Hall assisted forced magnetic reconnection

The role of the Hall effect in forced magnetic reconnection is investigated analytically for the so-called Taylor problem. In the latter, a tearing stable slab plasma equilibrium, which is chosen here to be a simple magnetic field reversal, is subjected to a small-amplitude boundary deformation that drives magnetic reconnection (hence the adjective "forced") at the neutral surface within the plasma. It is shown that such reconnection becomes substantially accelerated by the Hall effect when the nondimensional parameter di =(c ωpi) a exceeds S-15. Here, c ωpi is the ion inertial skin depth, a is the width of the plasma slab, and S1 is the Lundquist number of a highly conducting plasma. Two different types of external perturbation are considered. In the case of continuous quasistatic driving, with a frequency ω such that ω τA 1, τA being the Alfv́n transit time, various reconnection regimes are identified. The corresponding heating rates, which are determined by the parameters di, S, and ω τA, are derived. In the case of a "one-off" reconnection event, we demonstrate when and how the transition from the Hall regime to the magnetohydrodynamic regime occurs in the course of the reconnection process. It is found that the peak instantaneous reconnection rate scales as d ψ1 (0)dt∼ di 12 S-12 (B0 δ0 τA), where ψ1 (0) is the reconnected magnetic flux, B0 is the magnetic field strength, and δ0 is the amplitude of the boundary deformation. © 2006 American Institute of Physics.