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.

Based on three-dimensional simulations of the Braginskii equations, we identify two main parameters which control transport in the edge of tokamaks: the MHD ballooning parameter and a diamagnetic parameter. The space defined by these parameters delineates regions where typical L-mode levels of transport arise, where the transport is catastrophically large (density limit) and where the plasma spontaneously forms a transport barrier (H mode). [S0031-9007(98)07608-X]

Starting from the Braginskii fluid equations, a set of nonlinear reduced equations are derived which describe the low frequency dynamics of electron and ion energy and density in a toroidal plasma. The equations have an energy integral. The equations are appropriate for studying the relation between electron and ion thermal transport and particle transport in low temperature plasma near the edge of plasma confinement devices.

Electron magnetohydrodynamic ͑EMHD͒ turbulence is studied in two-and three-dimensional ͑2D and 3D͒ systems. Results in 2D are particularly noteworthy. Energy dissipation rates are found to be independent of the diffusion coefficients. The energy spectrum follows a k Ϫ5/3 law for kd e Ͼ1 and k Ϫ7/3 for kd e Ͻ1, which is consistent with a local spectral energy transfer independent of the linear wave properties, contrary to magnetohydrodynamic ͑MHD͒ turbulence, where the Alfvén effect dominates the transfer dynamics. In 3D spectral properties are similar to those in 2D.

[1] Three-dimensional (3-D) particle simulations are performed in a double current layer configuration to investigate the stability of current sheets and boundary layers which develop during magnetic reconnection of antiparallel fields in collisionless plasma. The strong current layers that develop near the x line remain surprisingly laminar, with no evidence of turbulence and associated anomalous resistivity or viscosity. Neither the electron shear flow instabilities nor kink-like instabilities, which have been observed in these current layers in earlier simulations, are present. The sharp boundary layers which form between the inflow and outflow regions downstream of the x line are unstable to the lower hybrid drift instability. The associated fluctuations, however, do not strongly impact the rate of reconnection. As a consequence, magnetic reconnection in the 3-D system remains nearly two dimensional.

Three-dimensional (3-D) simulations of drift-resistive ballooning turbulence are presented. The turbulence is basically controlled by a parameter α, the ratio of the drift wave frequency to the ideal ballooning growth rate. If this parameter is small [α≤1, corresponding to Ohmic (OH) or low confinement phase (L-mode) plasmas], the system is dominated by ballooning turbulence, which is strongly peaked at the outside of the torus. If it is large [α≥1, corresponding to high confinement phase (H-mode) plasmas], field line curvature plays a minor role. The turbulence is nonlinearly sustained even if curvature is removed and all modes are linearly stable due to magnetic shear. In the nonlinear regime without curvature the system obeys a different scaling law compared to the low-α regime. The transport scaling is discussed in both regimes and the implications for OH, L-mode, and H-mode transport are discussed.

Three-dimensional (3D) particle-in-cell simulations of collisionless magnetic reconnection are presented. The initial equilibrium is a double Harris-sheet equilibrium and periodic boundary conditions are assumed in all three directions. No magnetic seed island is imposed initially, and no flow conditions are imposed. The current sheet width is assumed to be one ion inertial length calculated with the density in the center of the current sheet. The ion to electron mass ratio is mi/me=150, which suppresses the growth of the drift kink instability. Two different runs have been performed: a simulation with exactly antiparallel magnetic field and a simulation with a constant guide field of the same magnitude as the antiparallel field superimposed. In the antiparallel case the inductive field of the waves excited by the lower hybrid drift instability (LHDI) leads to rapid acceleration of the electrons in the center of the current sheet and subsequently to a current sheet thinning. The current increase in the center is balanced by reverse currents in the gradient region. In the thin current sheet rapid reconnection sets in which self-organizes into a two-dimensional structure with a single X line. However, ∼15% of the total flux is reconnected while reconnection is still patchy and 3D. In the guide field case the growth rate of the LHDI is reduced, but leads nevertheless after a considerably longer time to electron acceleration in the current sheet center and to a thinning of the current layer, followed by single X line reconnection. It is suggested that electron acceleration due to LHDI in current sheets of the order of the ion scale results in rapid onset of reconnection.

Numerical simulations of 3D collisional drift-wave turbulence in a sheared magnetic field are presented which demonstrate that fluctuations are self-sustaining even though the linear eigenmodes of the system are all damped. An analytic calculation reveals that the source of the turbulence is a nonlinear streaming instability in which radial flows extract energy from the ambient density gradient and drive drift waves which then amplify the radial flow.