The role of non-linear Landau damping for cosmic-ray transport

We present the first assessment, using hybrid PIC simulations, of the role of non-linear Landau damping in the process of self-generated scattering in a high $\beta$ plasma, conditions appropriate for CR scattering in the halo of the Galaxy. This damping process manifests itself in the form of heating of the background plasma and reduction of the drift speed of CRs that yet remains super-Alfvenic. We also show that the damping leads to an inverse cascade process, consisting of producing non-resonant large scale modes, a novel result with many potential phenomenological implications.