  Diffusion of cosmic rays (CRs) is the key process of understanding their
propagation and acceleration. We employ the description of spatial separation
of magnetic field lines in MHD turbulence in Lazarian & Vishniac (1999) to
quantify the divergence of magnetic field on scales less than the injection
scale of turbulence and show this divergence induces superdiffusion of CR in
the direction perpendicular to the mean magnetic field. The perpendicular
displacement squared increases, not as distance $x$ along magnetic field, which
is the case for a regular diffusion, but as the $x^{3}$ for freely streaming
CRs. The dependence changes to $x^{3/2}$ for the CRs propagating diffusively
along magnetic field. In the latter case we show that it is important to
distinguish the perpendicular displacement in respect to the mean field and to
the local magnetic field. We consider how superdiffusion changes the
acceleration of CRs in shocks and show how it decreases efficiency of the CRs
acceleration in perpendicular shocks. We also demonstrate that in the case when
small-scale magnetic field is being generated in the pre-shock region, an
efficient acceleration can take place for the CRs streaming without collisions
along magnetic loops.
