Analytical Expressions For Diffusion Coefficients Research Articles

Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for revisions in the picture of cosmic ray transport. In this paper we use recently obtained scaling laws for MHD modes to obtain the scattering frequency for cosmic rays. Using quasilinear theory we calculate gyroresonance with MHD modes (Alfv\'{e}nic, slow and fast) and transit-time damping (TTD) by fast modes. We provide calculations of cosmic ray scattering for various phases of interstellar medium with realistic interstellar turbulence driving that is consistent with the velocity dispersions observed in diffuse gas. We account for the turbulence cutoff arising from both collisional and collisionless damping. We obtain analytical expressions for diffusion coefficients that enter Fokker-Planck equation describing cosmic ray evolution. We obtain the scattering rate and show that fast modes provide the dominant contribution to cosmic ray scattering for the typical interstellar conditions in spite of the fact that fast modes are subjected to damping. We determine how the efficiency of the scattering depends on the characteristics of ionized media, e.g. plasma $\beta$. We calculate the range of energies for which the streaming instability is suppressed by the ambient MHD turbulence.