Global diffusion of cosmic rays
  The propagation of charged particles, including cosmic rays, in a partially
ordered magnetic field is characterized by a diffusion tensor whose components
depend on the particle's Larmor radius $R_L$ and the degree of order in the
magnetic field. Most studies of the particle diffusion presuppose a scale
separation between the mean and random magnetic fields (e.g., there being a
pronounced minimum in the magnetic power spectrum at intermediate scales).
Scale separation is often a good approximation in laboratory plasmas, but not
in most astrophysical environments such as the interstellar medium (ISM).
Modern simulations of the ISM have numerical resolution of order 1 pc, so the
Larmor radius of the cosmic rays that dominate in energy density is at least
$10^{6}$ times smaller than the resolved scales. Large-scale simulations of
cosmic ray propagation in the ISM thus rely on oversimplified forms of the
diffusion tensor. We take the first steps towards a more realistic description
of cosmic ray diffusion for such simulations, obtaining direct estimates of the
diffusion tensor from test particle simulations in random magnetic fields (with
the Larmor radius scale being fully resolved), for a range of particle energies
corresponding to $10^{-2}\lesssim R_L/l_c \lesssim 10^{3}$, where $l_c$ is the
magnetic correlation length. We obtain explicit expressions for the cosmic ray
diffusion tensor for $R_L/l_c \ll 1$, that might be used in a sub-grid model of
cosmic ray diffusion. The diffusion coefficients obtained are closely connected
with existing transport theories that include the random walk of magnetic
lines.
