Magnetic helicity in multiply connected domains
David MacTaggart (University of Glasgow)
Tuesday 19th November 16:00-17:00 Maths 311B
Magnetic helicity is a fundamental quantity of magnetohydrodynamics (MHD) that carries topological information about the magnetic field. By ‘topological information’, we usually refer to the linkage of magnetic field lines. For domains that are not simply connected, however, helicity also depends on the topology of the domain.
In this talk I will first describe why helicity is a topological invariant of ideal MHD by introducing its classical definition in simply connected domains. After describing some applications, I will then describe how helicity can be calculated in any closed domain of arbitrary topology in R^3. The generalization of helicity to multiply connected domains makes use of the generators of the first homology groups (or, dually, the first de Rham cohomology groups) related to the domain and the complement of the domain in a ball containing the domain.