Coupled reactors kinetics equations

A general formulation of the kinetics equations of a system of coupled reactors is developed within the framework of neutron transport theory. The time behavior of the neutron population in a system of M interacting reactors is described by a set of M coupled generalized point kinetics equations. The kinetic behavior in each reactor being determined partly by its own characteristics and partly by the neutronic contribution from the rest of the system. The method of approach consists of describing the neutron population within a reactor by a single equation, the time dependent transport equation, and classifying neutrons on the surface of the reactor by groups according to the particular direction they travel with respect to a unit normal at the surface. This permits the use of the concept of surface coupling to account for the neutronic interaction between the reactors. To obtain the kinetics equation of the jth reactor in the system an adjoint equation is formulated in conjunction with the time dependent transport equation. The adjoint equation describes a fictitious steady state in the jth reactor when isolated from its environment. The mathematical procedure to derive the kinetics equations is basically the same as that used informulating generalized point kinetics equations. The coupled reactors kinetics equations are cast in terms of an amplitude time function and the reactor parameters defined as functions of a time dependent space flux shape. ..