Physical role of topological constraints in localized magnetic relaxation

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

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: Jan 15, 2015
• 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