CHARGEDPIONEMISSIONFROM 112 SN+ 124 SNAND 124 SN+ 112 SN REACTIONSWITHTHES ˇ RITTIMEPROJECTIONCHAMBER By JonathanElijahBarney ADISSERTATION Submittedto MichiganStateUniversity inpartialful˝llmentoftherequirements forthedegreeof PhysicsDoctorofPhilosophy 2019 ABSTRACT CHARGEDPIONEMISSIONFROM 112 SN+ 124 SNAND 124 SN+ 112 SNREACTIONS WITHTHES ˇ RITTIMEPROJECTIONCHAMBER By JonathanElijahBarney Heavyioncollisionsprovideaprobeofnuclearmatterinextremeconditions.Aparticular areaofinterestisthedensitydependenceofthesymmetryenergytermofthenuclearequation ofstate.Thesymmetryenergytermdescribesthedi˙erenceinbindingenergybetween pureneutronmatterandsymmetricnuclearmatter,whichhasanequalnumberofprotons andneutrons.Thedensitydependenceofthesymmetryenergya˙ectsthestructureof neutronstars,whichreachdensitiesfarexceedingwhatcanbeobservedinthelaboratory. Theemissionofchargedpionsfromheavyioncollisionsisexpectedtobesensitivetothe symmetryenergyatdensitieswhicharetypicallynototherwiseobservedinthelaboratory. Anexperimentalcampaigntomeasurechargedpionproductionwasperformedwiththe newS ˇ RITTimeProjectionChamber,usedintheSAMURAIspectrometeratRIKEN.The campaignincludedfoursecondarybeams,producedfromtwoprimarybeams.Thiswork focusesonthemeasurementofpionemissionfrom 124 Sn+ 112 Snand 112 Sn+ 124 Snsystems, probingasinglepointofasymmetryattwocenterofmassenergypoints.Thisworkserves tovalidateanalysismethods,andtoprovidecomparisonsbetweenthetwoexperiments ThedevelopmentoftheS ˇ RITTimeProjectionChamberisdiscussedindetail,from designconsiderationstoconstructionmethods.Upgradesperformedaftertheexperimental campaignarealsodescribed.Theentireexperimentalsetupisdescribed,withposition measurementsdiscussedandtabulated. TheanalysisofbeamdatafromtheBigRIPSfragmentseparatorisdescribedindetail, providingthebeamPID,momentum,andangleontarget.Theabsolutecrosssectionis determinedandabasic˝lterofimpactparameterisimplemented. Wedeterminethepionspectrafor 124 Sn+ 112 Snand 112 Sn+ 124 Snsystems,comparing themtoinformtherangeofpionkineticenergywhichareconsistentlyreconstructedfor bothsystems.Thisinformsthestudyofmoreasymmetricsystems,wherethepionratiois expectedtodi˙er. Dedicatedinlovingmemoryof: TimothyWhitneyBarney(1959-2016) NicholasAlexanderRoosa(1989-2012) iv ACKNOWLEDGMENTS Thisbodyofworkhasbeenmadepossiblebecauseofmanypeople,whosee˙ortsIwish toacknowledge.ThisworkbeganformeinNovember2010,whenKimCrosslansuggested thatIshouldjointheresearchgroupofProfessorBillLynch. ProfessorBillLynchhasbeenanexcellentadvisor,notonlybecauseofhisvastknowledge andexperience,butthepatientapproachhehashadwhilementoringme.FromBill,I've learnedthatsometimesthemostimportantquestionsarethemostsimple.NeitherBillnor IcouldhavepredictedallthechallengesthatIencounteredduringmytimeingraduate school,butBillhasalwayslistenedandunderstoodwhenIwasoperatingatlessthanfull capacity. ProfessorManYeeBettyTsanghasalsobeencloselyinvolvedwithmyadvisingandwork. I'mverygratefultoBettyforherexperienceinplanning,recordkeeping,andfacilitating communicationwithinacollaboration.Manyofthepositiveexperiencesandopportunities IhadingraduateschoolwereduetotherecommendationorhelpofBetty. Iwouldliketothanktherestofmyguidancecommittee:PawelDanielewicz,Edward Brown,andStuartTessmer.Thankyouforyourtime,expertise,thoughtfulcomments,and forlookingoutformybestinterests. IthasbeenmypleasuretoknowandworkwithJustinEsteefortheentiretyofmytime atMSU.Wehavesharedfailureandsuccess,wehavearguedandagreed,butinallcaseshe hasimprovedthequalityofmytimehere.Heisastalwartresearcher,andaloyalfriend. JuanManfredimadegraduateschoolmoreenjoyable,andwasagoodtravelcompanion. Also,Juan,youarewelcomeforthecat.Thankyoufortakingsuchgoodcareofhim.One ofthegreateststrengthsoftheHiRAgroupishowmuchhelpwegiveeachother:Iam v gratefultoalltheHiRAstudentsandpostdocsthatIhavehadthepleasuretoknowand workwith,thankyouforyourhelpinmyprojects,andforteachingmewhileIhelpedin yourendeavors. Iwouldliketothankmyfriendsandfamilyforsupportingmeonthisjourney.I'mtruly blessedtohavemysiblings:Deborah,Daniel,Elizabeth,Hannah,Mary,andSarah.Thanks toKoreyHurniforalwayshavinganopenear,andJonathanMayersformotivation.Thanks toTommyLeeforteachingmeit'salrighttomakemistakesontheway. ManyindividualshavejoinedtheS ˇ RITcollaboration,butfromthebeginning,thelead- ershipandvisionofWilliamG.Lynch(MSU),ManYeeBettyTsang(MSU),TetsuyaMu- rakami(KyotoUniversity),SherryYennello(TAMU),andTadaakiIsobe(RIKEN)enabled theconstructionoftheS ˇ RITTimeProjectionChamberandthesuccessfulexperimental campaigninwhichitwasused.AlanMcIntosh(TAMU)andRebeccaShane(MSU)not onlymadethedetectordesignandconstructionpossible,theymadeithappenasPostdocs: throughcarefulplanning,longdays,andweeklyinternationalconferencecalls.JustinEstee (MSU)andSuwatTangwancharoen(MSU,KMUTT)sharedresponsibilitieswithmyselffor designingandconstructingtheS ˇ RITTPC,andwewerejoinedfortheassemblybyWilliam Powell(UniversityofLiverpool),whoalsosuggestedthenamefortheS ˇ RITTPC.Ren- shengWang(THU,MSU)joinedforthetestingoftheTPC,producingthe˝rstobservation ofcosmicsintheTPC.Wewereassistedbymanyundergraduatestudents,whosee˙orts wereinvaluable.Inparticular,CorinneAndersonandHananielSetiawanwereintegralfor theTPCproject. Wehadagreatdealofhelpfrommanysta˙membersattheMSU.Inparticular,Iwishto thankJohnYurkon,JayPline,JohnPuro,JohnSantana,SusanLeCureux,RalphWitgen, BrianDrewyor,BarbaraPollockandBenShuartfortheirhelpandcontributionstothe vi project.TomPalazzolo,TomHudson,JimMuns,andRobBennettintheMSUDepartment ofPhysicsandAstronomymachineshophelpedwithmanydesignimprovements,andtaught meagreatdealaboutmachining.JayneTrueandBethanyHannonhelpedimmenselywith organizingallthetravelrequiredduringthisproject,thankyou! MizukiKurata-Nishimura(RIKEN)coordinatede˙ortsfromthearrivaloftheTPCat RIKENthroughthesuccessfulexperimentalcampaign,andwasadrivingforcebehindthe analysisoftheexperimentaldata.Thesoftwareusedforthedataanalysis(S ˇ RITROOT) wasdevelopedbyGenieJhang(KoreaUniversity,MSU),JungWooLee(KoreaUniversity) andGiordanoCerizza(MSU).MasanoriKaneko(KyotoUniversity)wasthegraduatestudent responsibleforthedevelopmentoftheMultiplicityTriggerArrayusedwiththeTPC,and hasbeenamajordrivingforceoftheanalysise˙orts.Jerzy−ukasik(INP),PiotrPawªowski (INP),KrzysztofPelczar(JU),andPaweªLasko(JU,INP)developedtheKATANAtrigger andvetoarrayusedwiththeTPC,aswellasthetriggerboxusedduringtheexperiment. YanZhang(fmr.THU)andZhigangXiao(THU)designedandproducedtheActiveVeto ArrayusedwiththeTPC.ClementineSantamaria(MSU,LBNL)joinedasaPostdocand helpedrunthecommissioningandexperiments,afterwardsdoingagreatdealofthebeam analysis.ShealsotaughtmehowtouseANAROOTandperformthebeamanalysis. IwouldliketoexpressmyappreciationtoHideakiOtsu(RIKEN),projectmanager fortheSAMURAIspectrometer,forhelpingusbringtheS ˇ RITandSAMURAItogether successfully.IalsoexpressmygratitudetotheBigRIPSteamforprovidingtherareisotope beams.IalsoamgratefultoHiroyoshiSakurai(RIKEN)forhostingmeasastudenttrainee fortheEAPSIsummerprogram.TheRIBFsecretaries,YuNayaandAsakoTakahashi helpedsomuchforallthepaperworkandtrainingnecessaryforallourvisitstoRIKEN. TheTPCdataanalysisrequiredagreatdealofwork,especiallyfromGenieJhang,Jung- vii WooLee,GiordanoCerizza,MizukiKurata-Nishimura,TadaakiIsobe,MasanoriKaneko, ChunYuenTommyTsang(MSU),RenshengWang,andJustinEstee.Theprocessinvolved developingphysicsanalysis,inparalleltestingandimprovingthereconstructionsoftware. Thisrequiredexcellentcommunicationbetweengroupmembers,andalotofhardwork. Below,IlistnamesofindividualswhohavecontributedtotheS ˇ RITproject.Thislist cannotbeentirelyinclusive,soIexpressmygratitudetoeveryonewhohashelpedalongthe way. MichiganStateUniversity(MSU),USA ‹ WilliamG.Lynch(Co-PIandSpokesperson) ‹ ManyeeBettyTsang(PIandSpokesperson) ‹ RebeccaShane(Postdoc,20112014) ‹ GiordanoCerizza(Postdoc,20152017) ‹ GenieJhang(Postdoc,2016) ‹ RenshengWang(VisitingScholar) ‹ JonathanBarney(Undergraduatestudent,20112013,Graduatestudent,2013 2019) ‹ JustinEstee(Undergraduatestudent,20112014,Graduatestudent,2014) ‹ SuwatTangwancharoen(Graduatestudent,20112016) ‹ ChunYuenTommyTsang(Graduatestudent,2016) ‹ ZbigniewChajecki(Postdoc) viii ‹ ClementineSantamaria(Postdoc,20152017) ‹ JohnYurkon(Sta˙) KyotoUniversity,Japan ‹ TetsuyaMurakami(JapanesePIandSpokesperson) ‹ MasanoriKaneko(Graduatestudent2014) RIBF,RIKEN,Japan ‹ HidetadaBaba(Sta˙) ‹ TadaakiIsobe(Spokesperson) ‹ MizukiKurata-Nishimura(Sta˙) ‹ HiroyoshiSakurai(Sta˙) ‹ DaisukiSuzuki(Sta˙) TexasA&MUniversity(TAMU),USA ‹ SherryJ.Yennello(Co-PI) ‹ BobOlsen(Sta˙) ‹ AlanB.McIntosh(Postdoc20102013,AssistantResearchScientist) KoreaUniversity,SouthKorea ‹ ByungsikHong(Faculty) ‹ GenieJhang(Graduatestudent,20132016) ix ‹ JungWooLee(Graduatestudent,2014) InstituteofNuclearPhysics(INP),Poland ‹ Jerzy−ukasik(Sta˙) ‹ PiotrPawªowski(Sta˙) ‹ PaweªLasko(GraduateStudent) JagiellonianUniversity(JU),Poland ‹ KrzysztofPelczar(Sta˙) TsinghuaUniversity(THU),China ‹ ZhigangXiao(Faculty) ‹ YanZhang(Ph.D.2017) Additionally,IwishtothankmembersoftheNeuLANDCollaboration: TechnischeUniversitätDarmstadt,Germany ‹ HeikoScheit(SeniorScientist) ‹ LeylaAtar(Postdoc) ‹ DominicRossi(Postdoc) ‹ HansTörnquist(Postdoc) ‹ AndreaHorvat(DoctoralResearcher) GSIHelmholtzCentreforHeavyIonResearch,Germany x ‹ ThomasAumann(Faculty) ‹ KonstanzeBoretzky(SeniorScientist) ‹ YvonneLeifels(SeniorScientist) RužerBo²kovi¢Institute,Croatia ‹ IgorGa²pari¢(ResearchAssociate) ComputingresourcesforanalysisinthisworkwereprovidedbytheHOKUSAI-GreatWave atRIKEN,theHighPerformanceComputingCenter(HPCC)atMSU,andtheNSCLcom- putingcluster. Finally,Iwanttothankthefundingsourceswhichhavemadethispossible:thiswork wassupportedbytheU.S.DOEunderGrantNos.DE-SC0014530,DE-NA0002923,USNSF GrantNo.PHY-1565546,andtheJapaneseMEXTKAKENHIgrantNo.24105004.The NSFEAPSIfellowshipsupportedmytravelandresearchatRIKENforthesummerof2014 (NSFaward1414979). xi TABLEOFCONTENTS LISTOFTABLES .................................... xv LISTOFFIGURES ................................... xvii Chapter1Introduction ............................... 1 1.1DensityDependenceoftheSymmetryEnergyTerm..............5 1.2PionProductionandtheSymmetryEnergy..................8 1.3MeasuringPionMultiplicities,andtheProposedExperiment.........10 1.4OrganizationofDissertation...........................12 Chapter2DevelopmentoftheS ˇ RITTimeProjectionChamber ..... 13 2.1GeneralDesignConsiderations..........................15 2.2DesignOverview.................................16 2.3GETElectronics.................................17 2.4TopPlate.....................................21 2.4.1MotionChassisandTableCon˝guration................22 2.5PadPlane.....................................22 2.5.1UnitCell..................................25 2.5.2LayerCrossSection............................26 2.5.3PadPlaneSignalMapping........................27 2.6PadPlaneGluing.................................28 2.6.1PadPlaneFlatnessMeasurement....................31 2.7WirePlanes....................................32 2.7.1AnodePlane...............................34 2.7.2GroundPlane...............................36 2.7.3GatingGridPlane............................38 2.7.4GatingGridTransmissionLine.....................42 2.7.5WirePlaneInstallation..........................43 2.7.6WirePlaneRepair............................46 2.8FieldCage.....................................47 2.8.1CathodePlateandVoltageStepDown.................51 2.8.2FieldCageWindows...........................53 2.8.3FieldCageGas..............................56 2.9TargetLadderandMotion............................57 2.10Enclosure.....................................59 2.11Shipping......................................61 2.12DisassemblyandReassemblyofTPC......................67 2.13TPCUpgrades..................................71 xii Chapter3ExperimentalSetupandTriggerSelection ............ 