PhD in Monte Carlo simulation for reactor physics

Neutron transport in nuclear reactor cores is described by the Boltzmann equation. The solution of this equation by the Monte-Carlo method is based on the simulation of a very large number of random trajectories of neutrons within the considered system. The averages over all the simulated trajectories allow easily accessing the physical observables of interest, which are governed by the Boltzmann equation. Each trajectory describes a random walk whose mathematical properties are determined in accordance with the underlying physical laws (probability of particle-matter interaction, angle-energy distribution laws, multiplicity of fission, etc.). As a result, Monte Carlo simulation has always been considered - since its introduction - as the reference method for calculating nuclear systems.

The TRIPOLI-4 Monte-Carlo code, developed at the Stochastic and Deterministic Transport Laboratory (LTSD) of CEA Saclay's Reactor Engineering and Applied Mathematics Research Department (SERMA), is used to simulate the transport of neutrons, photons, electrons and positrons in materials. It is therefore used in the fields of heart physics, radiation protection and nuclear instrumentation.

PhD Description 

To date, the Monte-Carlo methods have been almost exclusively devoted to the estimation of average physical quantities (which is also the case of the TRIPOLI-4 code), and this because of the very high calculation cost required by the realization of the particle paths in the material, which formally corresponds to solving the stationary Boltzmann equation.

Thanks to the increasing computer power, it is possible to use Monte Carlo simulation for design studies and reactor safety analyses, which requires the ability to carry out calculations of uncertainty propagation based on the variation of a parameter of the transport equation in response to the variation of the physical properties of the system.

In principle, the reactivity effect of a system perturbation can be estimated by taking the difference between the values computed in two independent calculations, one with the nominal system and the second with the perturbed system. In practice, for small perturbations, the computation time necessary to obtain a statistical uncertainty on the difference of these values ​​that is sufficiently low is prohibitive. Moreover, the number of sensitivity coefficients (or perturbations) required is often huge, and it is therefore difficult to resort to independent calculations.

Fortunately, parametric studies can be performed through perturbation calculations that directly evaluate the effects of small variations in the system. For example, according to the "Standard Perturbation Theory" (SPT) the estimation of reactor reactivity perturbations can be calculated by using the adjoint neutron flux, which however turns out to be a highly non-trivial task. Recently, the progress of the Monte-Carlo methods has made it possible to estimate the adjoint flow by means of an Iterated Fission Probability approach and thus to implement the perturbation techniques and to determine the variation of reactivity, within a single calculation, due to one or more perturbations of the compositions of the materials. The Monte Carlo TRIPOLI-4 code now includes a perturbation and sensitivity calculation feature.

The SPT theory is, however, limited to perturbations of reactivity. We are more generally interested in the effects induced by the variations of the material compositions of the reactor on other critical parameters of the Boltzmann equation. The goal of this thesis will be to extend the applications of perturbation techniques: we propose the development of mathematical and algorithmic methodologies to determine the variations of the reactivity, the reactor period or more generally of a physical observable such as a reaction rate in response to variations of a physical parameter of the system, such as temperature, geometric dimensions or nuclear data.

Further Infomation

Alexis JINAPHANH

alexis.jinaphanh@cea.fr ; tél. +33(0)1 69 08 62 75

DEN/DANS/DM2S/SERMA/LTSD

Andrea ZOIA

andrea.zoia@cea.fr ; tél. +33(0)1 69 08 79 76

DEN/DANS/DM2S/SERMA/LTSD