A proposal for a subcritical reactivity meter based on Gandini and Salvatores' point kinetics equations for multiplying subcritical systems

Multiplying Subcritical Systems were for a long time poorly studied and its theoretical description remains with plenty open questions. Great interest on such systems arose partly due to the improvement of hybrid concepts, such as the Accelerator-Driven Systems (ADS). Along with the need for new technologies to be developed, further study and understanding of subcritical systems are essential also in more practical situations, such as in the case of a PWR criticalization in their physical startup tests. Point kinetics equations are fundamental to continuously monitor the reactivity behavior to a possible variation of external sources intensity. In this case, quickly and accurately predicting power transients and reactivity becomes crucial. It is known that conventional Reactivity Meters cannot operate in subcritical levels nor describe the dynamics of multiplying systems in these conditions, by the very structure of the classical kinetic equations. Several theoretical models have been proposed to characterize the kinetics of such systems with special regard to the reactivity, as the one developed by Gandini and Salvatores among others. This work presents a discussion about the derivation of point kinetics equations for subcritical systems and the importance of considering the external source. From the point of view of the Gandini and Salvatores' point kinetics model and based on the experimental results provided by Lee and dos Santos, it was possible to develop an innovative approach. This article proposes an algorithm that describes the subcritical reactivity with external source, contributing to the advancement of studies in the field.