Neutron kinetics in subcritical cores with application to the source modulation method

The subject of this paper is an investigation of the performance of the so-called source modulation technique for the measurement of reactivity in subcritical, source-driven cores. Methods of measuring reactivity by a single detector, including the source modulation method, are based on the assumption of point kinetic behaviour of the core. Deviations from point kinetic behaviour will lead to an inaccurate estimation of the reactivity. Hence, first, the conditions of point kinetic behaviour in subcritical source-driven cores are revisited. In addition to the known conditions for such behaviour, which have an analogy to those in critical cores, some additional cases are found which only exist in subcritical cores. Then the performance of the source modulation technique is investigated. It is found that the error of the method, originally thought to be due exclusively to the deviation of the local detector signal from the amplitude factor of point kinetics, remains finite and non-zero even in the limit of exact point kinetic behaviour (e.g., with low frequencies or deep subcriticalities). This is demonstrated and explained by analytical formulae. Some remedies for this shortcoming of the method are also suggested and discussed.