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Neutron Flux Characterization and Design of Uftr Radiation Beam Port Using Monte Carlo Methods

Permanent Link: http://ufdc.ufl.edu/UFE0044814/00001

Material Information

Title: Neutron Flux Characterization and Design of Uftr Radiation Beam Port Using Monte Carlo Methods
Physical Description: 1 online resource (137 p.)
Language: english
Creator: Franca, Romel Siqueira
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: 47 -- barytes -- beam -- bias -- card -- carlo -- collimator -- concrete -- criticality -- definition -- distribution -- energy -- equation -- fission -- fixed -- flux -- foil -- geometry -- gold -- groups -- imp -- kcode -- mcnp -- method -- moderator -- monte -- neutron -- nonanalog -- phys -- port -- rate -- reaction -- read -- reduction -- roulette -- russian -- sdef -- silicide -- source -- spectrum -- splitting -- ssr -- ssw -- surface -- survival -- uftr -- uranium -- variance -- watt -- write
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This research presents the characterization, modeling, and design of the UFTR (University of Florida Training Reactor) radiation beam ports for reactor analysis applications. Extensive validation of beam port is required. Using MCNP5 results were produced for the multigroup neutron flux distributions, neutron spectrum and neutron reaction rates. Due to the strength of the neutron source in the reactor core, the neutron flux distribution and reaction rate can be monitored along the radiation beam port. The goal of the design in this research is to determine the neutron flux distribution, neutron energy flux and neutron reaction rate throughout the beam port. The calculation of the neutron flux distribution, neutron spectrum and neutron reaction rates along the beam port were tallied. To compute the multigroup neutron flux distributions, and neutron energy flux FMESH4 and *F4 tallies were used, respectively. Sets of 47 and 62 energy groups were analyzed for these tallies. To calculate neutron reaction rates, the tally F4 along with the tally multiplier FM4 was used.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Romel Siqueira Franca.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Schubring, Duwayne Lee.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044814:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044814/00001

Material Information

Title: Neutron Flux Characterization and Design of Uftr Radiation Beam Port Using Monte Carlo Methods
Physical Description: 1 online resource (137 p.)
Language: english
Creator: Franca, Romel Siqueira
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: 47 -- barytes -- beam -- bias -- card -- carlo -- collimator -- concrete -- criticality -- definition -- distribution -- energy -- equation -- fission -- fixed -- flux -- foil -- geometry -- gold -- groups -- imp -- kcode -- mcnp -- method -- moderator -- monte -- neutron -- nonanalog -- phys -- port -- rate -- reaction -- read -- reduction -- roulette -- russian -- sdef -- silicide -- source -- spectrum -- splitting -- ssr -- ssw -- surface -- survival -- uftr -- uranium -- variance -- watt -- write
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This research presents the characterization, modeling, and design of the UFTR (University of Florida Training Reactor) radiation beam ports for reactor analysis applications. Extensive validation of beam port is required. Using MCNP5 results were produced for the multigroup neutron flux distributions, neutron spectrum and neutron reaction rates. Due to the strength of the neutron source in the reactor core, the neutron flux distribution and reaction rate can be monitored along the radiation beam port. The goal of the design in this research is to determine the neutron flux distribution, neutron energy flux and neutron reaction rate throughout the beam port. The calculation of the neutron flux distribution, neutron spectrum and neutron reaction rates along the beam port were tallied. To compute the multigroup neutron flux distributions, and neutron energy flux FMESH4 and *F4 tallies were used, respectively. Sets of 47 and 62 energy groups were analyzed for these tallies. To calculate neutron reaction rates, the tally F4 along with the tally multiplier FM4 was used.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Romel Siqueira Franca.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Schubring, Duwayne Lee.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044814:00001


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NEUTRONFLUXCHARACTERIZATIONANDDESIGNOFUFTRRADIATIONBEAMPORTUSINGMONTECARLOMETHODSByROMELSIQUEIRAFRANCAATHESISPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEUNIVERSITYOFFLORIDA2012

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c2012RomelSiqueiraFranca 2

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Idedicatemythesistomymother. 3

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ACKNOWLEDGMENTS IhavedeeplyappreciationandrespectforDr.Schubringforhiswillingnesstohelpandtoguidemeonmyresearch.Dr.Schubringisawealthofknowledgeanddedicationalwaystryingtogetthebestoutoftheirstudents.TomeetsuchahumanbeinglikeDr.SchubringitwasauniqueopportunitythatIhadinmylife. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 14 CHAPTER 1INTRODUCTION ................................... 15 1.1UFTRReactorBackground .......................... 15 1.2UFTRReactorHorizontalBeamPorts .................... 16 1.3UFTRBeamPortChallenges ......................... 17 1.4ResearchGoalsandObjective ........................ 18 2REACTORMODELDEVELOPMENT ....................... 27 2.1UFTRReactorModel ............................. 27 2.2UFTRReactorCoreDesign .......................... 27 2.2.1UFTRFuelBox ............................. 28 2.2.2UFTRFuelPlate ............................ 28 2.3ReactorRadiationBeamPortsModeling ................... 29 3MCNP5BACKGROUNDANDCALCULATIONS ................. 34 3.1GeneralFeaturesofMCNP5 ......................... 34 3.2UFClusterPCComputers ........................... 34 3.3MCNP5Deck .................................. 34 3.3.1CriticalityDetermination ........................ 35 3.3.2FixedSourceMethodsApplied .................... 35 3.3.2.1Fixedsourcemethodwithsurfacesourceread(SSR) .. 36 3.3.2.2FixedsourcemethodwithSDEF .............. 37 4MCNP5MATHEMATICALANDTHEORETICALDISCUSSION ......... 53 4.1GeneralFeaturesofMCNP5 ......................... 53 4.2F4Tally ..................................... 53 4.3FMCard-TallyMultiplier ........................... 54 4.4FMESH4Tally ................................. 55 4.5RelativeError .................................. 56 4.6VarianceReductionMethods ......................... 58 4.6.1NonanalogMethods .......................... 58 4.6.1.1Geometrysplitting(G.S.) .................. 58 4.6.1.2Russianroulette(R.R.) ................... 58 5

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4.6.1.3Survivalbiasing(S.B.) .................... 59 4.6.2EfciencyoftheNonanalogMethod ................. 59 4.6.2.1PHYScard .......................... 60 4.6.2.2IMPcard ........................... 60 5MCNP5SIMULATIONRESULTS .......................... 61 5.1Introduction ................................... 61 5.2UFTRBeamPort ................................ 62 5.2.1UFTRReactorSouthBeamPortAnalyzes .............. 62 5.2.2EnergyGroupsAnalyzed ....................... 62 5.2.3SouthBeamPort3-DMulti-GroupNeutronFluxDistribution .... 63 5.2.4ImpactofDifferentModeratorsintheUFTR ............. 63 6NEUTRONIRRADIATIONCHARACTERIZATIONOFGOLDFOIL ....... 113 6.1Reaction-RateEquation ............................ 113 6.2ActivityEquations ............................... 115 6.2.1IrradiationActivity ............................ 116 6.2.2ActivityAfterA0 ............................. 118 6.3ReactionRateCalculationusingMCNP5 .................. 119 7CONCLUSION .................................... 124 APPENDIX AURANIUMSILICIDE ................................. 125 BALUMINUM ...................................... 126 CTHEEFFECTOFTHEIMPURITYINTHEFUELONTHEUFTRKe. ..... 127 DFISSIONCROSS-SECTIONS ........................... 131 E47ENERGYGROUPS ............................... 133 FBARYTES(BARITE)CONCRETE ......................... 135 REFERENCES ....................................... 136 BIOGRAPHICALSKETCH ................................ 137 6

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LISTOFTABLES Table page 1-1CollimatorComposition ............................... 19 1-2PuBeandSbBeneutronsourcesfeatures ..................... 19 1-3ReactorpowerrequirementsforPuBeneutronsource .............. 19 2-1Shieldingnominalspecications .......................... 27 3-1KCODEvalues-CriticalitySourceCard ...................... 35 3-2Surfacesourcewrite(SSW)andsurfacesourceread(SSR)cards ....... 36 3-3PossibleMCNP5constantsfortheWattFissionSpectrum ............ 40 5-1MCNP5-TotalTransportTime(ctm)-1CPU ................... 61 5-2MCNP5-RelativeError%fortallytypeF4 ..................... 62 5-3FigureofMerit(FOM) ................................ 62 5-4EnergyrangeforUFTRmeasurements ...................... 62 5-5Generalanalysesfor47energygroupsfor16CPU'susing(G.S.-R.R.) .... 63 5-6Generalanalysesfor47energygroupsfor16CPU'susing(G.S.-R.R.-S.B.) 63 5-7Casesofstudyfor47energygroups ........................ 63 5-8Physicalpropertiesofheavywater(D2O)andlightwater(H2O) ......... 64 5-9SlowingDownParametersofTypicalModerators ................. 64 6-1AbsorptiveReactions ................................ 113 6-2Recommended-raycalibrationenergiesandintensities ............ 120 6-3197Augoldfoilreactionrate ............................. 121 A-1UraniumSilicide-(U3Si2) .............................. 125 A-2UraniumSilicideImpurities ............................. 125 B-1Aluminum-(Al) .................................... 126 B-2AluminumImpurities ................................. 126 C-1no10BintheAluminumCladding ......................... 127 C-2KeandStandardDeviation ............................. 127 7

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C-310BintheAluminumCladding/VariationofCdconcentrationwhileLiisconstant 128 C-4KeandStandardDeviation ............................. 128 C-510BintheAluminumCladding/VariationofLiconcentrationwhileCdisconstant 129 C-6KeandStandardDeviation ............................. 129 E-147EnergyGroups .................................. 133 E-247EnergyGroupscont. ............................... 134 F-1Elementalcompositionofbarytesconcretesingramsofelementpercm3ofconcrete ........................................ 135 F-2Constantsforthermalneutronsforbarytesconcretes ............... 135 8

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LISTOFFIGURES Figure page 1-1AxialprojectionoftheUFTR,includingallaccessports. ............. 20 1-2AxialprojectionoftheUFTRwithitsRABBITsystem. .............. 21 1-3Horizontalbeamportsdrawing. ........................... 22 1-4Collimatorlteringastreamofraysinageneralproblem.Topwithoutacollimator.Bottomwithacollimator. ............................... 23 1-5ACollimator3Ddrawing. .............................. 24 1-6Collimator2Dprojection. .............................. 25 1-7MCNP5collimatorx-yprojection. .......................... 26 2-1RadialprojectionoftheUFTRcoreillustratingthefuelandthefuelboxarrangementassurroundedbygraphitestringers. ........................ 30 2-2HorizontalsectionoftheUFTRatbeamtubelevel. ................ 31 2-3Southbeamportmeasurements. .......................... 32 2-4MCNPmodelwithmaterials,generatedwithMCNPVisualEditor(VisEd). ... 33 3-1Neutronssiondensitydistribution]=cm3-secfortopviewoftheUFTRcore. 42 3-2Neutronssiondensitydistribution]=cm3-secforbottomviewoftheUFTRcore. 43 3-3Neutronssiondensitydistribution]=cm3-secwithinsixUFTRfuelboxesnumberedfromonetosixshowingthesouthview. ...................... 44 3-4Neutronssiondensitydistribution]=cm3-secwithinsixUFTRfuelboxesnumberedfromonetosixshowingthenorthview. ...................... 45 3-5Flowchartcalculation. ................................ 46 3-6AverageFissionNeutronspergroupforThermalNeutronsFissionin235U. ... 47 3-7AverageFissionNeutronspergroupforThermalNeutronsFissionin235U(LogScale). ......................................... 48 3-8AverageFissionNeutronspergroupforThermalNeutronsFissionin235U. ... 49 3-9AverageFissionNeutronspergroupforThermalNeutronsFissionin235U(LogScale). ......................................... 50 3-10TheWattFissionSpectrawhenThermalNeutronsInduceFissionin235Ufor(E)andf(a,b,E)(wherea=0.988b=2.249). ................. 51 9

