Unique Topological Characterization of Braided Magnetic Fields
arXiv:1208.2286 · doi:10.1063/1.4773903
Abstract
We introduce a topological flux function 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, and measures the average poloidal magnetic flux around any given field line, or the average pairwise crossing number between a given field line and all others. Moreover, its integral over the cross-section yields the relative magnetic helicity. Using the fact that the flux function is also an action in the Hamiltonian formulation of the field line equations, we prove that it uniquely characterizes the field line mapping and hence the magnetic topology.
6 pages, 2 figures, added interpretation as average crossing number, accepted in Phys. Plasmas
References in corpus (5)
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Cited by in corpus (16)
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- Braided magnetic fields: equilibria, relaxation and heating
- Evolution, structure and topology of self-generated turbulent reconnection layers
- Relative field-line helicity in bounded domains
- Magnetic helicity in multiply connected domains
- A complete topological invariant for braided magnetic fields
- Studying the transfer of magnetic helicity in solar active regions with the connectivity-based helicity flux density method
- Spatial Scales and Locality of Magnetic Helicity: Part 1
- A Life of Fun Playing With Solar Magnetic Fields (Special Historical Review)
- Topological Constraints in the Reconnection of Vortex Braids
- Evolution of Field Line Helicity in Magnetic Relaxation
- Higher Helicity of Magnetic Lines and Arf-invariants