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.
|Number of pages||10|
|Journal||Journal of Physics: Conference Series|
|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