An analytical solution for the point reactor kinetics equations with one group of delayed neutrons and the adiabatic feedback model

The point reactor kinetics equations with one group of delayed neutrons and the adiabatic feedback model are solved analytically. The analytical solution is based on an expansion of the neutrons density in powers of the small parameter, the prompt neutrons generation time, into the second order differential equation in the neutron density. The relation between the time and the reactivity for reactor excursions near prompt critical is derived. Also, the neutron density and the average density of delayed neutron precursors as functions of reactivity are presented. The relations of reactivity, neutron density and temperature with time are calculated, drawn, and compared with other analytic method.