Scalings Pertaining to Current Sheet Disruption Mediated by the Plasmoid Instability

TL;DR

This paper derives and validates analytical scaling relations for the plasmoid instability in evolving current sheets, considering effects of reconnection outflow and different triggering scenarios, enhancing understanding of current sheet disruption.

Contribution

It introduces new scaling relations for plasmoid instability considering outflow effects and distinguishes between initial perturbation and system noise triggers.

Findings

Scaling relations include power-law and logarithmic factors.

Relations agree with previous models when outflow effects are neglected.

Numerical validation confirms the analytical predictions.

Abstract

Analytic scaling relations are derived for a phenomenological model of the plasmoid instability in an evolving current sheet, including the effects of reconnection outflow. Two scenarios are considered, where the plasmoid instability can be triggered either by an injected initial perturbation or by the natural noise of the system (here referred to as the system noise). The two scenarios lead to different scaling relations because the initial noise decays when the linear growth of the plasmoid instability is not sufficiently fast to overcome the advection loss caused by the reconnection outflow, whereas the system noise represents the lowest level of fluctuations in the system. The leading order approximation for the current sheet width at disruption takes the form of a power-law multiplied by a logarithmic factor, and from that, the scaling relations for the wavenumber and the linear growth rate of the dominant mode are obtained. When the effects of the outflow are neglected, the scaling relations agree, up to the leading order approximation, with previously derived scaling relations based on a principle of least time. The analytic scaling relations are validated with numerical solutions of the model.