### 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.

Original language | English |
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Article number | 012002 |

Number of pages | 10 |

Journal | Journal of Physics: Conference Series |

Volume | 544 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2014 |

Event | Tangled Magnetic Fields in Astro- and Plasma Physics - International Centre for Mathematical Sciences (ICMS), Edinburgh, United Kingdom Duration: 15 Oct 2012 → 19 Oct 2012 http://www.icms.org.uk/workshops/tangled |

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## Cite this

*Journal of Physics: Conference Series*,

*544*(1), [012002]. https://doi.org/10.1088/1742-6596/544/1/012002