Stochastic and deterministic methods for the calculation of small-sample reactivity experiments

Several calculations methods for the analysis of small-sample reactivity experiments are presented, as their main advantages and drawbacks. A numerical benchmark has been defined for this study consisting in a regular lattice of UO₂ fuel pins, in which the central one is successively poisoned with isotopes of interest (actinides, absorbers, ...). A first method, based on a forward calculation (“eigenvalues difference method”), is presented, using either a deterministic or a stochastic calculation code. A first perturbative method studied is based on the “Exact Perturbation Theory” (EPT) implemented in the deterministic code APOLLO2.8, and gives consistent results against forward calculations. A second perturbative method, the “correlated sampling method”, implemented in the stochastic calculation code TRIPOLI4.7 is tested. It should be use carefully as it is generally validated against small atomic density changes, but can be useful for conception studies. An “hybrid method”, based on the EPT formalism, using both Monte Carlo and deterministic results is tested, and shows reliable results.