Numerical Analysis Seminars: Magnetic Braids
28 October 2011 14:00 in E 101
(with Gunnar Hornig, Uni of Dundee)
A magnetic field where all field lines connect between two planes resembles a mathematical braid with an infinite number of strands. Such “magnetic braids” occur in physical plasmas ranging from thermonuclear confinement devices to the coronae of stars. Here we are interested in the dynamical evolution of magnetic braids. Though often close to an ideal, “topology-preserving” evolution, even small amounts of dissipation can lead to large-scale topological changes via magnetic reconnection.
I will address the open question of how to quantify such changes by introducing a “topological flux function”. Defined on a cross section, this function is an ideal invariant. Moreover, its integral yields a well-known global invariant - the magnetic helicity. But a numerical relaxation simulation demonstrates that the new flux function contains far more information. In fact, by viewing the magnetic braid as a Hamiltonian system, the flux function may be shown to contain all essential topological information.
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