Do Potential Fields Develop Current Sheets Under Simple Compression or Expansion?

TL;DR

This paper challenges the assumption that potential fields remain potential under simple compression or expansion, providing a counterexample that questions previous conclusions about current singularity formation.

Contribution

It constructs an explicit counterexample to the assumption that potential fields stay potential during simple expansion or compression.

Findings

Counterexample shows potential fields can develop non-potential features

Previous results on current singularity formation may need revision

Questions the stability of potential fields under simple deformation

Abstract

The recent demonstration of current singularity formation by Low et al. assumes that potential fields will remain potential under simple expansion or compression (Low 2006, 2007; Janse & Low 2009). An explicit counterexample to their key assumption is constructed. Our findings suggest that their results may need to be reconsidered.