Fully nonlinear features of the energetic beam-driven instability

The so-called Berk–Breizman model is applied to a cold bulk, weak warm beam, one-dimensional plasma, to investigate the kinetic instability arising from the resonance of a single electrostatic wave with an energetic particle beam. A Vlasov code is developed to solve the initial value problem for the full-f distribution, and the nonlinear evolution is categorized in the whole parameter space as damped, steady-state, periodic, chaotic, or chirping. The saturation level of steady-state solutions and the bifurcation between steady-state and periodic solutions near marginal stability match analytic predictions. The limit of a perturbative numerical approach when the resonant region extends into the bulk is shown. Frequency sweeping is observed, with time-evolution approaching theoretical results. A new method to extract the dissipation rate from frequency diagnostics is proposed. For small collision rates, instabilities are observed in the linearly barely stable region.