Test and optimization of variance reduction methods in shielding problems with multiplicative media

During the start-up phase, for safety reasons, nuclear reactors must always be far from criticality. In this respect, it is common practice to monitor at each instant the neutron flux multiplication due to the start-up source located in the reactor core: this is achieved via in-core or ex-core detectors. The simulation of this type of problems is generally performed by means of Monte Carlo codes and constitutes a real scientific challenge. It combines the need for variance reduction methods, typical of fixed-source problems, with the need to correctly represent the fission neutron source, given by the fissile materials. The aim of this thesis is to test the potentialities of the Monte Carlo code TRIPOLI-4® (developed at CEA), and in particular of its variance reduction methods, in this domain. For this purpose, we have assessed the application of the Exponential Transform with Importance Biasing, the Adaptive Multilevel Splitting method (AMS) and the “Two-step” technique, a hybrid method commonly used at CEA. All the variance reduction techniques tested in this work require an importance function, which for our investigations has been produced using the IDT solver (part of the APOLLO3® deterministic code developed at CEA), the INIPOND module provided with TRIPOLI-4 and a geometric importance generator included in the AMS module. After presenting the methods, we performed some tests first on toy-models, taking into account single and multiple response evaluations, and then on a more realistic model representative of a generic PWR reactor. The Exponential Transform has been found to be unable to ensure a stable fission particle sampling within the simulation, producing estimations of neutron flux at the detector that were affected by evident biases and strongly altered convergence trends. This behavior was mitigated by increasing the distance between the source and the fissile material. The AMS method turned out to be little sensitive with respect to the type of importance function used, therefore extremely robust. It provided unbiased results with good performances. Finally, we observed that the Two-step method, which separates the calculation of the fission source from the neutron propagation towards the detector, allows exploiting the maximum performances obtainable with Exponential transform in simple propagation problems. On the other hand, we observed that the method presents a remarkable sensitivity to the quality of the fission source term, which might in turn favor the onset of bias within the propagation calculation.