A complete topological invariant for braided magnetic fields

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.

10 pages, 5 figures, submitted to conference proceedings on "Knotted, Linked and Tangled Flux in Quantum and Classical Systems" (Isaac Newton Institute for Mathematical Sciences)

References in corpus (5)

• Coronal Loops: Observations and Modeling of Confined Plasma
• Topological Constraints on Magnetic Relaxation
• Decay of helical and non-helical magnetic knots
• Unique Topological Characterization of Braided Magnetic Fields
• A Generalized Flux Function for Three-dimensional Magnetic Reconnection

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