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Department of Mathematical Sciences


Publication details for Anthony Yeates

Yeates, A. R. & Hornig, G. (2014). A complete topological invariant for braided magnetic fields. Journal of Physics: Conference Series 544(1): 012002.

Author(s) from Durham


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.