Nonlinear evolution of Buneman instability

The nonlinear evolution of one-dimensional electron-ion two-stream instability in a field-free plasma is studied both analytically and numerically (computer simulation). The instability is dominated by the fastest growing mode and its harmonics, provided that the initial fluctuation level is sufficiently small. A nonlinear dispersion relation is derived and solved numerically, taking into account; (a) the frequency and growth rate modulation, (b) the electric field up to ‖Ek‖4, and (c) the ’’renormalized’’ particle distribution functions. The model can successfully explain the results of a computer simulation, particularly the presence of an algebraic growth stage following the breakdown of the exponential linear growth, the appearance of harmonics, and the final saturation level. The minimum conductivity found scales as (M/m)0.61wpe, where M/m is the ion/electron mass ratio.