On the possibility of Alfvén wave resonance in collisionless magnetic reconnection

Alfvén wave resonance and magnetic reconnection are among the potential candidates for efficient dissipation of magnetic energy in space and astrophysical plasmas. In this paper, the correspondence between Alfvén resonance and the electron-inertia driven reconnection in a sheared force-free magnetic field is discussed. By analytical scaling the linear regimes of compressible tearing instability in the two-fluid magnetohydrodynamic (MHD) model, we present parametric conditions for the possibility of Alfvén resonance existence. Meanwhile, it is argued that the slow MHD Alfvénic resonance can take place only in the “intermediate” - called Hall-MHD regime when β>μ. β is the ratio of plasma thermal pressure to the pressure in equilibrium magnetic field and μ is the electron to ion mass ratio. There is no room for such a resonant dissipation phenomenon either in the single-fluid MHD or the electron-MHD regimes.