Quasilinear theory and simulation of Buneman instability

In a recently developed nonlinear theory of Buneman instability, a simplifying assumption of self-similarity was imposed for the electron distribution function, based upon which, a set of moment kinetic equations was derived and solved together with nonlinear wave kinetic equation [P. H. Yoon and T. Umeda, Phys. Plasmas 17, 112317 (2010)]. It was found that the theoretical result compared reasonably against one-dimensional electrostatic Vlasov simulation. In spite of this success, however, the simulated distribution deviated appreciably from the assumed self-similar form during the late stages of nonlinear evolution. In order to rectify this shortcoming, in this paper, the distribution function is computed on the basis of rigorous velocity space diffusion equation. A novel theoretical scheme is developed so that both the quasilinear particle diffusion equation and the adiabatic dispersion relation can be solved for an arbitrary particle distribution function. Comparison with Vlasov simulation over relatively early quasilinear phase of the instability shows a reasonable agreement, despite the fact that quasilinear theory lacks coherent nonlinear effects as well as mode-mode coupling effects.