Publication details for Anthony YeatesYeates, A. R. & Hornig, G. (2014). A complete topological invariant for braided magnetic fields. Journal of Physics: Conference Series 544(1): 012002.
- Publication type: Journal Article
- ISSN/ISBN: 1742-6588 (print), 1742-6596 (electronic)
- DOI: 10.1088/1742-6596/544/1/012002
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
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.