Mirror acceleration of cosmic rays in a high-$\beta$ medium

In a weakly compressible high-$\beta$ medium, pitch-angle scattering and the associated scattering acceleration of cosmic rays (CRs) by anisotropic Alfv\'{e}n and slow modes of magnetohydrodynamic (MHD) turbulence is inefficient. To tap the energy from magnetic compressions for efficient particle acceleration, a diffusion mechanism that can effectively confine particles in space without causing their trapping or pitch-angle isotropization is needed. We find that the mirror diffusion in MHD turbulence recently identified in Lazarian and Xu (2021) satisfies all the above conditions and serves as a promising diffusion mechanism for efficient acceleration of CRs via their stochastic non-resonant interactions with magnetic compressions/expansions. The resulting mirror acceleration is dominated by the slow-mode eddies with their lifetime comparable to the mirror diffusion time of CRs. Consequently, we find that the acceleration time of mirror acceleration is independent of the spatial diffusion coefficient of CRs. The mirror acceleration brings new life for the particle acceleration in a weakly compressible/incompressible medium and has important implications for studying CR re-acceleration in the high-$\beta$ intracluster medium.