A complete topological invariant for braided magnetic fields

A. R. Yeates (Lead / Corresponding author), G. Hornig (Lead / Corresponding author)

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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.

    Original languageEnglish
    Article number012002
    Number of pages10
    JournalJournal of Physics: Conference Series
    Volume544
    Issue number1
    DOIs
    Publication statusPublished - 2014
    EventTangled Magnetic Fields in Astro- and Plasma Physics - International Centre for Mathematical Sciences (ICMS), Edinburgh, United Kingdom
    Duration: 15 Oct 201219 Oct 2012
    http://www.icms.org.uk/workshops/tangled

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    Hornig, Gunnar

    • Mathematics - Professor & Personal Chair of Magnetohydrodynamics

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