Kinetic Simulations of the Cosmic-Ray Pressure Anisotropy Instability: Cosmic-Ray Scattering Rate in the Saturated State

Abstract Cosmic-ray (CR) feedback plays a vital role in shaping the formation and evolution of galaxies through their interaction with magnetohydrodynamic waves. In the CR self-confinement scenario, the waves are generated by the CR gyroresonant instabilities via CR streaming or CR pressure anisotropy and saturate by balancing wave damping. The resulting effective particle scattering rate by the waves, ν eff , critically sets the coupling between the CRs and background gas, but the efficiency of CR feedback is yet poorly constrained. We employ 1D kinetic simulations under the magnetohydrodynamic-particle-in-cell framework with the adaptive δ f method to quantify ν eff for the saturated state of the CR pressure anisotropy instability with ion-neutral friction. We drive CR pressure anisotropy by expanding/compressing the box, mimicking the background evolution of magnetic field strength, and the CR pressure anisotropy eventually reaches a quasi-steady state by balancing quasi-linear diffusion. At the saturated state, we measure ν eff and the CR pressure anisotropy level, establishing a calibrated scaling relation with environmental parameters. The scaling relation is consistent with quasi-linear theory and can be incorporated to CR fluid models, in either the single-fluid or p -by- p treatments. Our results serve as a basis for accurately calibrating the subgrid physics in macroscopic studies of CR feedback and transport.