On the Growth and Saturation of the Gyroresonant Streaming Instabilities

The self-regulation of cosmic ray (CR) transport in the interstellar and intracluster media has long been viewed through the lenses of linear and quasilinear kinetic plasma physics. Such theories are believed to capture the essence of CR behavior in the presence of self-generated turbulence, but cannot describe potentially critical details arising from the nonlinearities of the problem. We utilize the particle-in-cell numerical method to study the time-dependent nonlinear behavior of the gyroresonant streaming instabilities, self-consistently following the combined evolution of particle distributions and self-generated wave spectra in one-dimensional periodic simulations. We demonstrate that the early growth of instability conforms to the predictions from linear physics, but that the late-time behavior can vary depending on the properties of the initial CR distribution. We emphasize that the nonlinear stages of instability depend strongly on the initial anisotropy of CRs -- highly anisotropic CR distributions do not efficiently reduce to Alfvenic drift velocities, owing to reduced production of left-handed resonant modes. We derive estimates for the wave amplitudes at saturation and the time scales for nonlinear relaxation of the CR distribution, then demonstrate the applicability of these estimates to our simulations. Bulk flows of the background plasma due to the presence of resonant waves are observed in our simulations, confirming the microphysical basis of CR-driven winds.