Shannon entropy of nuclear fuel transmutation

Abstract

The paper concerns a transmutation of UO2, MOX and ThO2 fuels in the typical PWR geometry. The problem is solved by the linear chain method implemented in the MCB code. In the study, it was applied the novel trajectories period folding method which allows for tracking nuclide formation process for a whole fuel cycle. This approach aims to identify pathways for isotopes build-up during entire fuel evolution. The simulated system can be represented by a linear tree graph of all possible transmutation chains. The positions in a graph represent transmutation chain history while its values define the assigned transitions and passages. This model allows us to represent the evolution of nuclide field as a series of physically occurring nuclide transitions over the entire fuel irradiation time. It was used the tree graph approach together with the concept of network entropy as a characteristic measure of network topology. The Shannon entropy applied to the considered numerical problem is a measure of uncertainty and it was compared with the numerical uncertainties of nuclide field. The numerical uncertainties were obtained using the independent replica calculations, which allowed assessment of statistical error propagation in the considered model of the PWR fuel element.