  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 (ECS)
(thickness ~ an electron inertial length) formed in collisionless magnetic
reconnection, electron shear flow instabilities (ESFI) 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 investigate the evolution of ESFI in guide field magnetic
reconnection. The properties of the resulting plasma turbulence and their
dependence on the strength of the guide field are studied. Utilizing 3-D
electron-magnetohydrodynamic simulations of ECS we show that, unlike the case
of ECS self-consistently embedded in anti-parallel magnetic fields, the
evolution of thin ECS in the presence of a 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 cause the development of,
first, a wavy structure of the ECS. The turbulence, developed later, consists
of current filaments and electron flow vortices. As a result of the nonlinear
evolution of the instability, the ECS broadens simultaneously with its
flattening in the central region mimicking a viscous-like turbulent
dissipation. Later, the flattened ECS bifurcates. During the time of the
bifurcation, the rate of the change of the 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.
