Scaling of forced magnetic reconnection in the Hall-magnetohydrodynamic Taylor problem

Abstract

Two-dimensional, incompressible, zero guide-field, nonlinear Hall-MHD (magnetohydrodynamical) 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 being such as to drive magnetic reconnection within the plasma. This type of reconnection, which is not due to an intrinsic plasma instability, is generally known as “forced reconnection.” The inclusion of the Hall term in the plasma Ohm’s law is found to greatly accelerate the rate of magnetic reconnection. In the linear Hall-MHD regime, the peak instantaneous reconnection rate is found to scale like dΨ/dt∼diη1/3Ⅺ0, where Ψ is the reconnected magnetic flux, di the collisionless ion skin depth, η the resistivity, and Ⅺ0 the amplitude of the boundary perturbation. In the nonlinear Hall-MHD regime, the peak reconnection rate is found to scale like dΨ/dt∼di3/2Ⅺ02.