On the formation of current sheets in response to the compression or expansion of a potential magnetic field

TL;DR

This paper investigates how potential magnetic fields respond to compression or expansion, revealing that only fields with null points develop current sheets, while others relax smoothly without singularities.

Contribution

It provides a numerical analysis showing that magnetic null points are essential for current sheet formation during magnetic field deformation.

Findings

Fields with null points develop current singularities.

Fields without null points relax to smooth equilibria.

Null points are critical for current sheet formation.

Abstract

The compression or expansion of a magnetic field that is initially potential is considered. It was recently suggested by Janse & Low [2009, ApJ, 690, 1089] that, following the volumetric deformation, the relevant lowest energy state for the magnetic field is another potential magnetic field that in general contains tangential discontinuities (current sheets). Here we examine this scenario directly using a numerical relaxation method that exactly preserves the topology of the magnetic field. It is found that of the magnetic fields discussed by Janse & Low, only those containing magnetic null points develop current singularities during an ideal relaxation, while the magnetic fields without null points relax toward smooth force-free equilibria with finite non-zero current.