Estimation of reactivity worth with differential operator sampling method

Nagaya, Yasunobu  ; Mori, Takamasa

Nuclear reactor analysis requires calculations of reactivity worth such as control rod worth, void reactivity worth, sample reactivity worth, etc. It is, however, difficult to perform such calculations with the Monte Carlo method if the worth is small. In the present work, we extend the differential operator sampling method such that the derivative terms up to the fourth-order and the perturbed source effect up to the fourth-order can be estimated, and examine the applicability of the fourth-order differential operator sampling method to reactivity worth calculations. As a benchmark calculation, we perform the reactivity worth calculation for Godiva. The perturbation is introduced by decreasing the density in the central region of a radius of 1 cm. The result with the fourth-order differential operator sampling method agrees well with the reference one. As a practical calculation, we also perform Np sample worth calculation for TCA. The calculated sample reactivity worth with the differential sampling method approaches to the reference value as the higher-order effect is taken into account up to the fourth order. However, there still exists a discrepancy of 17%. It is, thus, found that many more higher-order effects must be taken into account or another method must be applied in this case.