Using a Higher-order Numerical Scheme to Study the Hall Magnetic Reconnection

Abstract

We use our recently developed higher-order conservation element and solution element scheme to investigate the evolutionary process of Hall magnetic reconnection. The purpose of this paper is twofold: (1) to take advantage of higher-order numerical schemes to capture some fine structures very well with fewer grid points and reduced computational cost; (2) to develop a better understanding of the magnetic reconnection described by Hall MHD; as Birn et al. pointed out, the Hall effect is a critical ingredient in determining collisionless reconnection rates in the magnetosphere. The contributions of this paper mainly include the following: (1) we capture a two-step magnetic reconnection process and describe the formation mechanism; (2) the simulations show complex formation and interaction of magnetic islands and we provide the ways by which the magnetic islands form and disappear; (3) we find an oscillatory nature of the reconnection and the transfer of energy from magnetic field to kinetic energy and thermal energy; (4) we identify the merging process of the central magnetic island and the outflow region magnetic island.