Kinetic–MHD simulations of gyroresonance instability driven by CR pressure anisotropy

The transport of cosmic rays (CRs) is crucial for the understanding of almost all high-energy phenomena. Both pre-existing large-scale magnetohydrodynamic (MHD) turbulence and locally generated turbulence through plasma instabilities are important for the CR propagation in astrophysical media. The potential role of the resonant instability triggered by CR pressure anisotropy to regulate the parallel spatial diffusion of low-energy CRs ($\lesssim 100$ GeV) in the interstellar and intracluster medium of galaxies (ISM and ICM) has been showed in previous theoretical works. This work aims to study the gyroresonance instability via direct numerical simulations, in order to access quantitatively the wave-particle scattering rates. For this we employ a 1D PIC-MHD code to follow the growth and saturation of the gyroresonance instability. We extract from the simulations the pitch-angle diffusion coefficient $D_{\mu\mu}$ produced by the instability during the linear and saturation phases, and a very good agreement (within a factor of 3) is found with the values predicted by the quasilinear theory (QLT). Our results support the applicability of the QLT for modeling the scattering of low-energy CRs by the gyroresonance instability in the complex interplay between this instability and the large-scale MHD turbulence.