AnewversionofthereflectedcoreinhourequationanditssolutionOriginalResearchArticle

Thestudyoftheneutronevolutioninnuclearsystemsisachallengingmathematicalandphysicalproblemsinceitconstitutesafundamentaltopicinthedesignofcriticalandsubcriticalreactors.Theobjectofthispaperistoderiveamathematicalframeworktocharacterizeanewversionofthetwo-pointinhourequationtodetermineitsrootsforreflectedreactors.Toattainsuchscope,ananalyticalapproachisalwaysusedforanalyzingthediffusiontheorymodelwithoneenergygroupofneutronandGdelayedfamilyofprecursors.Themodifiedtwo-pointinhourequationisdeducedandananalysisofitsrootsisperformedtakingintoaccounttheabilitytomodifysourcereactivityvariation.Inaddition,theworkproposedanumberofdelayedneutronmodelsusingmorethanthetraditionalsixgroups,wheretheeffectofthereflectorisconsideredmathematicallyequivalenttoanadditionaldelayedpseudo-neutrongroup.Forthecaseofsourcereactivityvariationanasymptoticreactorperiodisdeducedasasolutionofthismodifiedinhourequation.Theexactsolutionofthetwo-pointreactorkineticequationsisobtained;inwhicheachtransientintheneutronpopulationisalinearcombinationofexponentialfunctionsatdifferenttimeconstants,theirrespectivecontributionsdependsontheirprevioushistory.Finally,thenumericalresultsobtainedwiththesealgorithmsareappliedandverifiedforfourcasesofreflectedreactors.