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A complete topological invariant for braided magnetic fields.

Yeates, A. R. and Hornig, G. (2014) 'A complete topological invariant for braided magnetic fields.', Journal of physics : conference series., 544 (1). 012002.


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.

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Publisher statement:Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd.
Date accepted:No date available
Date deposited:27 October 2014
Date of first online publication:20 October 2014
Date first made open access:27 October 2014

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