Generalization of the analytical solution of neutron point kinetics equations with time-dependent external source

Abstract

Point reactor kinetics equations with one group of delayed neutrons in the presence of the time-dependent external neutron source are solved analytically during the start-up of a nuclear reactor. Our model incorporates the random nature of the source and linear reactivity variation. We establish a general relationship between the expectation values of source intensity and the expectation values of neutron density of the sub-critical reactor by ignoring the term of the second derivative for neutron density in neutron point kinetics equations. The results of the analytical solution are in good agreement with the results obtained with numerical solution.

"Prediction the Performance of the Iaea 10 Mw MTR Research Reactor at Transient Startup"

“…For validation of the developed modeling, comparison between this work and other analytical solutions of point reactor kinetic equations for one-group of delayed neutrons is accomplished with computed the change in neutron density as soon as reactivity is increased introduced unevenly. The comparison is applied with the solutions using at eidi et al [7], Reisch et al [8] and Zhang et al [5].…”