Monte Carlo for Low Power Reactors

Monte Carlo methods and the mathematical theory of low power reactor physics

At the start-up stage of a nuclear reactor, the power in the reactor is low, resulting in a high level of uncertainty when measuring neutron flux. 

Under this regime, spatial clustering of neutrons will also result in an uneven burn-up of fissile materials, affecting the long-term stability of the nuclear reactor. To counter this problem, we are proposing novel framework of branching particle systems inspired by seed bank models in population genetics to model the neutronic dynamics of reactor at the start-up phase.

By writing a neutron generating process and taking a diffusion limit, we can model the growth and fluctuation of the number of neutrons during the start-up process as Feller diffusions that solve a specific form of linear stochastic differential equation. Then, by leveraging well-established techniques in the field of population genetics, we can express the probability of extreme fluctuations in neutron numbers as solutions to systems of ordinary and partial differential equation. Such analytical method can provide a much faster way to calculate the probability of extinction and neutron spikes, crucial to determining nuclear reactor safety.

In the long run, we aim to use our model to obtain the optimal configuration of nuclear rod assembly that is most cost-efficient with guaranteed reliability and safety. We will also develop new Monte Carlo methods to evaluate the safety and reliability of reactor design during its initial stage.

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

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