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3-11SchematicNeutronFissionCrossSectionforU23592andU23892(LogScale). ... 52 5-1Neutronssiondensitydistribution]=cm3-secthroughoutthefuelbox2facingthereactorcore. ................................... 67 5-2Neutronssiondensitydistribution]=cm3-secthroughoutthefuelbox2facingsouthbeamport. ................................... 68 5-3xycross-sectionatz=-1mid-sectionofthefuelbox2 ............... 69 5-42-DNeutronFluxDistributionfor47energygroupsalongY-axis(cm)beforeCollimatorregion. .................................. 70 5-52-DNeutronFluxDistributionRelativeErrorfor47energygroupsalongtheY-axis(cm)beforeCollimatorregion. ........................ 71 5-62-DNeutronFluxDistributionfor47energygroupsalongY-axis(cm)beforeCollimatorregion. .................................. 72 5-72-DNeutronFluxDistributionRelativeErrorfor47energygroupsalongtheY-axis(cm)beforeCollimatorregion. ........................ 73 5-82-DNeutronFluxDistributionfor47energygroupsalongY-axis(cm)intheCollimatorregion. .................................. 74 5-92-DNeutronFluxDistributionRelativeErrorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. ......................... 75 5-102-DNeutronFluxDistributionfor47energygroupsalongY-axis(cm)intheCollimatorregion. .................................. 76 5-112-DNeutronFluxDistributionRelativeErrorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. ......................... 77 5-122-DNeutronFluxDistributionWithoutCollimatorfor47energygroupsalongtheY-axis(cm)BeforeCollimatorregion. ...................... 78 5-132-DNeutronFluxDistributionRelativeErrorfor47energygroupsWithoutCollimatoralongtheY-axis(cm)BeforeCollimatorregion. .................. 79 5-142-DNeutronFluxDistributionWithoutCollimatorfor47energygroupsalongtheY-axis(cm)BeforeCollimatorregion. ...................... 80 5-152-DNeutronFluxDistributionRelativeErrorfor47energygroupsWithoutCollimatoralongtheY-axis(cm)BeforeCollimatorregion. .................. 81 5-162-DNeutronFluxDistributionWithoutCollimatorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. ....................... 82 10

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5-172-DNeutronFluxDistributionRelativeErrorfor47energygroupsWithoutCollimatoralongtheY-axis(cm)intheCollimatorregion. ................... 83 5-182-DNeutronFluxDistributionWithoutCollimatorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. ....................... 84 5-192-DNeutronFluxDistributionRelativeErrorfor47energygroupsWithoutCollimatoralongtheY-axis(cm)intheCollimatorregion. ................... 85 5-202-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)BeforeCollimatorregion. .................. 86 5-212-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)BeforeCollimatorregion. .................. 87 5-222-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)BeforeCollimatorregion. .................. 88 5-232-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. ................... 89 5-242-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. ................... 90 5-252-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. ................... 91 5-263-DthermalneutronuxdistributionalongtheY-axis(cm)southbeamportbeforecollimatorregion. ............................... 92 5-273-DthermalneutronuxrelativeerroralongtheY-axis(cm)southbeamportbeforecollimatorregion. ............................... 93 5-28Contour3-DthermalneutronuxdistributionalongtheY-axis(cm)southbeamportbeforecollimatorregion. ............................ 94 5-29xysouthbeamportcrosssection. ......................... 95 5-303-DepithermalneutronuxdistributionalongtheY-axis(cm)southbeamportbeforecollimatorregion. ............................... 96 5-313-DepithermalneutronuxdistributionrelativeerroralongtheY-axis(cm)southbeamportbeforecollimatorregion. ......................... 97 5-323-DfastneutronuxdistributionalongtheY-axis(cm)southbeamportbeforecollimatorregion. ................................... 98 5-333-DfastneutronuxdistributionrelativeerroralongtheY-axis(cm)southbeamportbeforecollimatorregion. ............................ 99 11

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5-343-DthermalneutronuxdistributionalongtheY-axis(cm)southbeamportcollimatorregion. ................................... 100 5-353-DthermaluxdistributionrelativeerroralongtheY-axis(cm)southbeamportcollimatorregion. ................................ 101 5-363-DfastneutronuxdistributionalongtheY-axis(cm)southbeamportcollimatorregion. ......................................... 102 5-373-DfastuxdistributionrelativeerroralongtheY-axis(cm)southbeamportcollimatorregion. ................................... 103 5-38Neutronenergyuxfordifferentmoderatorsregionfor62energygroups. ... 104 5-39Thermalneutronenergyuxforthreedifferentmoderatorswithin62energygroups. ........................................ 105 5-40Improvementofthermalneutronenergyuxforthethreedifferentmoderatorswithin62energygroups. ............................... 106 5-41Fastneutronenergyuxforthreedifferentmoderatorswithin62energygroups. 107 5-42Improvementoffastneutronenergyuxforthethreedifferentmoderatorswithin62energygroups. .................................. 108 5-43Neutronscatteringcrosssectionsforhydrogen,deuteriumandCinH2O,D2O,andGraphiterespectively. .............................. 109 5-44NeutronabsorptioncrosssectionsforhydrogenanddeuteriuminH2OandD2Orespectively. ................................... 110 5-45Neutroncrosssectionsforhydrogen(H1) ..................... 111 5-46Neutroncrosssectionsfordeuterium(H2) ..................... 112 6-1MCNP5calculationsfor197Aufoilsat3differentlocations. ............ 122 6-2197Au(n,)198Aucross-sectionasafunctionofneutronenergy ......... 123 C-1Keff1. ......................................... 127 C-2Keff2. ......................................... 128 C-3Keff3. ......................................... 129 C-4Keffnal. ........................................ 130 D-1232Thssioncross-sectionversusneutronenergy(MeV). ............ 131 D-2238Ussioncross-sectionversusneutronenergy(MeV). ............. 131 D-3240Pussioncross-sectionversusneutronenergy(MeV). ............ 132 12

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D-4242Pussioncross-sectionversusneutronenergy(MeV). ............ 132 13

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AbstractofThesisPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofMasterofScienceNEUTRONFLUXCHARACTERIZATIONANDDESIGNOFUFTRRADIATIONBEAMPORTUSINGMONTECARLOMETHODSByRomelSiqueiraFrancaAugust2012Chair:DuWayneSchubringMajor:NuclearEngineeringSciences Thisresearchpresentsthecharacterization,modeling,anddesignoftheUFTR(UniversityofFloridaTrainingReactor)radiationbeamportsforreactoranalysisapplications.Extensivevalidationofbeamportisrequired.UsingMCNP5resultswereproducedforthemultigroupneutronuxdistributions,neutronspectrumandneutronreactionrates. Duetothestrengthoftheneutronsourceinthereactorcore,theneutronuxdistributionandreactionratecanbemonitoredalongtheradiationbeamport.Thegoalofthedesigninthisresearchistodeterminetheneutronuxdistribution,neutronenergyuxandneutronreactionratethroughoutthebeamport. Thecalculationoftheneutronuxdistribution,neutronspectrumandneutronreactionratesalongthebeamportweretallied.Tocomputethemultigroupneutronuxdistributions,andneutronenergyuxFMESH4andF4tallieswereused,respectively.Setsof47and62energygroupswereanalyzedforthesetallies.Tocalculateneutronreactionrates,thetallyF4alongwiththetallymultiplierFM4wasused. 14

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CHAPTER1INTRODUCTION 1.1UFTRReactorBackground TheUniversityofFloridaTrainingReactor(UFTR),wasoneoftherstreactorsbuiltinauniversityintheUnitedStatesofAmerica.TheUFTRwasbuiltin1959foreducation,research,andtotrainstudentstooperatereactors.TheUFTRoperatesatamaximumthermalpowerof100kW. Detailsoffuelenrichment,mass,andgeometryareexcludedfromthisthesisforsafeguards-relatedreasons.DetailedinformationontheUFTRfuelisavailabletoallUFTRstaffandthoseperformingUFTR-relatedwork.Accuratefuelparameterswereemployedinthepresentwork TheUFTRpresentlyusesalow-enrichedAluminum-UraniumSilicide(U3Si2-Al)alloymeatwithAluminumcladding(compositioninAppendix A and B ).ThemainimpuritiesintheUFTRnuclearfuelandgraphiteare10BandCdwhichcanimpactneutronmultiplicationiftheirconcentrationsarechanged[Appendix C ],duetohighneutronthermalabsorptioncross. UFTRalsousestwodifferentneutronsourceswhicharepositionedintheverticalports,nearthecenterofthereactor.TherstisaremovablePlutoniumBerylliumsource(239PuBe).ThesecondisaregenerableAntimonyBerylliumsource(124SbBe). Tables 1-2 and 1-3 showthefeaturesof239PuBeand124SbBeneutronsources. TheUFTRalsocontainsprimaryandsecondarycoolingsystems.Theprimarysystemoperatesatalltimesthatthereactoriscritical.Ifthepowerisgreaterthan1kWthesecondarycoolingsystemisrequiredtocooltheprimarysystem.UFTRhasfourcontrolblades.Threearesafetycontrolbladeswhiletheforthoneisaregulatingblade.Theregulatingbladeisusuallyusedforpoweradjustment. TheUFTRhasthreeverticalportsgoingthroughthereactorcore.Theyareusedtoplacetheneutronsourcesandsampleirradiation.Theverticalportsinclude,the 15

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westverticalport(W.V.P.),thecentralverticalport(C.V.P.),andtheeastverticalport(E.V.P.).Thesethreeverticalholesareapproximately1.5inchesindiameterandarecentrallypositionedbetweensixfuelcompartments.Portsrunthroughalargeroundremovableplugthataccessesaboralplateontopofthereactorgraphite.SeeFigure 1-1 forverticalaccessplugs. Thegraphitestringersaredrilledouttothecenterofthecore;theseholeshaveremovablegraphiteplugs.Allnuclearfuelhasgraphitestringersaroundit. Besidesthat,thereisaneast-westthroughportwhichbarelytouchesthethreeverticalportsandthisportispartoftheRABBIT. SeeFigure 1-2 fortheRABBITtubeaccess. UFTRalsohasradiationbeamportsonthereactorcenterplanewherethestudyofmulti-groupneutronuxdistributionandneutronreactionratewillbeperformed.SeeFigures 1-3 forhorizontalsectionoftheUFTRatbeamtubelevel. 1.2UFTRReactorHorizontalBeamPorts TheUFTRiscomposedofsixhorizontalradiationbeamportsandonethermalcolumn.TheradiationbeamportsweremodeledwiththeMonteCarlocodeMCNP5.Radiationbeamportsarealsousedtoperformsampleirradiationandconductspecialexperiments.Thereactorcoreiscomposedofsixfuelboxessurroundedbygraphitereectorusedasamoderator. ThebeamportsaresurroundedbybarytesconcreteshieldingasshowninFigure 1-3 whichisusedtoreectandabsorbneutronsthroughoutthebeamport.Thebeamportsarelocatedinthenorth,northeast,northwest,south,southeast,andsouthwestsidesofthereactor.Thethermalcolumnislocatedtotheeastsideofthereactor.Thebeamportsareapproximately2.50mdeepwithacylindricalcollimatorrestingattheendoftheport. 16

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1.3UFTRBeamPortChallenges Themaincomplexityofthisworkwastoachievegoodstatisticsofthemulti-groupneutronuxdistributionthroughouttheradiationbeamportatdifferentenergies.Thisdifcultywasaddressedthroughofvariancereduction,whichisaverypowerfultoolusedinMonteCarlocalculations. GeometrySplittingandGeometrySplittingwithRussianrouletteworkedverywell.Cellimportancewasoneofthevariancereductiontechniquesapplied,duetogeometriccharacteristicsoftheproblem.Theneutronimportancewasincreasedbyfactoroftwothroughoutthesecellstokeeptheneutronpopulationroughlyconstant.Neutronimportancewaschosenbylookingattheneutronpopulation.Thesourcebiasingorimplicitcapturewasalsoappliedtotheproblem. Collimator Acollimatorisadevicethataltersastreamofrayssothatonlythoseraystravelingparalleltoaspecieddirectionareallowedthrough.Ithasalongnarrowtubewithstronglyabsorbingmaterialandreectingwalls(Figure 1-4 ).Divergingneutronsgetrepeatedlyreectedorscatteredandabsorbedbytheformingwallsofthecollimator. TheUFTRcylindricalcollimatorismountedinsideofthebarytesconcreteshielding[Appendix F ]ofthereactor,andcanberemovedasdesired.Thecollimatorisalongsteeltubesurroundedbybaryticconcretewithsteelalloyontheoutside(Figure 1-5 ).Baryticconcreteisalow-costshieldingmaterialthatiseffectiveevenwithouttheusualadmixtureoftheneutronabsorberboron.[ 16 ]Thiscombinationofscatteringandabsorbingmaterialoptimizestheshieldingefciencyofaneutrondiaphragmwithrespecttovolumeandweight.[ 6 ] Theconcreteusuallyismadeof3%to5%ofordinarywater(H2O)withlowZelements.Becauseordinarywatercontainshydrogen(H1)whichabsorbsneutrons,barytesconcreteiscommonlyusedforneutronshieldingduetoitslowprice.However,alargeamountisrequiredtoshieldareactor. 17

