Abstract. The Geospace Environmental Modeling (GEM) Reconnection Challengeproject is presented and the important results, which are presented in a series of companion papers, are summarized. Magnetic reconnection is studied in a simple Harris sheet configuration with a specified set of initial conditions, including a finite amplitude, magnetic island perturbation to trigger the dynamics. The evolution of the system is explored with a broad variety of codes, ranging from fully electromagnetic particle in cell (PIC) codes to conventional resistive magnetohydrodynamic (MHD) codes, and the results are compared. The goal is to identify the essential physics which is required to model collisionless magnetic reconnection. All models that include the Hall effect in the generalized Ohm's law produce essentially indistinguishable rates of reconnection, corresponding to nearly Alfv6nic inflow velocities. Thus the rate of reconnection is insensitive to the specific mechanism which breaks the frozen-in condition, whether resistivity, electron inertia, or electron thermal motion. The reconnection rate in the conventional resistive MHD model, in contrast, is dramatically smaller unless a large localized or current dependent resistivity is used. The Hall term brings the dynamics of whistler waves into the system. The quadratic dispersion property of whistlers (higher phase speed at smaller spatial scales) is the key to understanding these results. The implications of these results for trying to model the global dynamics of the magnetosphere are discussed.

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Abstract. The Geospace Environment Modeling (GEM) Challenge Harris current sheet problem is simulated in 2 1/2 dimensions using full particle, hybrid, and Hall MHD simulations. The same gross reconnection rate is found in all of the simulations independent of the type of code used, as long as the Hall term is included. In addition, the reconnection rate is independent of the mechanism which breaks the frozen-in flux condition, whether it is electron inertia or grid scale diffusion. The insensitivity to the mechanism which breaks the frozen-in condition is a consequence of whistler waves, which control the plasma dynamics at the small scales where the ions become unmagnetized. The dispersive character of whistlers, in which the phase velocity increases with decreasing scale size, allows the flux of electrons flowing away from the dissipation region to remain finite even as the strength of the dissipation approaches zero. As a consequence, the throttling of the reconnection process as a result of the small scale size of the dissipation region, which occurs in the magnetohydrodynamic model, no longer takes place. The important consequence is that the minimum physical model necessary to produce physically correct reconnection rates is a Hall MHD description which includes the Hall term in Ohm's law. A density depletion layer, which lies just downstream from the magnetic separatrix, is identified and linked to the strong in-plane Hall currents which characterize kinetic models of magnetic reconnection.

Three-dimensional particle simulations of magnetic reconnection reveal the development of turbulence driven by intense electron beams that form near the magnetic x-line and separatrices. The turbulence collapses into localized three-dimensional nonlinear structures in which the electron density is depleted. The predicted structure of these electron holes compares favorably with satellite observations at Earth's magnetopause. The birth and death of these electron holes and their associated intense electric fields lead to strong electron scattering and energization, whose understanding is critical to explaining why magnetic explosions in space release energy so quickly and produce such a large number of energetic electrons.

We consider ion heating by turbulent Alfvén waves (AWs) and kinetic Alfvén waves (KAWs) with wavelengths (measured perpendicular to the magnetic field) that are comparable to the ion gyroradius and frequencies ω smaller than the ion cyclotron frequency Ω. As in previous studies, we find that when the turbulence amplitude exceeds a certain threshold, an ion's orbit becomes chaotic. The ion then interacts stochastically with the time-varying electrostatic potential, and the ion's energy undergoes a random walk. Using phenomenological arguments, we derive an analytic expression for the rates at which different ion species are heated, which we test by simulating test particles interacting with a spectrum of randomly phased AWs and KAWs. We find that the stochastic heating rate depends sensitively on the quantity ε = δv ρ /v ⊥ , where v ⊥ (v ) is the component of the ion velocity perpendicular (parallel) to the background magnetic field B 0 , and δv ρ (δB ρ ) is the rms amplitude of the velocity (magnetic-field) fluctuations at the gyroradius scale. In the case of thermal protons, when ε ≪ ε crit , where ε crit is a dimensionless constant, a proton's magnetic moment is nearly conserved and stochastic heating is extremely weak. However, when ε > ε crit , the proton heating rate exceeds the cascade power that would be present in strong balanced KAW turbulence with the same value of δv ρ , and magnetic-moment conservation is violated even when ω ≪ Ω. For the random-phase waves in our test-particle simulations, ε crit ≃ 0.2. For protons in low-β plasmas, ε ≃ β −1/2 δB ρ /B 0 , and ε can exceed ε crit even when δB ρ /B 0 ≪ ε crit , where β is the ratio of plasma pressure to magnetic pressure. The heating is anisotropic, increasing v 2 ⊥ much more than v 2 when β ≪ 1. (In contrast, at β 1 Landau damping and transit-time damping of KAWs lead to strong parallel heating of protons.) At comparable temperatures, alpha particles and minor ions have larger values of ε than protons and are heated more efficiently as a result. We discuss the implications of our results for ion heating in coronal holes and the solar wind.