Investigation of the validity of the point-kinetic approximation for subcritical heterogeneous systems in 2-group diffusion theory for measurement of the reactivity in ADS

In this paper, calculations are performed on a 2-D heterogeneous reflected subcricital system to determine the spatial distribution of the neutron noise induced by fluctuations of a neutron source located in the middle of the core. Likewise, the point-kinetic component of the neutron noise is determined and compared to the actual neutron noise. It is found that close to the source, the amplitude of the actual neutron noise is larger than its point-kinetic component, while smaller close to the core periphery. For increasing core subcriticalities and/or decreasing frequencies, the deviation of the reactor response from point-kinetics becomes smaller. Based on these observations, the source modulation method is considered for the evaluation of the core subcriticality, since this method is based on point-kinetics. Although the reactor response only deviates slightly from point-kinetics in practical cases such as for an ADS (i.e. a deeply subcritical medium), the reactivity estimated from the source modulation technique significantly deviates from its actual value. Small deviations of the reactor response from point-kinetics lead to large inaccuracies in the estimation of the reactivity, whereas perfect agreement with point-kinetics leads to a pathological case where the formula for estimating the reactivity is ill-posed. Therefore, the source modulation technique seems to be of limited applicability