76 3.1S ˇ RITTPCinsidetheSAMURAISpectrometer................76 3.2TPCalignmentandMeasurement........................77 3.3TriggerDetectors.................................81 3.3.1ScintillatingBeamTrigger........................82 3.3.2KyotoMultiplicityArray.........................82 3.3.3KrakowKATANAArray.........................84 3.3.4ActiveVetoArray.............................86 3.4TriggerSelection.................................87 3.4.1FastTriggerandFastClear.......................88 3.4.2GGDLogic................................89 3.4.3BusyCircuit................................91 3.4.4KATANATriggerBox..........................91 3.4.5TriggerforDAQ.............................92 3.4.6Di˙erencesBetweenPrimaryBeamTriggers..............93 3.5OtherAncillaryDetectors............................95 3.5.1BeamDriftChambers..........................95 3.5.2NeuLANDArray.............................95 3.6DAQ........................................96 Chapter4DataAnalysis .............................. 98 4.1RIBFFacilityandProductionofPrimaryBeam................98 4.2BeamAnalysis..................................100 4.2.1AnalysisofPPACsignals.........................104 4.2.1.1Positiondeterminationwithpartialinformation.......108 4.2.1.2BeamRateCalculationwithPPAC..............111 4.2.2AnalysisofBeamTimeofFlight....................112 4.2.3DeterminationofChargewiththeIonChamber............114 4.2.4BeamPileupandBackground......................119 4.2.5ReconstructedBeamPIDplots.....................122 4.2.6BeamPurity................................123 4.2.7ReconstructionE˚ciency.........................126 4.2.8BeamDriftChambersandProjectiontoTarget............127 4.3AbsoluteCrossSection..............................133 4.3.1MeasurementofReactedSn.......................134 4.3.2MeasurementofIncidentSn.......................134 4.3.3MeasuredCrossSection.........................137 4.4ImpactParameterSelection...........................138 4.5TPCAnalysis...................................142 4.5.1TrackValidation.............................146 4.5.2DetectionE˚ciencyfromEmbeddingStudies.............148 4.6CalibrationwithCocktailBeam.........................149 4.6.1CocktailBeamSettings..........................149 4.6.2RigiditywithinTPC...........................150 4.7Mixed 124 Sn-likebeam..............................152 xiii 4.8 112 Sn+ 124 Snand 124* Sn+ 112 Snpionproduction...............153 4.8.1PID˝ttingandpionselection......................154 4.8.2BackgroundEstimation..........................155 4.8.3PionMultiplicities............................157 4.8.4ComparisonofPionSpectrafor 124 Sn-likebeamsand 124 Snbeam..161 4.8.5ErrorinPionSpectra...........................162 4.8.6PionRatios................................163 4.8.7Examinationoflesscentralcollisions..................168 4.8.8PreliminaryComparisontoTransportCode..............170 Chapter5SummaryandOutlook ......................... 173 APPENDIX ........................................ 176 BIBLIOGRAPHY .................................... 184 xiv LISTOFTABLES Table1.1:BeamsusedintheS ˇ RITTPCexperimentalcampaign..........11 Table2.1:AGETchanneltoPadsignalmapping.Theconventionforpadnumber isdetailedinFigure2.10.FourFixedPatternNoise(FPN)channelsare presentperAGETcard,buttheyarenotconnectedtothepadplane. Channel35isNotConnected(NC)toanypad................29 Table2.2:Wireplaneproperties..............................33 Table4.1:BeamsusedintheS ˇ RITTPCexperimentalcampaign..........99 Table4.2:ResultingquantitiesforPPACreconstructionwithout(method1)andwith (method2)PPACpositionrecovery.....................111 Table4.3:Beampuritiesandtriggeredpuritiesforthesecondarybeams.......126 Table4.4:Eventreconstructione˚ciencyforeachbeam, 108 Snand 112 Snbothhad twodistinctreconstructione˚ciencies,describedinthetext........127 Table4.5:Average x and y o˙setsbetweenTPCvertexandBDCprojectedposition, foreachbeam.Theseo˙setsalsore˛ectthefactthattheBDCandTPC verticesarede˝nedindi˙erentcoordinateframes..............131 Table4.6:TotalabsorptioncrosssectionsfortheSnbeamsusedintheS ˇ RITexper- iment......................................136 Table4.7:Averageabsolutecrosssection, ˙ ,withstandarddeviationofthecross sectionmeasuredforthedataruns.......................137 Table4.8:Averageabsolutecrosssection, ˙ ,withstandarddeviationofthecross sectionmeasuredforthedataruns.......................142 Table4.9:Comparisonofmeasuredtargetpositionandreconstructedreactionvertex. DimensionsareintheTPCframe.......................146 Table4.10:Magneticrigidityforeachparticleincocktailbeams............150 Table4.11:Beamisotopesincludedformixed 124* Snbeam...............152 Table4.12:E˚ciencycorrected(E˙.Corr.)pionyieldsforthiswork..........159 xv Table4.13:Rawpionyieldsforeventswithimpactparameter5fm-7fm.......168 xvi LISTOFFIGURES Figure1.1:Thechartofnuclides,withprotonnumber( Z )ontheY-axis,andneu- tronnumber( N )ontheX-axis.Stableisotopesareshowninblack,and unstableisotopeswithcolorcorrespondingtolifetime.Figuremodi˝ed from[1].Forinterpretationofthereferencestocolorinthisandallother ˝gures,thereaderisreferredtotheelectronicversionofthisthesis...2 Figure1.2:Parameterizationsfordensitydependenceofsymmetryenergy,forthree valuesof .Figurefrom[2]..........................6 Figure1.3:Cartoongraphicshowingimpactparameter b ,andclassi˝cationofspec- tatorandparticipantnucleons........................7 Figure1.4:Maximumdensityachievedincollisionasfunctionoftime,simulatedfor twovaluesof .................................8 Figure2.1:OperationprincipleoftheS ˇ RITTPC,modi˝edfrom[3].........14 Figure2.2:S ˇ RITexplodedview.............................17 Figure2.3:SchematicofAGETfunction,from[4]....................18 Figure2.4:GETarchitectureemployedforS ˇ RITTPC,from[5]...........19 Figure2.5:AdapterandZAPboards...........................20 Figure2.6:Schematicviewoftopplateandribs(a),andphotographofTPCwith GETelectronicspartiallyinstalled(b)....................21 Figure2.7:Thetopplateandmotionchassisin(a)doorwaycon˝gurationand(b) tablecon˝guration...............................22 Figure2.8:Relativeerrorofmomentummeasurementfordi˙erentpadsizes.....24 Figure2.9:Padplanesymmetry,withhatchedregionsrepresentingthegroundstrip, andarrowsrepresentingthesymmetryofthepadlayout.Nottoscale..25 Figure2.10:Circuitschematicofthepadplaneunitcell.................26 Figure2.11:Padplaneoveralldimensionsinmm,withthepro˝leofaunitcell(cross hatched),andtheareaservicedbyoneAsAdboard(hatched).......27 xvii Figure2.12:Crosssectionalviewofthepadplane.ThegreenhatchedlayersareG-10, withthethicknessindicatedinmil......................28 Figure2.13:Gluingdoublegasketstotopplate(a)andapplicationofAralditeepoxy forpadplaneinstallation(b).........................30 Figure2.14:Vacuumtableinuseforpadplaneinstallation...............31 Figure2.15:DaveSanderson(NSCLsta˙)measuringtopplateandpadplane˛atness (a),withtopographicalmapofmeasured˛atness(b)............32 Figure2.16:Wireplanesmountedonthetopplate....................33 Figure2.17:Wireplanefeedthroughmapping......................34 Figure2.18:Anodeplanecircuitandtermination.Thiscircuitisrepeatedforeachof the14sections.................................35 Figure2.19:Anodeplanecircuitboard.Dimensionsinmm...............36 Figure2.20:Groundplanecircuit.Dashedlinesindicatethepatternrepeatsoverthe entireplane..................................37 Figure2.21:Groundplanecircuitboard.Dimensionsinmm...............38 Figure2.22:Gatinggridoperationprinciple[6]......................39 Figure2.23:Gar˝eldsimulationofgatinggrid[6].Theleftpanelshowstheopened gatinggrid,allowingelectronstoreachandterminateontheanodewires. Therightpanelshowstheclosedgatinggrid,whichcauseselectronsto terminateonthe V H wires..........................40 Figure2.24:Gatinggridclosingwithmagnetic˝eld[6]..................41 Figure2.25:Gatinggridcircuitforasinglesectionofthewireplane..........42 Figure2.26:Gatinggridplanecircuitboard.Dimensionsinmm.............42 Figure2.27:Crosssectionofgatinggridtransmissionline.Dimensionsininches....43 Figure2.28:Anodecircuitboardsattachedtospacerboards...............44 Figure2.29:Windingmachineforwireplanes.......................45 Figure2.30:Gluingtheanodewirestotheanodebars..................46 xviii Figure2.31:Schematicofwireplaneremoval˝xtureonupside-downtopplate.....47 Figure2.32:Dimensionsof˝eldcageinmm,withdetailsAandBhighlightingthetop perimeter....................................48 Figure2.33:Fieldcagecircuitlayout.Modi˝edfrom[7].................50 Figure2.34:E˙ectivecircuitdiagramfor˝eldcage....................51 Figure2.35:JustinEstee(GS)appliesepoxytothecathodeplate............52 Figure2.36:Cornerofvoltagestepdown.Thepaintedconductivesurfaceisvisible insidethecopperrings.............................53 Figure2.37:Explodedviewof˝eldcagewindowsandframes..............54 Figure2.38:Fieldcageentrancewindow.Assembledwindowshownin(a),inserted windowshownfrom(b)insideand(c)outsidethe˝eldcage........55 Figure2.39:Fieldcageexitwindow.Silverepoxyconnectingwindowandframestrips shownin(a),copper˝ngersandPCforelectricalconnectionofwindow framein(b),andinstalledwindowin(c)..................55 Figure2.40:TargetLadder.................................58 Figure2.41:TargetMotionCarriage............................59 Figure2.42:TPCenclosurewithtopplateremoved...................60 Figure2.43:TPCenclosuredesign,withouttopplate...................61 Figure2.44:Thecratebaseandplatform.Abedofphasechangematerialissecured totheplatformwithsteelstraps.......................62 Figure2.45:TheTPCinstalledonthecrateplatform.Thebedofphasechangema- terialisvisiblein(a),andthesidepro˝leshownin(b)showsoneofthe HEPAwindow˝lters..............................63 Figure2.46:TheTPCinsidethecratewiththecratewallsinstalled..........64 Figure2.47:Weighingthepackedcrate.Inadditiontotheoverallweight,thecrate wasmeasuredfromeachend(a)allowingustodetermineandmarkthe centerofgravity(markedwithorangepaintin(b)).............65 xix Figure2.48:StrappingthecratetotheforkliftattheNSCL.Twoliftingstraps(yellow) aresecuredtotheforkliftwithachain,visibleonthetopofthecrate..66 Figure2.49:MovingtheTPCcrateatRIKEN.(a)removingthecratefromtheside- loadedtruckwithaforklift,and(b)loweringthecratetotheB2Fareaof RIBFusingacrane..............................66 Figure2.50:Liftingthetopplateand˝eldcageoutoftheenclosure..........68 Figure2.51:Rotatingthetopplateand˝eldcage(a),andmovingthetopplateand ˝eldcageindoorwaycon˝guration(b)....................69 Figure2.52:Removingthe˝eldcagefromthetopplate(b),androtatingthetopplate without˝eldcage(b).............................69 Figure2.53:Alternativeprocedureforremoving˝eldcagewithoutrotation:liftingtop plate(a),stabilizedtopplate(b),purpose-builtcartfor˝eldcageremoval (c),slidingthe˝eldcageawayfromtopplate(d)..............70 Figure2.54:Illustrationofelectronleakagepriortorepair................71 Figure2.55:Upgradetopreventleakagearoundgatinggrid...............72 Figure2.56:Theinstalled˝eldcageupgrade(April2018)................73 Figure2.57:Theinstalledtargetmotionnut,whichaccommodatesawarpedleadscrew (April2018)..................................73 Figure2.58:Floatingleadnutdesigntoaccommodatewarpingofleadscrew......74 Figure2.59:Motionlinkingsystem(a)designand(b)installed.............75 Figure3.1:Schematicviewofexperimentallayout....................77 Figure3.2:Laseralignmentoftargetheight.......................78 Figure3.3:Flashphotographhighlightingretrore˛ectivephotogrammetrymarkers.79 Figure3.4:PhotographoftheTPCandancillarydetectorsinstalledintheSAMURAI spectrometer..................................81 Figure3.5:SBTarray...................................82 Figure3.6:DesigndrawingoftheKyotoMultiplicityArraymountedontheTPC..83 xx Figure3.7:DesigndrawingoftheKATANAarray.Thickscintillatorsareshownin blueandvetoscintillatorsareshowninpurple.Theleftsideshowsthe entirearray,andtherightsideshowsthearraywithvetopaddlesisolated85 Figure3.8:PhotographoftheActiveVetoArray.....................86 Figure3.9:BreakoutviewoftheTPCwithActiveVetoArrayinstalled.......87 Figure3.10:Fasttriggerlogic...............................89 Figure3.11:Fastclearlogic................................89 Figure3.12:GatingGridDriverLogic..........................90 Figure3.13:KATANATriggerBoxarchitecture.....................92 Figure3.14:KATANATriggerBoxlogic.........................92 Figure3.15:LogicforMasterTrigger,orDAQtrigger,duringthe 124 Xeprimarybeam experiment..................................93 Figure3.16:LogicforMasterTrigger,orDAQtrigger,duringthe 