Analytical solution of the point reactor kinetics equations with temperature feedback

In this paper the point reactor kinetics equations with one group of averaged delayed neutrons and the adiabatic feedback model are solved analytically. The relations of reactivity, and neutron density with neutron lifetime are calculated. The numerical results of the delayed-supercritical process in a pressurized-water reactor with 235U as a fissile material under constant step reactivity of ρ0 = β/2 are given. Our investigations report one of the most accurate results. However this method is valid and applicable as long as the adiabatic condition of heat transfer from fuel rods to the coolant is met.

► Supercritical process in a pressurized-water reactor with 235U as fissile materials.
► Solution of the point reactor kinetics equation with a temperature feedback.
► The linear relationship between reactivity and neutron generation time.