Abstract：We reproduce nonlinear behaviors, including frequency chirping and mode splitting, referred to as bump-on-tail instabilities. As has been reported in previous works, the generation and motion of phase-space hole-clump pairs in a kinetically driven, dissipative system can result in frequency chirping. We provide examples of frequency chirping, both with and without pure diffusion, in order to illustrate the role of the diffusion effect, which can suppress holes and clumps; Asymmetric frequency chirpings are produced with drag effect, which is essential to enhance holes, and suppress clumps. Although both diffusion and drag effect suppress the clumps, downward sweepings are observed, caused by a complicated interaction of diffusion and drag. In addition, we examine the discrepancies in frequency chirping between marginally unstable, and far from marginally unstable cases, which we elucidate by means of a dissipative system. In addition, mode splitting is also produced via BOT code for a marginal case with large diffusion.
2021, Vol. 38 
