Evolution of field line helicity during magnetic reconnection

TL;DR

This paper analyzes how field line helicity evolves during magnetic reconnection, revealing that reconnection efficiently redistributes helicity locally without significantly changing the total helicity, using derived evolution equations and kinematic examples.

Contribution

It derives the evolution equation for field line helicity and demonstrates its dominant work-like term during localized reconnection, highlighting efficient local helicity redistribution.

Findings

Reconnection redistributes helicity in a pairwise manner.

The evolution of field line helicity is dominated by a work-like term at endpoints.

Reconnection efficiently redistributes helicity with minimal change to total helicity.

Abstract

We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finite-B magnetic reconnection. Total (relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a work-like term that is evaluated at the field line endpoints, namely the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a well-organized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity.