During reactor start-up, the reactor generally starts from a state where it is critical with a 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 explicitely using Monte Carlo simulations. In the latter case, it is computationally costly, as one needs to check individually every thresholds 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.

The most recent progress is being able to validate the SDE framework with SCONE. The medium is a mixture of water and uranium in continuous energy (with SCONE), which can be reproduced accurately with the SDE solver (which is 1 group and 1 precursor family). The next step of the project will be to validate the deterministic solver based on the SDE model with SCONE, for models of increasing complexity.

Project team: Theophile Bonnet, Matt Evans, Valeria Raffuzzi, Oliver Tough and Terence Tsui