Unified Framework of Forced Magnetic Reconnection and Alfven Resonance

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 $\omega_0\gg S^{-3/5}$.