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Buneman instability is often driven in magnetic reconnection. Understandinghow velocity shear in the beams driving the Buneman instability affects thegrowth and saturation of waves is relevant to turbulence, heating, anddiffusion in magnetic reconnection. Using a Mathieu-equation analysis for weakcosine velocity shear together with Vlasov simulations, the effects of shear onthe kinetic Buneman instability are studied in a plasma consisting of stronglymagnetized electrons and cold unmagnetized ions. In the linearly unstablephase, shear enhances the coupling between oblique waves and the shearedelectron beam, resulting in a wider range of unstable eigenmodes with commonlower growth rates. The wave couplings generate new features of the electricfields in space, which can persist into the nonlinear phase when electron holesform. Lower hybrid instabilities simultaneously occur at$k_{\shortparallel}/k_{\perp} \sim \sqrt{m_e/m_i}$ with a much lower growthrate, and are not affected by the velocity shear.

Buneman instability in a magnetized current-carrying plasma with velocity shear