A complete topological invariant for braided magnetic fields

Yeates, A.R.; Hornig, G.

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.

Citation

Yeates, A., & Hornig, G. (2014). A complete topological invariant for braided magnetic fields. Journal of Physics: Conference Series, 544(1), Article 012002. https://doi.org/10.1088/1742-6596/544/1/012002

• Journal Article Type: Article
• Online Publication Date: Oct 20, 2014
• Publication Date: Oct 20, 2014
• Deposit Date: Oct 27, 2014
• Publicly Available Date: Oct 27, 2014
• Journal: Journal of Physics: Conference Series
• Print ISSN: 1742-6588
• Electronic ISSN: 1742-6596
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 544
• Issue: 1
• Article Number: 012002
• DOI: https://doi.org/10.1088/1742-6596/544/1/012002