Quantifying three dimensional reconnection in fragmented current layers

TL;DR

This paper develops an analytical framework to quantify magnetic reconnection rates in fragmented current layers, especially in high Lundquist number plasmas like the Solar Corona and Earth's Magnetosphere, where reconnection occurs in multiple sites.

Contribution

It introduces two measures for reconnection rate—total and net—applying to fragmented current layers without magnetic nulls, supported by two analytical models.

Findings

The total reconnection rate captures all connection formations.

The net rate reflects the dominant change in magnetic connectivity.

Models demonstrate how to apply these measures in practice.

Abstract

There is growing evidence that when magnetic reconnection occurs in high Lundquist number plasmas such as in the Solar Corona or the Earth's Magnetosphere it does so within a fragmented, rather than a smooth current layer. Within the extent of these fragmented current regions the associated magnetic flux transfer and energy release occurs simultaneously in many different places. This investigation focusses on how best to quantify the rate at which reconnection occurs in such layers. An analytical theory is developed which describes the manner in which new connections form within fragmented current layers in the absence of magnetic nulls. It is shown that the collective rate at which new connections form can be characterized by two measures; a total rate which measures the true rate at which new connections are formed and a net rate which measures the net change of connection associated with the largest value of the integral of $E_{\|}$ through all of the non-ideal regions. Two simple analytical models are presented which demonstrate how each should be applied and what they quantify.