A derivation of the time-dependent adjoint equations for neutron importance in the transport, continuous slowing-down and diffusion models

Abstract

A generalization of the conventional importance concept is to consider the contribution of any one neutron to some final operationally determinable characteristic of a nuclear reactor. Consistency requires that one neutron is as important as its progeny. From these ideas, the adjoint equations and boundary conditions are derived for the Boltzmann transport model, for simple and multigroup diffusion theory and for the continuous slowing-down model. This more general concept for the time-dependent importance includes the conventional expressions of iterated fission probability, etc. as special cases.