Abstract
The aim of this article is to describe a mathematical model and an associated numerical method for the basic problem of evaluating the void fraction of a slab material from the responses of a typical source-detector system for backscattered neutrons. The mathematical model and void fraction evaluation method reported herein: i) enable us to treat explicitly and exactly a mixed neutron beam, i.e. a neutron beam consisting of a monodirectional component with normal incidence upon the slab material and a component that is a smooth function of the angular variable and ii) allow for an arbitrary order of anisotropy of the neutron scattering phase function. In addition, the associated void fraction evaluation method is free from computer overflow exceptions, even for the challenging problems where the angular quadrature set is of high order and/or the slab material is exceedingly thick. We perform a numerical experiment to illustrate the positive features of both the mathematical model and evaluation method reported here, and we conclude this article with a discussion and directions for future work.
Highlights
We have been working on deterministic models in the subject of radiation transport theory [1] for the development of faster yet accurate alternatives to stochastic models such as Monte Carlo for both theoretical investigations and practical applications
The testing equipment upon which the ZB model was based is very simple: an isotropic neutron beam shines the test slab on one side, and a collimated neutron detector is positioned at the incidence side along a number of angular directions to get the angular fluxes of backscattered neutrons in corresponding angular directions [6]
To do away with some of these flaws, we have recently developed and reported on an improved mathematical model [11], which is based on a more accurate SN formulation and on some analytic and numerical schemes adapted from a hybrid analytic/numerical method developed by the present author for more general radiation transport problems [12, 13]
Summary
We have been working on deterministic models in the subject of radiation transport theory [1] for the development of faster yet accurate alternatives to stochastic models such as Monte Carlo for both theoretical investigations and practical applications. In this article we take a step further, and while keeping the positive features (ii) and (iii) above, we incorporate into the model described in DE ABREU [11] the practical case of a mixed beam, i.e. a beam consisting of a monodirectional component with normal incidence upon the slab material (as we have far considered) and a component that is a smooth function of the angular variable (not necessarily isotropic) This step was in order because it enables us to model beam transport problems associated with even more realistic neutron beams; an actual collimated beam can be thought of as a beam with a weakly divergent component and a monodirectional component.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
