The Role of Alfvén Resonances in Forced Magnetic Reconnection and its impacts on Kelven Helmholtz Instability

Alfvén resonance and magnetic reconnection are fundamental plasma processes which have received much attention in the past because of their role in heating space and laboratory plasmas. We demonstrate here that magnetic reconnection induced by an external driver, or forced magnetic reconnection, is a limiting case of Alfvén resonance parameterized by the frequency of the driver. In addition to demonstrating the transition between these processes, we determine several scalings, such as the dependence of the constant-psi reconnected flux on the driver frequency, showing that a small but finite frequency above the inverse of the reconnection time strongly suppresses reconnection. As a non-linear application of this study on Alfven resonances, we extend prior work by analyzing the saturation of a Kelvin-Helmholtz instability in the presence of Alfvén resonances. The width of the island resulting from a KH roll-up is parameterized as a function of the initial Mach number and the ratio of velocity and magnetic field shear widths. Finally, we study the analytic form of the saturated equilibrium state to understand the nonlinear behavior of this system.