On the limitations of magneto-frictional relaxation

Yeates, A.R.

Abstract

The magneto-frictional method is used in solar physics to compute both static and quasi-static models of the Sun’s coronal magnetic field. Here, we examine how accurately magneto-friction (without fluid pressure) is able to predict the relaxed state in a one-dimensional test case containing two magnetic null points. Firstly, we show that relaxation under the full ideal magnetohydrodynamic equations in the presence of nulls leads necessarily to a non-force-free state, which could not be reached exactly by magneto-friction. Secondly, the magneto-frictional solutions are shown to lead to breakdown of magnetic flux conservation, whether or not the friction coefficient is scaled with magnetic field strength. When this coefficient is constant, flux is initially conserved, but only until discontinuous current sheets form at the null points. In the ensuing weak solution, we show that magnetic flux is dissipated at these current sheets. The breakdown of flux conservation does not occur for an alternative viscous relaxation scheme.

Citation

Yeates, A. (2022). On the limitations of magneto-frictional relaxation. Geophysical and Astrophysical Fluid Dynamics, 116(4), 305-320. https://doi.org/10.1080/03091929.2021.2021197

• Journal Article Type: Article
• Acceptance Date: Dec 17, 2021
• Online Publication Date: Jan 14, 2022
• Publication Date: 2022
• Deposit Date: Jan 4, 2022
• Publicly Available Date: Jan 17, 2023
• Journal: Geophysical & Astrophysical Fluid Dynamics
• Print ISSN: 0309-1929
• Electronic ISSN: 1029-0419
• Publisher: Taylor and Francis Group
• Peer Reviewed: Peer Reviewed
• Volume: 116
• Issue: 4
• Pages: 305-320
• DOI: https://doi.org/10.1080/03091929.2021.2021197
• Public URL: https://durham-repository.worktribe.com/output/1221468