A Generalized Flux Function for Three-dimensional Magnetic Reconnection

TL;DR

This paper introduces a generalized flux function for 3D magnetic fields, enabling the measurement of magnetic reconnection rates in complex configurations without null points, advancing understanding of magnetic topology changes.

Contribution

It extends the 2D flux function concept to 3D fields using hyperbolic fixed points and manifolds, providing a new method to quantify reconnection in complex magnetic structures.

Findings

The generalized flux function allows measurement of reconnection rates in 3D fields.

The flux partition responds predictably to isolated reconnection events.

The method relates to the integrated parallel electric field in reconnection analysis.

Abstract

The definition and measurement of magnetic reconnection in three-dimensional magnetic fields with multiple reconnection sites is a challenging problem, particularly in fields lacking null points. We propose a generalization of the familiar two-dimensional concept of a magnetic flux function to the case of a three-dimensional field connecting two planar boundaries. Using hyperbolic fixed points of the field line mapping, and their global stable and unstable manifolds, we define a unique flux partition of the magnetic field. This partition is more complicated than the corresponding (well-known) construction in a two-dimensional field, owing to the possibility of heteroclinic points and chaotic magnetic regions. Nevertheless, we show how the partition reconnection rate is readily measured with the generalized flux function. We relate our partition reconnection rate to the common definition of three-dimensional reconnection in terms of integrated parallel electric field. An analytical example demonstrates the theory, and shows how the flux partition responds to an isolated reconnection event.