Differential equation for reactivity monitoring using the superposition principle

• A differential form of the inverse point kinetics equation is proposed. • The formulation avoids integral terms used in classical reactimeters. • Reactivity is computed using only power and its time derivatives. • Reactivity calculation does not require power history accumulation. • Results are consistent with standard inverse kinetics benchmarks. This paper presents a different approach to reactivity in nuclear reactors. By introducing the concept of separating reactivity into contributions from delayed and prompt neutrons, this work proposes a new method to solve the inverse point kinetics equations. This formulation is independent of the nuclear power history and solves for all six groups of neutron precursors by applying a superposition principle to the reactivity. These new equations are solved numerically for various nuclear power profiles and different values of the mean neutron generation time. Scenarios involving reactimeter shutdown are also considered. The approach yields accurate results with minimal error and significantly reduces computation time, with time steps up to 1 s. This perspective provides an alternative way of understanding the well-established physical phenomena that occur in a nuclear reactor. Furthermore, because reactivity can be obtained independently of the nuclear power history, this approach offers an attractive alternative for reactimeter design.