## 1. Introduction

[2] Collisionless magnetic reconnection facilitates the conversion of magnetic energy to high-velocity plasma flows, energetic beams, and thermal motion. In the case of a simple reversed magnetic field a fairly detailed understanding has been developed by comparing two-fluid, hybrid and full particle simulations [*Birn et al.*, 2001]. Nevertheless, the overall physical picture remains incomplete since this investigation was restricted to a system with spatial variation in the two-dimensional (2-D) plane perpendicular to the direction of the current. Such a model necessarily eliminates instabilities with a variation along the current sheet transverse to the plane of reconnection. A number of instabilities have been discussed as candidates for producing structure in the out-of-plane direction. These include the drift kink [*Zhu and Winglee*, 1996; *Ozaki et al.*, 1996; *Pritchett and Coroniti*, 1996; *Daughton*, 1999; *Horiuchi and Sato*, 1999] and sausage [*Büchner*, 1999] instabilities at the ion scales. These instabilities are at a large enough scale that they would substantially modulate reconnection in the out-of-plane direction. There is now substantial evidence that the prominence of the drift kink instability in early simulations was a consequence of an unrealistic electron-to-ion mass ratio and that at realistic mass ratios the drift kink mode would be suppressed [*Daughton*, 1999]. In recent 3-D particle simulations, therefore, symmetry constraints were imposed to eliminate the drift-kink instability, and the resulting simulations indicated that reconnection remained largely two-dimensional [*Hesse et al.*, 2001; *Pritchett*, 2001]. Buneman [*Krall and Trivelpiece*, 1973], lower hybrid drift [*Huba et al.*, 1980; *Brackbill et al.*, 1984; *Horiuchi and Sato*, 1999; *Pritchett and Coroniti*, 2001; *Rogers et al.*, 2000], and electron shear flow [*Drake et al.*, 1997; *Rogers et al.*, 2000] instabilities arise at smaller scales and may therefore in the nonlinear state be represented as an anomalous resistivity or viscosity. Electron shear flow instabilities specifically were found to broaden the electron current layer, which develops at the *x* line during collisionless reconnection to several times the electron skin depth, *d*_{e} = *c*/ω_{pe} [*Rogers et al.*, 2000]. Fluid simulations, however, must be interpreted with care since kinetic effects are expected to play a major role, in particular, in the vicinity of the neutral line where electrons and ions become unmagnetized. Using massively parallel computers, it becomes feasible to challenge the previous fluid results with full particle simulations and to extend earlier full particle simulations to much larger ion-to-electron mass ratios.

[3] In the present paper, using a full particle simulation model, we therefore explore the growth of secondary instabilities in the current and density layers that self-consistently develop during magnetic reconnection. The goal is first to determine whether reconnection has a tendency to self-modulate in the out-of-plane direction and second to determine whether small-scale instabilities develop in these layers and produce anomalous resistivity or viscosity, which feeds back on the rate of reconnection. In this paper we will not explore the role of instabilities that develop in realistic magnetotail equilibria in triggering reconnection during substorms. For this reason we focus primarily on the late time behavior of the dynamics after the current layer near the *x* line and the slow shocks separating the inflow and outflow regions have approached their steady state structure. A true steady state cannot, of course, be achieved in the present simulations because computational constraints limit the macroscopic size of the system. Nevertheless, as near as we can tell, the late time results are relatively insensitive to the initial widths of the current layers. The goal is also not to obtain an asymptotic scaling of the reconnection rate. This requires the exploration of reconnection in very large systems so that the macroscopic and microscopic scales are well separated. This is not possible within the constraints of the present computer systems while at the same time achieving sufficient separation of the ion and electron inertial scale lengths and the Debye length. We do find reconnection rates that are comparable with those measured in the Geospace Environmental Modeling (GEM) Reconnection Challenge [*Birn et al.*, 2001].

[4] The high-resolution 3-D simulations have been completed on a massively parallel T3E systems with typically 250 million electrons and 250 million ions using a newly developed relativistic particle code. Our simulations confirm the importance of the lower hybrid drift instability at the boundary between the inflow and outflow regions downstream of the *x* line, where the gradient in the plasma pressure steepens as a result of the formation of “slow shocks.” The strong current layers that develop near the *x* line remain surprisingly laminar. The lower hybrid drift instability, the drift kink instability and electron shear flow driven instabilities all remain stable in the vicinity of the *x* line. The lower hybrid drift mode is stabilized by finite β effects in the region of large density gradient, which forms very close to the *x* line and is also stable in the region of lower β farther from the *x* line, where gradients are more modest. The electron shear flow instability, however, which destabilizes narrow electron current sheets in the two-fluid limit, is totally absent in our full particle simulations. Stability is a consequence of the increased width of the electron current layers in the kinetic versus the two-fluid model. The electron heating that occurs as the electrons become demagnetized at the *x* line prevents the width of the current layer from falling below *d*_{e}, which is required for onset of the electron shear flow instability. The electron heating at the *x* line also suppresses the onset of the Buneman instability. Electron drift speeds in the center of the current sheet are comparable with but do not exceed the electron thermal velocity of electrons near the *x* line. No evidence of the Buneman instability and associated anomalous resistivity has been measured.

[5] The present results are limited to the case of no initial out-of-plane (guide) magnetic field. In a subsequent paper we will show that the behavior of the system with a finite guide field is much more dynamic [*Drake et al.*, 2002]. We also note that the conclusion that secondary instabilities do not play an important role during reconnection at late times does not extend to reconnection onset. During substorm onset in the magnetotail, for example, a substantial component of the magnetic field normal to the current sheet is present in the equilibrium [*Pritchett and Coroniti*, 1995]. We have not explored the stability of this equilibrium nor its nonlinear development and therefore cannot comment on the role of secondary instabilities in this configuration.