Generalized Contributon Response Theory

Abstract

A general theory is developed to describe the mechanism by which the response observed on a detector propagates throughout a system. The response is transferred between a particle source and the detector by special particles called contributons. The distribution in phase-space of the response carried by contributons defines a new quantity called the “response continuum,” which depends on solutions to the forward and adjoint Boltzmann equations. A transport equation for the response distribution is derived, and properties of the response continuum are discussed. The response concentration is described by the contributon response density and flux, which are used to locate regions containing large amounts of potential response contribution. The flow of response through space is described by streamlines of a vector field called the “response current.” This field is related to two new variables called the “response potential” and “vorticity,"respectively. Sample results are presented for “contributon dipole” configurations. A spherical harmonic expansion of the angular flux is given to describe directional characteristics of the response continuum. The “contributon slowing-down equation” is derived to describe the simultaneous transfer of response through space and energy. A new contributon Monte Carlo method to simulate response transport is discussed.