Fundamental burn-up mode in a pebble-bed type reactor (original) (raw)

The material composition of nuclear fuel changes constantly due to nuclides transforming to other nuclides via neutron-induced transmutation reactions and spontaneous radioactive decay. The objective of burnup calculations is to simulate these changes over time. This thesis considers two essential topics of burnup calculations: the numerical solution of burnup equations based on computing the burnup matrix exponential, and the uncertainty analysis of neutron transport criticality equation based on perturbation theory. The burnup equations govern the changes in nuclide concentrations over time. They form a system of first order differential equations that can be formally solved by computing the matrix exponential of the burnup matrix. Due to the dramatic variation in the half-lives of different nuclides, the system is extremely stiff and the problem is complicated by vast variations in the time steps used in burnup calculations. In this thesis, the mathematical properties of burnup m...