The Buneman instability is a beam-driven instability, essentially a variation on the two-stream instability or bump-on-the-tail.
The top plot shows electrons streaming through stationary ions. The instability comes from the Doppler-shifted electron plasma frequency resonating with the ion plasma frequency and, in the limit of large ion mass and non-relativistic streaming velocity, this becomes a resonance condition of roughly
k vbeam ~ ωp,e. In this setup, the expected wavelength is roughly about 1.0 in normalized units (very slightly less than 1.0).
The middle plot of the ion charge density, electron charge density, and total charge density shows that quasi-neutrality is preserved (dashed line shows the mean charge density).
The bottom plot shows the electric field in the y-direction (transverse), and electric field in the x-direction (longitudinal). As expected, the longitudinal field is dominated by the resonant wavelength (~1.0) and grows until the nonlinear breakup and saturation of the instability.