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.

A general stability analysis is performed for the Kelvin‐Helmholtz instability in sheared magnetohydrodynamic flow of finite thickness in a compressible plasma. The analysis allows for arbitrary orientation of the magnetic field B0, velocity flow v0, and wave vector k in the plane perpendicular to the velocity gradient, and no restrictions are imposed on the sound or Alfvén Mach numbers. The stability problem is reduced to the solution of a single second‐order differential equation, which includes a gravitational term to represent coupling between the Kelvin‐Helmholtz mode and the interchange mode. In the incompressible limit it is shown that the Kelvin‐Helmholtz mode is completely stabilized for any velocity profile as long as the condition is satisfied, where V0 is the total velocity jump across the shear layer. Numerical results are obtained for a hyperbolic tangent velocity profile for the transverse (B0 ⊥ v0) and parallel (B0∥v0) flow configurations. Only modes with kΔ < 2 are unstable, where Δ is the scale length of the shear layer. The fastest growing modes occur for kΔ ∼ 0.5‐1.0. Compressibility and a magnetic field component parallel to the flow are found to be stabilizing effects. For the transverse case, only the fast magnetosonic mode is destabilized, but if k · B0 ≠ 0, the instability contains Alfvén‐mode and slow‐mode components as well. The Alfvén component gives rise to a field‐aligned current inside the shear layer. In the parallel case, both Alfvén and slow magnetosonic components are present, with the Alfvén mode confined inside the shear layer. The results of the analysis are used to discuss the stability of sheared plasma flow at the magnetopause boundary and in the solar wind. At the magnetopause boundary, the fastest growing Kelvin‐Helmholtz mode has a frequency of 0 (V0/2Δ), which overlaps with the frequency range of geomagnetic pulsations (Pc 3‐5). It is suggested that the MHD Kelvin‐Helmholtz instability could serve as a dynamo process driving small‐scale field‐aligned currents in the presence of the sheared plasma flow in the magnetosphere.

Abstract. The objective of the Geospace Environment Modeling (GEM) magneticreconnection challenge is to understand the collisionless physics that controls the rate of magnetic reconnection in a two-dimensional configuration. The challenge involves investigating a standard model problem based on a simple Harris sheet configuration by means of a variety of physical models in order to isolate the essential physics. In the present work the challenge problem is modeled using an electromagnetic particle-in-cell code in which full particle dynamics are retained for both electrons and ions and Maxwell's equations are solved without approximation.

[1] Previous investigations of collisionless magnetic reconnection in a standard Harris neutral sheet configuration have demonstrated the importance of the Hall term for producing near-Alfvénic rates of reconnection and the existence of a very thin ($c/w pe ) electron current layer and sharp density/pressure gradients on c/w pi scales. The present work uses three-dimensional (3-D) particle-in-cell simulations with an open geometry to investigate the changes in the reconnection physics produced by a ''guide field'' component B 0y of the magnetic field. With B 0y ] B 0 , the nonlinear reconnection rate is not substantially modified from that for the Harris case. The properties of the reconnection fields and particle dynamics, however, are strongly altered. The familiar quadrupole B y pattern is replaced by an enhancement of jB y j between the separatrices. The enhanced parallel electric field and parallel electron velocity are confined to one pair of separatrix arms (which are positively charged), while the electron current peaks on the other pair (which are negatively charged). The ion outflow along the current sheet polarizes the separatrices, thereby creating large components of the in-plane electric field. The electrons are accelerated to form a beam structure with parallel speed limited by the electron Alfvén speed. The beam-dominated electron distribution produces some y-dependent structures in E k . For B 0y ) B 0 , the reconnection rate is reduced by a factor of 2-3, and the parallel fields and velocities are somewhat smaller; the Hall current produced perturbations in B y are considerably reduced.

[1] Three-dimensional electromagnetic particle-in-cell simulations are used to investigate the stability properties of a plasma sheet equilibrium with a minimum in the magnetic normal (B z ) component. Such a configuration is found to be unstable to a ballooning/ interchange type mode that is localized tailward of the B z minimum. The mode has a relatively short dawn-dusk wavelength of the order of the ion Larmor radius in the B z field (∼2000 km) and a phase velocity in the direction of the ion diamagnetic drift with a magnitude about one-fifth of the drift speed. The real frequency is about 60% of the midplane ion cyclotron frequency. The dominant mode polarization is d and dB k . A linear kinetic analysis including bounce and drift resonance interactions for the electrons and an orbit average over the flux tube volume for the Boltzmann term in the ion density perturbation produces agreement with the simulation mode properties and permits identification of the mode as the low-frequency extension of the lower hybrid drift instability in straight magnetic geometry. In its nonlinear evolution, the mode develops Rayleigh-Taylor fingers that extend across the B z minimum and into the near-Earth dipole region. These fingers transport magnetic flux earthward, and the flux is redistributed by electron Hall currents that flow around the fingers. This mode is likely to contribute to the nearly continuous presence of turbulence in the center of the plasma sheet.

[1] The process of collisionless magnetic reconnection in an ion-scale current sheet containing strong gradients in the density and magnetic field strength across the layer is investigated using two-dimensional particle-in-cell simulations. Such a current sheet configuration contains a strong normal polarization electric field on the high field/low density (magnetospheric) side of the layer. In initial-value simulations for such an asymmetric sheet, the reconnection rate and saturation level are found to be smaller by factors of 2-3 compared with a similar-scale symmetric current sheet. These rates are probably too small to explain observations at the dayside magnetopause. The addition of an external-driving electric field increases the reconnection rate substantially. This driven reconnection configuration is characterized by a nearly parallel inflow of electrons along the magnetosheath separatrices as the electrons attempt to flow from the high density side to the low density side of the layer, a strong outward flow of Poynting flux along the magnetospheric separatrices associated with the normal electric field and out-of-plane magnetic field, and a strong ion outflow jet. The outflow region on the magnetospheric side also exhibits a patchy parallel electric field structure and parallel electron velocity distributions with a counterstreaming feature. The addition of a moderate uniform magnetic guide field component (shear angle^110°) has no appreciable effect on the reconnection rate but does produce a drift of the X line in the direction of the electron diamagnetic drift at a small fraction of the magnetosheath Alfvén speed.

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The linear behavior of the double-tearing mode is investigated within the framework of magnetohydrodynamics. A two-space-scale analysis in which resistive solutions valid near the rational surfaces are joined to ideal solutions outside these regions is performed and used to derive the dispersion relation for the mode. If the separation of the rational surfaces at x=±xs is sufficiently small [xs/a&lt;(kya)−7/9S−1/9], the growth rate is predicted to scale as S−1/3, and the structure of the mode proves to be essentially identical with that of the m=1 tearing mode in cylindrical geometry. With increasing separation, the mode makes a transition to the S−3/5 scaling and structure of the standard tearing mode. These predictions are confirmed by direct numerical solution of the magnetohydrodynamic equations, and the S−1/3 scaling is shown to be correlated with violations of the constant-ψ approximation. Possible physical implications of the double-tearing mode are discussed.