On transition from Alfvén resonance to forced magnetic reconnection

Abstract

We revisit the transition from Alfvén resonance to forced magnetic reconnection with a focus on the property of their singularities. As the driven frequency tends to zero, the logarithmic singularity of Alfvén resonance shifts to the power-law singularity of forced reconnection, due to merging of the two resonance layers. The transition criterion depends on either kinetic effects or dissipations that resolve the singularity. As an example, a small but finite resistivity η is introduced to investigate the transition process. The transition threshold is then obtained as the driven frequency reaches a level of ∼O((η/k)1/3).