Unified Framework of Forced Magnetic Reconnection and Alfven Resonance

TL;DR

This paper develops a unified linear theory linking forced magnetic reconnection and Alfvén resonance, analyzing how boundary perturbations influence plasma behavior and reconnection rates.

Contribution

It introduces a comprehensive framework that describes the transition from Alfvén resonance to forced reconnection under various boundary perturbation frequencies.

Findings

Alfvén resonance arises from residues at resonant poles in the complex frequency plane.

Reconnection transitions to a constant-psi regime for low forcing frequencies.

Reconnection rate diminishes significantly at high forcing frequencies.

Abstract

A unified linear theory that includes forced reconnection as a particular case of Alfv\'en resonance is presented. We consider a generalized Taylor problem in which a sheared magnetic field is subject to a time-dependent boundary perturbation oscillating at frequency $\omega_0$. By analyzing the asymptotic time response of the system, the theory demonstrates that the Alfv\'en resonance is due to the residues at the resonant poles, in the complex frequency plane, introduced by the boundary perturbation. Alfv\'en resonance transitions towards forced reconnection, described by the constant-psi regime for (normalized) times $t\gg S^{1/3}$, when the forcing frequency of the boundary perturbation is $\omega_0\ll S^{-1/3}$, allowing the coupling of the Alfv\'en resonances across the neutral line with the reconnecting mode, as originally suggested in [1]. Additionally, it is shown that even if forced reconnection develops for finite, albeit small, frequencies, the reconnection rate and reconnected flux are strongly reduced for frequencies $\omega_0\gg S^{-3/5}$.