi.org/10.1063/1.4773903 |
| Publisher 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 |
| Date accepted: | No date available |
| Date deposited: | 10 January 2013 |
| Date of first online publication: | January 2013 |
| Date first made open access: | No date available |
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