Scaling of forced magnetic reconnection in the Hall-magnetohydrodynamical Taylor problem with arbitrary guide field

Two-dimensional, nonlinear, Hall-magnetohydrodynamical (MHD) numerical simulations are used to investigate the scaling of the rate of forced magnetic reconnection in the so-called Taylor problem. In this problem, a small amplitude boundary perturbation is suddenly applied to a tearing stable, slab plasma equilibrium. The perturbation is such as to drive magnetic reconnection within the plasma. This type of reconnection, which is not due to an intrinsic plasma instability, is generally termed “forced reconnection.” Hall effects are found to greatly accelerate the rate of magnetic reconnection, relative to the well-known Sweet–Parker rate. In the nonlinear Hall-MHD regime with arbitrary guide field, the peak reconnection rate is found to be independent of the resistivity, and to scale like dψ/dt∼[β/(1+β)]3/4di3/2Ⅺ02, where β is the plasma beta calculated using the guide field, di the collisionless ion skin depth, and Ⅺ0 the amplitude of the boundary perturbation.