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arXiv · 1304.8064

A complete topological invariant for braided magnetic fields

A. R. Yeates·G. Hornig
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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.

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A. R. Yeates, G. Hornig. 2013-04-30. A complete topological invariant for braided magnetic fields. https://doi.org/10.1088/1742-6596/544/1/012002

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