Kinetics of a point reactor in the presence of reactivity oscillations

The response of a subcritical system to reactivity oscillations is investigated in the point-kinetics limit, for both the undriven and driven case, with a fully analytic approach. For simplicity, purely-sinusoidal reactivity oscillations are considered, although extensions to generic, periodic oscillations are immediate. It is shown how information on the long-term behavior of the system can be inferred by considering an equivalent algebraic problem, for which accurate approximations can be obtained very efficiently. As the procedure leads to reliable results even when low-order approximations are considered, this approach proves particularly convenient when the stability of the system has to be investigated over a large range of variation of the parameters characterizing the reactivity oscillations. Considerations about the asymptotic behavior of the system driven by a generic, periodic external source are also provided.