238 Uprimarybeam experiment..................................93 Figure3.17:ThepartialNeuLANDarrayisshownin(a),andthechargedparticleveto arrayborrowedfromNEBULAisshownin(b)...............96 Figure4.1:Mode1oftheRIBFheavy-ionacceleratorsystem[8]...........99 Figure4.2:RIBFfacilityatRIKENcirca2012.Althoughthis˝gurewillnotrepresent thelatestupgrades,itwellrepresentstheBigRIPSandSAMURAIbeam lineduringtheS ˇ RITexperimentin2016.Figurefrom[9].........100 Figure4.3:Simpli˝edschematicofBigRIPS.DipolemagnetsarelabeledD1-D6.A singleenergydegraderwasusedbetweenD1andD2.FocalplanesF3,F5, andF7areshownwithbeamlinedetectors.Descriptionsofthesedetectors aregiveninthetext..............................101 Figure4.4:StructuralschematicofBigRIPS240 150mm 2 PPAC,fromReference[10] 104 Figure4.5:Anexample T sum spectra.Thedistributionis˝ttedwithaGaussian function,showninred.............................107 xxi Figure4.6:CorrelationplotforPPACsignalsfortheF7-1B(left)andF7-2B(right) PPACs.SignalissuesareevidentfortheF7-2BPPAC...........109 Figure4.7:BeamPIDfromreconstructionwithout(a)andwith(b)positionrecovery. RefertoTable4.2fornumericalcomparisonofthesetwoplots.......110 Figure4.8:Theuncalibrated(a)andcalibrated(b)time-of-˛ightspectrafromrun 2894.......................................112 Figure4.9:RelationshipbetweenTOFo˙setusedandreconstructed A=Q ratioof 132 Sn......................................113 Figure4.10:PIDreconstructedwithout(left)andwith(right)plasticslewingcorrec- tion.Resolutionin A=Q isvisiblyimprovedbyusingtheslewingcorrection.114 Figure4.11:MUSICside-viewschematic,fromReference[11].............115 Figure4.12:GeometricalmeanofADCresponsecomparedtosimulatedenergyloss.116 Figure4.13:Ionchambersignalandsimulatedenergylossbefore(leftpanel)andafter (rightpanel)pedestalsubtraction......................117 Figure4.14: 112 SnbeamPIDplotforrun2580,using3ADCchannels(left),andall6 ADCchannels(right).............................118 Figure4.15:Ionchambersignalfor 124 Snbeam.....................119 Figure4.16:Multi-hitTDCspectra,fromaPPACattheF7focalplane,for 132 Snbeam120 Figure4.17:(Left)Ionchamberresponseplottedagainstpile-uptimeaftermainpar- ticle,for 132 Snbeam.(Right)ResultingPIDspectrumfortheseevents. Bothplotsarerestrictedtoeventswithtimedi˙erencegreaterthan3 µ s.121 Figure4.18:Fromtoptobottom,lefttoright,beamPIDplotsfor 108 Sn(TL), 112 Sn (TR), 124 Sn(BL),and 132 Sn(BR)......................122 Figure4.19:Fromtoptobottom,lefttoright,wideperspectivebeamPIDplotsshow- inglighterbeamparticlesfor 108 Sn(TL), 112 Sn(TR), 124 Sn(BL),and 132 Sn(BR)...................................123 Figure4.20:BeamPIDfromlow-intensity 124 Snruns,usedtodeterminemaincon- taminants...................................124 Figure4.21:BeamPIDfor 124 Sn,withfoundisotopeshighlightedincolor......125 xxii Figure4.22:Beampurityfor 132 Snbyrun........................126 Figure4.23:Yaw( )andpitch( p )anglesusedfortheBDCprojection.......128 Figure4.24:Di˙erencesbetweenBDCprojectionandTPCvertexfor x (left)and y (right).....................................130 Figure4.25:CorrelationsbetweenBDCprojectionandTPCvertexfor x (left)and y (right)......................................130 Figure4.26:Foreachbeam,typical x o˙set witherrorbarsof 1standarddeviation.131 Figure4.27:Vertex Z probabilitydistributionfor 132 Sndata.A˝tonthetargetpeak isshowninred.................................135 Figure4.28:Calculatedcrosssectionforeachsystem,organizedbytotalsystemmass138 Figure4.29:Chargedparticlemultiplicitydistributionforthefourbeamsystems...140 Figure4.30:Relationshipbetween b and N C forthefourbeamsystems,witherror shownbyshadedregions...........................141 Figure4.31:Analysis˛owfortheS ˇ RITROOTsoftwarepackage,showingbranches forexperimentaldataaswellassimulation.................143 Figure4.32:ExampleADCspectraforapad.SignalheightisinADCchannels,and eachtimebucketcorrespondsto40ns.Figurefrom[12]..........144 Figure4.33:Normalizeddistributionof z positionofreconstructedvertex,forallsystems.146 Figure4.34:AtypicaleventintheTPCviewedfrom(toppanel)aboveand(bottom panel)theside.Thehighdensityregionoutlinedinredisexcludedfrom dataanalysis..................................147 Figure4.35:ThePIDfor 124 Snevents,(left)withoutcuts,and(right)withcuts....148 Figure4.36:CocktailPIDusing(left)propergeometryand(right)shiftedmagnetic˝eld151 Figure4.37: ^ b spectrafor 124* Snmixedbeam......................153 Figure4.38:Comparisonofenergylosstotypicalenergylossfor(top) 124* Snsystem and(bottom) 112 Snsystem.Y-projectionsareshowntotheleftfor ˇ , andtotherightfor ˇ + ............................155 xxiii Figure4.39:Projectionof˛attenedPIDbetween380and400MeV/c.The ˇ + (green) andproton(blue)peaksare˝tsimultaneously,withthetotal˝t(red)and separatecontributionsshown........................156 Figure4.40:Averagebackground/signalratiosfor ˇ + ,asafunctionofmomentum. Thee˙ectsofpositronandprotoncontaminationareevident.......158 Figure4.41:PionkineticenergyspectrainCOMframe. ˇ aredrawnontheleftside, ˇ + ontheright.Thetoppanelsareforthe 124* Snsystem,whilethe bottompanelsareforthe 112 Snsystem...................159 Figure4.42:Relativepionproductionforthe 124* Snsystemandthe 112 Snsystem,for ˇ (left)and ˇ + (right)...........................160 Figure4.43: p t - y 0 distributions,withrapiditynormalizedtobeamrapidity. ˇ are drawnontheleftside, ˇ + ontheright.Thetoppanelsareforthe 124* Sn system,whilethebottompanelsareforthe 112 Snsystem.........161 Figure4.44:PionKE COM spectrafor 124* Snand 124 Snbeams.Thetoppanelis e˚ciencycorrected,andthebottomistherawspectra...........162 Figure4.45:The ˇ =ˇ + spectralratiofor(left)the 124* Snsystemand(right)the 112 Snsystem.................................164 Figure4.46:ThedoubleratioasafunctionofKE COM for 124* Sn+ 112 Snand 112 Sn+ 124 Sn.165 Figure4.47:The ˇ =ˇ + spectralratioasafunctionofrapidity(left)andthedouble ratioasafunctionofrapidity(right).....................166 Figure4.48:The ˇ =ˇ + spectralratio,withtherapidityofthe 112 Snbeamreversed.166 Figure4.49:The ˇ (left)and ˇ + (right) p t - y 0 spectra,withtherapidityofthe 112 Sn beamreversedandaddedtothe 124* Snbeamtoformacompletespectra. Redlinescorrespondtokineticenergiesof50(bottom)and200(top)MeV intheCOMframe...............................167 Figure4.50:The ˇ =ˇ + spectralratioasafunctionofrapidity(left)andthedouble ratioasafunctionofrapidity(right),forlesscentralevents........169 Figure4.51:The ˇ (left)and ˇ + (right) p t - y 0 spectra,withtherapidityofthe 112 Sn beamreversedandaddedtothe 124* Snbeamtoformacompletespectra, forlesscentralevents.Redlinescorrespondtokineticenergiesof50 (bottom)and200(top)MeVintheCOMframe..............169 xxiv Figure4.52:The ˇ =ˇ + spectralratio,withtherapidityofthe 112 Snbeamreversed, forlesscentralevents.............................170 Figure4.53:The ˇ =ˇ + spectralratiofor 124* Sn(left)and 112 Sn(right),compared tosimulationforsoft(blue)andsti˙(red).................171 Figure4.54:Thedoubleratiofor 124* Snand 112 Sn,comparedtosimulationforsoft (blue)andsti˙(red).............................172 xxv Chapter1 Introduction Afundamentallyusefulpropertyofphysicallawsisthattheyareuniversal:thelawsof physicsarethesameonEarthastheyareinthecosmos.Discoveriesmadeinthecosmos increaseourunderstandingofthepalebluedotweoccupy,andmeasurementsinEarth-based laboratoriescanshedlightonthestars.Tolearnmoreabouttheprocesseswhichoccurin stars,weturntonuclearphysics.Nuclearphysicsisthestudyofthenucleusofanatom, thebasicbuildingblockofallmatter.Bystudyingthephysicsofthesetinysystems,we gaininformationabouttheentireuniverse,fromnuclearprocessesonEarthtothenuclear processesoccurringinastrophysicalenvironments. Everyatomconsistsofthreetypesofparticles:protons,neutrons,andelectrons.The protonsandneutronsarelocalizedatthecoreoftheatom,comprisingthenucleusofthe atom.Theelectrons,whichweighalmost2,000timeslessthanaprotonorneutron,forma cloudaroundthenucleuswhichextendsmanytimesbeyondthesizeofthenucleus:typically, anatomhasaradiusabout10,000timeslargerthantheradiusofitsnucleus.Nuclearphysics focusesonstudyingthenucleusofanatom:theprotonsandneutronswhicharebound togetherbythestrongnuclearforce.Thenumberofprotonsis˝xedforagivenchemical element,butthenumberofneutronscanvary,resultingintheexistenceofdi˙erentisotopes ofthesameelement.Oneisotopeofanelementmayberadioactive,whileanotherisstable. Thechartofthenuclides,showninFigure1.1,depictsisotopesasafunctionofproton 1 number(alongtheY-axis)andneutronnumber(alongtheX-axis).Stableisotopesare showninblack,andradioactiveisotopesareshownwithcolorcorrespondingtohalflife. Figure1.1:Thechartofnuclides,withprotonnumber( Z )ontheY-axis,andneutron number( N )ontheX-axis.Stableisotopesareshowninblack,andunstableisotopeswith colorcorrespondingtolifetime.Figuremodi˝edfrom[1].Forinterpretationofthereferences tocolorinthisandallother˝gures,thereaderisreferredtotheelectronicversionofthis thesis. Thestabilityofanucleusdependsonitsbindingenergy BE :theamountofenergy requiredtodissociatethenucleus.Ifwemodelthenucleusasanincompressibledropof nuclearmatter[13],thebindingenergycanbeapproximatedusingtheBethe-Weizsäcker liquiddropmodel,asemi-empiricalformulawhichgivesthebindingenergyasafunctionof thenumberofprotons Z ,neutrons N ,andmass A = N + Z : BE = a V A a S A 2 = 3 a C Z 2 A 1 = 3 a A ( N Z ) 2 A + O : (1.1) The˝rstcoe˚cient a V isthevolumeterm:thenuclearinteractionsbetweennucleiare attractive,bindingthedroptogether.Theenergycontributionfromvolumescaleslinearly with A .Thesurfaceterm a S isacorrectiontothevolumeterm,necessarysincenucleonsat 2 thesurfaceofthedropinteractwithfewerneighborsthanthoseinsidethenucleus,reducing theattractiveinteractionsandthusthebindingenergy.TheCoulombterm a C accounts fortherepulsivee˙ectoftheCoulombforce,scalingwith Z 2 toaccountforprotoncharge, anddividedby A 1 = 3 toaccountfortheradiusofthedrop,providingascaleforthedistance betweenprotons.Theasymmetryterm a A isnecessarytodescribethedecreaseinbinding energythatoccursduetoasymmetryinthenumberofprotonsandneutrons.Baryons inthedropcannotoccupythesamequantumstates,asrequiredbythePauliexclusion principle.However,aneutronandaprotoninanucleuscanoccupythesamespatialand spinstates,astheyhavedi˙erentisospinprojections(+1/2and-1/2,respectively).An imbalanceofnucleontypescausesonenucleontypeinexcesstooccupyhighersingleparticle energylevelsthanthede˝cientnucleontype,resultinginareducedbindingenergythan foranucleuswithsymmetricprotonandneutronnumbers.Additionally,thestrongnuclear forceinteractionsprefersymmetric( N = Z )systems,leadingtoreducedbindingenergyfor asymmetricsystems.Thisenergydi˙erenceismodeledwiththeasymmetryterm a A .Other termssuchaspairing( O )canbeaddedtore˝nethismodel,butforourpurposes,itis su˚cienttoonlydiscussuptotheasymmetryterm. Ifweextendourliquiddroptoamacroscopicnuclearsystem(suchasaneutronstar), wecanconsiderthelimitwhere A !1 .Thesurfacetermbecomesnegligible,andwecan neglectlong-rangeCoulombforces(insystemssuchasaneutronstar,theCoulombforces arescreenedbythepresenceofmobileelectrons),givingbindingenergypernucleon BE A = a V a A 2 ; (1.2) with astheasymmetry: =( N Z ) =A .Forasymmetricsystem, BE=A isdescribedby 3 onlythevolumeterm a V ,whileforpureneutronmatter, BE=A = a V a A .Todescribe astrophysicalsystemsthatexistatarangeofdensities,wemustmovebeyondtheliquid dropmodel,sinceitsmodelingofamacroscopicsystemasanincompressible˛uidatnormal nucleardensityisnotvalid.Forexample,thegravitationalforceofaneutronstarcompresses thenuclearmattertoextremelimitsofmuchhighernucleondensities,requiringanEquation ofState(EoS)todescribepropertiesofnuclearmatteroverarangeofdensities.Anequation ofstaterelatesanimportantpropertyofasystem,suchasitsenergy/nucleon,tostate variables,suchaspressure,temperature,andasymmetry.Forlargenuclearsystems,the asymmetrycanbedescribedintermsoftheneutronandprotondensities, = ˆ n ˆ p ˆ : (1.3) Asastartingpoint,weusetheinsightslearnedfromtheliquiddropmodeltoformanuclear EoS: E ( ˆ; )= E ( ˆ; =0)+ S ( ˆ ) 2 ; (1.4) withseparablecontributionsfromsymmetricmatter( E ( ˆ; =0) )andasymmetricmatter ( S ( ˆ ) 2 ).Theterm S ( ˆ ) isthesymmetryenergy:thedi˙erencebetweentheEoSforpure neutronmatter( =1 )andsymmetricnuclearmatter( =0 ).Fromsuchanequationof state,thepressurecanbecalculated, P ( ˆ )= E ( ˆ ) =V; (1.5) atzerotemperature,fora˝xednumberofparticles.Bymodelingthethermalpropertiesof nuclei,onecanextrapolatetonon-zerotemperatures.Determinationofthepressure-density 4 relationshipisnecessarytomodelthestructureofaneutronstarwherethenuclearmatter isinhydrostaticequilibrium. 