Relative magnetic helicity in multiply connected domains

MacTaggart, D. and Valli, A. (2023) Relative magnetic helicity in multiply connected domains. Journal of Physics A: Mathematical and Theoretical, 56(43), 435701. (doi: 10.1088/1751-8121/acfd6c)

Abstract

Magnetic helicity is a conserved quantity of ideal magnetohydrodynamics (MHD) that is related to the topology of the magnetic field, and is widely studied in both laboratory and astrophysical plasmas. When the magnetic field has a non-trivial normal component on the boundary of the domain, the classical definition of helicity must be replaced by relative magnetic helicity. The purpose of this work is to review the various definitions of relative helicity and to show that they have a common origin—a general definition of relative helicity in multiply connected domains. We show that this general definition is both gauge-invariant and is conserved in time under ideal MHD, subject only to closed and line-tied boundary conditions. Other, more specific, formulae for relative helicity, that are used frequently in the literature, are shown to follow from the general expression by imposing extra conditions on the magnetic field or its vector potential.

• Item Type: Articles
• Additional Information: A V acknowledges the support of INdAM-GNCS and Prin201752HKH8/NA-FROM-PDEs.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Mactaggart, Dr David
• Authors: MacTaggart, D., and Valli, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Physics A: Mathematical and Theoretical
• Publisher: IOP Publishing
• ISSN: 1751-8113
• ISSN (Online): 1751-8121
• Published Online: 09 October 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Journal of Physics A: Mathematical and Theoretical 56(43): 435701
• Publisher Policy: Reproduced under a Creative Commons License

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