Hybrid Methods in Calculating Extinction Probability for Low Power Reactors

During reactor start-up, the reactor generally starts from a state where it is critical with an external source. Initially, the neutron population is very small and suffers from large statistical fluctuations. One is thus interested in the probability that the neutron population vanishes before some time boundary or exceeds some threshold. Traditionally, this probability is solved using either approximation schemes, or explicitly using Monte Carlo simulations. In the latter case, it is computationally costly, as one needs to check individually every threshold for different initial conditions or sources. In this work, we recast the problem in an SDE framework and use the theory of Feller diffusions to obtain a deterministic solver for any initial condition or source.