Reactivity effects of the random dispersal of nuclear materials

Nuclear reactors are in general deterministic with respect to the distribution of materials, consequently the reactivity of their configurations are fixed (disregarding the fluctuations of the number of neutrons per fission). This is not the case of High Temperature Gas Cooled Reactors (HTGCR), where the fuel is constructed with a random distribution of fuel kernels with positions at random; additionally the pebble version of the HTGCR is build with the pebbles positions at random therefore having two degrees of randomness. In this study we analyze the fuel cell with one pebble at its center, an ensemble of fuel cells is constructed by the simulation for each pebble of the random dispersal of the several thousands fuel kernels per pebble. The objective is to calculate the width of the random dispersal of keff; a simple model that simulates the effects of the random dispersal on the space averaged thermal cross sections was developed for this purpose. A limited set of calculations with the continuous energy Monte Carlo code MCNP gives a reactivity width compatible with the results of the simple model. Deterministic versions of the random dispersal are proposed to calculate the ensemble average keff based on the positioning of the kernels according to cubic and hexagonal lattices.