Earlier linear and 2-dimensional nonlinear studies on a sheared electron current channel at fast electron time scales have shown the existence of unstable sausage like perturbations which lead to partial stopping of electron flow and formation of coherent structures in nonlinear stage. In this work a complete three dimensional linearized perturbation analysis is carried out for the shear flow configuration. It is shown that the instability criterion in this case is much more relaxed than for the earlier two dimensional modes and results in a considerable enhancement of the domain of unstable modes in the wave number space. Based on the increased number of unstable modes and the relaxation of the two dimensional constraint of the existence of two non dissipative square invariants it can be argued that the three dimensional case would lead to a turbulent state, which may cause effective anomalous damping of the electron flow.
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