SUPERDIFFUSION OF COSMIC RAYS: IMPLICATIONS FOR COSMIC RAY ACCELERATION

Diffusion of cosmic rays (CRs) is the key process for understanding their propagation and acceleration. We employ the description of spatial separation of magnetic field lines in magnetohydrodynamic turbulence in Lazarian & Vishniac to quantify the divergence of the magnetic field on scales less than the injection scale of turbulence and showthat this divergence induces superdiffusion ofCRin the direction perpendicular to themean magnetic field. The perpendicular displacement squared increases, not as the distance x along the 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 the magnetic field. In the latter case, we show that it is important to distinguish the perpendicular displacement with 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 the small-scale magnetic field is generated in the pre-shock region, an efficient acceleration can take place for the CRs streaming without collisions along the magnetic loops.