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On the limitations of magneto-frictional relaxation

Yeates, A.R.

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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.


Yeates, A. (2022). On the limitations of magneto-frictional relaxation. Geophysical and Astrophysical Fluid Dynamics, 116(4), 305-320.

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


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Copyright Statement
© 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group<br /> This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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