Cosmic-rays (CRs) are relativistic particles that pervade galaxies and intergalactic space. They likely play a dynamically important role in a wide range of astrophysics systems by interacting with thermal gas via magnetic fields, whose consequence is known as CR feedback. The key to understanding CR feedback lies in how well the gas and CRs are coupled, which is in most cases described by a CR diffusion coefficient that is largely unconstrained, leading to substantial uncertainties in recent studies of galaxy formation and evolution. At microphysical level, the coupling is known to be mediated by resonant wave scattering, with waves excited by the gyro-resonant instabilities for the bulk of CR particles, yet the multi-scale nature of the problem precludes numerical studies over decades. I will describe the first effort in studying such instabilities from first principles using the novel magnetohydrodynamic-particle-in-cell technique, which precisely reproduces such instabilities and allows us to study their non-linear evolution. I will further discuss ongoing works by gradually incorporating more realistic physics, towards the long-term goal of offering faithful sub-grid models for macroscopic studies of CR feedback.
