The Trajectory Period-Folding Method For Transmutation Analysis

The evolution of the nuclide composition over time is described by the first-order differential equation known as the Bateman equation. The formation of new isotopes can take place due to natural radioactive decay or due to nuclear reactions induced by neutrons (or other particles). Reaction rates in the depletion problem are time-dependent; therefore, the procedure is performed in calculation steps. One of the methods used to solve fuel evolution for a single time period is the linear chain approach. Calculated linear chains represent a series of physically occurring nuclide transitions from the source nuclide to the resulting nuclide. Within this solution, the obtained chains preserve all quantitative information about the transmutation process for the calculated time period. In a multi-step problem, nuclide concentrations are propagated from step to step and the information about how transmutation chains are formed after more than one step is lost. The newly proposed approach uses a methodology which extends the representation of transmutation chains with trajectories described by transition and passage functions and allows to track the nuclide transmutation process beyond one step. Trajectories prepared for each computing time step are combined in the process of period folding, thus enabling broader representation of the nuclide field evolution. This procedure corresponds to the period-folding trajectory. It can be recursively repeated by adding consecutive steps obtained through the standard solution in order to build time-dependent physical evolution of transmutation chains and observe the simulated system with a new specific tool. The novel period-folding method is implemented in the Monte Carlo