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Theentranceandtheexitofthecollimatorhasacircularapertureof2.54cmwithaapproximatelylengthof1.4m.ThechemicalcompositionofacollimatorisshowninTable 1-1 Thecollimatorhasagapthatislledwithairtoallowtheneutronbeamtotravelthroughit.Itispossibletocalculatethedoserateattheoutsideofthesouthbeamport,whichprovidesaneutronbeamwithadoserateof100R/hrimmediatelyfollowingshutdownfrompowerrun.[ 13 ] Figure 1-5 showsthe3Ddrawingofthecylindricalcollimator,andFigure 1-7 showsitscorrespondingx-yprojectionoftheMCNP5model. 1.4ResearchGoalsandObjective Theprimarygoalofthisresearchistodevelopmodelsforthedeterminationofmulti-groupneutronuxdistributionandneutronreactionratesthroughouttheradiationbeamport.Inadditionanalysisonthecriticalcorecongurationtoinvestigatethecombinedeffectsoftheimpuritiesinthefuelandreactorstructurewasperformed[Appendix C ]. Thespecicobjectivesofthisresearchwerethefollowing: CalculationofkeusingMCNP5,anddeterminationofneutronssionintensitydistributionineachfuelboxandinthewholereactorcoreusingWattssionSpectrum. DevelopmentofMCNP5modelsforradiationbeamport. Determinationofmulti-groupneutronuxdistributionsfor47energy-groupstructuresthroughouttheradiationbeamportusingtheFMESH4tallyoption. DeterminationofneutronreactionrateforgoldfoiltargetusingMCNP5. 18

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Table1-1. CollimatorComposition Density(g/cm3)TemperatureLimit(0C)Z SteelAlloy7.8214000C-VeryHighlowBarytesConcrete3.1<1000ClowAir0.0011858-Table1-2. PuBeandSbBeneutronsourcesfeatures PuBeSbBe Non-regenerableRegenerable1Ci10CiRemovablesourceRemovablesourceInstalledasneeded/desiredinC.V.P.orE.V.P.PermanentlyinstalledinW.V.P.Sourcealarmat100wattsHighradiationtolerance C.V.P.=CentralVerticalPort,E.V.P.=EastVerticalPort,W.V.P.=WestVerticalPort Table1-3. ReactorpowerrequirementsforPuBeneutronsource PuBe Preferat1wattShouldberemovedbefore10wattsSourcealarmat100wattsShallberemovedbeforeexceeding1kW 19

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Figure1-1. AxialprojectionoftheUFTR,includingallaccessports. 20

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Figure1-2. AxialprojectionoftheUFTRwithitsRABBITsystem. 21

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Figure1-3. Horizontalbeamportsdrawing. 22

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Figure1-4. Collimatorlteringastreamofraysinageneralproblem.Topwithoutacollimator.Bottomwithacollimator. 23

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Figure1-5. ACollimator3Ddrawing. 24

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Figure1-6. Collimator2Dprojection. 25

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Figure1-7. MCNP5collimatorx-yprojection. 26

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CHAPTER2REACTORMODELDEVELOPMENT 2.1UFTRReactorModel ThischapterdiscussestheUniversityofFloridaTrainingReactor(UFTR)structureandmeasurementsalongwithanexplanationofitspartssuchascoreandradiationbeamports.AtwoaxialprojectionsoftheUFTRareshowninFigures 1-1 and 1-2 UFTRFeatures TheUFTRisalightwater(H2O)andgraphitemoderated,watercooledreactor.TheUFTRcontainssixhorizontalbeamports,onehorizontalthermalcolumn,threeverticalportsthroughthecore,sixverticalfuelboxes,graphitestacking,shieldingblocks,andothergeometricalfeatures.TheUFTRdesignfeaturesarespeciedtoensurethatitemsimportanttosafetyarenotchangedwithoutappropriatereview. Thereactorisaccommodatedbyareinforcedoctagonshapedconcretecellwithatotalareaof30ftx60ftsquarefeetand29ftofheadroom.ThespecicationsoftheconcretebiologicalshieldareprovidedinTable 2-1 Table2-1. Shieldingnominalspecications ConcreteshieldingSpecications Sides,center6ft.,cast,barytesSides,end6ft.9in.,cast,barytesMiddleBaritesconcreteblockTop5ft.10in.End3ft.4in. 2.2UFTRReactorCoreDesign TheUFTRcoreiscomposedofthesixverticalfuelboxesasshowninFigure 2-1 S1=SafetyBlade]1 S2=SafetyBlade]2 S3=SafetyBlade]3 RB=RegulatingBlade F=ActiveFuelBundle D=DummyFuelBundle 27

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AfullcoremodelfortheUFTRwasgeneratedwithHummingbirdExceedprogramandMonteCarloNeutronParticlecodeversion5(MCNP5)toobtainacompletedetailforthereactorsystemcomponents. Thereactorcore'ssixfuelboxesaresurroundedbyreactor-gradegraphite(yellowinFigure 2-1 ),thatprovidesadditionalmoderation.The5ftx5ftx5ft(152.4cmx152.4cmx152.4cm)reactorgradegraphitestringerisusedtoslowdownneutronsreleasedduringssionandreectneutronsbacktothereactorcore. Thesixfuelboxesarearrangedintwoparallelrowsofthreeboxeseach,whichareseparatedbyabout30cmofgraphite.Inaddition,thesixboxesareoodedwithlightwater.Thewaterowsatalowmassvelocitythroughthepipingatthebottomofthefuelboxes,goesupthroughthefuelboxescoolingthecore,andowsoutofthecorethroughthepipingatthetop. 2.2.1UFTRFuelBox TheUFTRcoreiscomposedof6verticalfuelboxesmadeofaluminumandlledwithH2O.ThereareuptofourfuelbundlesforeachUFTRfuelbox(i.e,atotalof64=24fuelbundles);twooftheboxescontainadummybundleasshownintheFigure 2-1 .Eachfuelbundlecontains14plates. 2.2.2UFTRFuelPlate TheUFTRfuelplateismadeofAluminumcladdingduetoitslowabsorptioncross-sectionwithadimensionof(0.635cmx0.0381cmx2.54cm).Thefuelbundleiscomposedoffourteenplatescontaininglow-enrichedUraniumSilicide(U3Si2)[Appendix A ]andAluminum[Appendix B ]. 28

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2.3ReactorRadiationBeamPortsModeling Thereactorissurroundedbyaconcretewall.Thebeamportconsistsofacylindricalportvaryingindiameteralongthelengthfromthecoretotheoutsideoftheconcretewall.Thereisacollimatorplugwhichconsistsofaconcreteplugwitha2.54cmdiametersteelalloyaboutthecenterasshowninFigure 1-5 .Whenthebeamportisnotbeingused,asolidconcreteplugreplacesthecollimatorplug.MeasurementsforthebeamportgeometryaretakenfromblueprintsoftheUFTRandveriedbyphysicalmeasurementswhenappropriate.SeeFigure 2-2 forUFTRradiationbeamports. UFTRReactorSouthBeamPort Themodelofthereactorsouthbeamportrunsinthesouthdirection(-ydirection)from-28.654cmto-279.38cmandinthenorthdirection(+ydirection)from28.654cmto279.38cm.ThesurfacesourceforthemodelwastakenfromUFTRfullcoremodelsurfacetalliesaty=-28.2575cm.Calculationsaredonewithandwithouttheinsertionofthecollimatorpluganddiscussedinchapter5. 29

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Figure2-1. RadialprojectionoftheUFTRcoreillustratingthefuelandthefuelboxarrangementassurroundedbygraphitestringers. 30

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Figure2-2. HorizontalsectionoftheUFTRatbeamtubelevel. 31

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Figure2-3. Southbeamportmeasurements. 32

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Figure2-4. MCNPmodelwithmaterials,generatedwithMCNPVisualEditor(VisEd). 33

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CHAPTER3MCNP5BACKGROUNDANDCALCULATIONS 3.1GeneralFeaturesofMCNP5 MonteCarloisastochasticmethodwell-suitedtosolvecomplicatedthreedimensionalandtime-independentneutrontransportproblems.TheMonteCarlotechniqueispre-eminentlyrealistic(atheoreticalexperiment).FurtherdetailsoftheMonteCarlomethodasusedinMCNP5canbefoundintheMCNP5manual. 3.2UFClusterPCComputers TheMCNP5codewasrunonan8node(16processor)clusterwiththefollowingfeatures: AMDDualOpteronprocessorsat2.4Ghz 8GBDDRRAMpernodeona533Mhzsystembus. 1000Mbitfullduplexnetworkinterfaces. 8-portkeyboard,video,mouse(KVM)switch. 3.3MCNP5Deck Thegeometryofthefullreactormodelwascreatedina3DCartesiancoordinatesystemtogiveabetterviewofthegeometry.AMCNP5deckwasbuiltandrunwithExceed(version6.1)usedtoacquirethegeometryplots. TherststepofthisresearchwastomodeltheauthenticradiationbeamportinMCNP5.Thesixhorizontalbeamportsweresetupinthemodelsuchthattheirpositioncanbeadjustedbasedontheactualreactoroperations.TheportswereplacedinthemodelbyusingtheTRncard(coordinatetransformation).Afterthat,thebeamportdesignswereattachedtotheUFTRcoredesignprovided.PlotsofthesedesignsweremadewithExceed. Thesecondstepwasthecalculationofthecoremultiplication(ke)andthecollectionofneutronssionsourceresultsfromthesixfuelboxesoftheUFTRcore.ThekewasfoundwithMCNP5usingKCODE.Tocollecttheneutronssionsourcedensitydistributionatxedpoints,theWattFissionSpectruminputwasusedwith 34

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KCODEandKSRCcards,wheretheKSRCcardwasusedtoxthelocationoftheinitialneutronssionsourceinthesixfuelboxesinthereactorcore. Thethirdstepwas(a)determinationofmulti-groupneutronuxdistributionandneutronuxintensityfor47energygroupsthroughouttheradiationbeamport,and(b)determinationofneutronreactionrateforgoldfoiltarget. 3.3.1CriticalityDetermination ThefollowingisavericationoftheoverallcriticalityanalysisoftheUniversityofFloridaTrainingReactor(UFTR)coremodelusingMCNP5.ThedeckwasrunasaKCODEsourceproblemforcriticalitycalculations.TheKCODEcardspeciestheMCNP5criticalitysourcethatisusedfordeterminingke.ThisrequiresKSRCorSDEForSRCTPlesfortheinitialspatialssionsourceanduseenoughsettlecyclestoreachfundamentalspatialmode. TheKCODEsourcecardvaluesweresetasshowninTable 3-1 .TheinitialsourcepointsforKCODEcalculationsweresetas3points(xiyizi)perfuelplateusingtheKSRCcard. Table3-1. KCODEvalues-CriticalitySourceCard ParametersValues Numberofparticlehistoriespercycle5104Numberofskippedcycles100Totalnumberofcycles800 3.3.2FixedSourceMethodsApplied OncethedeckwasrunasaKCODEsourceproblem,thesourcecanbeexpressedusingtwodifferentmethods: 1. FixedSourceMethodwithSSRcard(byRSSAle) 2. FixedSourceMethodwithSDEFcard Thesecondmethodwasemployed,asdiscussedinthenextsection 35

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3.3.2.1Fixedsourcemethodwithsurfacesourceread(SSR) Toobtaintheneutronsource,onaMCNP5calculationwasperformedusingthecriticalitysourceKCODEcard,theKSRCsourcepointscardforaxedsourceproblem,andthesurfacesourcewrite(SSW)cardtoacquiretheWSSAsurfacesourcele. ForKCODEcalculations,particlesarewrittenonlyforactivecycles.TheSSWcardwasusedtoobtainthesourceinformation.ThiscardisusedtowriteasurfacesourceleortowriteaKCODEssionvolumesourceleforuseinasubsequentMCNP5calculation. TheSSWinthiscasewasusedtowritetheKCODEssionvaluesourceleanditwasusedinthejunctionofthereactorcorewithradiationsouthbeamport. InaKCODEcalculation,thessionneutronsourcesandpromptphotonsproducedfromssionduringeachcyclearewrittentotheWSSAle.CalculationtoaWSSAleisdonewithaCELoptiononaSSWcard.ThessionsourceiswrittenbytheKCODEcard.ParticlescrossingspeciedsurfacescanalsobewrittenbyspecifyingSi(problemsurfacenumber).Inthiscase,SSWusedsurface-20(Table 3-2 ). Particle-crossinginformationiswrittentotheWSSAle.Atrackthatcrossesacertainsurfaceinthecorrectdirectionwillberecordedonlyifitentersorleavestherightcell.Duringexecution,surfacesourceinformationiswrittentothescratchleWXXA.Uponnormalcompletion,WXXAbecomesWSSA.ThesimulationtogettheWSSAsourcecardforthereactorcorewascarriedoutusingtheinformationoforiginalrunfromTable 3-2 ThevaluesoftheSSW/SSRcardsweresetasfollows: Table3-2. Surfacesourcewrite(SSW)andsurfacesourceread(SSR)cards SurfaceCardSurface Reactorcorerun-originalrunSSW-20Southbeamportrun-currentrunSSRold20new500 36

