Spatial corrections for pulsed-neutron reactivity measurements

For pulsed-neutron experiments performed in a subcritical reactor, the reactivity obtained from the area-ratio method is sensitive to detector positions. The spatial effects are induced by the presence of both the prompt neutron harmonics and the delayed neutron harmonics in the reactor. The traditional kinetics distortion factor is only limited to correcting the spatial effects caused by the fundamental prompt-α mode. In this paper, we derive spatial correction factors fp and fd to account for spatial effects induced by the prompt neutron harmonics and the delayed neutron harmonics, respectively. Our numerical simulations with the FX2-TH time-dependent multigroup diffusion code indicate that the high-order prompt neutron harmonics lead to significant spatial effects and cannot be neglected in calculating the spatial correction factors. The prompt spatial correction factor fp can be simply determined by the ratio of the normalized detector responses corresponding to the fundamental k-mode and the prompt neutron flux integrated over the pulse period. Thus, it is convenient to calculate and provides physically intuitive explanations on the spatial dependence of reactivity measured in the MUSE-4 experiments: overestimation of the subcriticality in regions close to the external neutron source and underestimation of the subcriticality away from the source but within the fuel region.