Modeling nonlinear development of Buneman instability with linear dispersion theory

In this paper, spectra in the nonlinear phases of the Buneman instability are described by instantaneous linear dispersion theory. One-dimensional Vlasov simulation of the Buneman instability shows that nonlinear development is characterized by particle trapping in large-amplitude waves. Trapped particles form counter-streaming beam distribution function in velocity space. In addition to the low-frequency Buneman mode, the simulation also shows excitations of high-frequency electron plasma waves as well as wave modes propagating in the direction opposite to the original electron beam. The actual physics of the wave dynamics is very complicated to analyze. However, by employing linear dispersion theory on the basis of instantaneous electron distributions it is possible to relate the generation of waves to the particle distribution. Specifically, it is shown that excitations of various waves are intimately related to the counter-streaming electron beam distribution. The present approach can be a useful diagnostic tool based upon which an intuitive understanding of the complicated nonlinear physics can be attained.