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Thesurface20andsurface500aresetatpositionpy-28.575ofthejunctionofthereactorcoreandthesouthbeamport. Then,theparticlesweresentthroughoutthesouthbeamporttoobtainthemulti-groupneutronuxdistribution.Duetopoorstatisticsachievedonthemulti-groupneutronuxdistributioncalculationswhenusingtheFMESH4cardfor47energygroups,theFixedSourceMethodwithSDEFcardwasusedinstead.Multi-groupneutronuxdistributionisdiscussedonchapter4. 3.3.2.2FixedsourcemethodwithSDEF TodetermineaneutronssiondensitydistributionintheMCNP5code,acriticalitysourceKCODEcalculationisperformed.AKSCRCsourcepointscardisusedforaxedsourceproblemwithneutronssionenergysampledfromtheWattssionspectrum. Totallyneutronssionsourcedensityforeachfuelplate,100meshesweredened.Fivemeshesacrossthewidthoftheplate,onemeshrepresentingthethickness,andtwentymeshesaxially. The3-Dneutronssiondensitydistribution(]=cm3-sec)plotsthroughoutthesixfuelboxesisrepresentedintheFigs. 3-1 3-2 3-3 and 3-4 Togeneratethespectrumoftheneutronssionsourcedistribution,assionspectrumwasgeneratedbasedonthecontinuousenergyWattspectrumformulation[ 9 ].TheMCNP5WattssionspectrumcontinuousenergyformisgivenbyEqn. 3 .Theveriedssionspectraformisobtainedbyplotting(Fig. 3-10 )Eqns. 3 and 3 overtheenergiesofthe47energygroups[Appendix E ]intheBUGLE-96cross-sectionlibrary[ 15 ].ThespectrainFig. 3-10 arenotidenticaldueto235Uenrichmentdifferences. Thederivativeofthessionspectrum,(E),inrespecttoEisdenedastheaveragenumberofssionneutronsemittedperunitenergywithenergyEinEtoE+dEandexpressedby 37

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(E)=0.453e)]TJ /F3 7.97 Tf 6.59 0 Td[(1.036Esinhp 2.29E(3)(E)representsthessionspectrumwhenthermalneutronsinducessionin235U.Thessionspectrumof235Uispreferredoverthessionspectrumof238Udueto235f238falongtheenergydistribution(Fig. 3-11 ).Thegroup-wiseneutronssionsourcedistributionsfor47[Appendix E ]energygroupsareshownintheFigs. 3-6 3-7 3-8 ,and 3-9 Performingacriticalitycalculationfollowedbyaxedsourcecalculation(comparedtoonlyperformingacriticalitycalculation)allowssignicantreductionofcomputationtimesinceaproperlyconvergedsourceisassumedtobeobtainedfromthecriticalitycalculation,anysubsequentcalculationscanbeperformedbyusingthemorecomputationallyefcientxedsourcesimulation. Thexedsourcerequiresoneofthethreecards: SDEF SSR(withRSSAle) Userdenedsourcesubroutine Here,SDEFwasusedincombinationwithsi(sourceinformation)andsp(sourceprobability).Onceobtainedtheneutronssionsource,thesourcewascollectedandsettoanewleforasecondrunwithSDEFcardwheresiisthexedsourcelocationsfromKSCRCcard,andspistheneutronssionsourcevalues. SDEFwassetas sdefpos=d1erg=d3VEC=0-10dir=1 six1y1z1x2y2z2... spa1b2c3d4... 38

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Threedifferentmethodswereappliedtoobtainmoreefcientresultsinthecalculationofmulti-groupneutronuxdistributionthroughouttheradiationsouthbeamport: 1. AsingleshotofthexedsourcewasgivenusingtheSDEFcard.Totalsimulationtimewas24days 2. AsingleshotofthexedsourcewasgivenusingtheSDEFandphys:ncards.Thephys:ncardwasusedtoreduceneutronabsorptioninthecollimatorregion.Totalsimulationtimewas9days. 3. AsingleshotofthexedsourcewasgivenusingtheSDEFandphys:ncardsuptothebeginningofthecollimatorregion.ThentheSSRandphys:ncardswereusedforthesecondrun.Totalsimulationtimewas8hours. TheSSRcardwasusedtowritethesurfacesourceleinsteadtowriteaKCODEssionvolumesourceleasintheprevioussection. Inconclusion,thecombinationofthexedsourcemethodwithSDEFandSSRcardsshowedtohaveabetterstatisticsresultsfortherelativeerrorthantheSSRmethodbyitselfwhenthesourcewasshotthroughouttheradiationsouthbeamporttocalculatethemulti-groupneutronuxdistributions. MCNPWattFissionSpectrum.TheenergydependentWattssionspectrum(Fig. 3-10 )hastwofunctionsa(E1)andb(E1)whicharetabulatedwithincidentenergy.Thespectrumiscalculatedusingthefollowingequation: g(E1,E2)=e)]TJ /F4 7.97 Tf 6.59 0 Td[(E2=a Isinh(p bE2)(3) Where: I=1 2r a3b 4ex0[erf(p x)]TJ 11.96 8.55 Td[(p x0)+erf(p x+p x0)])]TJ /F7 11.955 Tf 11.96 0 Td[(ae)]TJ /F4 7.97 Tf 6.59 0 Td[(xsinh(abx)(3) x=E1)]TJ /F7 11.955 Tf 11.96 0 Td[(U a(3) 39

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Table3-3. PossibleMCNP5constantsfortheWattFissionSpectrum NeutronInducedFissionIncidentNeutronEnergy(MeV)a(MeV)b(MeV)]TJ /F3 7.97 Tf 6.59 0 Td[(1) n+235UThermal0.9882.249q10.9882.249q141.0282.084n+238UThermal0.881113.4005q10.895063.2953q140.965342.8330 x0=ab 4(3) TherangeofnalenergiesallowedisfromzerotoE1-U,whereUisaconstantfromthelibrary.However,theWattssionspectraintheEvaluatedNuclearDataLibrary,ENDL[ 7 ]isdenedbyasimpleanalyticalfunction[ 12 ]: f(a,b,E2)=Ce)]TJ /F4 7.97 Tf 6.58 0 Td[(E2=asinh(p bE2)(3) where C=r 4 a3be)]TJ /F4 7.97 Tf 6.59 0 Td[(ab=4(3) andE2isthesecondaryneutronenergy.Thecoefcientsaandbvaryweaklyfromoneisotopetoanother(Table 3-3 ).Theconstantsforneutron-inducedssionaretakendirectlyfromtheENDF/B-Vlibrary.Atypicalpromptneutronssionspectrumof235UisgivenbyEqn. 3 ;itwillbeusedtorepresenttheveriedWattssionspectra(Fig. 3-10 ).[ 4 ] Uranium235Uand238U.238Uundergoesassiononlywhenstruckwithaneutronof1MeVormore.Eventhoughthisssionablenuclideplaysanimportantroleinnuclearfuel,isunabletosustainastablessionchainreactionbyitselfandhencemustalwaysbeusedincombinationwithassilenuclidesuchas235Uor239Pu.Fissilenuclidesrepresenttheprincipalfuelsusedinssionchain-reactionsystems. 40

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Figure 3-11 showsthetotalssioncross-sectionfeaturesofthessileandssionablenuclidespresentintheUFTR.ThedatawereacquiredfromENDF/B-VIIatatemperatureof300K(26.85C).The235Ussioncrosssectionhasaconsiderablydifferentbehaviorthanssionablenuclide238Utheentireenergyrange. 41

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Figure3-1. Neutronssiondensitydistribution]=cm3-secfortopviewoftheUFTRcore. 42

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Figure3-2. Neutronssiondensitydistribution]=cm3-secforbottomviewoftheUFTRcore. 43

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Figure3-3. Neutronssiondensitydistribution]=cm3-secwithinsixUFTRfuelboxesnumberedfromonetosixshowingthesouthview. 44

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Figure3-4. Neutronssiondensitydistribution]=cm3-secwithinsixUFTRfuelboxesnumberedfromonetosixshowingthenorthview. 45

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Figure3-5. Flowchartcalculation. 46

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Figure3-6. AverageFissionNeutronspergroupforThermalNeutronsFissionin235U. 47

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Figure3-7. AverageFissionNeutronspergroupforThermalNeutronsFissionin235U(LogScale). 48

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Figure3-8. AverageFissionNeutronspergroupforThermalNeutronsFissionin235U. 49

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Figure3-9. AverageFissionNeutronspergroupforThermalNeutronsFissionin235U(LogScale). 50

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Figure3-10. TheWattFissionSpectrawhenThermalNeutronsInduceFissionin235Ufor(E)andf(a,b,E)(wherea=0.988b=2.249). 51

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Figure3-11. SchematicNeutronFissionCrossSectionforU23592andU23892(LogScale). 52

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CHAPTER4MCNP5MATHEMATICALANDTHEORETICALDISCUSSION 4.1GeneralFeaturesofMCNP5 TheMonteCarloN-Particletransportcodeversion5.0(MCNP5),isageneralpurpose,continuous-energy,generalgeometry,time-independentMonteCarlotransportcode.MCNP5isageneralMonteCarloradiationtransportcodecapableoftransportingneutrons,photons,andelectronsthroughvirtuallyanymaterialprovidedproblemgeometry. TheMonteCarlomethodwasdevelopedduringthe1940s.Randomsamplesofparametersorinputsareusedtoassessthebehaviorofacomplexsystemorprocess.MonteCarlomethodsarefrequentlyusedwhenthemodeliscomplex,nonlinear,orinvolvesmanyuncertainparameters. 4.2F4Tally Attheinitiationofaparticlefromasourcepoint,aparticletrackiscreated.Thetrackreferstoeachcomponentofasourceparticleduringitsentirehistory.AtallyofparticletracklengthinagivenspaceisusedinMCNP5tocalculateux.FurthertallyingofthecollisionsalongthetracklengthareusedtocomputereactionratesandforsourcegenerationinKCODEcalculations. Letthefollowingvariablestobedenedas: )777(!r=particlelocationinspace E=particleenergy t=time )777(!=unitvectorindirectionoparticlemotion =particleangularux v=particlespeed s=tracklength V=volume(cm3) N=particledensity(]/cm3) 53

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TheF4tallyinMCNP5willconversetothefollowing: F4=1 VZVZtZE()777(!r,E,t)dEdtdV(4) Scalaruxisdenedastheintegralofangularuxoveralldirections, ()777(!r,E,t)=Z4()777(!r,b,E,t)db(4) tocalculatenuclearreactionratesandhencethechainreactions.Thescalaruxisalsoafunctionofposition,energyandtime.Theangularuxisusefulforthecalculationofreactionsratesandofboundarycrossings.Itisdenedas: ()778(!r,b,E,t)=vN()778(!r,b,E,t)(4) wherevistheparticlespeed.ThescalaruxcanalsobedenedasamultipleofparticlevelocityvtimestheparticledensityN: ()778(!r,E,t)=Z4dbvN()777(!r,b,E,t)(4) Hence, F4=1 VZVZtZEvN()777(!r,E,t)dEdtdV(4) Sinceds=vdt, F4=1 VZVZtZEN()777(!r,E,t)dEdsdV(4) ThequantityN()778(!r,E,t)isthetracklengthdensity;therefore,theuxcanbeestimatedbysummingtracklengths. 4.3FMCard-TallyMultiplier TheFMcardcanmodifyanyuxorcurrenttallyoftheformR'(E)dEintoRR(E)'(E)dE,whereR(E)isanycombinationofsumsandproductsofenergy-dependentquantitiesknowntoMCNP. 54

