Trapped particle instability in : I homogeneous Vlasov plasmas

Abstract

Kinetic instability due to trapped particles in non-linear evolution of large amplitude electrostatic waves i.e BGK (Bernstein-Greene-Kruskal) mode is investigated in a one dimensional, collisionless, homogeneous Vlasov-Poisson plasma with immobile ions and kinetic electrons. Considering a cosinusoidal density perturbation with non-linear perturbation amplitude α = 0.05 as starting point, we have demonstrated that long time BGK solutions with scale k>kmin (where kmin−1 corresponds to the longest length scale in the system) are not stable due to Landau growth in the secondary sideband modes. This growth in the sideband modes is primarily related to trapped particles in the potential well of the perturbation which leads to trapped particle instability when the amplitude of the sidebands become comparable to that of the primary nonlinear mode. In the past, to explain trapped particle instability, two physical mechanisms were held responsible, namely, wave particle interaction phenomenon at resonance location v ϕ = ω/k and mode coupling interaction phenomenon between primary and secondary sideband modes. We have demonstrated and emphasized both the phenomena in our study. In addition, effect of primary mode perturbation amplitude on trapped particle instability is investigated and growth rates corresponding to secondary sideband modes are reported alongwith a new scaling law for detrapping time as a function of perturbation amplitude. Also, scaling of growth rates corresponding to lower and upper sideband modes with respect to perturbation amplitude is obtained which demonstrates the existence of a transition point at α = 0.075 between small and large perturbation amplitudes and growth rate scales as γ ∼ α 2 for α < 0.075 whereas γ ∼ α 1/2 for α > 0.075.