Kinetics of parametric instabilities of Alfvén waves: Evolution of ion distribution functions

Using numerical simulations in a hybrid regime, we studied the evolution of large-amplitude Alfvén waves subject to modulational and decay instabilities, including the effects of ion kinetics. We considered both a monochromatic and incoherent spectrum of waves, different wave polarizations and amplitudes, and different plasma regimes, ranging from β < 1 to β > 1. We found in all cases that ion dynamics affects the instability evolution and saturation; as a feedback, wave-particle interactions provide a nonlinear trapping of resonant particles that importantly change the properties of the ion velocity distribution functions. In particular, we observed a proton acceleration along the magnetic field and in some cases the formation of a parallel velocity beam traveling faster than the rest of the distribution. For the range of parameters used in our simulations, the fundamental ingredient in generating an ion beam is observed to be the parallel electric field carried by the density fluctuations driven by the ion-acoustic modes generated by the parametric instabilities.