1.1DensityDependenceoftheSymmetryEnergyTerm Thenuclearsaturationdensity ˆ 0 isde˝nedtobethedensitywhichminimizesthebinding energypernucleon,andisexperimentallydeterminedas ˆ 0 =0 : 16 fm 1 = 3 .Fordensities atorbelowsaturationdensity,thesymmetryenergycanbedeterminedusinginformation aboutboundnucleiandbystudyingnuclearcollisions.Muchworkhasbeendonetoconstrain thesymmetryenergyaroundthesaturationdensity,butthevalueofsymmetryenergyfor higherdensitiesmustalsobeconstrained.Inparticular,thevalueofthesymmetryenergy attwicesaturationdensity( 2 ˆ 0 )iscrucialfordeterminingthestructureofneutronstars. Thesymmetryenergydensitydependenceisoftenparametrizedbyde˝ningthequantity x ˆ ˆ 0 3 ˆ 0 (1.6) andperformingaTaylorexpansionaroundthesymmetryenergyatsaturationdensity: S ( ˆ )= J + Lx + 1 2 K sym x 2 + 1 6 Q sym x 3 + ::: ,(1.7) with J = S ( ˆ 0 ) ,and L , K sym ,and Q sym theslope,curvature,andthirdderivativeofthesym- metryenergyatsaturationdensity.Thisformcanbeveryusefulforinvestigationsaround saturationdensity,aswellasformakingcomparisonstosymmetricnuclearmatter[14].An 5 alternativeformalismistodescribethebehaviorasapowerlaw,asinReference[2]: S ( ˆ )= S kin ˆ ˆ 0 2 = 3 + S int ˆ ˆ 0 ; (1.8) whichhastheadvantageofusingasingletunableparameter todescribethedensity dependenceofthesymmetryenergy.Theterm S kin ˇ 12 : 3 MeVisthekineticterm,and S int ˇ 20 MeVtheinteractionterm.Figure1.2showsthesymmetryenergydependence usingthisformalismforthreevaluesof .Avalueof =1 wouldindicateanearlylinear dependenceondensity.Withinthiswork,avalueof above1willbereferredtoas andavaluebelow1willbereferredtoas Figure1.2:Parameterizationsfordensitydependenceofsymmetryenergy,forthreevalues of .Figurefrom[2]. Tostudythesymmetryenergyataroundtwicesaturationdensity,weturntoHeavy-Ion Collisions(HIC),whichenableustoproduceshort-lived,high-densityregionsofnuclear matter.ByemployingRare-Isotope(RI)beams,wecanprobesystemswitharangeof asymmetry.Inthepast,HIChavebeensuccessfullyusedtostudythesymmetryenergy, usingprobessuchastheneutron/protonratioemittedfromHIC[15],isospindi˙usion[16], 6 electricdipolepolarizabilityandthe 208 Pbneutronskin[17],andtransverse˛ow[18].The fundamentalchallengethatmustbefacedwhenusingHICtoconstrainthesymmetryenergy athigherdensityistoseparatehighdensityandlowdensitye˙ects. Figure1.3:Cartoongraphicshowingimpactparameter b ,andclassi˝cationofspectatorand participantnucleons. InHIC,therelativecentralityofacollisionhasalargee˙ectonthereactiondynamics. Centralityisdescribedbytheimpactparameter b ,thetransversedistancebetweenthe centersofatargetnucleusandanapproachingbeamnucleus.Themostcentralregion ofthecollisionwillachievethehighestdensity,andmodelsindicatethatthedensitycan reach2 ˆ 0 [19].Nucleonsinthemostcentralregionarereferredtoasparticipantnucleons, andnucleonsoutsidethisregionarereferredtoasspectatornucleons.Figure1.3shows acartoonrepresentationofparticipantandspectatornucleons.Particlesemittedfromthe centralregionofthecollisioncanprovideinformationaboutthesymmetryenergyat 2 ˆ 0 ,but particleswillalsobeproducedfromlowerdensityregions.Tospeci˝callystudysymmetry energye˙ects,itisnecessarytoselectaprobewhichwillpreferablybeproducedinthe high-densityregion.Onesuchprobeispions[20,21,22],whicharepredominatelyproduced intheearlystagesofthereaction,whenthehighdensitymatterisproduced(asshownin Figure1.4),whichshowsmaximumdensityachievedinapBUUsimulation(discussedin Section1.3)ofa 124 Sn+ 112 Snreaction,withacentralcollision( b =3 fm). 7 Figure1.4:Maximumdensityachievedincollisionasfunctionoftime,simulatedfortwo valuesof . 1.2PionProductionandtheSymmetryEnergy Withinaheavyioncollision,pionscanbeproducedthroughnucleon-nucleonscatterings,or throughthedecayof resonances.Ifourbeamenergyisbeloworslightlyabovethepion productionthreshold( ˘ 300 MeV/u),mostpionproductionwillbeduetothedecayof resonances[19].Therearefourdistinct resonances: ++ , + , 0 ,and .These resonancesareproducedbynucleon-nucleoninteractionsinthehighdensityregionofthe HIC,wherethecollectivemotionofnucleiprovidestheenergyrequiredtoformthe reso- nances.Thetypeof resonance(++,+,0,-)produceddependsonthenucleonsinvolved intheproduction.Therelativeprobabilitiesforaspeci˝cnucleon-nucleoninteraction( p - p , n - p , n - n )toproducea canbedeterminedusingconservationlawsandClebsch-Gordan 8 coe˚cients(seeAppendixAforderivation): p + p ! r 3 4 ++ + n r 1 4 + + p n + p ! r 1 2 + + n r 1 2 0 + p n + n ! r 1 4 0 + n r 3 4 + p : (1.9) Usingthedecaymodesof s,wecandeterminetherelativeprobabilitiesofdi˙erentpions beingproduced,foraspeci˝cnucleon-nucleoninteraction, p + p ! r 5 6 ˇ + + p + n r 1 6 ( ˇ 0 + p + p ) n + p ! r 1 6 ( ˇ + + n + n )+ r 2 3 ( ˇ 0 + n + p )+ r 1 6 ( ˇ + p + p ) n + n ! r 1 6 ( ˇ 0 + n + n ) r 5 6 ˇ + n + p : (1.10) Fromthis,wecanseethattheproductionof ˇ willlargelydependon n - n collisionsin thehighdensityregion,while ˇ + productionwilllargelydependon p - p collisions.The productionof ˇ and ˇ + isequallylikelyfor n - p collisions.Itfollowsthattherelative productionof ˇ and ˇ + shoulddependontherelativenumbersofneutronsandprotonsin thehighdensityregion. Thesymmetryenergywilla˙ecttherelativenumberofprotonsandneutronsinthehigh densityregion.Alargesymmetryenergy(i.e.,sti˙)willfavorsymmetryinthenumber ofprotonsandneutrons,andwillcompetewiththeCoulombforcewhicha˙ectsonlythe expulsionofprotonsfromthehighdensityregion.Asmallsymmetryenergy(i.e.,soft) willleadtocomparativelyfewerprotonsinthehighdensityregion.Thereforetherelative numbersof ˇ and ˇ + producedshouldprovideanindicationoftherelativenumbersof 9 neutronsandprotonspresentinthehighdensityregion,andtherebyprovideameasureof thesymmetryenergy.Thisqualitativeargumentmustbemodeledtoaccountforreaction dynamicsanddi˙erencesinthe ˇ and ˇ + production.Thesymmetryenergydirectly a˙ectstherelativequantitiesandexpulsionofprotonsandneutronswithinthehighdensity region,butinferringthesymmetryenergyat 2 ˆ 0 fromexpelledprotonsandneutronsis di˚cult,mostnotablybecauseneutronsandprotonsareemittedfromallregionsofthe reaction,regardlessofdensity.Measurementsof n - p spectrawillthereforebea˙ectedbythe symmetryenergyatarangeofdensities. 1.3MeasuringPionMultiplicities,andtheProposedEx- periment Measuringchargedpionsrequiresamagnetic˝eldtoseparatepositiveandnegativecharge. Tomeasurearangeofasymmetry( ),largeisotopesarepreferable.Manychargedparticles areproducedintheHIC,andwemustbeabletoresolvethemomentaandParticleIden- ti˝cation(PID)oftheseparticlestodistinguishpions,especiallypositivepions,fromother chargedparticles.Todeterminethekineticenergyoftheparticlesinthereactioncenter- of-momentumframe,theangleofemissionmustbedeterminedinadditiontothemomenta andPID.Themeasurementofprotons,deuterons,tritons, 3 Heand 4 Hecanbeusedfor complimentarymeasurementsofthesymmetryenergy,andprovidenecessarysystematic information. TheuseofaTimeProjectionChamber(TPC)suitsthedesiredmeasurementperfectly.A TPC,usedinconjunctionwithamagnetic˝eld,isabletodistinguishbetweenpositivelyand negativelychargedparticles.ATPCcoversalargesolidangle,andcanbeusedtodistinguish 10 individualtracksinahighmultiplicitycollision.Sincetheexperimentwillbeperformedat sub-thresholdenergies,theorypredictsthatthepionproductionwillbearelativelyrare processcomparedtolightchargedparticlessuchashydrogenandheliumisotopes[2],soitis importanttomaximizethedetectione˚ciencyofpions.TheEOSTPC[23]haspreviously beenemployedtomeasurechargedpionspectrafor ˘ 1GeV/AAu+Aucollisions[24],thus demonstratingthefeasibilityofusingaTPCforsuchmeasurements. Forthepurposeofconstrainingthesymmetryenergy,anewTPC,calledtheS ˇ RIT (SAMURAIPion-ReconstructionandIon-Tracker)TPC[3],ajointprojectbetweenTexas A&MUniversityandMichiganStateUniversity,wasconstructedattheNationalSuper- conductingCyclotronLaboratory(NSCL)andusedinanexperimentalcampaignatthe RadioactiveIsotopeBeamFactory(RIBF)attheRIKENNishinaCenterforAccelerator- BasedScienceinWako,Japan.Twoprimarybeams( 124 Xeand 238 U)wereusedtoproduce fourbeams( 108 Sn, 112 Sn, 124 Sn,and 132 Sn)whichwereimpingedontwoisotopictargets ( 112 Snand 124 Sn),toprobealargerangeofasymmetry.Additionally,twobeamswerepro- ducedconsistingoflow-chargeparticles( Z rangingfrom1to3)formomentumcalibrations. Thebeam-targetsystemsusedislistedinTable1.1. PrimaryBeamSecondaryBeam IsotopeEnergyDesiredTargetEnergyatmidtarget (AMeV)IsotopeIsotope(MeV/u) 238 U345 132 Sn 124 Sn ˘ 270 238 U345 124 Sn 112 Sn ˘ 270 124 Xe345 112 Sn 124 Sn ˘ 270 124 Xe345 108 Sn 112 Sn ˘ 270 Table1.1:BeamsusedintheS ˇ RITTPCexperimentalcampaign Thisdissertationwillfocusonthepionmeasurementfromthe 124 Sn+ 112 Snsystem andthe 112 Sn+ 124 Snsystem,providinginitialresultsfromtheS ˇ RITTPCcampaignand 11 demonstratingthecapabilitiesoftheTPC.Theheavyioncollisionsaremodeledwithatrans- portcode,whichpredictsthepionproductionforgivenparameterizationsofthesymmetry energy[19,2].Inthisdissertation,apreliminarycomparisonofourdatatothepredictions ofonetransportmodel(pBUU)byPawelDanielewicz[25,26],whichusestheBoltzmann- Uehling-Uhlenbeckequation,isperformed.Therehasbeenongoinge˙ortstocomparetoa suiteoftransportcodes[27],whichmaybeusedinthefuturetointerpretpionproduction spectra,andtherebyconstrainthesymmetryenergy. 1.4OrganizationofDissertation ThisdissertationbeginswithadescriptionofthedesignandconstructionoftheS ˇ RIT TPCinChapter2.TheTPCshippingprocessisalsodetailedinChapter2,alongwitha descriptionofupgradesthatwereperformedtotheTPCaftertheexperimentalcampaign. TheexperimentalsetupisdescribedinChapter3,includingthepositionmeasurementofthe setup.AdescriptionofancillarydetectorsandtheexperimentaltriggerisincludedinChapter 3.AnalysisofthebeamandTPCdataispresentedinChapter4.Thebeamanalysisinvolves beamparticleidenti˝cationandtrajectoryreconstruction.Theabsolutecrosssectionis determinedusingscalerinformation,TPCinformation,andthebeaminformation.An overviewoftheTPCanalysissoftwareispresented,withdetailsonthepionextractionand analysis.AsummaryisprovidedinChapter5,alongwithanoutlookforfuturework. 12 Chapter2 DevelopmentoftheS ˇ RITTime ProjectionChamber TheSAMURAIpionReconstructionandIonTrackingTimeProjectionChamber(S ˇ RIT TPC)[3]wasdesignedtodetectpionsandotherlightchargedparticles,observableswhich aresensitivetothesymmetryenergy.TheoperationprincipleisshowninFigure2.1,with the˝eldcageandpadplaneillustrated,althoughnottoscale.TheS ˇ RITTPCwasdesigned tobeplacedinsidethemagnetgapoftheSAMURAISpectrometer[28],whichprovidesthe indicatedmagnetic˝eld.The˝eldcageproducesauniformelectric˝eldanti-paralleltothe magnetic˝eld,andis˝lledwithP10gas(90%Argon,10%CH 4 )atjustaboveatmospheric pressure.ARare-Isotope(RI)beamisimpingesona˝xedtargetattheentranceofthe˝eld cage.Whenabeamnucleuscollideswithatargetnucleus,neutronsandchargedparticles arereleased.Asthechargedparticlespassthroughthe˝eldcage,theyionizetheP10gas, creatingelectron-ionpairs.Thepositiveionsdriftdownwardstowardsthecathodeplate, whiletheelectronsdriftupwardstowardsthegroundwireplane,located8mmbelowthe padplane.Theelectronsaremultipliedbetweenthegroundplaneandtheanodewireplane, whichislocated4mmbelowthepadplane.Thehighvoltagepotentialbetweenthesetwo wireplanesacceleratesthedriftelectrons,givingthemsu˚cientenergytoliberateadditional electronsfromthegas.Theadditionalliberatedelectronswillalsobeaccelerated,liberating 13 Figure2.1:OperationprincipleoftheS ˇ RITTPC,modi˝edfrom[3]. furtherelectrons.Thischaine˙ectcausesanavalancheofelectrons;therefore,theregion betweenthegroundandanodewireplanesisreferredtoastheavalancheregion.The electronsterminateontheanodeplane,butthemotionofthepositiveionsproducedinthe avalancheregioninducesanimagechargeonthepadplane,creatingasignallargeenough tobeampli˝edanddigitizedbyreadoutelectronics. Thehighly-segmentedpadplaneallowsdeterminationofthetrajectoryofaparticlein the x - z plane,whilethethirddimension, y ,isinferredfromtherelativetimingofinduced signals.Theanti-parallelelectric˝eld,incombinationwiththeencompassingmagnetic˝eld, causestheelectronstodriftintightspiralsalongthe˝eldlines,mitigatingdi˙usionthat wouldotherwiseoccur.Acombinationofmagneticrigidity( Bˆ )andenergyloss( dE=dx ) providesthenecessaryinformationtodetermineparticleidenti˝cation,alongwithmomenta ofthechargedparticlescreatedintheRIcollision.Themagnetic˝eldseparatesthecharged particlesbymagneticrigidity,whiletheenergylossperunitlengthisdeterminedfromthe amountofchargeliberatedbeneathapad.Thischapterdescribesthedesignandconstruction 14 oftheS ˇ RITTPC.ItshouldbenotedthatthischaptersharesoverlapwithReference[7], whichwaswrittenbeforethe˝rstexperimentalrunoftheS ˇ RITTPC. 