Current Sheet Broadening due to Turbulence in Three-dimensional Collisionless Reconnection

The present study has investigated the statistical distribution of the current sheet width across the reconnection diffusion region by means of the 3D particle-in-cell simulations. The 3D reconnection layers are unstable to the flow shear instabilities, which results in electromagnetic (EM) turbulence generating effective magnetic dissipation around the x-line. The simulations are performed for several ion-to-electron mass ratios and computational domain sizes, which determine the fastest-growing mode in each simulation run. When the turbulence is weak, the current sheet width increases with the turbulence intensity, following a theoretical curve independent of the mass ratio and domain size. However, when the turbulence is stronger, the width saturates at a low level around 2 times the local electron inertia length, i.e., much smaller than the ion kinetic scales. It is found that the intense inductive electric field due to the EM turbulence is partly canceled out by the eddy viscous effect. As a result, the reconnection electric field is almost unchanged during the quasi-steady phase, regardless of the turbulence intensity. The result implies that the magnetohydrodynamic turbulence models are unlikely to be applicable to the reconnection diffusion region.