Abstract
In nuclear fission reactor, the decay constant of delayed neutron will often determine the time behavior of the neutron population in a subcritical system or supercritical system or in a critical system in which a neutron source or cross section change with time. In the treatment of these problems, it is frequently necessary to include the delayed neutrons. When the effect of delayed neutrons in a reactor system is considered, the time-dependent neutron transport equation will be supplemented with the balance equations for delayed-neutron precursors. The aim of this paper is to present an iterative method for the determination of the solution of transport equation with delayed neutrons and to establish an explicit relationship among these physical parameters of reactor so that one can determine the decay and growth property of the solution of the system. The iterative method consists of two monotone sequences which converge monotonically from above and below, respectively, to a unique solution. Quantitative conditions in terms of physical parameters of the reactor are found for eventual decay and growth of neutron population. Finally, in the special case of slab geometry, one of our results leads to a criterion on the macroscopic cross section and the slab length from which the growth property of the solution can be determined without explicit knowledge of solution. © 1990, Taylor & Francis Group, LLC. All rights reserved.