A complete topological invariant for braided magnetic fields

Yeates, A.R.; Hornig, G.

doi:10.1088/1742-6596/544/1/012002

A complete topological invariant for braided magnetic fields

Yeates, A.R.; Hornig, G.

Authors

Professor Anthony Yeates anthony.yeates@durham.ac.uk
Professor

G. Hornig

Abstract

A topological flux function is introduced 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, whose integral over the cross-section yields the relative magnetic helicity. Recognising that the topological flux function is an action in the Hamiltonian formulation of the field line equations, a simple formula for its differential is obtained. We use this to prove that the topological flux function uniquely characterises the field line mapping and hence the magnetic topology. A simple example is presented.

Citation

Yeates, A., & Hornig, G. (2014). A complete topological invariant for braided magnetic fields. Journal of Physics: Conference Series, 544(1), Article 012002. https://doi.org/10.1088/1742-6596/544/1/012002

Journal Article Type	Article
Online Publication Date	Oct 20, 2014
Publication Date	Oct 20, 2014
Deposit Date	Oct 27, 2014
Publicly Available Date	Oct 27, 2014
Journal	Journal of Physics: Conference Series
Print ISSN	1742-6588
Electronic ISSN	1742-6596
Publisher	IOP Publishing
Peer Reviewed	Peer Reviewed
Volume	544
Issue	1
Article Number	012002
DOI	https://doi.org/10.1088/1742-6596/544/1/012002

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