Understanding Total Monte Carlo uncertainty propagation in burn up calculations with Generalized Perturbation Theory
The last few years has seen Total Monte Carlo becoming the most used method for uncertainty propagation in burn up calculations. This straightfoward approach allows for the direct observation of output uncertainties (keff, isotopic concentrations etc. of the coupled Bateman equation (fuel depletion) and Boltzmann equation (neutron transport) The application of GPT in this coupled case implies not only the calculation of nuclide adjoint functions but also the calculation of a number of importance functions. The coupling is thus almost never done. In this paper, we compare the propagation of Pu239 fission, capture and (n,2n) cross sections' uncertainties with both TMC and GPT methods in a simple Na cooled fast reactor assembly. In such a case, the change of spectrum due to the change in in one nuclide's cross sections is expected to be smaller than in a thermal spectrum where the importance of individual resonances is high. We will see that it can't be negligeted. Thanks to the combined use of TMC and GPT we can separate the effects of uncertainties on a selection of other heavy nuclide densitities. The power normalisation gives minor, but important contributions. The sensitivities to depletion terms are the dominant terms for Pu239 and its direct daughters' evolution. The minor actinide density uncertainties are dominated by the impact of Pu239 on neutron spectrum and then on minor actinides' average cross sections. The results of uncertainty analyses could therefore be very different if basic uncertainties with complete energy and cross nuclide correlations were available.