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TheFMcardcanalsomodelattenuation.Herethetallyisconvertedto: Z'(E)e)]TJ /F12 7.97 Tf 6.58 0 Td[(t(E)axdE(4) ,wherexisthethicknessoftheattenuator,aisitsatomdensity,andtisitstotalcrosssection. TwospecialFMcardoptionsareavailable.TherstoptionsetsR(E)=1/'(E)toscoretracksorcollisions.ThesecondoptionsetsR(E)=1toscorepopulationorpromptremovallifetime. CrosssectionscanbeusedasresponsefunctionswiththeFMcardtodeterminereactionrates.MCNP5thermalS(,)tablesshouldbeusediftheneutronsaretransportedatsufcientlylowenergiesthatmolecularbindingeffectsareimportant. 4.4FMESH4Tally MeshtalliesareinvokedbyusingtheFMESHcard.AsintheFcard,auniquenumberisassignedtoeachmeshtally.Sinceonlytrack-lengthmeshtalliesareavailable,themeshtallynumbermustendwitha4,andmaynotbeusedtoidentifyanF4tally.Thetracklengthiscomputedoverthemeshtallycellsandnormalizedperstartingparticle,exceptinKCODEcriticalitycalculations. TheFMESHcardallowstheusertodeneameshtallysuperimposedovertheproblemgeometry.Resultsarewrittentoaseparateoutputle,withthedefaultnameMESHTAL.Bydefault,themeshtallycalculatesthetracklengthestimateoftheparticleux,averagedoverameshcell,inunitsofparticles/cm2.IfanasteriskprecedestheFMESHcard,energytimeparticleweightwillbetallied,inunitsofMeV/cm2. TheFMESH4tallywasusedtocomputethemulti-groupneutronuxdistributions.Setsof47and62energygroupswereanalyzedforthistally.Threedifferentenergyrangeswerestudieddependingontheneutronclassication.Therstclassisthermalneutronswithaenergyrangeof0.1eV1MeV). 55

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ThefollowingarekeywordsusedwithFMESHcardthatcanbeenteredinanyorder, GEOM=meshgeometry:Cartesianorcylindrical AXS=directionvectorofthecylindricalmeshaxis VEC=directionvector,alongwithAXSthatdenestheplaneforangletheta=0 ORIGIN=x,y,zcoordinatesinMCNPcellgeometrysuperimposedmeshorigin IMESH=coarsemeshlocationsinx(rectangular)orr(cylindrical)direction IINTS=numberofnemesheswithincorrespondingcoarsemeshes JMESH=coarsemeshlocationsiny(rectangular)orz(cylindrical)direction JINTS=numberofnemesheswithincorrespondingcoarsemeshes KMESH=coarsemeshlocationsinz(rectangular)ortheta(cylindrical)direction KINTS=numberofnemesheswithincorrespondingcoarsemeshes EMESH=valuesofcoarsemeshesinenergy EINTS=numberofnemesheswithincorrespondingcoarseenergymeshes FACTOR=multiplicativefactorforeachmesh TR=transformationnumbertobeappliedtothetallymesh 4.5RelativeError ForMonteCarlocalculations,thesignicanceofunderstandingandcalculatingthevarianceanderrorinthecalculatedresultscannotbeoveremphasized.MCNPreportsthestatisticalerrororuncertaintyassociatedwitheveryresult. Thevarianceisinverselyproportionaltothesquarerootthenumberofhistories(N),suchthatrelativeerrorinthetallydecreaseswithincreasingN.ThebruteforceofincreasingNtoimproveprecisionrapidlyreachesthepointofdiminishingreturns.TherearemanyvariancereductiontechniquesthatcanbeappliedwithMCNP5toachieveprecisionwithinreasonablecomputationaltime. Variance-reductiontechniquesinMonteCarlocalculationsreducethecomputertimerequiredtoobtainresultsofsufcientprecision.RelativeerrorRisdenedasratioofthevarianceSbxtothemeanestimatebxofthesamplexk, R=Sbx bx(4) TheestimatedvarianceofSbxisgivenby 56

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S2bx=S2 N(4) with S2=PNi=1(xi)]TJ /F13 11.955 Tf 11.96 .49 Td[(bx)2 N)]TJ /F5 11.955 Tf 11.95 0 Td[(1bx2)]TJ /F13 11.955 Tf 11.96 .49 Td[(bx2(N0)(4) wherethequantitySistheestimatedstandarddeviationofthepopulationofxbasedonthevaluesofxithatwereactuallysampled. Let bx2=1 NNXi=1x2i(4) and bx2= 1 NNXi=1xi!2(4) CombiningEqs.(3.10),(3.11),(3.12),and(3.13),Rcanbewritten(forN0)as R=vuut 1 N bx2 bx2)]TJ /F5 11.955 Tf 11.95 0 Td[(1!=vuuut N2 N2PNi=1x2i PNi=1xi2)]TJ /F5 11.955 Tf 14.71 8.08 Td[(1 N(4) R=vuuut PNi=1x2i PNi=1xi2)]TJ /F5 11.955 Tf 14.72 8.09 Td[(1 N(4) Hence,iftherearenonzeroscoresthatareidenticalandequaltox,Rbecomes R=s nx2 (nx)2=1 p n,Nn(4) Toreducetheerrorinthetallyresultsbyz,z2timestheoriginalnumberofhistories(n)mustbecalculated. 57

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4.6VarianceReductionMethods 4.6.1NonanalogMethods ThenonanalogMonteCarlomethodsareapowerfultoolusedformanycalculations,andtraditionallytheyhavebeendevelopedaccordingtotheneed.AnonanalogMonteCarlomodelattemptstofollowinterestingparticlesmoreoftenthanuninterestingones.Aninterestingparticleisonethatcontributesalargeamounttothequantity(orquantities)thatneedstobeestimated.Here,acombinationofthreevariancereductiontechniquesareusedtoobtainbetterresultsinMonteCarlocalculations.Thesetechniquesareasfollows:GeometrySplitting,RussianRoulette,SurvivalBiasing. 4.6.1.1Geometrysplitting(G.S.) Thistechniqueisusedwhentheratiowi (Ei)isgreaterthananupperboundwi=2.[ 5 ]ItconsistsofreplacingaparticleofweightwibyMiparticlesofweight(Ei).[ 5 ]Miisdenedinthefollowingway: Mi=8>><>>:Aintwi (Ei),withprobability(1)]TJ /F7 11.955 Tf 11.95 0 Td[(p)Aintwi (Ei)+1,withprobabilityp (4) Where p=wi (Ei))]TJ /F7 11.955 Tf 11.95 0 Td[(Aintwi (Ei) (4) Aint(x)isthelargeintegersuchthatAint(x)x.[ 5 ] 4.6.1.2Russianroulette(R.R.) Thisisaprocedureinwhichaprobabilityp=w (E)ispredetermined.TheweightwofaparticleatenergyEcanbereplacedwithanincreasedweightw'=(E)orwithprobability(1-p)theparticleisterminated.[ 5 ] 58

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4.6.1.3Survivalbiasing(S.B.) Survivalbiasingalsoknownasimplicitabsorptionorimplicitcaptureallowsmoreparticlestohavenon-zerocontributiontothescorethantheanalogsimulation(naturalsimulation).Whenparticlescollideinanalogsimulation,thereisaprobabilitythatthisparticletobeabsorbedbythenucleusandkilled.However,insurvivalbiasing(nonanalogsimulation)theparticleisneverkilledbyabsorption;instead,theparticle(neutron)withweightWnisreducedtown.Where wn=1)]TJ /F6 11.955 Tf 13.15 8.09 Td[(a t.Wn (4) Wn-neutronweight. a-microscopicabsorptioncrosssection. t-totalmicroscopiccrosssection. MCNP5implementssurvivalbiasing.Bydefaultsettingthisparametertotheneutronenergyintervaldesiredfulladvantageofthismethodwillbeachieved.Herein,thePHYS:NcardfromMCNP5issetfrom20to1e-14.IfnosurvivalbiasingisneededjustsetthePHYS:Ncardtothemaximumenergyv20Mevforbothedges(PHYS:N2020). 4.6.2EfciencyoftheNonanalogMethod TheefciencyofaMonteCarlosimulationdependsonthetypeofvariancereductionappliedtotheprobleminquestion.TheMCNP5codeusesdifferentcardstorepresentdifferenttypesofvariancereduction.However,onlythePHYSandIMPcommandswereused.ThecommandPHYSisusedtoavoidtime-consumingtracking,physics,orunimportanttallycontributionsinthebeamport.ThecommandIMPisusedtoimprovestatistics. 59

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4.6.2.1PHYScard ThePHYScommandisusedtospecifyenergycutoffsandthephysicstreatmentstobeusedforphotons,neutronsandelectrons.[ 11 ]ThePHYScardissetasfollows:PHYS:N201E-14wherecrosssectiontablebelow20MeVisretainedandforneutronsbelow1E-14MeVanalogabsorption(naturalsimulation)willbeused,whileabove1E-14MeVsurvivalbiasingisused. 4.6.2.2IMPcard Theimportancecard(imp:n)speciestherelativecellimportanceforneutrons,oneentryforeachcelloftheproblem.Theimp:ncardcangointhedatacardsectionoritcanbeplacedonthecellcardlineattheendofthelistofsurfaces.Theimp:ncardthroughoutoutthebeamportcellshadaincreaseofafactoroftwotokeepneutronpopulationroughlyconstant. 60

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CHAPTER5MCNP5SIMULATIONRESULTS 5.1Introduction UsingtheMonteCarloNeutronTransportCode(MCNP),neutronssiondensitydistribution,multi-groupneutronuxdistribution,neutronenergyux,andneutronreactionratewerecomputedusingaxedsourcemethodwiththesdefcard.Tocomputeneutronssiondensitydistribution,theWattssionspectrumwasused.Tocomputethemulti-groupneutronuxdistribution,FMESH4.Theneutrontalliesenergyuxwerefoundwith*F4tallycards.Tocalculateneutronreactionrateatcertainlocationsoftheradiationbeamportusingthegoldfoil(197Au)asatarget,thetallyF4withthetallymultiplierFM4wasapplied.ThetallymultiplierFM4modiesthetallytoachievedesiredunitcalculations.WiththeapplicationofMonteCarlovariancereductionmethodsarelativeerroroflessthan10%wasobtained. Applicationofnonanalogmethods Theresults,fromTable 5-1 ,provethatthesurvivalbiastechniqueisaveryusefultoolinreducingcomputertime. Table5-1. MCNP5-TotalTransportTime(ctm)-1CPU npsG.S.-R.R.G.S.-R.R.-S.B. 5million111min.29min.10million195min.57min.50million768min.288min. However,whenthetwononanalogsimulationsarecomparedtheimprovementoftherelativeerrorisnotsignicant(Table 5-2 );survivalbiasinghasminimalimpactinthestatisticsofthetally. Thegureofmerit(FOM),inTable 5-3 isusedtodemonstratetheeffectivenessofaMonteCarlosimulationwhensurvivalbiastechniqueisapplied.TheFOMincreasesascomputertimedecreasessuchthatalargerFOMmeansaneffectiveMonteCarlosimulation. 61

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Table5-2. MCNP5-RelativeError%fortallytypeF4 npsAnalogSimulationNon-Analog(noS.B.)Non-Analog(S.B.) 5million57.74%55.53%53.86%10million50.21%40.98%38.86%50million26.76%19.38%19.24% G.S.=GeometrySplitting,R.R.=RussianRoullete,S.B.=SurvivalBiasing Table5-3. FigureofMerit(FOM) npsVarianceReductionFOM10)]TJ /F3 7.97 Tf 6.59 0 Td[(3 5millionG.S.-R.R.1.85millionG.S.-R.R.-S.B.4.610millionG.S.-R.R.1.910millionG.S.-R.R.-S.B.7.2 G.S.=GeometrySplitting,R.R.=RussianRoullete,S.B.=SurvivalBiasing 5.2UFTRBeamPort 5.2.1UFTRReactorSouthBeamPortAnalyzes Inthissection,the47energy-groupcaseswillbeanalyzedforthesouthbeamport.Forthesouthbeamportmulti-groupneutronuxdistributionstudy,theneutronssiondensitydistributionwascalculatedthroughoutthereactorcore.Howeverthessionneutroncontributionwasmainlyfromthefuelplatesinfuelbox2asshowninFigs 3-3 3-4 5-1 and 5-2 5.2.2EnergyGroupsAnalyzed ThespecicationsinTable 5-4 areinaccordwithUFTRenergyrangemeasurements.Tables 5-7 showthegroupI.D.'sandcasesthatwerestudiedfortheradiationsouthbeamport. Table5-4. EnergyrangeforUFTRmeasurements EnergyEnergyRange Thermal0.1eV-1.0eVEpithermal1.0eV-1.0MeVFast1.0MeV-17.332MeV 62

