  In the standard picture of cosmic ray transport the propagation of charged
cosmic rays through turbulent magnetic fields is described as a random walk
with cosmic rays scattering on magnetic field turbulence. This is in good
agreement with the highly isotropic cosmic ray arrival directions as this
diffusion process effectively isotropizes the cosmic ray distribution.
  High-statistics observatories like IceCube and HAWC have however observed
significant deviations from isotropy down to very small angular scales. This is
in strong tension with this standard picture of cosmic ray propagation. While
large scale multipoles arise naturally, for example due to the earth's motion
relative to the isotropic cosmic ray distribution, there is no intuitive
mechanism to account for the observed anisotropies at smaller angular scales.
  By relaxing one of the standard assumptions of quasi linear theory and
treating correlations between fluxes of cosmic rays from different directions
explicitly we show that higher multipoles also are to be expected from particle
propagation through turbulent magnetic fields. We present a first analytical
calculation of the angular power spectrum assuming a physically motivated model
of the magnetic field turbulence and find good agreement with numerical
simulations.
