Methods for calculating coupled reactor systems

Abstract

803Theoretical approaches to analyzing neutron kinetics in coupled reactor systems are reviewed. A systematic exposition of methods based on the use of integral parameters and an integral equation decribing neutron transport with the energy and angular variables eliminated is given. Special attention is given to a reactor-subcritical assembly as a coupled system.Coupled reactor systems are one area of modern reactor physics that is undergoing intense development. Interest in such systems has increased substantially in the last few years in connection with the development of nuclear systems for various purposes where coupled reactor systems are to be used.The term "coupled reactor systems" (coupled in the neutron-physical sense), which was first introduced into the theory of nuclear reactors by R. Avery [1], signifies that in each reactor some neutrons are emitted as a result of fissions caused by neutrons produced in other reactors. It should be noted that in general a separate component of such a system can be a deeply subcritical and a self-critical nuclear reactor, which makes it possible new ways of controlling coupled systems and increasing their nuclear safety.There are many types of coupled reactor systems. Examples are power systems with enhanced breeding of fuel [2], systems of coupled small pulsed reactors [3][4][5], sectioned reactor systems and neutron-multiplying boosters [3, 5, 6], blankets for a thermonuclear reactor [5,7], subcritical target-blanket complexes for accelerator-driven systems [8-10], reactorlaser systems [5], and other types. Such systems have been used to perform a combination of computational-theoretical and experimental studies of physical processes. It has been shown that such systems have special features which conventional reactors do not. All this required specialists to develop not only a specific theory of coupled systems but also new approaches to the numerical simulation of the neutron-physical, kinetic, and thermal processes occurring in them. In the present paper, a systematic exposition of methods for solving such problems is given.As already noted above, the theoretical approaches which R. Avery was the first to expound in the most systematic manner form the methodological foundation for studying neutron kinetics in coupled reactor systems. In Avery's formalism, integral parameters characterizing individual reactors (individual multiplying zones or regions) and their couplings are used to study a system. The quantity k ij is the probability that a fission neutron in the jth reactor will produce a next-generation fission neutron in the ith reactor and is called the coupling coefficient for i ≠ j; k ij is itself the neutron multiplication coefficient in the ith reactor. The quantity l ij is defined as the average lifetime of prompt neutrons for the process where the neutrons are transferred from the jth into the ith reactor with i ≠ j and is, strictly speaking, the average lifetime of prompt neutrons with i = j. We note that in general k ij ≠ k ji and l ij ≠ l ji .Explic...