Magnetic reconnection is recognized as a dominant mechanism for converting magnetic energy into the convective and thermal energy of particles, and the driver of explosive events in nature and laboratory. Magnetic reconnection is often modeled using resistive magnetohydrodynamics, in which collisions play the key role in facilitating the release of energy in the explosive events. However, in space plasma the collisional resistivity is far below the required resistivity to explain the observed energy release rate. Turbulence is common in plasmas and the anomalous resistivity induced by the turbulence has been proposed as a mechanism for breaking the frozen-in condition in magnetic reconnection. Turbulence-driven resistivity has remained a poorly understood, but widely invoked mechanism for nearly 50 years. The goal of this project is to understand what role anomalous resistivity plays in fast magnetic reconnection.

Turbulence has been observed in the intense current layers that develop during magnetic reconnection in the Earth's magnetosphere. Electron streaming is believed to be the source of this turbulence. Using kinetic theory and 3D particle-in-cell simulations, we study the nonlinear development of streaming instabilities in 3D magnetic reconnection with a strong guide field. Early in time an intense current sheet develops around the x-line and drives the Buneman instability. Electron holes, which are bipolar spatial localized electric field structures, form and then self-destruct creating a region of strong turbulence around the x-line. At late time turbulence with a characteristic frequency in the lower hybrid range also develops, leading to a very complex mix of interactions.

The difficulty we face in this project is how to address a long-standing problem in nonlinear kinetic theory: how to treat large amplitude perturbations and the associated strong wave-particle interactions. In my thesis, I address this long-standing problem using particle-in-cell simulations and linear kinetic theory.Some important physics have been revealed.

1: The lower hybrid instability (LHI) dominates the dynamics in low $beta$ plasma in combination with either the electron-electron two-stream instability (ETS) or the Buneman instability (BI), depending on the parallel phase speed of the LHI.

2: An instability with a high phase speed is required to tap the energy of the high velocity electrons. The BI with its low phase speed, can not do this. The ETS and the LHI both have high phase speed.

3: The condition for the formation of stable electron holes requires $|v_p -v_g|< sqrt{2e|phi|/m_e}$, where $|phi|$ is the amplitude of the electric potential, and $v_p$ and $v_g$ are the phase and group velocity of the relevant waves. Like ETS and BI, LHI all can form electron holes.

4: The overlapping resonance in phase space is the dominant mechanism for transporting the momentum and energy from high velocity electrons to low velocity electrons, which then couple to the ions.