Analytical Solution of Neutron Point Kinetic Equations Taking into Account Oscillating External Neutron Source

Neutron external source plays an important role during the start-up of a nuclear reactor. Therefore, the analytical solutions of neutron point kinetics equations in the presence of external source are important in predicting the variation of the neutron population during the start-up of a nuclear reactor. For a constant external source, an analytical solution is worked out, as shown in the previously published articles. Due to fluctuations of the neutron source around a mean value, the source is actually time dependent. Thus, in this research, an alternative analytical solution with one group of delayed neutrons is proposed with the ramp reactivity insertion for the external source with sinusoidal fluctuation during the start-up of the nuclear reactor. The only approximation made in this study is to ignore the second time derivative of the neutron population. The present study is fully in agreement with other studies regarding the limit of very small amplitude fluctuations.