  We describe an analysis of neutron transport in the interior of model pebble
bed reactor (PBR) cores, considering both crystal and random pebble
arrangements. Monte Carlo codes were developed for (i) generating random
realizations of the model PBR core, and (ii) performing neutron transport
inside the crystal and random heterogeneous cores; numerical results are
presented for two different choices of material parameters. These numerical
results are used to investigate the anisotropic behavior of neutrons in each
case and to assess the accuracy of estimates for the diffusion coefficients
obtained with the diffusion approximations of different models: the atomic mix
model, the Behrens correction, the Lieberoth correction, the generalized linear
Boltzmann equation (GLBE), and the new GLBE with angular-dependent path-length
distributions. This new theory utilizes a non-classical form of the Boltzmann
equation in which the locations of the scattering centers in the system are
correlated and the distance-to-collision is not exponentially distributed; this
leads to an anisotropic diffusion equation. We show that the results predicted
using the new GLBE theory are extremely accurate, correctly identifying the
anisotropic diffusion in each case and greatly outperforming the other models
for the case of random systems.
