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The role of a super-Alfv\'enic plasmoid instability in the onset of fast reconnection is studied by means of the largest Hall magnetohydrodynamics simulations to date, with system sizes up to $10^{4}$ ion skin depths ($d_{i}$). It is demonstrated that the plasmoid instability can facilitate the onset of rapid Hall reconnection, in a regime where the onset would otherwise be inaccessible because the Sweet-Parker width is significantly above $d_{i}$. However, the topology of Hall reconnection is not inevitably a single stable X-point. There exists an intermediate regime where the single X-point topology itself exhibits instability, causing the system to alternate between a single X-point geometry and an extended current sheet with multiple X-points produced by the plasmoid instability. Through a series of simulations with various system sizes relative to $d_{i}$, it is shown that system size affects the accessibility of the intermediate regime. The larger the system size is, the easier it is to realize the intermediate regime. Although our Hall MHD model lacks many important physical effects included in fully kinetic models, the fact that a single X-point geometry is not inevitable raises the interesting possibility for the first time that Hall MHD simulations may have the potential to realize reconnection with geometrical features similar to those seen in fully kinetic simulations, namely, extended current sheets and plasmoid formation., Comment: Accepted for publication in Physics of Plasmas

Controversy has been raised regarding the cause of hysteresis, or bistability, of solutions to the equations that govern the geometry of the reconnection region in Hall magnetohydrodynamic (MHD) systems. This brief communication presents a comparison of the frameworks within which this controversy has arisen and illustrates that the Hall MHD hysteresis originally discovered numerically by Cassak et al. [Phys. Rev. Lett. 95, 235002 (2005)] is a different phenomenon from that recently reported by Zocco et al. [Phys. Plasmas 16, 110703 (2009)] on the basis of analysis and simulations in electron MHD with finite electron inertia. We demonstrate that the analytic prediction of hysteresis in EMHD does not describe or explain the hysteresis originally reported in Hall MHD, which is shown to persist even in the absence of electron inertia.

This paper presents linear analytical and numerical studies of plasmoid instabilities in the presence of shear flow in high-Lundquist-number plasmas. Analysis demonstrates that the stability problem becomes essentially two dimensional as the stabilizing effects of shear flow become more prominent. Scaling results are presented for the two-dimensional instabilities. An approximate criterion is given for the critical aspect ratio of thin current sheets at which the plasmoid instability is triggered.

This paper presents Sweet–Parker type scaling arguments in the context of hyper-resistive Hall magnetohydrodynamics. Numerical experiments suggest that both cusplike and modestly more extended geometries are realizable. However, the length of the electron dissipation region, which is taken as a parameter by several recent studies, is found to depend explicitly on the level of hyper-resistivity. Furthermore, although hyper-resistivity can produce more extended electron dissipation regions, the length of the region remains smaller than one ion skin depth for the largest values of hyper-resistivity considered here, significantly shorter than current sheets seen in many recent kinetic studies. The length of the electron dissipation region is found to depend on electron inertia as well, scaling like (me/mi)3/8. However, the thickness of the region appears to scale similarly, so that the aspect ratio is at most very weakly dependent on (me/mi).

This paper presents two-fluid simulations of forced magnetic reconnection with finite electron inertia in a collisionless three-dimensional (3D) cube with periodic boundaries in all three directions. Comparisons are made to analogous two-dimensional (2D) simulations. Reconnection in this system is driven by a spatially localized forcing function that is added to the ion momentum equation inside the computational domain. Consistent with previous results in similar, but larger forced 2D simulations [B. Sullivan, B. N. Rogers, and M. A. Shay, Phys. Plasmas 12, 122312 (2005)], for sufficiently strong forcing the reconnection process is found to become Alfvenic in both 2D and 3D, i.e., the inflow velocity scales roughly like some fraction of the Alfven speed based on the upstream reconnecting magnetic field, and the system takes on a stable configuration with a dissipation region aspect ratio on the order of 0.15.

This paper presents two-fluid simulations of forced magnetic reconnection with finite electron inertia in a collisionless three-dimensional (3D) cube with periodic boundaries in all three directions. Comparisons are made to analogous two-dimensional (2D) simulations. Reconnection in this system is driven by a spatially localized forcing function that is added to the ion momentum equation inside the computational domain. Consistent with previous results in similar, but larger forced 2D simulations [B. Sullivan, B. N. Rogers, and M. A. Shay, Phys. Plasmas 12, 122312 (2005)], for sufficiently strong forcing the reconnection process is found to become Alfvenic in both 2D and 3D, i.e., the inflow velocity scales roughly like some fraction of the Alfven speed based on the upstream reconnecting magnetic field, and the system takes on a stable configuration with a dissipation region aspect ratio on the order of 0.15.