Sub-critical reactor kinetics analysis using incomplete gamma functions and binomial expansions

Point reactor kinetics equations with one group of delayed neutrons are solved analytically to determine the neutron population as a function of time for any ramp reactivity insertion in the presence of external neutron source using prompt jump approximation. With the time dependent neutron population the other important kinetic parameters such as the reactor period also can be derived. Analytical solutions are available in the literatures for any ramp reactivity insertion into a critical reactor without considering the source term. Analytical solutions available in the literature by considering the source term also to study sub-critical reactor kinetics. But such a solutions either uses constant source approximation which under predicts the solution, or the available solution is not useful for all kind of sub-critical reactivity and external ramp reactivity insertion combination due to the computer precision incompatibility. In the present work, analyses are carried out to determine the reactivity boundary to which the existing results can converge to a true solution, beyond where the precision incompatibility arises. A new series solution is recommended in the region where existing solution converges to false solution due to precision incompatibility.