Estimation of axial diffusion processes by analog Monte-Carlo: theory, tests and examples

With the advent of fast, reasonably inexpensive computer hardware, it has become possible to follow the histories of several million particles and tally quantities such as currents and fluxes in a finite reactor region using analog Monte-Carlo. Here use is made of this new capability to demonstrate that it is possible to test various approximations that cumulatively are known as the axial diffusion approximation in a realistic, heterogeneous reactor lattice cell. From this, it proves possible to extract excellent estimates of the homogenized diffusion coefficient in few energy groups and lattice sub-regions for further comparison with deterministic methods of deriving the same quantity. The breakdown of the diffusion approximation near the endpoints of the axial lattice cell, as well as in the moderator at certain energies, can be observed