Variational Representations in Reactor Physics Derived from a Physical Principle

Abstract

A physical axiom is advanced that relates density of neutrons and their individual contribution to operationally determinable behavior of a reactor. The variational principle derived from this axiom is of a general form applicable to systems in which time dependency of coefficients of equations prevents a separation into conventional eigenfunctions and eigenvalues. The physical significance of independent variation of two field functions is investigated. The treatment of nonseparable systems and variational principle to which we are led are both independent of any particular physical model employed to represent system and appear to be applicable to a variety of nonconservative, continuous, and time-dependent systems in mathematical physics. The more well-known properties of separable problem are derived from principle as the exception proving rule in an attempt to associate physical meaning with commnonly . employed forms. Thus a discussion is given of relation of Greens function to both fields and Joint Error is introduced as a criterion for completeness of biorthegonal sets. Although variational principle derived is not applicable to variation of coefficients of equations through nonlinearities, it is indicated how themore » present approach may be extended to account for nonlinearities. (auth)« less