Phenomenological studies of cosmic-ray self-confinement often hinge on the linear theory for the growth rate of the streaming instability and for the damping rate of the generated magnetic modes. Largely different expressions exist, especially for the rate of nonlinear Landau damping, which is often assumed to be the most important damping mechanism in warm ionized plasmas. Using hybrid-particle-in-cell simulations in the resonant streaming instability regime, we present a comprehensive assessment of nonlinear Landau damping and show that the damping rate at a given scale depends on the power in magnetic fields on larger scales. Furthermore, we find that an inverse cascade develops, which produces magnetic fields on scales larger than the resonant ones. Here, we extend previous results obtained for a monoenergetic distribution of nonthermal particles to the case of broader cosmic ray (CR) distributions, as a first step toward developing phenomenological models. Preexisting turbulence of Alfvénic nature at large scales severely affects the damping of waves produced by low-energy CRs; depending on its amplitude, such a turbulence may inhibit the growth of streaming instability so that CRs are either self-confined at all energies or not at all.

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• Cosmic ray propagation
• Cosmic rays & astroparticles
• Plasma instabilities
• Plasma turbulence
• Plasma waves
• Wave-wave, wave-particle interactions
• Hybrid model
• Particle-in-cell methods