On the limitations of magneto-frictional relaxation

TL;DR

This paper investigates the limitations of the magneto-frictional method in modeling the Sun's coronal magnetic field, revealing issues with flux conservation and the inability to reach force-free states in null point regions.

Contribution

It demonstrates that magneto-friction cannot accurately reproduce relaxed states with null points and highlights flux dissipation issues not present in alternative viscous schemes.

Findings

Magneto-frictional relaxation leads to non-force-free states near nulls.

Flux conservation breaks down at current sheets during relaxation.

Alternative viscous relaxation maintains flux conservation.

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.