Convergence of Monte Carlo algorithms for power reactor noise

Power reactor noise refers to the small periodical variations of the neutron flux in nuclear reactor cores, induced by various perturbations. A prominent example is the vibration of fuel assemblies due to fluid-structure interactions. Although noise is generally an unwanted phenomenon, its analysis is useful for core monitoring. In this respect, several state-of-the-art deterministic or Monte Carlo solvers have been developed to solve the equations describing neutron noise. In this paper, we investigate the convergence properties of Monte Carlo methods for neutron noise analysis, within the orthodox linearization approximation. For this purpose, we establish a theoretical framework for complex-weighted Monte Carlo games and we show that convergence of such algorithms can be assessed using two sets of eigenvalues. In order to substantiate our findings, we examine a few relevant benchmark configurations for noise problems.