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Unique topological characterization of braided magnetic fields

Yeates, A.R.; Hornig, G.

Unique topological characterization of braided magnetic fields Thumbnail


G. Hornig


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.

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
Public URL


Published Journal Article (897 Kb)

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

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