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 $S−1∕5$⁠. Here, $c∕ωpi$ is the ion inertial skin depth, $a$ is the width of the plasma slab, and $S≫1$ 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 $ωτA≪1$⁠, $τA$ being the Alfvén transit time, various reconnection regimes are identified. The corresponding heating rates, which are determined by the parameters $di$⁠, $S$⁠, and $ωτA$⁠, 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 $dψ1(0)∕dt∼di1∕2S−1∕2(B0δ0∕τA)$⁠, where $ψ1(0)$ is the reconnected magnetic flux, $B0$ is the magnetic field strength, and $δ0$ is the amplitude of the boundary deformation.