Geospace Environment Modeling (GEM) magnetic reconnection challenge: Resistive tearing, anisotropic pressure and Hall effects

The nonlinear evolution of resistive tearing is studied in various regimes, including one-fluid isotropic MHD, anisotropic (gyrotropic) MHD with terms approximating the effects of anisotropy driven instabilities, and HaIl-MHD. Both uniform resistivity and spatially localized resistivity are investigated. The initial state is a plane one-dimensional current sheet with an initial perturbation representing a periodic structure with magnetic islands and x type neutral points, chosen for the “GEM magnetic reconnection challenge” [Birn et al., this issue]. In the absence of dissipation, within ideal MHD, the initially imposed x type configuration collapses into a thin current sheet of finite length, while the magnetic islands contract, conserving their magnetic flux. The current density in the thin sheet becomes significantly enhanced, so that microscopic dissipation mechanisms can be expected to be ignited, even if they were absent in the initial state. Finite resistivity enables reconnection, and the growth of magnetic islands as in particle simulations. A comparison of reconnection rates shows that for the chosen initial current sheet thickness, a localized resistivity, corresponding to a Lundquist number (magnetic Reynolds number) of order unity, is necessary to approximate the growth and the reconnection electric field in the particle simulations. Pressure anisotropy, governed by double adiabatic conservation laws (modified by Ohmic heating), leads to reduced growth rates. This reduction is drastic for uniform resistivity. Isotropizing terms, modeling the effects of anisotropy driven microinstabilities again destabilize. HaIl-MHD simulations can reproduce the fast growth of the particle simulations. The various models show both similarities and dissimilarities in their spatial structure. For similar amounts of reconnected flux, the variation of the normal magnetic field and of the (ion) flow speed along the current sheet are similar, but electric field and current density show significant differences.