Study on kinetics of subcritical system: Contribution of delayed neutrons to the transient after a reactivity insertion

It is generally difficult to employ three dimensional spaces and time dependent kinetics by using a Monte Carlo method for nuclear reactor kinetics, because the random work analysis of a neutron becomes extremely difficult when conditions for neutron transport change with time. However, in most cases of kinetic analysis, in particular relevant to ADS systems, we meet with many cases, where the lifetime of prompt neutron is much shorter than that of the neutron transport condition. In calculating the kinetic evolution of a subcritical (SC) system, in this paper we propose a new calculation technique where a steady state equation for the neutron flux and a time-dependent one for the delayed neutron precursor density will be treated. In this paper, the accuracy of this theory is investigated by using a simple point reactor equation for several cases typical for ADS system. We obtained strict solution Φ* as a reference solution, Φ1 as a solution by the present method, and Φ2 as a solution where both neutrons and delayed neutron precursors are treated by using static equations. The obtained results show a good agreement between Φ1 and Φ*, though the Φ2 agrees with Φ* poorly in all our cases. Finally, we can employ a conventional Monte Carlo code for neutron transport and analysis many kinetics problems of ADS systems with the help of delayed neutron precursor analysis.