Nonlinear evolution of electron shear flow instabilities in the presence of an external guide magnetic field

The dissipation mechanism by which the magnetic field reconnects in the presence of an external (guide) magnetic field in the direction of the main current is not well understood. In thin electron current sheets (half thickness close to an electron inertial length) formed in a quasi-steady state of collisionless magnetic reconnection, electron shear flow instabilities are potential candidates for providing an anomalous dissipation mechanism which can break the frozen-in condition of the magnetic field affecting the structure and rate of reconnection. We present the results of investigations of the evolution of electron shear flow instabilities, from linear to nonlinear state, in guide field magnetic reconnection. The properties of the plasma turbulence resulting from the growth of instability and their dependence on the strength of the guide field are studied. For this sake, we utilize the three dimensional electron-magnetohydrodynamic simulations of electron current sheets. We show that, unlike the case of current sheets self-consistently embedded in anti-parallel magnetic fields, the evolution of thin electron current sheets in the presence of a finite external guide field (equal to the asymptotic value of the reconnecting magnetic field or larger) is dominated by high wave number non-tearing mode instabilities. The latter causes the development of, first, a wavy structure of the current sheet. The turbulence, developed later, consists of current filaments and electron flow vortices. As a result of the nonlinear evolution of instability, the current sheet broadens simultaneously with its flattening in the central region mimicking a viscous-like turbulent dissipation. Later, the flattened current sheet bifurcates. During the time of bifurcation, the rate of the change of mean electron flow velocity is proportional to the magnitude of the flow velocity, suggesting a resistive-like dissipation. The turbulence energy cascades to shorter wavelengths preferentially in the direction perpendicular to the guide magnetic field. The degree of anisotropy of the turbulence was found to increase with the increasing strength of the guide field.