Extended theory of the Taylor problem in the plasmoid-unstable regime

TL;DR

This paper extends the theory of forced magnetic reconnection by incorporating plasmoid instability, deriving thresholds and reconnection rates, supported by simulations, revealing conditions for fast reconnection in tearing-stable plasmas.

Contribution

It introduces an extended analytical framework for the Taylor problem considering plasmoid instability, including threshold conditions and reconnection rates, validated by simulations.

Findings

Plasmoid instability enables fast reconnection even in tearing-stable plasmas.

Derived threshold perturbation amplitude for plasmoid onset.

Analytical expression for reconnection rate in plasmoid regime.

Abstract

A fundamental problem of forced magnetic reconnection has been solved taking into account the plasmoid instability of thin reconnecting current sheets. In this problem, the reconnection is driven by a small amplitude boundary perturbation in a tearing-stable slab plasma equilibrium. It is shown that the evolution of the magnetic reconnection process depends on the external source perturbation and the microscopic plasma parameters. Small perturbations lead to a slow nonlinear Rutherford evolution, whereas larger perturbations can lead to either a stable Sweet-Parker-like phase or a plasmoid phase. An expression for the threshold perturbation amplitude required to trigger the plasmoid phase is derived, as well as an analytical expression for the reconnection rate in the plasmoid-dominated regime. Visco-resistive magnetohydrodynamic simulations complement the analytical calculations. The plasmoid formation plays a crucial role in allowing fast reconnection in a magnetohydrodynamical plasma, and the presented results suggest that it may occur and have profound consequences even if the plasma is tearing-stable.