  This paper studies cosmic ray (CR) transport in magneto hydrodynamic (MHD)
turbulence. CR transport is strongly dependent on the properties of the
magnetic turbulence. We perform test particle simulations to study the
interactions of CR with both total MHD turbulence and decomposed MHD modes. The
spatial diffusion coefficients and the pitch angle scattering diffusion
coefficients are calculated from the test particle trajectories in turbulence.
Our results confirm that the fast modes dominate the CR propagation, whereas
Alfv\'en and slow modes are much less efficient and have shown similar pitch
angle scattering rates. We investigate the cross field transport on large and
small scales. On large/global scales, normal diffusion is observed and the
diffusion coefficient is suppressed by $M_A^\zeta$ compared to the parallel
diffusion coefficients, with $\zeta$ closer to 4 in Alfv\'en modes than that in
total turbulence as theoretically expected. For the CR transport on scales
smaller than the turbulence injection scale, both the local and global magnetic
reference frames are adopted. Super diffusion is observed on such small scales
in all the cases. Particularly, CR transport in Alfv\'en modes show clear
Richardson diffusion in the local reference frame. Our results have broad
applications to CRs in various astrophysical environments.