2.1GeneralDesignConsiderations Toachievethedesiredphysicsresults,theTPCmustbeabletoresolvelightchargedparticles inreactionswhichcanincludeprojectile-likefragmentsandintermediatemassfragment particlesinhighmultiplicity[29].Tothisend,thedesignwasbasedontheEOSTPC[23]. Totakeadvantageofthe2mpolefaceoftheSAMURAIspectrometer,theS ˇ RITTPC hasalargepadplane(1344mmby864mm).Structuralboltcoverswithinthepolegap ofSAMURAIreducetheavailablepolegapto75cm(of80cmmaximum).Thepadplane isreadoutbyfront-endelectronics,whichmustbemountedascloseaspossibletothepad planetoavoidsignallossandnoisepickup.Thecombinationofreadoutelectronicsand availablepolegaplimitsthedriftlengthofthe˝eldcageto50.49cm. TheS ˇ RITTPCwasdesignedtostudycentral,heavy-ioncollisionsataround E =300 MeV/u,whichresultinahighmultiplicityofproducedparticles.Theparticleidenti˝cation andmomentummeasurementforpions,hydrogenisotopes,andheliumisotopesarenecessary forthephysicsgoals.Speci˝cgoalsfocusedonwithinthisworkaremeasuringcharged- pionspectraandratios,aswellasdeterminingmultiplicitycrosssections.Asdiscussedin Chapter1,thepionratiomeasuredwithdi˙erentbeam/targetsystemsisexpectedtoprovide constraintsofthedensitydependenceofthesymmetryenergy.Measurementsofmultiplicity crosssectionsprovideimpactparameterconstraints,whichisimportantforcomparisonto theory. Typically,alargerpadplanesizeisrequiredforalargerrangeofmomentumacceptance, 15 whileasmallerindividualpadsizeallowsa˝nerresolutionofhighermomentumvalues. Thetotalnumberofpadsislimitedbychannelcost,andasmallpadsizerequireshigh densityelectronicsforreadout.Thedesignofthepadplanehadtooptimizethemomentum measurementoverarangeofmomentumacceptance,withoutusingacost-prohibitivenumber ofchannels.Additionally,thepadplaneshould˝tinsidetheregionofuniformmagnetic˝eld oftheSAMURAIspectrometer. TosafelyoperatewithintheSAMURAImagnetat0.5T,allpartshadtobemadeofnon- magneticmaterials.Manystainlesssteelpartsandscrewscanbeused,butmustbechecked formagnetism.Type316stainlesssteel,whichcontainsasmallamountofmolybdenum,is typicallynon-magnetic,butcanbecomemagneticwhenthemetalisworked.Toavoidusing anymagneticelectricalcomponents,weavoidedcomponentswhichwerenickelcoatedorhad ironpins.Eachcomponentusedwascheckedformagnetismusingarare-earthmagnet. Anadditionalconsiderationmadeformaterialsusedwastoavoidintroducingimpurities inthe˝eldcagegas.Oxygenandhalogenideshavearelativelylargeelectrona˚nity,and thuscanabsorbdriftelectrons,whichdonottypicallyhaveenoughenergytoformnegative ionswithnoblegasesormostorganiccompounds[30].Materialswerespeci˝callychosento behalogenfree,toavoidintroducingsuchimpurities. 2.2DesignOverview AnexplodedviewoftheS ˇ RITTPCisshowninFigure2.2.Thepadplaneandwireplanes aremountedtothetopplate,whichiskept˛atwithribs.The˝eldcagesealsagainstthe topplate,formingagastightdetectionvolume.CleanP10gasentersthe˝eldcagethrough aninletatthebottomofthe˝eldcage,andexitsthe˝eldcagethroughanoutletonthetop, 16 Figure2.2:S ˇ RITexplodedview. ˛owingthroughtherestoftheenclosurevolume,andexitingviaabubbler.Thevoltagestep downbridgestheelectricpotentialbetweenthe˝eldcagecathodeandthegroundpotential oftheenclosure.Theseparts,alongwiththetargetmechanism,arehousedwithinthe enclosure.Anentrancewindowismountedonthefront˛angeoftheTPC,allowingRI beamstoentertheenclosure. 2.3GETElectronics Forthepadplanereadout,theGenericElectronicsforTPC(GET)systemisemployed[31]. ThissectiondrawsheavilyfromReferences[31]and[5].TheApplication-Speci˝cIntegrated Circuit(ASIC)andAnalog-to-DigitalConverter(ADC)board,orAsAdboard,isusedto amplify,shape,anddigitizethesignalsfrompads.EachAsAdboardhas4ASICforGET (AGET)chips,whichamplifyandshapethesignalsfrom64inputpads.Aschematicdiagram 17 Figure2.3:SchematicofAGETfunction,from[4]. oftheAGETfunctionisshowninFigure2.3.Eachofthe64shaperoutputsissampled andstoredona512-cellswitchedcapacitorarray,whichprovidesacircularbu˙erforthe analogsignal.Uponreceivingatrigger,thesesampledsignalsaresentsequentiallytoa fourchannelADContheAsAdboard,withonechannelhandlingsignalsfromoneAGET chip.AsingleAsAdboardthereforehandlesupto256inputsignals,witheachinputsignal containingasmanyas512samplesofthesignalinducedonthecorrespondingTPCpad.The samplingfrequencyisadjustablefrom1MHzto100MHz,allowingatimerangefrom512 µ sto5.12 µ stobesampled.Eachofthe512cellsoftheswitchedcapacitorarraystorethe ampli˝edandshapedchargesignalforitspadduringthetimecorrespondingtothesampling frequency,formingagranularket"withassociatedsignalheight.Inadditiontothe inputsignals,eachAGEThas4FixedPatternNoise(FPN)channels,whichcanbeusedto determinenoiselevels.Thereisalsoadiscriminatorforeachinputsignalthatcanbeused forpartialreadoutofpadswithdataabovethethresholdvalues.Asthechanneloccupancy ratesfortheTPCarehigh,thisfeaturewasnotused.Instead,allchannelsarewrittento diskoneveryevent. ThedigitizeddatafromtheAsAdboardsareconcentratedbyConcentrationBoards (CoBo).EachCoBocanhandlesignalsfrom4AsAdboards,foratotalof1024input signals.TheseCoBoboardssendtheconcentrateddatatoaDAQserver,whichwritesthe 18 Figure2.4:GETarchitectureemployedforS ˇ RITTPC,from[5]. eventtodisk.TheCoBohaveDDRAMforeventbu˙ering,storingthetimesequenced, digitizeddatafromthe512-cellswitchedcapacitorarrays.AcontrolpathontheCoBos isusedtoreceivethetriggerfromtheMultiplicity,TriggerandTime(MuTanT)module (see[4]forfurtherdetails)andtransferittotheAsAdboards,andtocon˝guretheAsAd boardspriortodatataking.Whenaneventtriggerisreceived,thebu˙ereddatafromthe CoBomodulesarewrittentodisk. FortheS ˇ RITTPC,48AsAdboardsareusedwith12CoBos.TheCoBosaremounted in2 µ -TCAcrateslocatedoutsidethemagnetic˝eld,with8CoBosandoneMuTanTmodule inonecrateand4CoBosandoneMuTanTmoduleintheother.TheAsAdandCoBowere connectedwith8mlongcommercialVery-High-Density-CableInterconnect(VHDCI)cables. 19 Figure2.5:AdapterandZAPboards. The µ -TCAcratessenddatafromtheCoBomodulesthrougha10Gbpsnetworkswitchto2 DAQservers,whichemployNARVAL[32]astheDAQframework.TheGETarchitectureas employedfortheS ˇ RITTPCexperimentisshowninFigure2.4.Duringexperimentalruns, theAsAdsamplingfrequencywas25MHz,with270ofthe512timebucketsdigitized[5]. TheconnectionbetweenAsAdandpadplaneishandledwithcustommadeinterface boards,asshowninFigure2.5.Theinterfaceuses2typesofrigidcircuitboards,connected with˛exibleribboncables.Push-typeconnectorsonthesmallerrigidboardsareusedto interfacetothepadplane,andthelargerboardisconnectedtotheAsAd.Spacersareused toensurethattheforceontheSAMTECconnectorissu˚cienttoensureelectricalcontact onallsignalandgroundlines,butnotanymore.Excessiveforceonthepadplanecanbreak thegassealbetweenthepadplaneandthetopplate.ThelargerboardiscalledaZAP board,asituseslowcapacitancediodearraystoprotecttheAsAdfromhugesignalswhich couldbecausedbysparkingaroundthepadplane.The˛exibleribboncablesallowthe AsAdboardtobeinstalledinatiltedfashion,maximizingthelimitedspacebudget. 20 (a) (b) Figure2.6:Schematicviewoftopplateandribs(a),andphotographofTPCwithGET electronicspartiallyinstalled(b). 2.4TopPlate Arigidaluminumplateisusedasa˛atreferencesurfaceforthepadplane,wireplanes,˝eld cage,andtargetmechanism,andasthemountingpointforthereadoutelectronics.This plateisreferredtoastheplate".Thetopplateismadeofa3/4inchthickaluminum plate,2035.2mmlongand1498.6mmwide.Arecessismachinedonthebottomsideto˝t thepadplane,andslotsthroughtheplatearemachinedfortheinterfaceboards(described previously)toconnecttothepadplane.Machiningthefeed-throughsandrecessescauses theplatetowarp,asthemachiningprocessrelievesstresswithinthemetal,soaseriesof ribsisinstalledonthetopplatetomaintainplanarity.Thetopplateandsupportingrib structureisshowninFigure2.6a,withasingleAsAdandinterfaceboardinstalled.The ribsareusedtoholdasupportstructureforreadoutelectronics,madeof80-20aluminum extrusion.Figure2.6bshowstheTPCwithGETreadoutelectronics(describedpreviously) installedonhalfofthepadplane. 21 (a) (b) Figure2.7:Thetopplateandmotionchassisin(a)doorwaycon˝gurationand(b)table con˝guration. 2.4.1MotionChassisandTableCon˝guration AmotionchassisfortheTPCwasdesignedandfabricatedatTexasA&MUniversity.The motionchassisconnectsdirectlytotheribsofthetopplate,allowingthetopplatetobe movedandworkedoneasilyandsafely.Themotionchassisisshowninstalledonthetopplate inFigure2.7a,intheorwaymotion"con˝guration.Castersonthemotionchassisallow smoothmotionacross˛oorsandthroughdoors.Anadditionalsetofcastersareemployed foracon˝guration,showninFigure2.7b.Inthiscon˝guration,thebottomofthetop platecanbeworkedoneasily,andmotionisalsopossible,althoughinthetablecon˝guration, theassemblywillnot˝tthroughatypicaldoorway. 2.5PadPlane Anarrayofconductive,charge-sensitivepadscalledtheplane"ismountedtothe bottomofthetopplate.Eachpadis11.5mminthebeamdirectionand7.5mminthe transversedirection,with0.5mmisolationbetweeneachpad.Anelectronavalanchewill 22 induceasignalonthenearestcharge-sensitivepads:ifanavalancheoccursoveranisolation area,thesignalwillspreadoverthetwoneighboringpads.Therefore,eachpadcoversan e˙ectiveareaof12mm 8mm.Thepadplanespans112padsinthebeamdirectionand 108padsinthetransversedirection,for12,096padsandoveralldimensionsof1344mm 864mm.ThepaddimensionsmatchedtheEOSTPC,whichhadpreviouslybeenused tomeasurepions.TheoverallpadplanesizeissomewhatsmallerthanthatoftheEOS TPC,butisareasonablematchtotheavailableregionofuniformmagnetic˝eldinsidethe SAMURAIspectrometer. Thee˙ectofpaddimensiononmomentumresolutioncanbeinvestigatedfora˝xed numberofchannels.Foranarrayof108 112padsof˝xedlength,weexaminetherelative errorindeterminingmomentumforpadsofdi˙erentwidths.Forparticlesstartingatthe originofthepadplanewithmomentumalignedalongtheZ-axis,themagneticrigiditycan beusedtodeterminethepathlengthandnumberofpadscrossed.Weassumetheerror ofpointmeasurementvariesas " 2 / W 2 + L 2 ,with W and L thepadwidthandlength, respectively.Themomentumresolutionisdeterminedfromtheabilitytomeasuretrack curvature.From[30],thevarianceforcurvaturemeasurementcanbedescribedas ˙ 2 = " 2 L 4 720 N 3 ( N 1)( N +1)( N +2)( N +3) ; (2.1) where " istheerrorofmeasurementforeachpointalongthecurve, L isthetracklength, and N +1 isthenumberofpointsmeasured. Usingthe8mm 12mmpadsizeasareference,relativemomentummeasurement errorisshowninFigure2.8asafunctionofmagneticrigidity(inMeV/c/e).Forlow rigidityparticles,widerpadsincreasethepathlength(byincreasingthetotalpadplane 23 Figure2.8:Relativeerrorofmomentummeasurementfordi˙erentpadsizes. size),whichincreasesthemomentumresolution.Forhigherrigidityparticles,thenarrow padsincreasethenumberofmeasurementpointsalongthepath,increasingresolution.A narrowpadsize(andthereforenarrowpadplane)drasticallyreducesthepathlengthforlow rigidityparticles,disproportionatelyincreasingthemomentumerror.Sinceourpionswill typicallybeofrigiditylessthan1000MeV/c/e,thewiderpadsarebettersuitedforourpion measurement. Thepadplaneismadefroma6-layerPrintedCircuitBoard(PCB),withconductive surfacescoatedingold.Duetothecomplexityandsizeofthepadplane,itistechnically di˚cultandcost-prohibitivetoproduceasasingleboard,soinstead4di˙erentpieceswere producedthatcouldbecombinedtoformthepadplane.Theperimeterofthepadplan isboundedbyagroundstrip,causinganasymmetrywhichrequires2designsforthe4 pieces.Opposingcornerssharethesamedesign,asillustratedinFigure2.9.Thewidthof thegroundstripisexaggeratedinthe˝gure.Dowelpinholesinthethreeoutercornersare usedtosettherelativepositionofthe4boardswhenmountingtotherigidtopplate. 24 Figure2.9:Padplanesymmetry,withhatchedregionsrepresentingthegroundstrip,and arrowsrepresentingthesymmetryofthepadlayout.Nottoscale. 