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The arrival directions of multi-TeV cosmic rays show significant anisotropiesat small angular scales. It has been argued that this small scale structure isreflecting the local, turbulent magnetic field in the presence of a globaldipole anisotropy in cosmic rays as determined by diffusion. This effect isanalogous to weak gravitational lensing of temperature fluctuations of thecosmic microwave background. We show that the non-trivial power spectrum inthis setup can be related to the properties of relative diffusion and we studythe convergence of the angular power spectrum to a steady-state as a functionof backtracking time. We also determine the steady-state solution in ananalytical approach based on a modified BGK ansatz. A rigorous mathematicaltreatment of the generation of small scale anisotropies will help in unravelingthe structure of the local magnetic field through cosmic ray anisotropies.

Small-scale anisotropies of cosmic rays from relative diffusion