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Energyrangefor47energygroups Whengeometrysplitting(G.S.)andrussianroullete(R.R.)variancereductionswerecombinedwithsurvivalbias(S.B.),thesimulationtimewasreducedsignicantly. Table5-5. Generalanalysesfor47energygroupsfor16CPU'susing(G.S.-R.R.) GroupI.D.]npsTotalCPUTime(min)RelativeError% 452.2billion418,9449.84372.9billion558,7469.83172.9billion558,7469.02 G.S.=GeometrySplitting,R.R.=RussianRoullete Table5-6. Generalanalysesfor47energygroupsfor16CPU'susing(G.S.-R.R.-S.B.) GroupI.D.]npsTotalCPUTime(min)RelativeError% 452.2billion167,5789.80372.9billion223,4989.80172.9billion223,4989.00 G.S.=GeometrySplitting,R.R.=RussianRoullete,S.B.=SurvivalBiasing Table5-7. Casesofstudyfor47energygroups CasesGroupI.D.]EnergyRange Case1450.87640eV-0.41400eVCase2371.5850e-03MeV-4.5400e-04MeVCase3171.653MeV-1.3530MeV 5.2.3SouthBeamPort3-DMulti-GroupNeutronFluxDistribution Thescatteringandcountourplotsofthemulti-groupneutronuxdistributionswerecalculatedalongtheradiationsouthbeamportbeforeandalongthecollimatorintwoseparaterunstoshowplotoftheneutronuxintensitydistributionwithmoredetails.It'snoticedthatthereisahighintensityofneutronuxwherethesouthbeamportisclosertothefuelbox2duetoahighintensityofneutronsinthisregionasobservedintheguresbelow. 5.2.4ImpactofDifferentModeratorsintheUFTR Herein,theneutronenergyuxfor62energygroups[Appendix??]willbestudiedwithdifferentmoderatorstochecktheeffectivenessofparticularmoderatorssurrounding 63

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theUFTRcore.Twoothermoderators(lightandheavywater)willbecomparedtographitetoanalyzetheirimpactontheneutronenergyuxinthesouthbeamportregionclosetothefuelbox2(Fig. 3-3 ). Graphite-Graphite(carbon)couldbeusedasareectoraswell.Nucleargraphiteisspecicallyproducedforuseasamoderatororreectorinsideofanuclearreactor. LightWater(H2O)-Innaturalwater,almostallofthehydrogenatomsareprotium,1H.Lightwaterislargelyusedinnuclearreactorsbecauseitisextremelyinexpensive. HeavyWater(D2Ocoolant)-Heavywaterischemicallythesameasregular(light)water,butwiththetwohydrogenatoms(asinH2O)replacedwithdeuterium(2H)atoms(hencethesymbolD2O,deuteriumoxide).Thepresenceoftheneutronsinthedeuteriumatomsofheavywateriswhatmakesitheavy,about11%denserthanwater. Power-generatingreactorsuselightwatercoolantasmoderator.However,heavywaterisbetterthanlightwateratmoderating(slowing)neutronsforseveralreasons,whichmakeitusefulinsomenuclearreactorcores.Tables 5-8 and 5-9 showphysicalpropertiesandparametersofthemoderatorsinstudy. Table5-8. Physicalpropertiesofheavywater(D2O)andlightwater(H2O) PropertyD2OH2O Freezingpoint(C)3.820.00Boilingpoint(C)101.4100.0Density(at20C,g/cm3,liquid)1.10560.9982Temp.ofmaximumdensity(C)11.64.0 Table5-9. SlowingDownParametersofTypicalModerators ModeratorA[g/cm3]s[cm)]TJ /F3 7.97 Tf 6.59 0 Td[(1]s=a H2O--0.9200.99821.3571D2O--0.5091.10560.1765670C120.7160.1581.60.060192 64

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TheparametersinTable 5-9 areusefultoidentifywhichmoderatorismoreefcienttoslowdownneutronscomingfromthereactorcore.Themathematicalequationsofthesequantitiesarepresentedasfollows: =(A)]TJ /F3 7.97 Tf 6.59 0 Td[(1 A+1)2,whereAisthenuclearmass isthemeanlethargygainpercollisionaveragenumberofcollisionsnecessarytoslowdownassionneutronfrom2MeVto1.0eVisfoundby <]>=ln2106 1.0 =14.5 (5) wherethemeanlethargygainpercollisionisgivenby =ZEiEi[lnE0 Ef)]TJ /F5 11.955 Tf 11.96 0 Td[(lnE0 Ei]1 1)]TJ /F6 11.955 Tf 11.95 0 Td[(dEf(5) or =1+ 1)]TJ /F6 11.955 Tf 11.95 0 Td[(ln=1)]TJ /F5 11.955 Tf 13.15 7.92 Td[((A)]TJ /F5 11.955 Tf 11.96 0 Td[(1)2 2AlnA+1 A)]TJ /F5 11.955 Tf 11.95 0 Td[(1(5) sisthemoderatingpowerofamaterial.However,thisparameterisnotenoughtodescribetheeffectivenessofamaterialforneutronmoderationbecausethemoderatorhastobeaweakabsorberofneutronsaswell. s aisthemoderatingratio. Thebestmoderator(D2O)isheavywaterbecauseithasthebiggestmoderatingratio. NeutronSpectraintheModerator Inthissectiontheneutronspectrawillbeanalyzedfordifferentmoderators.Bychangingthegraphite(moderator)thatsurroundstheUFTRreactorcoretoothertypesofmoderators,changesintheneutronspectraareobserved.ThiscanbeobservedintheFigures 5-39 and 5-41 AsshowninFigure 5-39 thethermalneutronenergyuxismoreintenseinlightwater(H2O)thanheavywater(D2O)andGraphite(C).Thishappensduetotheneutroncrosssectionofanisotope(Figs. 5-43 5-44 5-45 ,and 5-46 ). 65

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Ingeneral,thevaluesofabsorptioncross-sectionforlightwaterarehigherthanforheavywater(Fig. 5-44 ).Thisiswhylightwatercoolanthasalowermoderatingratiothanheavywater.However,thescatteringcrosssectionforhydrogenisapproximatelyover10timesthatofdeuterium,mostlyduetothelargeincoherentscatteringlengthofhydrogen(Fig. 5-43 ).Thisisthereasonwhythethermalneutronuxforlightwaterismoreintensethanthatofheavywater. Whenfastneutronenergyuxisalsoconsideredgraphiteperformedbetterthanlightwaterandheavywaterduetotheresonanceoftheneutronscatteringcrosssectionofgraphite(C)forhighenergygroups(Fig. 5-43 ). 66

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Figure5-1. Neutronssiondensitydistribution]=cm3-secthroughoutthefuelbox2facingthereactorcore. 67

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Figure5-2. Neutronssiondensitydistribution]=cm3-secthroughoutthefuelbox2facingsouthbeamport. 68

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Figure5-3. xycross-sectionatz=-1mid-sectionofthefuelbox2 69

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Figure5-4. 2-DNeutronFluxDistributionfor47energygroupsalongY-axis(cm)beforeCollimatorregion. 70

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Figure5-5. 2-DNeutronFluxDistributionRelativeErrorfor47energygroupsalongtheY-axis(cm)beforeCollimatorregion. 71

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Figure5-6. 2-DNeutronFluxDistributionfor47energygroupsalongY-axis(cm)beforeCollimatorregion. 72

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Figure5-7. 2-DNeutronFluxDistributionRelativeErrorfor47energygroupsalongtheY-axis(cm)beforeCollimatorregion. 73

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Figure5-8. 2-DNeutronFluxDistributionfor47energygroupsalongY-axis(cm)intheCollimatorregion. 74

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Figure5-9. 2-DNeutronFluxDistributionRelativeErrorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. 75

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Figure5-10. 2-DNeutronFluxDistributionfor47energygroupsalongY-axis(cm)intheCollimatorregion. 76

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Figure5-11. 2-DNeutronFluxDistributionRelativeErrorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. 77

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Figure5-12. 2-DNeutronFluxDistributionWithoutCollimatorfor47energygroupsalongtheY-axis(cm)BeforeCollimatorregion. 78

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Figure5-13. 2-DNeutronFluxDistributionRelativeErrorfor47energygroupsWithoutCollimatoralongtheY-axis(cm)BeforeCollimatorregion. 79

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Figure5-14. 2-DNeutronFluxDistributionWithoutCollimatorfor47energygroupsalongtheY-axis(cm)BeforeCollimatorregion. 80

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Figure5-15. 2-DNeutronFluxDistributionRelativeErrorfor47energygroupsWithoutCollimatoralongtheY-axis(cm)BeforeCollimatorregion. 81

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Figure5-16. 2-DNeutronFluxDistributionWithoutCollimatorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. 82

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Figure5-17. 2-DNeutronFluxDistributionRelativeErrorfor47energygroupsWithoutCollimatoralongtheY-axis(cm)intheCollimatorregion. 83

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Figure5-18. 2-DNeutronFluxDistributionWithoutCollimatorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. 84

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Figure5-19. 2-DNeutronFluxDistributionRelativeErrorfor47energygroupsWithoutCollimatoralongtheY-axis(cm)intheCollimatorregion. 85

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Figure5-20. 2-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)BeforeCollimatorregion. 86

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Figure5-21. 2-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)BeforeCollimatorregion. 87

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Figure5-22. 2-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)BeforeCollimatorregion. 88

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Figure5-23. 2-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. 89

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Figure5-24. 2-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. 90

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Figure5-25. 2-DNeutronFluxDistributionWithandWithoutCollimatorfor47energygroupsalongtheY-axis(cm)intheCollimatorregion. 91

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Figure5-26. 3-DthermalneutronuxdistributionalongtheY-axis(cm)southbeamportbeforecollimatorregion. 92

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Figure5-27. 3-DthermalneutronuxrelativeerroralongtheY-axis(cm)southbeamportbeforecollimatorregion. 93

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Figure5-28. Contour3-DthermalneutronuxdistributionalongtheY-axis(cm)southbeamportbeforecollimatorregion. 94

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Figure5-29. xysouthbeamportcrosssection. 95

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Figure5-30. 3-DepithermalneutronuxdistributionalongtheY-axis(cm)southbeamportbeforecollimatorregion. 96

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Figure5-31. 3-DepithermalneutronuxdistributionrelativeerroralongtheY-axis(cm)southbeamportbeforecollimatorregion. 97

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Figure5-32. 3-DfastneutronuxdistributionalongtheY-axis(cm)southbeamportbeforecollimatorregion. 98

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Figure5-33. 3-DfastneutronuxdistributionrelativeerroralongtheY-axis(cm)southbeamportbeforecollimatorregion. 99

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Figure5-34. 3-DthermalneutronuxdistributionalongtheY-axis(cm)southbeamportcollimatorregion. 100

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Figure5-35. 3-DthermaluxdistributionrelativeerroralongtheY-axis(cm)southbeamportcollimatorregion. 101

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Figure5-36. 3-DfastneutronuxdistributionalongtheY-axis(cm)southbeamportcollimatorregion. 102

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Figure5-37. 3-DfastuxdistributionrelativeerroralongtheY-axis(cm)southbeamportcollimatorregion. 103

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Figure5-38. Neutronenergyuxfordifferentmoderatorsregionfor62energygroups. 104

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Figure5-39. Thermalneutronenergyuxforthreedifferentmoderatorswithin62energygroups. 105

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Figure5-40. Improvementofthermalneutronenergyuxforthethreedifferentmoderatorswithin62energygroups. 106

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Figure5-41. Fastneutronenergyuxforthreedifferentmoderatorswithin62energygroups. 107

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Figure5-42. Improvementoffastneutronenergyuxforthethreedifferentmoderatorswithin62energygroups. 108

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Figure5-43. Neutronscatteringcrosssectionsforhydrogen,deuteriumandCinH2O,D2O,andGraphiterespectively. 109

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Figure5-44. NeutronabsorptioncrosssectionsforhydrogenanddeuteriuminH2OandD2Orespectively. 110

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Figure5-45. Neutroncrosssectionsforhydrogen(H1) 111

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Figure5-46. Neutroncrosssectionsfordeuterium(H2) 112

