  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.
