A complete topological invariant for braided magnetic fields
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.
Cite
@article{arxiv.1304.8064,
title = {A complete topological invariant for braided magnetic fields},
author = {A. R. Yeates and G. Hornig},
journal= {arXiv preprint arXiv:1304.8064},
year = {2015}
}
Comments
10 pages, 5 figures, submitted to conference proceedings on "Knotted, Linked and Tangled Flux in Quantum and Classical Systems" (Isaac Newton Institute for Mathematical Sciences)