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Physical role of topological constraints in localized magnetic relaxation

Yeates, A.R.; Russell, A.J.B.; Hornig, G.

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Authors

A.J.B. Russell

G. Hornig



Abstract

Predicting the final state of turbulent plasma relaxation is an important challenge, both in astro-physical plasmas such as the Sun's corona and in controlled thermonuclear fusion. Recent numerical simulations of plasma relaxation with braided magnetic fields identified the possibility of a novel constraint, arising from the topological degree of the magnetic field-line mapping. This constraint implies that the final relaxed state is drastically different for an initial configuration with topological degree 1 (which allows a Taylor relaxation) and one with degree 2 (which does not reach a Taylor state). Here, we test this transition in numerical resistive-magnetohydrodynamic simulations, by embedding a braided magnetic field in a linear force-free background. Varying the background force-free field parameter generates a sequence of initial conditions with a transition between topological degree 1 and 2. For degree 1, the relaxation produces a single twisted flux tube, whereas for degree 2 we obtain two flux tubes. For predicting the exact point of transition, it is not the topological degree of the whole domain that is relevant, but only that of the turbulent region.

Citation

Yeates, A., Russell, A., & Hornig, G. (2015). Physical role of topological constraints in localized magnetic relaxation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2178), Article 20150012. https://doi.org/10.1098/rspa.2015.0012

Journal Article Type Article
Acceptance Date Apr 30, 2015
Online Publication Date Jun 8, 2015
Publication Date Jun 3, 2015
Deposit Date Jan 5, 2015
Publicly Available Date Mar 29, 2024
Journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print ISSN 1364-5021
Electronic ISSN 1471-2946
Publisher The Royal Society
Peer Reviewed Peer Reviewed
Volume 471
Issue 2178
Article Number 20150012
DOI https://doi.org/10.1098/rspa.2015.0012
Related Public URLs http://arxiv.org/abs/1412.7314

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Copyright Statement
© 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.





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