Analytical solution of the point reactor kinetics equations for one-group of delayed neutrons for a discontinuous linear reactivity insertion

The understanding of the time-dependent behaviour of the neutron population in a nuclear reactor in response to either a planned or unplanned change in the reactor conditions is of great importance to the safe and reliable operation of the reactor. It is therefore important to understand the response of the neutron density and how it relates to the speed of lifting control rods. In this study, an analytical solution of point reactor kinetic equations for one-group of delayed neutrons is developed to calculate the change in neutron density when reactivity is linearly introduced discontinuously. The formulation presented in this study is validated with numerical solution using the Euler method. It is observed that for higher speed, r = 0.0005 the Euler method predicted higher values than the method presented in this study. However with r = 0.0001, the Euler method predicted lower values than the method presented in this study except for t = 1.0 s and 5.0 s. The results obtained have shown to be compatiblewith the numerical method.