1OverviewHowaFissionReactorworks:Avoiding‘Chernobyl’2EnergyfromfissionNuclearenergycanbereleasedfromanyreaction(e.g.fusion,fissionetc)ifityields…anincreaseintotalbindingenergy(sameas)adecreaseintotalmassThus:massconvertedtoenergy(E=mc2)Numberofnucleons,ABindingEnergypernucleon(MeV)EnergyfromfissionEnergyfromfusion3EnergyfromfissionE.g.–one238Unucleus(Z=92)splitsintotwo119Pdnuclei(Z=46):applyconservationofmass-energy…WhereQ=energyreleased.soQ/c2=0.20538u,1u=931.5MeV/c2,soQ=191MeVNote:Qispositive–i.e.energyisreleased(massisreduced)Enormousenergyreleased–mostlyinKEoffissionfragments4EnergyfromfissionQuestion:Whydoesn’t238Usimplyfissionspontaneously?Itobviouslywantsto!Infact,Q+veformostnucleioverA=100,sowhydon’ttheyALLfission?Considerpotenergyoftwo“separating”119Pdfragments…EnergyQMeVSeparationCoulombpotentialNuclearPotentialFissionbarrier,D5Neutron-inducedfissionSo,nucleusneedstobegivenenergy(D)beforeitcanfission.Wherecanyougetitfrom?Consider“firing”aneutronata235Unucleustomakeitfission…(thisisatypicalfissionreactionfrom235U).Forthisfissionevent,D=6.2MeV.Now,lookatthefirststep…Fromthemasses,wefindthatQ’=6.54MeVSimplyabsorbingtheneutronprovidesenoughenergytocausefissionThus,235UisFISSILEHowmanynaturally-occurringfissilenuclidesarethere?

238U,however,isFISSIONABLE.Q’isnotquiteenough,needsabitmoreenergy6Neutron-inducedchainreactionNow–achainreactionisfeasible…Energyreleased=178MeVOneofthese(onaverage)needstogoontocauseanotherfissionevent…Lookseasy!Putalargelumpof235Utogether,andrelaxtoenjoyfireworks!However….otherthingscanhappentoneutronsnaturalUis0.715%235U(fissile)and99.285%238U(fissionable)7Neutron-inducedchainreactionNeutroninteractions

Fastfissionneutrons(~2MeV)areemittedinanamountofUraniumDifferentprobabilitiesofdifferentinteractionsProbabilitycalledacross-section(s)measuredin“barns”(b)Scattering(elasticandinelastic)–simplyreducesenergyofneutronastravelsthoughmaterial.s~fewbarnsRadiativeCapture–neutronabsorbedbynucleus,whichthendecaysbybetaandgammadecay.s~0to1000’sbarnsFission–neutroninducedfission.s~1to500barns,increasingasenergyreducesFastenergies(MeV)ThermalenergiesCaptureresonances8Nat.UNat.UNeutron-inducedchainreactionLookatcross-sections…Fastneutrons(2MeV)fissionscatt.captureThermalneutrons(kT~0.02eV)fissionscatt.captureChainreactionfeasibleatthermalenergies…IMPLIESNeutronsslowingdowntothermalenergies–NOTinuranium(avoidcaptureresonances)capture9LOSSESFROMCHAINREACTIONFastneutronsfromfissionSomefissionin235U+somecapturein235/238USomefastfissionin238Un-fluxincreasesbyfactoreSlowingdowninfuelandmoderatorFractionnotleakingoutPNLfLeakageoffastneutronsfromcoreSlowedto10eV→1keVFractionnotcaptured=pRadiativecapturein238UresonancesThermalneutronsFractionnotleakingoutPNLthLeakageofthermalneutronsfromcoreThermalneutronsabsorbedincoreFractionabsorbedinfuel=fThermalneutronscapturedinnon-fuelmaterial(e.g.moderator)Numberofneutronsemittedperneutronabsorbedinfuel=hForstablechainreaction,k=PNLFPNLthepfh=1Neutron-inducedchainreaction10ThermalReactorComponentsofareactor:Fuel:Uranium(usuallyenrichedwithmore235U,sometimesnatural)OfteninUO2form,surroundedby‘cladding’,usuallyrods.Moderator:Needstobeefficientinthermalisingneutrons,smallnumberofcollisions…so,Aneedstobesmall(n~18forH,~115forC)Needssmallcapturecross-sectionCoolant:ForcarryingawayenergytoheatexchangerforturbineNeedssmallcapturecross-section11MagnoxReactor(UK–beingdecommissioned)ControlRodchannels-BoronsteelrodsGraphitemoderatorConcreteshieldCO2coolantcirculatingat~360oCFuelRods-NatUmetal,magnoxcladdingHeatexchangerSteamtoturbinesandwaterreturnPressureVessel12Pressurisedwaterreactor(typicalexisting)ConcreteshieldH2Omoderator/coolantcirculatingat~320oCand~150atmpressure.FuelRods-UO23%-4.5%enrichment,steelSteamgeneratorSteamtoturbinesandwaterreturnControlRodchannels-BoronsteelrodsPressureVessel13Reactorcontrolanddesign–PhysicsinActionStablereactorrunsatk=1(critical)Controlledbyinsertion,retractionofcontrolrods(highcapturec.s.)Howstableisareactor?Howquicklycanareactorrespondtosmalltransientchangesink?Suddencatastrophicincidents?PhysicsinAction–PARTI:Late(delayed)neutrons14Reactorcontrolanddesign–PhysicsinActionHowlongdowehavetorespondifreactorgoessuper-critical?Determinedby:Timebetweenemissionofpromptneutronandabsorptioninreactor(promptneutronlifetime,tp),andDegreeofsuper-criticality(k-1)tp=thermalisingtime+diffusiontime(thermalneutron“walk”)~10-5s~10-3sSo,timebetweenneutron“generations”~milliseconds15Reactorcontrolanddesign–PhysicsinActionNeutronflux(andhencepower)inareactorvarieswithtimeapproximatelyas…Forverysmallexcesscriticality,k-1=0.001,andtp~1ms,powerincreasesas…e10increaseinpowerin10seconds~22,000!!Wouldbeimpossibletocontrol,butphysicscomestotherescue…1687Br87Kr87Rb87Sr87Kr*neutron86Krb-b-b-b-NotallneutronsinareactorarepromptfissionneutronsSomefissionfragmentsareveryrichinneutronsCanbeta-decaytonuclearstateswhichemitneutronsReactorcontrolanddesign–PhysicsinActionForexample….Half-lifeof87Bris55.7sMeantimeforemission(thenabsorption)ofthisneutronafterfissionis~55.7/ln2~80seconds…NOT1ms17Reactorcontrolanddesign–PhysicsinAction0.6%ofallreactorneutronsarebeta-delayed,averagelifetime12.5seconds,soforALLneutrons…So,smallexcesscriticality,k-1=0.001,andteff~80ms,powerincreasesas…e1.3increaseinpowerin10seconds~3.7(not22,000)

