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 threedimensional 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

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... 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. Magnetic reconnection is the driver of explosions in laboratory, space, and astrophysical plasmas, including solar and stellar flares and storms in Earth's magnetosphere. In the classic picture of magnetic reconnection, oppositely directed components of the magnetic field cross-link, forming a magnetic x-line configuration. The expansion of the newly reconnected field lines away from the x-line releases the magnetic energy and pulls in the oppositely directed magnetic flux to sustain the energy release process. Some form of dissipation is required to allow the plasma and magnetic field to decouple so that the topological change in the magnetic field can take place. The rate of reconnection, however, is sensitive to the plasma resistivity (1-3) such that reconnection based on classical resistivity is orders of magnitude too slow to explain the fast release of magnetic energy observed in nature. To explain the large discrepancy between observations of energy re-lease times and the predictions, it was postulated that the plasma resistivity is enhanced above the classical values by electron scattering associated with electric field fluctuations (4). These fluctuations could be driven by the intense currents that form during magnetic reconnection. The resulting anomalous resistivity fortuitously also facilitates fast reconnection, which is insensitive to resistivity (5, 6). The concept of anomalous resistivity also has a secondary benefit. Observations of solar flares indicate that up to half of the energy released in magnetic reconnection is carried by energetic electrons (7) . The direct production of very energetic electrons during magnetic reconnection in Earth's magnetotail has also been reported (8). The mechanism for such strong electron heating remains unclear. The flows that develop during reconnection are typically of the order of the Alfvén speed c A ϭ B/[(4) 1/2 ], where B is the magnetic field strength and is the plasma mass density, and are therefore too slow to produce the near relativistic electron velocities observed. The development of high-frequency turbulence, which could cause the electron scattering associated with anomalous resistivity, would also heat electrons and perhaps produce the broad spectrum of energetic electrons observed in nature. Anomalous resistivity has been widely invoked to explain the fast release of energy observed in nature, but the concept remains poorly understood (4). The strongest evidence for its existence comes from observations in the auroral region of the ionosphere, where localized regions of large parallel electric field have been measured (9, 10). These localized structures take the form of double layers (which support a net drop in the electric potential) or electron holes (regions of depressed electron density that exhibit a bipolar parallel electric field). We carried out three-dimensional (3D) particle simulations of magnetic reconnection to explore the self-consistent development of current-driven instabilities and anomalous resistivity and compared the results with observations from the Polar spacecraft at Earth's magnetopause. In earlier simulations of a system with a reversed field and no imposed ambient guide (out-of-plane) magnetic field, no current-driven instabilities developed around the x-line (11). The intrinsic electron heating around the null field region was sufficient to stabilize current-driven instabilities. In our simulations, an imposed guide field prevents the demagnetization of electrons and associated heating. The initial equilibrium is a double current layer with two magnetic field components B x and B z dependent on the spatial coordinate y: where B 0 is the asymptotic field strength outside of the current layers; B z ϭ (B 2 -B x 2 ) 1/2 is chosen so that the total field B is constant. For the 3D simulations shown, the computational domain has dimensions L x ϭ 4d i , L y ϭ 2d i , L z ϭ d i and periodic boundary conditions. The scale length d i is the ion inertial length c/ pi , where pj is the plasma frequency of a particle species j, and w 0 ϭ 0.25d i is the current layer thickness. The initial plasma pressure is constant with the density n 0 and electron and ion temperatures T e ϭ T i ϭ 0.04 m i c A 2 , where c A ϭ B 0 /[(4 n 0 m i ) 1/2 ]. Other parameters are B