2.5.1UnitCell Thepadsaregroupedintocells"whichspan7padsinthebeamdirectionand9pads inthetransversedirectionforatotalof63pads.Theunitcellisdesignedtobereadout usingeithertwoSTARFrontEndElectronics(FEE)cardsorbyoneAGETchip(described inSection2.3).ThelayoutandsignalroutingoftheunitcellisshowninFigure2.10.Pads areshowninblue,withpadnumberinwhiteshownforonerowandonecolumn.The padnumberincreasesfromlefttoright,andtoptobottom.Thesignallayerisshownin yellow.Thesignalroutingwaschosentominimizethetypicaltracelength.Thegreencircles representVerticalInterconnectAccess(VIA)holeswhichtransportsignalbetweencircuit boardlayers.ThefootprintfortwoSAMTECFSIconnectorsareshowninred.These connectorsarespring-loaded,andmustbeheldagainstthepadplanecircuitboard.Fora numberingconvention,wehavede˝ned4rowsfromthe2connectors,andlabeledthepins ineachoftheserowsfrom0-24.Thisnumberingisindicatedingrayinthe˝gure.Theunit 25 Figure2.10:Circuitschematicofthepadplaneunitcell. cellpatternisrepeatedacrossthepadplane,andhasmirrorsymmetryacrosstheZ-axis (orientedalongthetypicalbeamdirection). SinceeachAsAdboardhas4AGETchips,4unitcellsareservicedbyeachAsAdboard. ThepadplanedimensionsareillustratedinFigure2.11alongwiththepro˝leofaunitcell andtheareaservicedbyasingleAsAdboard.Thepadplanespans16unitcellsinthebeam direction,and12unitcellsinthetransversedirection.Thereare196unitcellsinthepad plane,and48AsAdboardsareusedtoreaditout. 2.5.2LayerCrossSection Toavoidcrosstalk,weuseamulti-layercircuitboard.Thesignalplaneisinthemiddle, shieldedoneithersidebygroundplanes,withthepadsideandreadoutsideontheoutside layers.Thisputsarequirementofaminimumof5layers,butitisbesttouseaneven numberoflayersinacircuitboardduetothemanufacturingprocess,soatotalof6layers wereused.ThecrosssectionisshowninFigure2.12,notdrawntoscale.Thelayersof 26 Figure2.11:Padplaneoveralldimensionsinmm,withthepro˝leofaunitcell(cross hatched),andtheareaservicedbyoneAsAdboard(hatched). copperareall0.7mil(1mil=0.001inch)thick,andaredrawninanorangecolor.To simplifythemanufacturingprocess,thereareonlytwoVIArouteswithonerouterunning throughtheentireboard,andoneroutegoingfromthetoplayertolayer5.Theinsulating layers,drawningreenhavethicknessindicatedwithunitsofmil.Theinsulatingmaterials aremadeofnon-brominatedG10glass-epoxyresin.TheVIAroutewhichrunsthroughall layersisusedtoconnectthepadstothesignallayers.Onthetoplayer,theVIAiscovered withinsulatingsoldermaskmaterialtoavoidgroundingtothetopplate.TheVIAroute whichrunsfromthetoplayertolayer5isusedtobringthesignalfromthesignallayerto thetoplayer,aswellastointerconnectallgroundlayers. 2.5.3PadPlaneSignalMapping TheinterfaceboardconnectingtheAsAdboardstothepadplanewasdescribedpreviously, andshownschematicallyinFigure2.5.ThesignalmappingfromoneAGETchiptooneunit cellisenumeratedinTable2.1,withpadnumbersfollowingtheconventioninFigure2.10. Inadditionto64signalchannels,theAGETchiphas4FixedPatternNoise(FPN)channels, 27 Figure2.12:Crosssectionalviewofthepadplane.ThegreenhatchedlayersareG-10,with thethicknessindicatedinmil. whichareincludedinthemap.Sinceeachunitcellhas63padsinsteadof64,onechannel isNotConnected(NC).Themappingisthesameforeachunitcell/AGETchipinthepad plane. 2.6PadPlaneGluing ThepadplanewasfastenedtothetopplateusingAraldite2013epoxy.Sincethepad planeformsagastightbarrier,thegluingprocedurewasdesignedwithredundancyfor leaks.Adoublegasketfabricatedfrompolycarbonatewasgluedtothetopplatearound eachsetofholesusedfortheGETelectronics,asshowninFigure2.13a.Forthisgluing, EZ-poxywasused.Analuminumjigwasusedtoapplyeachgasket,toensureuniform application.Uniformpressurewasappliedtothegasketswhiletheepoxycuredusingte˛on- coated,weightedaluminumplates.Thismadeagas-tightsealbetweenthegasketsandthe topplate.EZ-poxydoesnotprovidethestrongeststructuralbondtoeitheraluminumor polycarbonate,butitislowviscosity,whichallowsthegasketstobepressed˛atagainstthe topplate.Thisisessentialtoensureagas-tightseal. Withthegasketsinstalled,thepadplanewassecuredtothetopplateusingAraldite 28 AGETPad AGETPad AGETPad AGETPad 014 1733 3449 5152 19 1810 35NC 5230 215 1934 3642 5359 316 203 3743 5438 421 2126 3850 5560 57 22FPN 3944 56FPN 622 234 4051 5739 78 2425 4135 5861 823 255 4256 5940 90 2627 4336 6062 1031 276 4457 6141 11FPN 2820 45FPN 6255 121 2912 4637 6348 1324 3018 4758 6453 142 3111 4828 6546 1532 3219 4945 6654 1617 3313 5029 6747 Table2.1:AGETchanneltoPadsignalmapping.Theconventionforpadnumberisdetailed inFigure2.10.FourFixedPatternNoise(FPN)channelsarepresentperAGETcard,but theyarenotconnectedtothepadplane.Channel35isNotConnected(NC)toanypad. 29 (a) (b) Figure2.13:Gluingdoublegasketstotopplate(a)andapplicationofAralditeepoxyfor padplaneinstallation(b). 2013epoxy,whichbondsstronglytothepadplanecircuitboardandtothealuminumtop plate.Thepadplanecornerswereinstalledoneatatime,usingavacuumtabletoensure planarity.TheepoxywasappliedtothetopplateasshowninFigure2.13b,insquare patternscoveringeachofthepreviouslydescribedgaskets.AlthoughmostoftheAraldite applicationisnotdirectlyonthealuminumsurface,itissqueezedoverthealuminumwhen thepadplaneispushedagainstit.Eachscrewholewas˝lledwithTe˛on-coatedscrewsto preventtheAraldite2013epoxyfrom˛owingintothem.Kaptontapewasplacedoverthe electricalconnectionsofthepadplane,tokeepthemcleanofepoxy. Withtheepoxyapplied,thepadplanecornerisloweredintoplaceusingavacuumtable, asshowninFigure2.14.Thevacuumtablehasaprecision˛atsurfacewithmanyholes which,whenusedwithavacuumpump,holdsthepadplanecircuitboard˛atwhilethe epoxycures.Precisionshimsareusedtosettheheightandlevelofthevacuumtable.Metal weightsontopofthevacuumtableapplypressuretothepadplaneandepoxy.Theepoxy wascuredinthiscon˝gurationfor24hoursforeachpadplanecorner. Withthispadplanegluingprocedure,eachgasketwasgluedbytworectangularbeads 30 Figure2.14:Vacuumtableinuseforpadplaneinstallation. ofAraldite2013epoxytothetopplate.Theinnermostrectanglesurroundstheelectrical contactsfortheSAMTECpushconnector,andtheoutermostrectanglesurroundstwoscrew holesusedtosecuretheSAMTECconnectortothetopplateandpadplane.Whentesting theTPCwithP10gas,someleaksweredetectedonthetopplateusingacombustiblegas detectorwithsensitivitytomethaneatthe5ppmlevel.Allsuchleakswerethensealed byinjectingEZ-poxythroughthetwoscrewholes,intothecaptivevolumebetweenthetwo rectangularseals. 2.6.1PadPlaneFlatnessMeasurement Afterthepadplanewasinstalledonthetopplate,the˛atnessofboththepadplaneand topplatewerechecked.Thetopplatewasmovedtoacleantent,andsecuredintable con˝guration.AFARObrandlaseralignmentsystemwasusedtoprobetherelativeheight ofmanypointsoverthesurfaceofthepadplaneandtopplate.Apictureofthemeasurement inprogressisshowninFigure2.15a,andtheresultingmeasurementisshowninFigure2.15b, withdimensionsininches.Themeasurementindicateddeviationfromplanarityofupto 0.125mmforthepadplane,andupto 0.203mmforthetopplate.Thepadplaneis 31 o˙setfromthebottomsurfaceofthetopplateby1mm. (a) (b) Figure2.15:DaveSanderson(NSCLsta˙)measuringtopplateandpadplane˛atness(a), withtopographicalmapofmeasured˛atness(b). 2.7WirePlanes Thewireplanesareusedtocreateanelectronavalancheandproduceasignalonthepad planethatisreadoutbythefrontendelectronics.Eachwireplaneisdividedinto14 sections,whichallowsustoreplaceorrepairindividualsectionswithoutreplacingtheentire wireplane.Thewiresfromeachwireplanearemountedunderthepadplane,running transversetothebeamdirection.Foreachsection,apairofcircuitboardsaremountedon spacerbarsoneithersideofthepadplane,screwedtothetopplate.Thewiresareepoxied andsolderedtothesecircuitboardstoformasectionofthewireplane.Figure2.16shows thewireplanesmountedonthetopplate.Thepropertiesforthewireplanesarelistedin Table2.2. Theampli˝cationoccursbetweenthegroundandanodewireplanes,andthegating gridplaneisusedtopreventampli˝cationofeventswhicharenotofinterest.Therelative 32 PlaneWirematerialDiameterPitchDistancetoTensionNominal ( µ m)(mm)padplane(mm)(N)voltage(V) AnodeAu-platedW20440.51420 GroundBeCu76181.20 GatingBeCu761141.2-110 70 Table2.2:Wireplaneproperties. Figure2.16:Wireplanesmountedonthetopplate. voltagebetweengroundandanodeplanesdeterminestheelectronmultiplication,andsince thegroundplaneremains˝xedatgroundpotential,thegainisadjustedbyvaryingonlythe anodevoltage.Theaveragevoltageofthegatinggridissettomatchthelocalelectric˝eld, withalternatingwireso˙setinoppositepolarityfromtheaveragevoltagewhenthegating gridisclosed. Thewireplanesareconnectedtofeed-throughsinthetopplate,withthefeed-through mappingshowninFigure2.17.The˝gureperspectiveshowsthetopplatefromunderneath, withthewireplanesvisibleandnumbered1-14,with1attheupstreamendand14atthe 33 Figure2.17:Wireplanefeedthroughmapping. downstreamend.Adesignerrorblockedtwoanodeplanefeed-throughs,asindicatedbyred hatchedfeed-throughs.Duetothis,thehighvoltagesuppliesfortwopairsofanodeplanes wereprovidedthroughthesamefeed-throughs,thus,thevoltagesonanodeplanes12and14 arelinkedtogether,asarethevoltagesonanodeplanes11and13.Theanodehighvoltage issuppliedusingMHVfeed-throughs(Amphenolmodel10400),andthegroundissupplied usingBNCfeed-throughs(Amphenolmodel031-4237).Thegroundplaneisconnectedon bothleftandrightsideswithBNCfeed-throughs(Amphenolmodel031-220H),withtwo sparefeed-throughs.Thegatinggridplaneisconnectedonbothleftandrightsidesusing Dual-Lemofeed-throughs(LEMOmodelHGP.0S.302.CLLPV)andtransmissionlinesthat areshownalongsidethegatinggridboards. 2.7.1AnodePlane Theanodeplaneconsistsof364gold-platedtungstenwires,26wiresoneachofthe14 sections.Thethindiameterof20 µ misnecessaryforahighgain,andalthoughthewires 34 arebiasedtoahighelectricalpotential,theyarevulnerabletoahighelectriccurrent. Therefore,theanodeplanecircuitrequiresprotectionagainstsuddenelectricaldischarge, whichcanoccurwhenanelectronavalancheterminatesonawire.Thecircuitforasingle anodesectionisshowninFigure2.18,withwiresrepresentedbyarrows. Figure2.18:Anodeplanecircuitandtermination.Thiscircuitisrepeatedforeachofthe 14sections. Thebiasisprovidedononesideofthepadplanethrougha10M resistor,withavirtual groundmadeusinga1nFcapacitor.Whennegativechargeisdepositedonananodewire, thepositivechargeonthecapacitorcancelsthenegativecharge,partiallydischargingthe capacitor.Thecapacitorisrechargedthroughtheresistor,withanRCtimeconstantof10 ms.Thismaintainsthevoltageonthewirewhilegas-ampli˝cationoccursontheanodewire duringanevent.Italsolimitsthecurrentonthewireintheeventofasparkandallowsa controlledrechargingoftheanodewires.Thehighvoltageforeachsectionissuppliedusing anSHVfeed-throughinthetopplate,andaBNCfeed-through,J1,islocatedonthetop plate,whichallowstheindividualanodesignalstobeobservedorgrounded.Aswitchboard installedtoallowthiscon˝gurationtoberemotelyswitchedbetweengroundandaLEMO terminal,whichcanbeattachedtoapre-ampreadout.Thecomplementingcircuitboardon theoppositesideofthepadplaneisleftunconnectedtohighvoltageorground. 35 Figure2.19:Anodeplanecircuitboard.Dimensionsinmm. ThelayoutoftheanodeboardsisshowninFigure2.19.Eachsectionconsistsof26wires, andincludespadsforinstallingtheresistorandcapacitor.Thetop(blue)isthesignallayer, towhichthewiresarea˚xed.Thebottom(red)isthelayertowhichtheresistorsand capacitorsaresoldered.VIAsareshowningreenwhichlinkthetwolayers. 2.7.2GroundPlane Thegroundplaneconsistsof1456beryllium-copperwires,104wiresoneachofthe14 sections.Themainpurposeofthegroundplaneistode˝neagroundpotentialforelectron ampli˝cation.Additionally,thegroundplanecanbepulsedsoastoinduceregularsignals onthepadplane.Thisisaveryusefulfeaturefortestingandcalibration.Thewiresfor eachsectionareconnectedtoanimpedancelinewhichisbuiltintothecircuitboard.The impedancewasintroducedtomatchtheintrinsiccapacitanceofthegroundplanewires. Thisimpedancelinehasasetimpedanceperunitlength,andisrepresentedasanindividual capacitorandinductorforeachwireinFigure2.20.Thearrowsrepresentwiresfromeither side,andthedashedlinesindicaterepetitionforthe1452wireswhicharenotshown.The 36 Figure2.20:Groundplanecircuit.Dashedlinesindicatethepatternrepeatsovertheentire plane. circuitismirroredontheoppositesideofthepadplane,sothatthereare2BNCfeed- throughsusedtocontrolthegroundplane.TheBNCfeed-throughsarealsoconnectedto switchboards,allowingapulsersignaltobeinjectedonthebeamrightside,orallowingthe groundplanetobeshortedtogroundthrougha7 resistor.Thebeamleftsidecanbe shortedthrougha50 resistor,orthroughthe50 anda7 resistor,ore˙ectively6.14 . Thesignallinerunsacrossthetopoftheboard,withthesignallineofeachboard connectedtoadjacentsectionsinseries.Thegroundlinerunsalongthebottomsideofthe board,andthislineisalsoconnectedtothegroundlinesofadjacentsections.Theground lineandthesignallineforasectioncanbeseeninFigure2.21.Thebottom(blue)layeris atgroundpotential,andthetop(red)layeristhesignallayer.Thewiresarea˚xedtothe signallayer.VIAs,showningreen,connectthesignalandbottomlayer. 