{"title":"A quasistatic asymptotic limit for reactor kinetics","authors":"","doi":"10.1016/j.anucene.2024.110864","DOIUrl":null,"url":null,"abstract":"<div><p>We propose a “quasistatic” asymptotic limit for reactor kinetics in which the material properties vary much more slowly in time than the solution itself. We further develop an asymptotic approximation of the solution in this limit using the method of multiple scales that, to leading order, takes the form of the product of a function that depends only on time and a function that depends on all independent variables but varies on the same time scale as the material properties. Determining when an approximation of this form is valid is of interest as several methods for performing reactor-kinetics calculation rely on such a representation of the solution. With an example reactor-kinetics problem, we demonstrate our asymptotic approximation becomes more accurate as the material properties vary more slowly in time, as expected.</p></div>","PeriodicalId":8006,"journal":{"name":"Annals of Nuclear Energy","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Nuclear Energy","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0306454924005279","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"NUCLEAR SCIENCE & TECHNOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a “quasistatic” asymptotic limit for reactor kinetics in which the material properties vary much more slowly in time than the solution itself. We further develop an asymptotic approximation of the solution in this limit using the method of multiple scales that, to leading order, takes the form of the product of a function that depends only on time and a function that depends on all independent variables but varies on the same time scale as the material properties. Determining when an approximation of this form is valid is of interest as several methods for performing reactor-kinetics calculation rely on such a representation of the solution. With an example reactor-kinetics problem, we demonstrate our asymptotic approximation becomes more accurate as the material properties vary more slowly in time, as expected.
期刊介绍：
Annals of Nuclear Energy provides an international medium for the communication of original research, ideas and developments in all areas of the field of nuclear energy science and technology. Its scope embraces nuclear fuel reserves, fuel cycles and cost, materials, processing, system and component technology (fission only), design and optimization, direct conversion of nuclear energy sources, environmental control, reactor physics, heat transfer and fluid dynamics, structural analysis, fuel management, future developments, nuclear fuel and safety, nuclear aerosol, neutron physics, computer technology (both software and hardware), risk assessment, radioactive waste disposal and reactor thermal hydraulics. Papers submitted to Annals need to demonstrate a clear link to nuclear power generation/nuclear engineering. Papers which deal with pure nuclear physics, pure health physics, imaging, or attenuation and shielding properties of concretes and various geological materials are not within the scope of the journal. Also, papers that deal with policy or economics are not within the scope of the journal.
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