1995/08/01 by H. L. Berk, B. N. Breizman, B. N. Breǐzman +1
Physics and Astronomy · #Astro and Planetary Science #Astrophysics and Star Formation Studies #Solar and Space Plasma Dynamics
paper · doi:10.1063/1.871198
openalex publication_date 1995/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
A numerical procedure has been developed for the self-consistent simulation of the nonlinear interaction of energetic particles with discrete collective modes in the presence of a particle source and dissipation. A bump-on-tail instability model is chosen for these simulations. The model presents a kinetic nonlinear treatment of the wave–particle interaction within a Hamiltonian formalism. A mapping technique has been used in this model in order to assess the long time behavior of the system. Depending on the parameter range, the model shows either a steady-state mode saturation or quasiperiodic nonlinear bursts of the wave energy. It is demonstrated that the mode saturation level as well as the burst parameters scale with the drive in accordance with the analytical predictions. The threshold for the resonance overlap condition and particle global diffusion in the phase space are quantified. For the pulsating regime, it is shown that when γL≳0.16 ΔΩ, where γL is the linear growth rate for the unperturbed system and ΔΩ is the frequency separation of neighboring resonances, overlap occurs together with an amplification of the free energy release compared to what is expected with the saturation of nonoverlapping modes. The effect of particle losses on the wave excitation is included in the model, which illustrates in a qualitative way the bursting collective losses of fast ions/alpha particles due to Alfvén instabilities.