Particle-in-cell simulation of Buneman instability beyond quasilinear saturation

Spatio-temporal evolution of Buneman instability has been followed numerically till its quasilinear quenching and beyond, using an in-house developed electrostatic 1D particle-in-cell (PIC) simulation code. For different initial drift velocities and for a wide range of electron to ion mass ratios, the growth rate obtained from simulation agrees well with the numerical solution of the fourth order dispersion relation. Quasi-linear saturation of Buneman instability occurs when the ratio of electrostatic field energy density to initial electron drift kinetic energy density reaches up to a constant value, which, as predicted by Hirose [Plasma Phys. 20, 481 (1978)], is independent of initial electron drift velocity but varies with the electron to ion mass ratio (m/M) as approximate to(m/M)(1/3). This result stands verified in our simulations. The growth of the instability beyond the first saturation (quasilinear saturation) till its final saturation [Ishihara et al., PRL 44, 1404 (1980)] follows an algebraic scaling with time. In contrast to the quasilinear saturation, the ratio of final saturated electrostatic field energy density to initial kinetic energy density is relatively independent of the electron to ion mass ratio and is found from simulation to depend only on the initial drift velocity. Beyond the final saturation, electron phase space holes coupled to large amplitude ion solitary waves, a state known as coupled hole-soliton, have been identified in our simulations. The propagation characteristics (amplitude-speed relation) of these coherent modes, as measured from present simulation, are found to be consistent with the theory of Saeki et al. [PRL 80, 1224 (1998)]. Our studies thus represent the first extensive quantitative comparison between PIC simulation and the fluid/kinetic model of Buneman instability. Published by AIP Publishing.