Zero-variance schemes for kinetic Monte Carlo simulations

Solving time-dependent transport problems for neutrons and precursors in a nuclear reactor is a daunting task in a naive Monte Carlo framework, mainly because of the enormous difference between the time scale associated with the prompt fission chains and that associated with the decay of delayed neutron precursors. Recently, the development of variance reduction techniques specific for reactor kinetics and the rapidly increasing computer power have paved the way towards the possibility of obtaining reference solutions to the time-dependent transport problem. However, the application of time-dependent Monte Carlo to large systems (i.e. at the scale of a full reactor core) is still considerably hindered by the huge computational requirements. In this paper, we construct an ideal Monte Carlo game that results in a zero-variance estimator for specific observables in time-dependent transport. Our derivation follows the pattern of the existing schemes for stationary problems. To the best of our knowledge, zero-variance Monte Carlo schemes for time-dependent transport including delayed neutrons precursors have never been considered before. As a proof of principle, we verify our construction for a simplified benchmark configuration where analytical reference solutions for the transport problem can be explicitly obtained.