Comparison of neutron diffusion and Monte Carlo simulations of a fission wave

Simulations by many groups have shown that fission waves could form in uranium and potentially be used as the basis for a power reactor. The vast majority of studies have been done using a neutron diffusion approximation. Monte Carlo simulations are typically considered to be the benchmark against which other computational approaches are tested. However, a direct comparison of Monte Carlo and diffusion results for fission waves has not been made. In the present work we show the results of 1-D and 3-D simulations of a fission wave system done using MCNPX 2.7.0. The results are compared with those from a one-dimensional, one-group neutron diffusion code. The diffusion simulations produce a wave speed of 5.9 cm/year versus 7.9 cm/year for the 3-D Monte Carlo simulations and 5.3 cm/year for the 1-D simulations. The 1-D diffusion and Monte Carlo simulations produce flux profiles with a correlation of R2 = 0.93, and their 238U burnup profiles have R2 = 0.98.