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Magnetohydrodynamic Relaxation Theory

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Topics in Magnetohydrodynamic Topology, Reconnection and Stability Theory

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 591))

Abstract

This chapter is concerned with the magnetic relaxation problem, in which an electrically conducting fluid is initialised in some non-trivial state, and is subsequently allowed to relax to some minimum-energy state, subject to the magnetohydrodynamic (MHD) equations. No driving or forcing is applied during this relaxation process and some form of dissipation allows energy to decrease until the system reaches a relaxed state. Our problem is simple: can we understand or predict this relaxed state?

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Notes

  1. 1.

    While you can make A ⋅B into a material scalar by choosing an appropriate gauge (Webb et al. 2010), this would remove the utility of field-line helicity as a measure of changes in magnetic topology. Instead, a gauge of A should be chosen that is fixed in time (at least on the boundaries where it affects the h(V t)).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Durham University, Durham, UK

    Anthony R. Yeates

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  1. Anthony R. Yeates
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Correspondence to Anthony R. Yeates .

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Editors and Affiliations

  1. School of Mathematics and Statistics, University of Glasgow, Glasgow, UK

    David MacTaggart

  2. College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK

    Andrew Hillier

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Yeates, A.R. (2020). Magnetohydrodynamic Relaxation Theory. In: MacTaggart, D., Hillier, A. (eds) Topics in Magnetohydrodynamic Topology, Reconnection and Stability Theory. CISM International Centre for Mechanical Sciences, vol 591. Springer, Cham. https://doi.org/10.1007/978-3-030-16343-3_4

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  • DOI: https://doi.org/10.1007/978-3-030-16343-3_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-16342-6

  • Online ISBN: 978-3-030-16343-3

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