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

The compression or expansion of a magnetic field that is initially potential is considered. It was recently suggested by Janse & Low 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 nonzero current.