Magnetic winding: what is it and what is it good for?

David MacTaggart (University of Glasgow)

Thursday 29th October, 2020 14:00-15:00 ZOOM (ID: 928 8535 6036)

Abstract

Topic: Applied Mathematics Seminar David MacTaggart
Start Time : Oct 29, 2020 01:48 PM

Meeting Recording (as a onedrive accessble to University of Glasgow):

https://gla-my.sharepoint.com/personal/david_mactaggart_glasgow_ac_uk/_layouts/15/onedrive.aspx?id=%2Fpersonal%2Fdavid%5Fmactaggart%5Fglasgow%5Fac%5Fuk%2FDocuments%2Fdmac%5Fglasgow%5Fseminar%5F2020&originalPath=aHR0cHM6Ly9nbGEtbXkuc2hhcmVwb2ludC5jb20vOmY6L2cvcGVyc29uYWwvZGF2aWRfbWFjdGFnZ2FydF9nbGFzZ293X2FjX3VrL0VzN01wcjJRV2twUHN4QTNHa2FlT0hRQjBNZ0NXMldxeUtGc3FyQ01qazY0Tnc_cnRpbWU9Q25uSnowTjgyRWc

Magnetic helicity is a topological invariant of ideal magnetohydrodynamics that encodes information about field line topology (the connectedness of field lines). For closed magnetic fields, the classical result is that this topological description is given by the Gauss linking number. In this talk, we extend this description to open magnetic fields (fields that have non-trivial normal components on a boundary) and show that field line winding provides a suitable description of the underlying field line topology. We give examples to show how magnetic winding can be used to understand the topological complexity of magnetic fields emerging into the solar atmosphere and discuss the implication of these results for predicting solar eruptions. 

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