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.