An accurate solution of point reactor neutron kinetics equations of multi-group of delayed neutrons

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. In this study, an accurate analytical solution of point reactor kinetics equations with multi-group of delayed neutrons for specified reactivity changes is proposed to calculate the change in neutron density. The method is based on formulating a coefficient matrix of the homogenous differential equations of the point reactor kinetics equations and calculating the eigenvalues and the corresponding eigenvectors of the coefficient matrix. A small time interval is chosen within which reactivity relatively stays constant. The analytical method was applied to solve the point reactor kinetics equations with six-groups delayed neutrons for a representative thermal reactor. The problems of step, ramp and temperature feedback reactivities are computed and the results compared with other traditional methods. The comparison shows that the method presented in this study is accurate and efficient for solving the point reactor kinetics equations of multi-group of delayed neutrons.

► Analytical solution is proposed to solve the point reactor kinetics equations (PRKE).
► The method is based on formulating a coefficient matrix of the PRKE.
► The method was applied to solve the PRKE for six groups of delayed neutrons.
► Results shows good agreement with other traditional methods in literature.
► The method is accurate and efficient for solving the point reactor kinetics equations.