中子的减速教学教程电子教案

SLOWINGDOWNOFNEUTRONSElasticscatteringofneutrons.Lethargy.AverageEnergyLossperCollision.Neutronmoderationwithoutspacedistribution.Spacedependentmoderation.AgeTheory.NeutronSpectruminaCore.HT2004:RectorPhysics1SlowingdownChainReaction235U2MeV

nνβγγβν235Un

0.1eV235UnnHT2004:RectorPhysics2SlowingdownHT2004:RectorPhysics3SlowingdownPrinciplesofaNuclearReactornn/fissionN1N2LeakageFastfissionResonanceabs.Non-fuelabs.LeakageNon-fissileabs.FissionSlowingdownEnergyE2MeV1eV200MeV/fission

ν≈2.5HT2004:RectorPhysics4SlowingdownHT2004:RectorPhysics5SlowingdownHT2004:RectorPhysics6SlowingdownHT2004:RectorPhysics7SlowingdownHT2004:RectorPhysics8SlowingdownDifferentialCrossSectionsrxyzHT2004:RectorPhysics9SlowingdownHardSpheresModelrTotalscattering

crosssectionσs=2πr2nrθHT2004:RectorPhysics10Slowingdownrb(θ)θimpactparametercrosssection

σ(θ)dθIσ(θ)IisthenumberofneutronsdeflectedbyananglegreaterthanθHT2004:RectorPhysics11SlowingdownUnitspherer=1IHT2004:RectorPhysics12SlowingdownDetectorIHT2004:RectorPhysics13SlowingdownNeutronSlowingDownu0U0Uuvcvq

HT2004:RectorPhysics14Slowingdownθ=0θ=180EvE+dEv+dvHT2004:RectorPhysics15SlowingdownEE-dEEaE0E0p(E)??HT2004:RectorPhysics16SlowingdownQuantummechanics+detailednuclearphysicsanalysisconcludeElasticscatteringisisotropicinCMsystemfor:neutronswithenergiesE

<10MeVlightnucleiwithA<13HT2004:RectorPhysics17SlowingdownEaE0E0HT2004:RectorPhysics18SlowingdownHT2004:RectorPhysics19SlowingdownNumberofcollisionrequiredforthermalisation:Fornon-homogenuousmedium:Averagecosine

valueofthescatteringangleinCM-systemHT2004:RectorPhysics20SlowingdownAveragecosine

valueofthescatteringangleinLab-systemHT2004:RectorPhysics21SlowingdownMaterialAαm01H100.6672D20.1110.3334He40.3600.1676Li60.5100.0959Be90.6400.07410B100.6690.06112C120.7160.056238U2380.9380.003H2O**0.037D2O**0.033HT2004:RectorPhysics22SlowingdownSlowing-downfeaturesofsomemoderators

ModeratorξNξΣsξΣs/ΣaH2O0.92719.71.3662D2O0.510360.1805860Be0.209870.153138C0.1581150.060166U.00842170.00400.011N-numberofcollisiontothermalenergyxSs-slowingdownpowerxSs/Sa-moderationratio(qualityfactor)HT2004:RectorPhysics23SlowingdownNeutronvelocitydistribution

Att.!!kB=1.381×10-23J/K=8.617×10-5eV/KVelocityspace:v+dvv4πv2dvProbabilitythatenergylevel

E=mv2/2isoccupied:HT2004:RectorPhysics24SlowingdownThemostprobablevelocity:andcorrespondingenergy:Maxwell-DistributionforNeutronDensityHT2004:RectorPhysics25SlowingdownDon’tforget:Maxwell-DistributionforNeutronFluxHT2004:RectorPhysics26SlowingdownHT2004:RectorPhysics27SlowingdownAverageenergyforneutronsNeutronfluxdistribution:ForthermalneutronsHT2004:RectorPhysics28SlowingdownAveragecosineofscatteringangle:CM:LAB-system:Theconsequenceofµ0¹0inthelaboratory-systemisthattheneutronscatterspreferablyforward,speciallyforA=1i.e.hydrogenandpracticallyisotropicscatteringforA=238i.e.Uranium,becauseµ0»0i.e.Y=90oinaverage.Thiscorrespondstoisotropicscattering.ltrisdefined

aseffectivemeanfreepathfornon-isotropicscattering.HT2004:RectorPhysics29SlowingdownYYYlscosYlscosY2TransportMeanFreePathlsltrHT2004:RectorPhysics30SlowingdownSlowing-downofFastNeutronsInfinitemediumHomogeneousmixtureofabsorbingandscatteringmatterContinuesslowingdownUniformlydistributedneutronsourceQ(E)Φ(E)=[n/(cm2×s×eV)]Φ(E)dE=numberofneutronswithenergiesindEaboutEHT2004:RectorPhysics31SlowingdownContinuesSlowing-DownEtdEdtassumedslowing-downrealslowing-downHT2004:RectorPhysics32SlowingdownSlowing-downdensityq(E)-numberofneutrons,whichpercubic-centimeterandsecondpassenergyE.Ifnoabsorptionexistsinmedium,so:

q(E)=Q;Q

-sourceyield(n×cm-3s-1)Assumingnoorweakabsorption(withoutresonances)EnergyEq(E)HT2004:RectorPhysics33SlowingdownEnergyLethargyEmax0LethargyEuq(E)u+duE-dEu-ξduξHT2004:RectorPhysics34SlowingdownNeutronspectrumEF(E)uF(u)E0.025eV2015105010MeVHT2004:RectorPhysics35SlowingdownSlowing-downwithresonanceabsorptionProbabilityforabsorptionpercollision:NumberofcollisionsinduordE:ProbabilityforabsorptioninduordE:Thiscorrespondsenrelativedecreaseinq:HT2004:RectorPhysics36SlowingdownF(u)Eust=ss+sc~scsF0(u)q0F(u)qHT2004:RectorPhysics37SlowingdownExample.Howlongtimeexiststheneutronunderslowing-downphaserespectivelyasthermal?Slowing-downintime-ts:Numberofcollisionsindu:Numberofcollisionsindt:v(1eV)=1.39·106cm/s

v(0.1MeV)=4.4·108cm/sThermallife-length-tt:HT2004:RectorPhysics38SlowingdownMaterialtfast(ms)tthermal(ms)H2O1200D2O81.5105Be104300C251.2104Neutrons