Conservation of writhe helicity under anti-parallel reconnection

TL;DR

This paper demonstrates that writhe, a topological property of flux tubes, remains conserved during anti-parallel reconnection, implying helicity conservation depends on local twist modifications at the reconnection site.

Contribution

It establishes the conservation of writhe during anti-parallel reconnection and clarifies conditions under which helicity is conserved in flux tube interactions.

Findings

Writhe is conserved during anti-parallel reconnection.

Helicity conservation depends on the sum of original twists.

Local twist changes at reconnection affect helicity.

Abstract

Reconnection is a fundamental event in many areas of science, from the interaction of vortices in classical and quantum fluids, and magnetic flux tubes in magnetohydrodynamics and plasma physics, to the recombination in polymer physics and DNA biology. By using fundamental results in topological fluid mechanics, the helicity of a flux tube can be calculated in terms of writhe and twist contributions. Here we show that the writhe is conserved under anti-parallel reconnection. Hence, for a pair of interacting flux tubes of equal flux, if the twist of the reconnected tube is the sum of the original twists of the interacting tubes, then helicity is conserved during reconnection. Thus, any deviation from helicity conservation is entirely due to the intrinsic twist inserted or deleted locally at the reconnection site. This result has important implications for helicity and energy considerations in various physical contexts.