Consistent multipoint kinetics for source-driven systems

The application of the multipoint method to the analysis of the dynamic behavior of subcritical source-driven systems is studied. The system domain is divided into a small number of macro-regions and the neutron flux is factorized in the product of shape and amplitude functions on each subdomain. The flux, factorized in the multipoint fashion, is then introduced into the variational formulation of the kinetic equations for neutrons with delayed emissions. The objective of the analysis is the derivation of a consistent formulation of the multipoint equations and the correct definition of the weighting functions adopted in the projection procedure. Different choices for the integral functional introduced in the variational formulation are considered, leading to different forms of the system of first-order differential equations in time for the amplitudes. Their characteristics are addressed and their performances in terms of accuracy of time-dependent predictions are discussed.