On turbulent magnetic reconnection: fast and slow mean steady-states

TL;DR

This paper analyzes a turbulent magnetic reconnection model, demonstrating that only the classic Sweet-Parker and Petschek solutions are steady states, with Petschek reconnection being self-similar and capable of producing a universal steady rate.

Contribution

It shows that these two steady-state solutions are the only possibilities and provides criteria for their selection based on turbulent energy growth and current density.

Findings

Sweet-Parker occurs without turbulent energy growth

Petschek occurs when current density exceeds a critical value

Petschek reconnection is self-similar and yields a universal rate

Abstract

We investigate a model of turbulent magnetic reconnection introduced by Higashimori, Yokoi and Hoshino (Phys. Rev. Lett. 110, 255001) and show that the classic two-dimensional, steady-state Sweet-Parker and Petschek reconnection solutions are supported. We present evidence that these are the only two steady-state reconnection solutions, and we determine the criterion for their selection. Sweet-Parker reconnection occurs when there is no growth in turbulent energy, whereas Petschek reconnection occurs when the current density in the reconnecting current sheet is able to surpass a critical value, allowing for the growth of turbulent energy that creates the diffusion region. Further, we show that the Petschek solutions are self-similar, depending on the value of the turbulent time scale, and produce a universal steady reconnection rate. The self-consistent development of Petschek reconnection through turbulence, within the model, is an example of fast and steady magnetic reconnection without an explicit need for the collisionless terms in an extended Ohm's law.