Cosmic ray transport in anisotropic magnetohydrodynamic turbulence

Observations of interstellar turbulence imply that the power spectrum of the wave turbulence must be highly anisotropic. This anisotropy has to be included when transport of high energy cosmic rays in the Galaxy is discussed. Here we evaluate the relevant cosmic ray transport parameters in the presence of anisotropic shear Alfvèn wave turbulence, which have no contribution from the transit-time damping interaction and are entirely due to gyroresonant interactions. By averaging the respective Fokker-Planck coefficient over the particle pitch-angle we calculate the momentum and spatial diffusion coefficients for different anisotropy parameters. For strongly perpendicular turbulence ($\Lambda \ll 1$) we obtain that the momentum diffusion coefficient is proportional to $\Lambda ^{(s+1)/2}$, whereas for strongly parallel turbulence ($\Lambda \gg 1$) the momentum diffusion coefficient is a constant. We also calculate the anisotropy dependence of the spatial diffusion coefficient and the mean free path for pure Alfvèn turbulence. For all coefficients we discuss the rigidity dependence for different cosmic ray particles and compare with earlier calculations of transport parameters for slab-type Alfvèn turbulence