Monte Carlo methods for reactor period calculations

Several technological issues, such as reactor start-up analysis or kinetics studies of accelerator-driven systems, demand the asymptotic time behaviour of neutron transport to be assessed. Typically, this amounts to solving an eigenvalue equation associated to the Boltzmann operator, whose precise nature depends on whether delayed neutrons are taken into account. The inverse of the dominant eigenvalue can be physically interpreted as the asymptotic reactor period. In this work, we propose a Monte Carlo method for determining the dominant alpha eigenvalue of the Boltzmann operator and the associated fundamental mode for arbitrary geometries, materials, and boundary conditions. Extensive verification tests of the algorithm are performed, and Monte Carlo calculations are finally validated against reactor period measurements carried out at the ORPHEE facility of CEA/Saclay.