37 Figure2.21:Groundplanecircuitboard.Dimensionsinmm. 2.7.3GatingGridPlane Thegatinggridwireplaneisusedtoblockdriftelectronsfromreachingtheavalanche region.Duringanexperiment,reactionsoccurwithinthedetectorthatareeithernotof scienti˝cinterest,orarenotabletoberecordedwhilethedataacquisitioniswritingthe lastevent.Oneparticularlyproblematicsituationisthatofunreactedbeamparticlesthat passthroughthe˝eldcage.Thehighchargeandenergyofthebeamparticleresultsin heavyionizationwithinthe˝eldcage.Iftheionizedelectronspasstotheavalancheregion, thereareundesirableresults.The˝rstproblemarisesfromtheproductionofpositiveions withintheavalancheregion.Asustainedproductionofpositiveionscancauseabuildup ofcharge",netchargewithinthegaswhichdistortstheelectric˝eldwithinthe˝eld cage,a˙ectingthedriftspeedofelectrons,driftpathofelectrons,andthedetectorgain,all inanunpredictablemanner.Further,thebuildupofpositiveionscanleadtotheproduction ofpolymerchainswhichbindtothethinanodewires,changingtheire˙ectiveradiusand irreversiblyreducingthegain.Thise˙ectiscommonlyknownasdetectoraging[33].Finally, theampli˝cationofahighlyionizingeventproducesasaturatingsignaloncorresponding pads,causingthecorrespondingreadoutchanneltobeunresponsiveforupto35ms[5]. Forthereasonsoutlinedabove,itisnecessarytohaveagatinggridwireplanewhich 38 Figure2.22:Gatinggridoperationprinciple[6]. servestoclosetheavalancheregiontodriftelectronsfromundesiredevents.Thisisachieved byusingtwoalternatingsetsofwires,witheachwireneighboredbywiresoftheopposite set.Inthepen"con˝guration,bothsetsofwiresarebiasedtoavoltage V avg ,allowing driftelectronstopassthroughunimpeded.Thebestvalueof V avg wasdeterminedusing GARFIELDsimulations.Inthed"con˝guration,bothsetsareo˙setfrom V avg bya voltage V ,withonesetabovetheaveragevoltageat V H = V avg + V andonesetbelow theaveragevoltageat V L = V avg V .Thiscausesanelectric˝eldbetweenwires,sothat driftelectronsareattractedtothesetat V H .Theclosedandopenstatesareillustratedin Figure2.22,withtheopenstateallowingelectronstopassthrough,andtheclosedstate resultinginelectrondriftlinesterminatingonthe V H setofwires. Thechoiceof V mustaccountfortwofactors: V mustbesu˚cientlyhightoprevent driftelectronsfrompassingthrough,butas V isincreased,thetimerequiredtoswitch totheopenstateincreases.Agatinggriddriverisusedtochangethestateofthegating grid,andisdescribedinReference[6].GARFIELDsimulationswereusedtodeterminethe minimumnecessaryo˙setvoltagetoclosethegatinggrid.Figure2.23showstheelectron 39 Figure2.23:Gar˝eldsimulationofgatinggrid[6].Theleftpanelshowstheopenedgating grid,allowingelectronstoreachandterminateontheanodewires.Therightpanelshows theclosedgatinggrid,whichcauseselectronstoterminateonthe V H wires. driftlinesfortheopen(left)andclosed(right)states,fromaGARFIELDsimulation[6]. ThesimulationassumesP10gasatatmosphericpressure,with V A = 110 Vand V =70 V.Thedrift˝eldis131V/cmandthesimulationisperformedwithoutmagnetic˝eld.The quanti˝cationofopenorclosedisdeterminedbytransparency".Forexample,if 1000electronswereinitialized,and995passedthroughthegatinggrid,terminatingonthe anodeplane,thecon˝gurationwouldhaveanelectrontransparencyof0.995,or99.5%. Theinclusionofamagnetic˝eldincreasesthedi˚cultytoclosethegatinggrid.Since thedrift˝eldandmagnetic˝eldareanti-parallel,theLorentzforcesuppressestransverse di˙usionandcausestheelectronstofollowtheanti-parallelelectricandmagnetic˝eldlines closelyastheydriftupwards.Theseelectric˝eldlinesterminateonthegatinggridwhen itisclosed.Aselectronsapproachtheregionwheretheelectric˝eldhasalargetransverse componentduetotheclosedgatinggrid,theyareguidedawayfromtheelectric˝eldlines bythe E B e˙ect,inadirectionparalleltothewires,withsomeelectronsmissingthe 40 Figure2.24:Gatinggridclosingwithmagnetic˝eld[6]. gatinggridwiresbiasedat V H .Thisresultsinahigherelectrontransparency,whichmust beovercomebyincreasing V [30].Todeterminethe V requiredforclosingwithmag- netic˝eld,GARFIELDsimulationswereperformedusing4000electronspersimulationand determiningtheelectrontransparencyforvariousvaluesof V withamagnetic˝eldsetat 0,0.5,and1.0T[6].TheresultsareshowninFigure2.24. Thee˙ectivecircuitforoneofthegatinggridboardsisshowninFigure2.25.The matchinggatinggridboardontheoppositesideofthepadplanemirrorsthiscircuit.Two distinctsetsofwiresareused(V H andV L ),andtheyareconnectedtotheopposingpolarities ofthetransmissionline(showninFigure2.17).Thetransmissionlineisrepresentedbythe capacitorandinductorinFigure2.25,andisdescribedinthenextSection. ThegatinggridcircuitboardsareshowninFigure2.26,witharelativelystraightforward circuitboardlayout.Themainconsiderationthatmustbetakenistoallowsu˚cientspace betweenthefrontrowofpadsandthewiresfromtherearrowthatrunbetweenthosepads. Theelectricalconnectionsmadetotheboardmustbedoneonboththetopandbottom 41 Figure2.25:Gatinggridcircuitforasinglesectionofthewireplane. Figure2.26:Gatinggridplanecircuitboard.Dimensionsinmm. sides,andsoitisrequiredthattheboardsarelargerthanthespacerbarsthattheyare mountedon. 2.7.4GatingGridTransmissionLine Abi-polargatinggriddriver[6]isusedtodrivethegatinggridbetweenopenandclosed states.Thegatinggridplanehasaninherentimpedanceduetocapacitancewithneighboring gatinggridwiresaswellasneighboringgroundplanewires,andthusatransmissionlinemust beusedbetweenthegatinggriddriverandthegatinggridwirestoimprovetheimpedance matching.Openingofthegatinggridmustbedoneasrapidlyaspossiblewithoutintroducing 42 largesignalsonthepadplane,asevery1 µ srequiredtoopenthegatinggridresultsin5.5 cmofdriftdistancebeingnotdetectable,orapproximately9%ofthedetectionvolume. Figure2.27:Crosssectionofgatinggridtransmissionline.Dimensionsininches. Twotransmissionlines,oneforeachsideofthewireplane,runthelengthofthepad planeasshowninFigure2.17,andareconnectedtoeachsectionofthegatinggridplane throughconnectionsforeach V H and V L ,placedevery104mm.Thedesigncopiesthe dimensionsofcommerciallyavailabletransmissionline.Forthesignallines,a1.4milthick by0.25inchwidecopperfoilwasused.A2milthickKaptonstripwasusedtosetthe distancebetweensignallines.ThecrosssectionisshowninFigure2.27.TheKaptonhas adielectricconstantof3.4,sothetransmissionlinehascapacitanceof3.8nF/m,or5.5nF pertransmissionline.TheentireassemblyisencapsulatedinEZ-poxyforinsulation,and thesignallinesaresuppliedthroughadual-Lemofeed-throughonthedownstreamendof thetopplate.TheEZ-poxyinsulationiswrappedwithcopperforshielding;however,this changestheimpedancecharacteristicsofthetransmissionlineinanon-uniformmanner. 2.7.5WirePlaneInstallation The˝rststepofthewireplaneassemblyistoattachthecircuitboardstospacerbars usingepoxy.Thecircuitboardsandspacerboardsarealignedtoeachotherusingdowel pins.Uniformpressureisappliedtothecircuitboardsandspacerswhiletheepoxycures, usingavacuumbag.Theanodespacerboardshavecutoutstoaccommodatetheelectrical 43 componentsused.Afterthecircuitboardshavebeenattachedtothespacers,thesecutouts are˝lledwithepoxytoprovideelectricalinsulation,asshowninFigure2.28.Notethathalf theanodeboardsdonothaveelectricalcomponents,asthewiresarebiasedfromonlyone side. Figure2.28:Anodecircuitboardsattachedtospacerboards. Thewiresarewoundtoaprecisetensionandapproximatespacingbeforetheyare mountedtothecircuitboards.ThewirewindingwasperformedintheNSCLdetector lab,usingthewirewindingmachineshowninFigure2.29.Awire-feedingtableusesa springtensioningsystemtofeedthewireatasettension.Thismachinespinstwowire planeframesataconstantrate,wrappingthewirearoundtheframes.Themachinemoves thewire-feedingapparatusalongtheframeataratetosettheinitialpitchofthewires. Whenthewireiswoundtotheframes,itissecuredusing5-minuteepoxy.Thewirebetween thetwoframesisthentrimmed,andthewireplaneframesareremovedfromthemachine forinstallationonthewirebars.Thetensionofthewireplaneswasveri˝edusingaspeaker 44 Figure2.29:Windingmachineforwireplanes. tovibratethewires.Thedi˙ractionpatternofalowpowerlaserincidentonthemiddle ofawireindicateswhenthespeakerwastunedtoformastandingwaveonthewire.The frequencythatformsthesecondharmonicisusedtoinferthewiretension. Thewirebarsarenumberedandinstalledonthetopplate.Theheightofeachbarisset individuallyusingshimstockandaheightgauge,withthetopplateasareferencesurface. Thegatinggridandgroundplanebarsareremovedtoinstalltheanodewires.Thewire planeframe,withwoundwires,issetabovetheanodebars.Figure2.30showsthethe anodewiresbeinggluedtotheanodebars.Awirecomb,madewithanelectricaldischarge machineto1/10,000inchprecision,isusedtoalignthewireswhiletheyareglued.Afterthe epoxyhascured,eachwireissolderedtothecircuitboard.Excesswireistrimmedaway, andthewirecombsandwireplaneframeareremoved.Thesolderedregionisthencovered withEZ-poxytocoveranysharpedgesorpoints. 45 Figure2.30:Gluingtheanodewirestotheanodebars. 2.7.6WirePlaneRepair Repairingabrokenwireorwireplanerequiresonetoremoveallwireplanesabovethe damagedportion.Thus,toreplaceasinglesectionoftheanodewireplane,thecorrespond- inggatinggridandgroundplanesectionsmustbothberemoved.Duringfabrication,we discoveredthatthetensioningofoneanodeplanewasincorrectandthereforeitneededto bereplaced.Ideally,replacingsuchananodewireplanesectionshouldbedonewithout havingtoremakethegroundandgatinggirdplanesections.Aproceduretoremoveground andgatinggridwireplaneswasplannedandimplementedtocorrectthewronglytensioned anodeplane.ThuswetestedthisprocedureduringtheconstructionoftheTPCtoreplace anodeplane6,whichexhibitedsparkingissues. First,theelectricalconnectionsareremovedfromthewireplanesectionsthatmustbe removed.Aremoval˝xture,showninplaceinFigure2.31,wasdesignedwhichwouldscrew tothewirebarsfromeitherend.Thismaintainsthewireplanesectiontensionandoverall shapewhenthewireplanesectionisremovedfromthetopplate.Toinstalltheremoval 46 Figure2.31:Schematicofwireplaneremoval˝xtureonupside-downtopplate. ˝xture,thegatinggridtransmissionlinemust˝rstberemoved.Swivel-tipsetscrewson eachcorneroftheremoval˝xtureareusedtocontroltheheight,allowingustoliftthewire planesectiono˙thetopplateinacontrolledmanner.Oncethewireplanesectionisraised aboveneighboringsections,theentire˝xtureisremovedfromthetopplate.Theleftand rightsidescanbemarkedontheremoval˝xtureusingamarker.ALexancoverisinstalled ontheremoval˝xture,keepingthewiressafeuntiltheyarereinstalled.Boththegatinggrid andthenthegroundwireplanesectioncanberemovedinthisway. Whentherepairsare˝nished,thewireplanesarereinstalled,returningtheleftand rightbarstotheiroriginalposition,usingthedowelholesandpinstoreproducetheoriginal position.The˝rststepistoremovetheLexancover.Thentheremoval˝xtureandwire planecanbeplacedonthetopplateabovethepositionforthewireplane.Thewireplane isloweredintopositionusingtheswivel-tipscrews. 