MAKESreactorscontrollable…aswellas…..PromptLate18Reactorcontrolanddesign–PhysicsinActionConsider238UcaptureresonancesAtomsvibrateinlatticesite,neutronenergyincentreofmassoscillates–“smudges”resonanceenergyneutron238UHighertemperature–oscillations

increase–broaderresonancesneutron238UsrneutronenergyPhysicsinAction–PARTII:“ThermalFeedback”19Reactorcontrolanddesign–PhysicsinActionSuper-criticalreactorPowerincreasesTemperatureincreasesResonancesbroadenmoreresonantcaptureNeutronfluxreducesPowerreducesTemperaturereducesResonancesnarrowlessresonantcaptureNeutronfluxincreasesNaturalthermalfeedbackmechanism...20Reactorcontrolanddesign–PhysicsinActionHowmuchfuel-howmuchmoderator?

Toomuchmoderator–thermalneutronsmorelikelytobecapturedbymoderatornuclei…

Toolittlemoderator,andneutronsre-enterfuelbeforethermalised–canbecapturedbytheresonances.Moderator/fuelratiocrucialSuper-criticalSub-criticalOptimumM/Fover-moderatedunder-moderated21ReactorsSAFERifthey’reunder-moderated…Imaginewhathappensifa“hole”(void)appearsinareactorE.g.coolantleaksout

E.g.powerrunsawayandwaterboils(bubblesappear)E.g.actofterrorismUsually,ifVOIDappears…lessmoderation(allmaterials,esp.water,aremoderators)someneutronsdon’tslowdown–captureinresonancesfewerneutronscausefission,reactiondiesoutcalled“NEGATIVEVOIDCOEFFICIENT”ESSENTIALdesignfeatureReactorcontrolanddesign–PhysicsinAction22Super-criticalSub-criticalover-moderatedunder-moderatedABReactorcontrolanddesign–PhysicsinActionMakesureofNEGATIVEvoidcoeff→under-moderatedreactor23ChernobylChernobylaccident,26/04/1985at012348s

1GWpowerreactor,graphitemoderated,1.8%enrichedfuel,water-cooled,directwatercycleExperimentperformedtoimprovesafety.Manyoperatorerrors,over-rides,etccausedthefollowingconditions…Reactorwasrunningat7-10%offullpowerControlrodsfullywithdrawnEmergency