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CHAPTER6NEUTRONIRRADIATIONCHARACTERIZATIONOFGOLDFOIL 6.1Reaction-RateEquation Nuclearinteractionswithhighpurityactivationfoilshavebeenoneofthemostefcientwaysofdetectingneutronsandmeasuringtheradionuclidesproducedinthefoilsfromtheseinteractions.Neutronreactionsinclude: Table6-1. AbsorptiveReactions ReactionName (n,)10n+AZX!A)]TJ /F3 7.97 Tf 6.58 0 Td[(3Z)]TJ /F3 7.97 Tf 6.58 0 Td[(2Y+42He(n,p)10n+AZX!AZ)]TJ /F3 7.97 Tf 6.58 0 Td[(1Y+p(n,ssion)10n+A1Z1X!A2Z2X+A3Z3X+10n(n,2n)10n+AZX!A)]TJ /F3 7.97 Tf 6.58 0 Td[(1ZX+210n(n,)10n+AZX!A+1ZX+ Chargedparticles,ionizing(photons),andfastandthermalneutronshavebeenusedtoactivateelements.Chargedparticleshaveathreshold;photoncrosssectionsaregenerallysmallerthanneutroncrosssections.Thermalneutronsaregenerallythemosteconomicalchoiceforactivation.Ina(n,)reaction,thenucleusisleftinanexcitedstate.Thisnew,unstableconguration,eventuallydecaysbyemissionofoneormoredelayedgammas. The(n,)reaction,alsonamedtheradioactivecapturereaction,isofparticularsignicancebecauseitspansthecompleteenergyrangeofneutrons.TheotherreactionsonTable 6-1 arenormallythresholdreactionsandhappenjustaboveadeniteenergy. Thisexcitednucleusmayde-excitebyreleaseofaand/or.Thethreemostcommontypesofradioactivitydecayareasfollow:photons(),heavychargedparticles(),andelectronspositrons(). The(n,-)reactioncanbedenedwiththeclassicFredholmequationoftherstkind[ 2 ]: 113

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RRi=NZ10(E)(r,E)dE(6) where, RRi=rateatwhichreactionsareoccurringinthesensorfoili(reactions/s), N=numberoftargetatomsinthefoil, (E)=energy-dependentmicroscopiccross-section, (E)=energy-dependentneutronuxinthesample(n/cm2sec). Tosolveforneutronux,theEqn. 6 mustbechangedintoadiscreteenergygroupstructurefortheuxandcross-section.Dene'asthemagnitudeoftheneutronscalarux(inn/cm2sec)and (E)astheneutronenergyuxshape(in1/MeV).Then,Eq. 6 canbewrittenas: RRi=N'Z10(E) (E)dE(6) where, Z10 (E)dE=1(6) TheintegralinEqn. 6 isdiscretizedusinganemeshmultigroupenergybinstructurewithEg=1,2,...,G: RRi=N'GXg=1ZEg+1Eg(E) (E)dE(6) Forthisproceduretobeprecise,Eg+1hastobechosentobeanenergyabovewhichthecross-section(E)isinsignicant.Then,thegroupshapefunctionisgivenby: g=ZEg+1Eg (E)dE(6) Thegroupcross-sectionisthendenedas: 114

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g=REg+1Eg(E) (E)dE REg+1Eg (E)dE(6) IfwemultiplyanddivideEqn. 6 bythedenitionofgroupux,weobtain: RRi=N'GXg=1"REg+1Eg(E) (E)dE REg+1Eg (E)dE#ZEg+1Eg (E)dE(6) SubstitutionofEqn. 6 andEqn. 6 intoEqn. 6 yieldsthereactionrateequation: RRi=N'GXg=1g g(6) 6.2ActivityEquations Eqn. 6 ,whichrepresentsthereactionrate,willbefoundusingtheinducedactivityofthefoilirradiatedintheneutronenvironment.Afterirradiation,thefoilsarecountedonanefciency-calibratedhighpuritygermanium(HPGe)detector.HPGespectrometryisusedforanalyzingenvironmentalsamplesanddeterminingradioisotopeconcentrationsduetoitsexcellentresolution.Thisdetectorhasbettercharacteristicssuchasresolution,absoluteefciency"(E)andismoresensitivetothedetectionofimpurities.[ 3 14 ]Ifweignorethedecayofthefoiloverthetimethatitiscounted,thenthecountsrecordedonthedetectorovertimecanbelinkedtoactivityasinEqn. 6 : Ac=C "dItc(6) where, Acistheactivityattimeofcountingindps(desintegrationpersecond) Cisthetotalnumberofcountsortheareabelowthepeakgotfromtherayspectrum, "disthedetectorcountingefciency(counts/), Igamma-rayintensity!isthe-rayyieldforthespecic-raymeasured(/disintegration)[ 1 10 ] 115

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tccountingtime(seconds) 6.2.1IrradiationActivity WhileafoilwithNnumberoftargetnuclidesispositionedinaneutroneld,itwillcaptureneutronstocreateadaughternuclideNd. NN)302()302(!NdNd)362()363(!Ns(6) Therateofchangewithtime(dN dt)ofthenumberoftheparentnuclideNis: dN dt=)]TJ /F6 11.955 Tf 9.3 0 Td[(N(6) then, N(t)=N0e)]TJ /F12 7.97 Tf 6.59 0 Td[(t(6) Therateofchangeinrespecttotime(dNd dt)ofthenumberofthedaughternuclideNdisafunctionoftheproductionandlossrates: dNd dt=N)]TJ /F6 11.955 Tf 11.95 0 Td[(Nd(6) where, -spectrumaveragedcross-section -irradiationneutronux N-numberoftargetnuclides Nd-numberofdaughternuclides -decayconstantforthedaughternuclide N-productionrate Nd-lossrate Thedecayconstantisrelatedtothehalf-lifebyfollowingequation: =ln2 T1=2(6) 116

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IftheinitialconcentrationofthedaughternuclideNdis0att=0,then N(t)=N0e)]TJ /F12 7.97 Tf 6.59 0 Td[(t(6) becausethereisonlylossrate(N)insteadofproductionrate(N). Hence,thesolutiontotheequation 6 forthenumberofdaughternuclidespresentduringtheirradiationis: Nd(t)=N0 (1)]TJ /F7 11.955 Tf 11.96 0 Td[(e)]TJ /F12 7.97 Tf 6.58 0 Td[(t)(6) Thenumberofdisintegrationsofaradioactivesourceinagiventimeisgivenbyitsactivity.Anactivityofonebecquerel(Bq)meansoneatomofthesourcedisintegratespersecond.OneCurie(Ci)is37billionBq. TheactivityAofthefoilisgivenbyN.Hence,theactivity(A0)attheendoftheirradiationwillbe: A0=Nd(t0)(6) A0=N0(1)]TJ /F7 11.955 Tf 11.96 0 Td[(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t0)(6) Whentheinducedactivityapproachesahorizontalasymptoteorsaturatedactivity(A1)foraninnitelylongirradiationtime,theactivitywillberepresentedbyEqn. 6 Ifthefoilisirradiatedforaperiodofthreeorfourtimeslongerthanthevalueofdaughternuclide'shalf-life,thenumberofdaughternuclideshasnearlyreachedasteady-state.Theactivityatthispointiscalledsaturationactivity(A1).SolvingEqn. 6 forsteady-state,thefollowingisobtained: 0=N)]TJ /F6 11.955 Tf 11.96 0 Td[(Nd(6) Then, 117

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A1=N=Nd(6) where RR=N(6) Iftheirradiationhasproceededforatimet0atwhichtimethefoilisremovedwithanactivityA0: A0=A1(1)]TJ /F7 11.955 Tf 11.95 0 Td[(e)]TJ /F12 7.97 Tf 6.58 0 Td[(t0)(6) where, A1=A0 (1)]TJ /F7 11.955 Tf 11.96 0 Td[(e)]TJ /F12 7.97 Tf 6.58 0 Td[(t0)(6) 6.2.2ActivityAfterA0 Afterexposuretotheneutronux,thefoilistransferredtoanappropriateradiationcountertomeasureitsactivity.Becausetheactivitycontinuouslydecays;acarefulrecordmustbemadeofeachofthetimescounted.Ifthecountingiscarriedoutoveranintervalbetweent1andt2,thetotalnumberofcountsCwillbe: Zt2t1A(t)dt=C)]TJ /F7 11.955 Tf 11.96 0 Td[(B "d(6) C="dZt2t1A(t)dt+B(6) C="dZt2t1A0e)]TJ /F12 7.97 Tf 6.59 0 Td[((t)]TJ /F4 7.97 Tf 6.59 0 Td[(t0)dt+B(6) C="dA0 et0(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t1)]TJ /F7 11.955 Tf 11.96 0 Td[(e)]TJ /F12 7.97 Tf 6.58 0 Td[(t2)+B(6) 118

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whereBisthenumberofbackgroundcountsexpectedint2-t1.AftercombiningEqs. 6 and 6 ,weobtainthesaturatedactivity: A1=(Ccounts)]TJ /F7 11.955 Tf 11.96 0 Td[(B) "det0(1)]TJ /F7 11.955 Tf 11.96 0 Td[(e)]TJ /F12 7.97 Tf 6.58 0 Td[(t0)(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t1)]TJ /F7 11.955 Tf 11.96 0 Td[(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t2)(6) Theseequationswillbeusedtodeterminetheactivityofthegoldfoilsfollowingirradiation.Eqs. 6 and 6 showthatA1isequivalenttotherateatwhichthereactionsarehappeninginthesample.Hence,thereactionrateisrepresentedby: RR=(Ccounts)]TJ /F7 11.955 Tf 11.96 0 Td[(B) "det0(1)]TJ /F7 11.955 Tf 11.96 0 Td[(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t0)(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t1)]TJ /F7 11.955 Tf 11.95 0 Td[(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t2)(6) Ifthegamma-rayintensity(IfromTable 6-2 )isinsertedintoEqns. 6 and 6 thesaturatedactivityandthereactionratewillbe: A1=(Ccounts)]TJ /F7 11.955 Tf 11.96 0 Td[(B) "dIet0(1)]TJ /F7 11.955 Tf 11.96 0 Td[(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t0)(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t1)]TJ /F7 11.955 Tf 11.95 0 Td[(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t2)(6) RR=(Ccounts)]TJ /F7 11.955 Tf 11.96 0 Td[(B) "dIet0(1)]TJ /F7 11.955 Tf 11.96 0 Td[(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t0)(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t1)]TJ /F7 11.955 Tf 11.95 0 Td[(e)]TJ /F12 7.97 Tf 6.59 0 Td[(t2)(6) Activationfoilsarethuswidelyusedformappingthespatialvariationofsteady-stateneutronuxesinreactorcores,wheretheextremetemperature,pressure,andlimitedspaceseverelyconstrainthetypesofconventionaldetectorsthatmaybeused.[ 8 ] 6.3ReactionRateCalculationusingMCNP5 Thereactionratesandthecorrespondingsaturationactivitywerecalculatedforthegoldfoilatdifferentlocationsalongthebeamport.ThiswasaccomplishedusingtheFMtallyfromMCNP5.ThereactionnumberusedforFMtallywas102,whichcorrespondstothereactioncross-section(n,).TheresultsacquiredwillbeusedtodesignthefoilirradiationexperimentintheUFTRreactor. Itisclearthatthegoldfoiltargetinthebeamportshouldbelocatedclosetothemoderatorregionduetothehighintensityofuxinthisarea.However,thegoldfoils 119

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canberelocatedasdesired.Itisobservedwhengoldfoilisputfarfromthemoderatorregion,reactionratestatisticsfromMCNP5codebecomeverypoor;yet,withtheapplicationofvariancereductioncalledDXTRANgreatresultscanbeachieved. DXTRANisavariancereductiontechniquewhichisconsideredpartiallydeterministic.DXTRANusuallyshouldnotbeinproblemswhichhavereectingsurfacesorwhiteboundaries.Thistypeofvariancereductionhasgreatusabilityinregionswhereneutronsarehighlyabsorbedsuchasasmallgapinaconcretecollimator.DXTRANisavaryusefultypeofvariancereductionusedtoobtainparticlesinaverysmallregionbyincreasinginadesiredtally.TheDXTRANspherefollowtheprinciplethatitmustfullyencircletheareaoftoobtainasmuchaspossiblecollidedparticlesinacell.Thefailureofhavingthepropersphereradiuswouldgiveapoorstatisticsoutput.Uponsamplingacollisionorsourceemissionprobability,DXTRANestimatesthecorrectweightfractionthatshouldscatterorbeemittedtowardthesphereandarrivewithoutcollision.Therefore,theDXTRANmethodputsthiscorrectweightonthesphere. GoldFoilMaterialProperties: FoilReaction:197Au(n,)198Au Mass(g/mole):196.967 Density:19.3g/cm3 ThermalMicroscopicCrossSection:8.8010)]TJ /F3 7.97 Tf 6.59 0 Td[(23cm2 FastMicroscopicCrossSection:9.5010)]TJ /F3 7.97 Tf 6.58 0 Td[(23cm2 E:411.8KeV 411.8keVphotonsperdecay(I):95.54% IsotopeHalf-Life(T1=2):2.695days NumberDensity:5.9101022nuclei/cm3 Table6-2. Recommended-raycalibrationenergiesandintensities ParentE(KeV)I(%) 198Au411.8020595.54675.88360.8061087.68420.159 120

