The collision probability approach to neutron transport can be used to obtain the energy-dependent neutron spectrum in nuclear reactor systems as well as other quantities of interest. This method makes the approximation that the neutron distribution is constant within homogeneous regions, or cells, in the system. This assumption restricts geometries that can be modeled by the collision probability approach. The geometry modeled is typically an infinite lattice of two homogeneous cells: a fuel pin cylinder and the coolant that surrounds it. The transport of neutrons between the homogeneous cells is done using probabilities describing the chance that a neutron having a collision in one cell has its next collision in another cell. These collision probabilities can be cast in terms of escape and transmission probabilities for each cell. Some methods exist that extend the collision probability approach to systems composed of more than two homogeneous cells. In this work, we present a novel collision probability method, based on previous work by Schneider et al. (2006a), for an arbitrary number of cells. The method operates by averaging the transmission probabilities across cells of the same shape, and thus assumes a certain level of homogeneity across all cells. When using multigroup cross sections, which the collision probability approach requires, it is necessary to consider the effect that a system's geometry and composition has on those multigroup cross sections. The cross sections must be computed in a way that accounts for the resonance self-shielding that may reduce the reaction rates in the resonance region. The process of developing self-shielded cross sections in a heterogeneous system utilizes an escape cross section. We compute this escape cross section using the same collision probabilities used to obtain the energy spectrum. Results are presented for simple two-cell systems, and preliminary results for four-cell simulations are also given. An extension to the method is provided that accounts for the fact that in thermal systems the assumption of homogeneity is not always valid. / text

<p>Comprehensive sensitivity and uncertainty analysis has been performed for light-water reactor and heavy-water reactor lattices using three techniques; adjoint-based sensitivity analysis, Monte Carlo sampling, and direct numerical perturbation. The adjoint analysis was performed using a widely accepted, commercially available code, whereas the Monte Carlo sampling and direct numerical perturbation were performed using new codes that were developed as part of this work. Uncertainties associated with fundamental nuclear data accompany evaluated nuclear data libraries in the form of covariance matrices. As nuclear data are important parameters in reactor physics calculations, any associated uncertainty causes a loss of confidence in the calculation results. The quantification of output uncertainties is necessary to adequately establish safety margins of nuclear facilities. In this work, the propagation of uncertainties associated with both physics parameters (e.g. microscopic cross-sections) and lattice model parameters (e.g. material temperature) have been investigated, and the uncertainty of all relevant lattice calculation outputs, including the neutron multiplication constant and few-group, homogenized cross-sections have been quantified. Sensitivity and uncertainty effects arising from the resonance self-shielding of microscopic cross-sections were addressed using a novel set of resonance integral corrections that are derived from perturbations in their infinite-dilution counterparts. It was found that the covariance of the U238 radiative capture cross-section was the dominant contributor to the uncertainties of lattice properties. Also, the uncertainty associated with the prediction of isotope concentrations during burnup is significant, even when uncertainties of fission yields and decay rates were neglected. Such burnup related uncertainties result solely due to the uncertainty of fission and radiative capture rates that arises from physics parameter covariance. The quantified uncertainties of lattice calculation outputs that are described in this work are suitable for use as input uncertainties to subsequent reactor physics calculations, including reactor core analysis employing neutron diffusion theory.</p> / Doctor of Philosophy (PhD)