文档介绍：脉冲堆有限裂变链长的数学期望值分析
第24卷第1期
2007年3月
原子核物理评论
NuclearPhysicsReview
,
Mar.,2007
ArticleID:1007—4627(2007)01一OO8O—O5
ExpectedValueofFiniteFissionChainLengths
ofPulseReactors
LIUJian-jun,ZHOUZhi—gao,ZHANGBen—ai
(InstituteofAppliedPhysicsandC0mp"t口to口
ZMathematicsBeijing,Beijing100088,China)
Abstract:Theaverageneutronpopulationnecessaryforsponsoringapersistentfissionchainina
multiplyingsystem,,theprobabilityfunctionO(n,t0,,)
-linearpartial differentialequationfortheprobabilitygeneratingfunctionG(z;t0,t)
equation,wehaveobtainedanapproximateanalyticsolutionforaslightlypromptsupercriticalsys—
?,themeanvalueoffinitefissionchainlengthsisestimatedin
thisworkandshowsthattheestimatedvalueisreasonablefortheexperimentalanalysis. Keywords:pulsereactor;criticalnuclearsystem;finitefissionchain
CLCnumber:TL4Documentcode:A
1Introduction
Foranuclearmultiplyingsystemofaweak neutronsourcewiththereactivecoefficientk,neg—
lectingdelayedneutrons,ifasourceneutronleads to.
afissionandsponsorsapersistentfissionchain, thelengthofthefissionchainwillpresentinsto—
chasticfluctuationway,andtheprobabilitydistri—
butionofthechainswillbestronglycorrelatedto <1,thelengthofthefission chainwillbefinite,and,theprobabilityofsponso—
>1.
thelengthofthepersistentfissionchainmaybefi—
niteorinfinite,theprobabilitymainlyreliesonthe extentofk>.,eveninasupercriticalsys—
tem,thereisprobabilityforanuetronnottospon—
sorapersistentfissionchain.
Althoughinthesupercriticalsystemwitha permanentsourceS,theprobabilityofsponsoring apersistentfissionchainbythelastinginjectionof thesourceneutroninthetimespanfromzerotoin—
finityisunity,therandomicityofneutrontrans—
portationatmicrolaysoftenmakesthetime, lengthandprobability,ofpersisitent