  The arrival directions of TeV-PeV cosmic rays are remarkably uniform due to
the isotropization of their directions by scattering on turbulent magnetic
fields. Small anisotropies can exist in standard diffusion models, however,
only on the largest angular scales. Yet, high-statistics observatories like
IceCube and HAWC have found significant deviations from isotropy down to small
angular scales. Here, we explain the formation of small-scale anisotropies by
considering pairs of cosmic rays that get correlated by their transport through
the same realisation of the turbulent magnetic field. We argue that the
formation of small-scale anisotropies is the reflection of the particular
realisation of the turbulent magnetic field experienced by cosmic rays on time
scales intermediate between the early, ballistic regime and the late, diffusive
regime. We approach this problem in two different ways: First, we run test
particle simulations in synthetic turbulence, covering for the first time the
TV rigidities of observations with realistic turbulence parameters. Second, we
extend the recently introduced mixing matrix approach and determine the
steady-state angular power spectrum. Throughout, we adopt magneto-static,
slab-like turbulence. We find excellent agreement between the predicted angular
power spectra in both approaches over a large range of rigidities. In the
future, measurements of small-scale anisotropies will be valuable in
constraining the nature of the turbulent magnetic field in our Galactic
neighborhood.