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Table6-3. 197Augoldfoilreactionrate ReactionRatePosition(cm)nps16CPU-TotalComp.Time(min) 14.3680E-08-1494million3,304.368.88150E-09-1645million3,493.224.87450E-09-1895million1,925.04 Gold-198(19879Au) 19879Auisproducedbytheneutronactivationofthestable19779Au(Gold-197).The19879Audecaysbythebetaemission()withhalf-lifeof2.7daystoanisotopeofmercury: 19879Au!19880Hg++0)]TJ /F3 7.97 Tf 6.58 0 Td[(1e(6) Itemitsa412KeVgamma(plusinsignicantamountsofotherenergies).FormanyyearsGold-198grains,consistingofGold-198encapsulatedinplatinum,wereusedforpermanentimplant,especiallyfortheheadandneckregion.HoweverthemethodhaslargelyfallenintodisuseandGold-198grainsnolongerfeatureinUKsupplierscatalogue. 121

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Figure6-1. MCNP5calculationsfor197Aufoilsat3differentlocations. 122

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Figure6-2. 197Au(n,)198Aucross-sectionasafunctionofneutronenergy 123

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CHAPTER7CONCLUSION Thekeyobjectiveofthisresearchwastoacquirethe2-Dand3-Dnormalizedmulti-groupneutronuxdistributionthroughouttheUniversityofFloridaTrainingReactor(UFTR)radiationbeamport.Inadditiontothat,developanefcientmodelprovidingthemulti-groupneutronuxdistributioninareasonabletotalcomputationtimebyusingvariancereductionaMonteCarloTechnique. ThisresearchcreatedabenchmarkMonteCarloNeutralParticleversion5(MCNP5)modelsoftheUFTRradiationbeamportsthatcannowbeusedforfuturesimulationofthemulti-groupneutronuxdistributionandneutronuxintensityatthedifferentlocationsoftheradiationbeamports.TheMCNP5modelcanalsobeusedtobenchmarktheMCNP5neutronreactionratewithexperimentalvaluesfromthereactor. CriticalityanalysisoftheUFTRcoremodelusingMCNP5wasperformedtoobtain3-Dneutronssiondensitydistributioninthereactorcorebyusingxedsourcemethodathreepointsource. Onceneutronssiondensitydistributionwascalculatedthemulti-groupneutronuxdistribution,neutronenergyux,andneutronreactionratewerecomputedusingamonodirectionalsourcedenitiontosavecomputationaltime.Threedifferenttypesofvariancereductionwereappliedtotheworktoobtaindesiredoutput:GeometrySplitting,RussianRoulette,andSurvivalBias.Where,thePHYSandIMPcommandswereused. Multi-groupneutronuxdistributioncomparisonwithandwithoutcollimatorwasmadeintheradiationbeamporttoobservetheabsorptionandreectionofneutronsduetothecollimator. Additionalstudywasmadeintheneutronspectratoseetheimpactofdifferentmoderatorssurroundingthereactorcore. 124

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APPENDIXAURANIUMSILICIDE (0.1eV
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APPENDIXBALUMINUM (0.1eV
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APPENDIXCTHEEFFECTOFTHEIMPURITYINTHEFUELONTHEUFTRKEFF. (Keff) TableC-1. no10BintheAluminumCladding Cases10BCdLiKe ReferenceCase2ppm1ppm0.1ppm0.99958Case40.1ppm1ppm0.1ppm1.00114Case50.1ppm1ppm0.4ppm(4x)1.00102Case60.1ppm1ppm2ppm(20x)1.00098 TableC-2. KeandStandardDeviation CasesKeStandardDeviation ReferenceCase0.999580.00012Case41.001140.00015Case51.001020.00016Case61.000980.00015 FigureC-1. Keff1. 127

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TableC-3. 10BintheAluminumCladding/VariationofCdconcentrationwhileLiisconstant Cases10BCdLi ReferenceCase2ppm1ppm0.1ppmCase12ppm2ppm(2x)0.1ppmCase82ppm4ppm(4x)0.1ppm TableC-4. KeandStandardDeviation CasesKeStandardDeviation ReferenceCase0.999580.00012Case10.999160.00016Case80.998870.00016 FigureC-2. Keff2. 128

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TableC-5. 10BintheAluminumCladding/VariationofLiconcentrationwhileCdisconstant Cases10BCdLi ReferenceCase2ppm1ppm0.1ppmCase22ppm1ppm0.4ppm(4x)Case72ppm1ppm2ppm(20x) TableC-6. KeandStandardDeviation CasesKeStandardDeviation ReferenceCase0.999580.00012Case20.999390.00016Case70.999270.00012 FigureC-3. Keff3. 129

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FigureC-4. Keffnal. 130

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APPENDIXDFISSIONCROSS-SECTIONS (ENDF/B-VIIFissionableNuclidesCross-SectionPlotinLog10Scaleat300K(26.85C)) FigureD-1. 232Thssioncross-sectionversusneutronenergy(MeV). FigureD-2. 238Ussioncross-sectionversusneutronenergy(MeV). 131

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FigureD-3. 240Pussioncross-sectionversusneutronenergy(MeV). FigureD-4. 242Pussioncross-sectionversusneutronenergy(MeV). 132

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APPENDIXE47ENERGYGROUPS (Average]ofFissionNeutrons(E)d(E)) TableE-1. 47EnergyGroups Ehighest(MeV)Elowest(MeV)EnergyGroupI.D.]Average]ofFissionNeutrons 17.3314.1913.0873e-0514.1912.2121.4040e-0412.211038.8800e-04108.60742.1814e-038.6077.40855.0761e-037.4086.06561.4962e-026.0654.96672.9375e-024.9663.67987.8966e-023.6793.01297.5313e-023.0122.725104.2975e-022.7252.466114.5322e-022.4662.365121.9502e-022.3652.346133.7886e-032.3462.231142.3761e-022.2311.92157.1682e-021.921.653167.0559e-021.6531.353178.9275e-021.3531.003181.1618e-011.0038.208e-1196.4226e-028.208e-17.427e-1202.7925e-027.427e-16.081e-1214.8114e-026.081e-14.979e-1223.8767e-024.979e-13.688e-1234.3574e-02 133

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TableE-2. 47EnergyGroupscont. Ehighest(MeV)Elowest(MeV)EnergyGroupI.D.]Average]ofFissionNeutrons 3.688e-12.972e-1242.2689e-022.972e-11.832e-1253.2557e-021.832e-11.111e-1261.7150e-021.111e-16.738e-2278.4173e-036.738e-24.087e-2284.0687e-034.087e-23.183e-2291.1529e-033.183e-22.606e-2306.6001e-042.606e-22.418e-2312.0091e-042.418e-22.188e-2322.3566e-042.188e-21.503e-2336.2930e-041.503e-27.102e-3345.6438e-047.102e-33.355e-3351.8407e-043.355e-31.585e-3365.9873e-051.585e-34.540e-4372.4400e-054.540e-42.144e-4382.9855e-062.144e-41.013e-4399.6865e-071.013e-43.727e-4403.6195e-073.727e-51.068e-5418.8031e-081.068e-55.040e-6421.0780e-085.040e-61.860e-6434.0116e-091.860e-68.760e-7447.8460e-108.760e-74.140e-7452.5296e-104.140e-71.000e-7461.0729e-10 134

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APPENDIXFBARYTES(BARITE)CONCRETE (Barytesconcreteshielding) TableF-1. Elementalcompositionofbarytesconcretesingramsofelementpercm3ofconcrete ElementBA-aBA-bBA-HBAHABAHA-dBA-OR (g/cm3)3.503.392.572.352.283.30Hinwater0.02430.01220.0070.0260.02980.036inore---0.0045--Oinwater0.1950.09750.7100.02091.0840.291inore0.8720.8720.7100.4941.0840.971incement0.1180.1180.7100.1381.0840.971C--0.0233---Mginore----0.04410.0099incement0.00380.0038-0.00460.04410.0099Alinore--0.01230.05460.05650.0066incement0.01370.01370.01230.01610.05650.0066Siinore--0.1800.3080.2320.139incement0.03620.03520.1800.04140.2320.139S0.3640.3640.1800.1440.00940.287Cainore0.02030.02030.1480.1090.2090.135incement0.1470.1470.1480.1720.2090.135Feinore0.1510.1510.595-0.03380.277incement0.00910.00910.5950.01070.03380.277Ba1.5511.5510.7180.6180.5771.20 TableF-2. Constantsforthermalneutronsforbarytesconcretes ConcreteMixno.Density(g/cm3)aDLK BA-a3.50.01970.4404.720.212BA-b3.390.01760.6676.170.162BA-H2.570.02200.9126.450.155BAHA2.350.01280.4215.750.174BAHA-d2.280.01110.4126.100.164BA-OR3.300.02240.3343.860.259 135

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REFERENCES [1] StandardTestMethodsforDetectorCalibrationandAnalysisofRadionuclides.,1998. [2] Aghara,S.andCharlton,W.Characterizationandquanticationofanin-coreneutronirradiationfacilityataTRIGAIIresearchreactor.NuclearInstrumentsandMethodsinPhysicsResearchB248(2006):181. [3] Attix,F.H.IntroductiontoRadiologicalPhysicsandRadiationDosimetry.NewYork:JohnWileySons,1986. [4] Duderstadt,J.J.andHamilton,L.J.NuclearReactorAnalysis.NewYork:JohnWileySons,1976. [5] Ghassoun,J.andJehouani,A.RussianrouletteefciencyinMonteCarloressonantabsorptioncalculations.AppliedRadiationandIsotopes53(2000).4-5:881. [6] Grunauer,F.EntwicklungeinesNeutronen-Kollimatorsfureinmedizinischbiologis-chesBestrahlungssystem.Ph.D.thesis,1975. [7] Howerton,R.J.TheLLLEvaluatedNuclearDataLibrary(ENDL):EvaluationTechniques,ReactionIndex,andDescriptionofIndividualEvaluations.,1975. [8] Knoll,G.F.Radiationdetectionandmeasurement.NewJersey:JohnWileySons,Inc.,2000. [9] Lamarsh,J.R.IntroductiontoNuclearEngineering.MA:Addison-WesleyPublishingCompany,1983,2nded. [10] Lemmel,H.D.X-rayandGamma-rayStandardsforDetectorCalibration.,1991. [11] Shultis,J.K.andFaw,R.E.AMCNPPrimer.,2004. [12] Verbeke,J.M.,Hagmann,C.,andWright,D.SimulationofNeutronandGammaRayEmissionfromFissionandPhotossion.,2009. [13] Vernetson,W.G.UFTRDesignandOperationCharacteristics.,2004. [14] Vichaidid,T.,Soodprasert,T.,andVerapaspong,T.CalibrationofHPGeGamma-RayPlanarDetectorSystemforRadioactivityStandards.NaturalSci-ence41(2007):198. [15] White,J.E.,Ingersoll,D.T.,Slater,C.O.,andRoussin,R.W.BUGLE-96:ArevisedmultigroupcrosssectionlibraryforLWRapplicationsbasedonENDF/B-VIrelease3.,1996. [16] Wolber,G.,Hoever,K.,Krauss,O.,andMaier,W.Anewfast-neutronsourceforradiobiologicalresearch.PhysicsinMedicineandBiology42(1997):725. 136

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BIOGRAPHICALSKETCH RomelFrancaborninRiodeJaneiroandlivesinFlorida.HewasintheNavalAcademyforfewyearstobecomeanavyofcer.HehadtheopportunitytobetwiceMathematicalOlympicChampioninthestateofFloridaandbeacceptedtotheCornelUniversityinNewYork-IthacatoworkintheresearchareaofmathematicalmodelingofdiseasesintheMathematicalandTheoreticalBiologyInstitute(MTBI).ThenpursingadegreeinelectricalengineeringatUniversityofFloridadidworkatComputationalNeurologicalElectricalEngineeringLab(CNEL)buildingelectronicscircuits,andworkingwithMATLABsimulationsforthedynamicalanalysisoftheolfactorybrain.AmathematicalmodelcreatedatBerkeleyUniversity.Oncenishedtheelectricalengineeringdegree,hejoinedtheNuclearEngineeringDepartmenttobecomeanuclearengineerintheareaofReactorPhysics,andatthesametimeworkingwithsearchengineoptimization(SEO). 137