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Thesis
Home   /   Thesis   /   Monte Carlo methods for the adjoint transport equation: application to radiation shielding problems

Monte Carlo methods for the adjoint transport equation: application to radiation shielding problems

Engineering sciences Mathematics - Numerical analysis - Simulation

Abstract

The Monte Carlo method is the reference approach for simulating the transport of neutrons and photons, particularly in the field of radiation shielding, due to the very low number of approximations that it introduces. The usual Monte Carlo strategy is based on the sampling of a large number of particle histories, which start from a source, follow the physical laws of collision available in nuclear data libraries and explore the geometry of the system : the contributions of the particles to the response of interest (e.g. a count rate in a detector), averaged over all simulated stories, estimate the value predicted by the Boltzmann equation. If the detector region is "small", statistical convergence of the standard Monte Carlo approach becomes very difficult, because only an extremely limited number of stories will be able to contribute. It then becomes advantageous to use Monte Carlo methods for the solution of the adjoint transport equation: the histories of the particles are sampled from the detector backwards, and the collection region is the source of the starting problem (which is typically assumed to be “large” relative to the detector). This approach, simple in principle, offers the possibility of considerably reducing the statistical uncertainty. However, the adjoint Monte Carlo methods present scientific obstacles that are both practical and conceptual: how to sample the physical laws of collision “backwards”? How to control the numerical stability of adjoint simulations? In this thesis, we will explore different strategies in order to provide answers to these questions, in view of applying these methods to radiation shielding problems. The practical implications of this work could open up very encouraging perspectives for the new TRIPOLI-5® simulation code.

Laboratory

Département de Modélisation des Systèmes et Structures
Service des Réacteurs et de Mathématiques Appliquées
Laboratoire de Transport Stochastique et Déterministe
Paris-Saclay
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