2.8FieldCage The˝eldcageprovidesacontainmentboxforthecountergas,andproducesauniformelectric drift˝eldfortheelectronsionizedfromthecountergas.Togetherwiththerigidtopplate,the 47 Figure2.32:Dimensionsof˝eldcageinmm,withdetailsAandBhighlightingthetop perimeter. ˝eldcageformsasealedrectangularboxwhichcontainsP10gasatjustaboveatmospheric pressure.P10gasisusedintheSTARTPC[34],andperformancepropertieshavebeen studiedindetail[35].Keydesignconsiderationsincludedmaximizingthedriftdistance whilestill˝ttinginsidethemagnetgapoftheSAMURAIspectrometer,andmaintaining auniformelectric˝eldthroughoutthedetectionvolumeunderneaththepadplane.The overallexteriordimensionsareshowninFigure2.32,whichshowsviewsofthe˝eldcage fromthefront,side,andaperspectivefromthetop. The˝eldcageinterfaceswiththetopplateusinganassemblycalledthetopperimeter. ALexanring,formedoftwopieces,surroundsthewireplanes,whileanaluminumperimeter formsthesealbetween˝eldcagewallsandtheLexanring.The˝eldcageanditsenclosed 48 driftvolumecanthereforebemadegas-tightallowingthegasmixturesinthedriftregionand theinsulationgastobedi˙erent.ThetopperimeterisshowninFigure2.32,withdetailed closeups.O-ringgroovesaremachinedonbothsidesoftheLexanring,matingwiththetop plateononeside,andthealuminumperimeterplateontheother.The˝eldcagewallsare madewith1.575mmthickG10PrintedCircuitBoards(PCBs).CopperstripsonthePCBs de˝netheelectric˝eld,andusingPCBsallowsustomakethe˝eldcagegas-tight.Each sidewallismadeusing3PCBs,whilethefrontwallismadewith2PCBs,aswellasthe entrancewindow.Therearwallisformedentirelyusingtheexitwindowandframe.The cathodeplate(detailedinthefollowingsection)sealsthe˝eldcageonthebottom. Theheightofthe˝eldcageisconstrainedbytheverticalspacebudget.Theusablepole gapoftheSAMURAIspectrometeris75cm,duetoasetofboltcoversinsidethemagnet. Abovethe˝eldcagetheremustbespacefortheAsAdboards,andbelowthe˝eldcagethere mustbespacefortheVoltageStepDown(VSD),whichisdescribedinafollowingsection, andtheenclosurestructure.Thespaceusedaboveandbelowwasminimizedsothatthe ˝eldcageheightcouldbemaximized.Theresultingdriftlength,betweentheinteriorface ofthecathodeplateandthegatinggridwires,is497.3mm. Thehighvoltageissuppliedtothecathodethrougha10M resistor,asshownin Figure2.33.Therearetwopathstogroundfromthecathode:throughtheVSD(discussed inSection2.8.1),andthroughthe˝eldcageresistorchain.Thee˙ectiveresistanceofthe VSDisR VSD =700M .Each˝eldcagestripisconnectedtothenextthroughtwo10M resistors,oneonthebeamleftsideandoneonthebeamrightside.Thus,thee˙ective resistancebetweenadjacentstripsisR=5M .Thereare49resistorpairsinthe˝eldcage resistorchainbetweenthecathodeandtopperimeter,providingatotalresistanceofR FC =245M .A˝xed20M resistor(R TP1 )inparallelwithanadjustableresistor(R TP2 ) 49 Figure2.33:Fieldcagecircuitlayout.Modi˝edfrom[7]. connectsthetopperimetertoground.Thee˙ectivecircuitdiagramisshowninFigure2.34. ThechoiceofR TP2 isinprinciplemadetotunetheelectric˝eldbetweenthetopperimeter andgatinggrid,tomatchtheelectric˝eldbetweenthecathodeandtopperimeter.The˝eld matchingrequiresthat V tp V cath y tp-cath = V gg V tp y gg-tp ; (2.2) where y tp-cath =490mmisthedistancebetweenthecathodeandthemiddleofthetop perimeterequipotential,and y gg-tp =7.3mmisthedistancebetweenthegatinggridand themiddleofthetopperimeterequipotential.Withthisrequirement,theresistancebetween topperimeterandground, R TP =( R 1 TP1 + R 1 TP2 ) 1 ,canbedeterminedusingthestandard voltagedividerrelation 50 Figure2.34:E˙ectivecircuitdiagramfor˝eldcage. R TP = R FC y gg-tp y tp-cath V cath + V gg V cath V gg : (2.3) Testsoftheelectrontransparencyforvariousvaluesof R TP2 wereperformedduringthe commissioningrun,whichindicatedanidealvalueof R TP2 =19.77M .Byourcalculation, thiscorrespondsto V gg = 165V,althoughfortheexperimentalruns,thevoltagesupplied tothegatinggrid, V avg ,wassetto 171V. 2.8.1CathodePlateandVoltageStepDown Thecathodeplatesealsthebottomofthe˝eldcage,andde˝nestheelectric˝eld.The cathodeplatewasdesignedtobelightweightandtomitigatesparkingpoints.Thecathode plateismadeusingalightweighthoneycombaluminumplate,whichhasamachinablesolid aluminumperimeter.Incidentgammarayscanliberateelectronsfromthealuminumsurface, whichhasarelativelylowworkfunction.Toreducetheproductionofsuchelectrons,the interiorsurfaceofthecathodeiscoatedwithgraphitepaint,whichcanbeseeninFigure2.35. Anextrusionismachinedinthecathodewhichmatcheswiththe˝eldcagewallgeometry. Thecathodeis˝xedtothe˝eldcagewallsusingscrews,andsealedwithAralditeepoxy. 51 Figure2.35:JustinEstee(GS)appliesepoxytothecathodeplate. Duringtheexperiment,thecathodeplatewasbiasedto6.7kV.TheVoltageStepDown (VSD)wasrequiredtosafelybridgetheelectricpotentialofthecathodeplatetothegrounded enclosure.Aseriesofcopperrings,eachwith1.125cmseparationfromneighboringrings,are mountedwithstando˙stoaninsulatingplate,withtheinnermostringelectricallyconnected toaconductivesurfacepaintedona0.375"polycarbonateinsulatingplate.Theconductive surfacehasa4nFcapacitancetothegroundedenclosure.ThisgeometryisshowninFig- ure2.36.ThecathodeisconnectedtotheconductivesurfacewithCu-Bespring-loaded connections.Theinnermostringisconnecteddirectlytotheconductivesurface,andthe outermostringisconnecteddirectlytotheenclosure.Eachringisconnectedtotheneigh- boringring(s)witha100M resistor,creatingane˙ectiveresistancebetweencathodeand groundof700M inparallelwiththeaforementioned4nFcathodetogroundcapacitance. Thecapacitanceandthe10M HVtocathoderesistore˙ectivelyservesasalowpass˝lter 52 Figure2.36:Cornerofvoltagestepdown.Thepaintedconductivesurfaceisvisibleinside thecopperrings. withacuto˙frequencyofabout4Hz,removingnoisefromtheHVsupply. 2.8.2FieldCageWindows The˝eldcagehasentranceandexitwindows,toallowchargedparticlestoenterandexitthe ˝eldcage.AdesigndrawingisshowninFigure2.37,showingthe˝eldcagewithwindows andwindowframesaccentuated.Thewindowsaremountedtoremovablepolycarbonate frames(yellowandturquoiseinthe˝gure),whichinturnmountto˝xedpolycarbonate frames(greeninthe˝gure).Thisallowsremovalof˝eldcagewindowswhenneeded. Theentrancewindowismadewith4 µ mthickpolyp-phenyleneterephtalmide(PPTA), 5.73cmwideby7cmtall.Theremovablepolycarbonateframeis9.9cmwideby16.9cm tall.Figure2.38showstheentrancewindow,with(a)showingthewindowremovedfrom the˝eldcage,and(b)and(c)showingthewindowinstalledonthe˝eldcage.Notethat 53 Figure2.37:Explodedviewof˝eldcagewindowsandframes. thewindowisinsertedfrominsidethe˝eldcage.Aluminumstripsareevaporatedoverthe entiresurfaceofthewindowandframe,withsilverepoxyensuringelectricalcontactbetween windowstripsandframestrips.Copper˝ngersareusedtoconnectthestripsontheframe tothestripsofthe˝eldcage. Theexitwindowismadewith125 µ mthickpolyamide,80.8cmwideby38.9cmtall. Aluminumelectrodestripsareevaporatedontothepolyamide,andthewindowissand- wichedbetweentwopolycarbonateframes,whichhavestripspaintedonwithconductive paint.Figure2.39ashowsaclose-upofthesilverepoxyusedtoelectricallyconnectthewin- dowstripsandframestrips.Figure2.39(b)showsthe˝xedframe,withcopper˝ngerson theoutsidetoelectricallyconnecttheinnerstripsoftheremovableframe.Aprintedcircuit boardwithcopperstripsisusedtoelectricallyconnecttheoutsidestrips.Thiscircuitboard isshowninFigure2.39b,withawhitewiresolderedtoeachstrip.Whentheremovable windowframeisinstalled,thisprintedcircuitboardisscrewedtotheframe,asshownin Figure2.39c,formingtheelectricalconnection.Toensurethecontinuityoftheelectrical 54 (a) (b) (c) Figure2.38:Fieldcageentrancewindow.Assembledwindowshownin(a),insertedwindow shownfrom(b)insideand(c)outsidethe˝eldcage. (a) (b) (c) Figure2.39:Fieldcageexitwindow.Silverepoxyconnectingwindowandframestripsshown in(a),copper˝ngersandPCforelectricalconnectionofwindowframein(b),andinstalled windowin(c). 55 connectionaroundthe˝eldcage,1k resistorsareusedatthefront,beamrightcornerto completetheloop.Ifthestripsonthewindowarenotconnectedtothe˝eldcagestripson bothsides,resistancemeasuredacrossthe1k resistorwillbe1k ,butthisresistancewill beshortedifthewindowstripsareproperlyconnected. 2.8.3FieldCageGas Asuitablecountergasmustbeusedwithinthe˝eldcage.Thegasshouldhaveafast driftvelocity,andproducemanyionpairsduringprimaryionization.Thecountergas istypicallyamixofamonatomic˝llgasandapolyatomicquenchinggas.Duringthe avalanche,somegasmoleculeswillbeexcitedratherthanfullyionized,andthephotons emittedduringde-excitationcanionizethe˝llgas,therebycausingionizationatpointsaway fromtheavalanchelocation,andcreatingavalanchesthatarenotassociatedwithanactual hit.Thequenchinggashelpsreducethise˙ect:thephotonsarepreferentiallyabsorbedby thepolyatomicquenchinggas,whichhaslargephoto-absorptioncoe˚cientsoverawider rangeofwavelengthsthanthatofnoblegases,duetoitsmanydegreesoffreedom[30]. Thethinwallsofthe˝eldcageandenclosuremakeitnecessarytousea˝eldcagegas aroundatmosphericpressure.P10gaswaschosenasthecountergas,followingthecounter gaschoicefortheEOSTPCandtheSTARTPC.PropertiesofP10havebeenstudiedin detailforgasdetectors,anditisacommonchoiceofcountergas.Atatmosphericpressure, thedriftvelocityreachesalocalmaximumatanelectric˝eldtopressureratioof E=p =0.146 V/cm/mbar[35].Operatingatthis E=p resultsinadriftvelocitywhichhassmallchanges undersmallvariationsoftheoperatingconditions.Themaximaldriftvelocityisabout5.5 cm/ µ s,soforeachevent,itrequires9.2 µ sforthedriftelectronsnearthecathodetoreach theavalancheregion.Thisproducesanstrictupperlimitontheratewhichcanbeaccepted 56 bythedetector.Afasterdriftvelocitycanallowahigherratetobeaccepted;however,a gaswithfasterdriftvelocitywillhaveareducedinteractionwithchargedparticles,resulting inreducedprimaryionization. FortheS ˇ RITexperimentalcampaign,a6.7kVpotentialwasappliedtothecathode, producinganelectric˝eldof124.73V/cm.Thegas˛owwasabout1L/min,exhausting throughabubblerwith1cmofmineraloiloveratmosphere,correspondingtoapressure of0.78mbaroveratmosphericpressure.Barometricpressurerecordedduringtheexperi- ment˛uctuatedbetween995mbarand1020mbar,correspondingto E=p valuesof0.163 to0.167V/cm/Torr.ComparingtotheMAGBOLTZsimulationsperformedbytheSTAR collaboration[35],thiscorrespondstodriftspeedsbetween5.395cm/ µ sand5.403cm/ µ s. 2.9TargetLadderandMotion Tomountthe˝xedtargetsfortheTPC,atargetmotionassemblywasdesignedtohold5 targets.ThetargetladdercanbemovedseparatelyintheXandZdimensions.Thetarget ladderis˝xedatasetheightwhenitisinstalled;thisheightcanonlybechangedbyopening theTPC.TheXandZmotioniscontrolledfromoutsidethemagnet,usingaseriesofgears formotiontransfer.Thepositionofthetargetladderisdeterminedusingpotentiometers alongtheXandZaxis.ThetargetladderisshowninFigure2.40.Theentrancewindow framepreventsthetargetladderfrombeingpositionednexttothewindow,so3ofthe 5targetsaremountedwithstando˙s,allowingthemtobepositionedinsidethewindow frame.Thewidthoftheentrancewindowframedoesnotallowall5targetstobeplacedon stando˙s. Thetargetladderismountedonthemotioncarriage,showninFigure2.41.Themotion 57 Figure2.40:TargetLadder carriageisabletotraverseintheX-axis,withthecarriageplatformabletomoveintheZ axis.TheZmotionmechanismisinterfacedwiththemotioncarriagethroughabearingand aluminumrod,whicharefreetomoveintheX-axis,butconstrainedintheZ-axisthrough theZmotionmechanism,whichusesathreadedrodtosettheZ-positionofthebearing. TheXmotioniscontrolledusinga102cmlongbrassthreadedrod.AnAcetalnutcouples thethreadedrodandthemotioncarriage.TheAcetalnutwasinitially˝xed,butupgraded aftertheexperimenttohavefreedomofmotionintheZandYdimensions,toaccommodate warpinginthebrassrod. ThemotioncontrolispatchedoutoftheTPCusingrotaryfeed-throughsonthetopplate andbrassgearpairsforcorners.Forthefeed-throughs,2LeskerO-RingShaftSeals,model FMH-25A,wereused.Forthegears,18Bostonmitergears,modelG466Y,wereused.For theZ-motion,5gearpairsareusedtoroutethemotionandfortheX-motion,4gearpairs areused.ThemotionisdirectedoutoftheSAMURAImagnetwiththegears,allowingthe motiontobecontrolledfromoutsidethemagnet,consistentwithsafetyrulesoftheRIBF facility. 58 Figure2.41:TargetMotionCarriage. 2.10Enclosure TheTPCenclosureservesasanelectricallygrounded,gas-tightboxwhichkeepsdelicate componentsprotected,andkeepspotentiallyhazardousfacetscontained.Theenclosure ismadewithanangle-aluminumframe,sealedwithwindowsandplates.Theenclosureis showninFigure2.42,withaclearplasticcoverinplaceofthetopplate.Theangle-aluminum stockisweldedtoformtheframe,withweldscrossingtheO-ringsurfaces.Theseweldshad tobegroundandpolished,toachieveO-ringsealing.Mountingpointsareweldedtoeach corner,whichcanbeusedtomountwheels(asinFigure2.42),orheight-adjustingscrews. ThedesignisshowninFigure2.43,againwiththetopplateremoved.Theupstream endhasa1/2"thickaluminumplate,witha25.3cmdiameterholetoaccommodatethe activevetoarray(discussedinChapter3)andentrancewindow.Thebottomhasa1/2" plate,witha1/4"deeprecessforthevoltagestepdown.Twoclearplasticwindowson theupstreamendoftheleftandrightsidesprovideviewsofthetargetmechanism.Three aluminumwindows,0.032"thick,areusedontheleft,right,anddownstreamendsofthe 59 Figure2.42:TPCenclosurewithtopplateremoved. TPCtoallowchargedparticlestoleavetheTPCwithminimalenergyloss. Thethinaluminumwindowsaresetin1/2"thickaluminumframes.Screwsareusedto mechanically˝xthewindowpanelstothewindowframes,andepoxyisusedtoproducea gas-tightseal.ThewindowframeshavedoubleO-ringgroovesfor1/8"diameterViton(a ˛ouroelastomer)O-ringstosealagainsttheenclosureframe.Theclearplasticwindowsare setin1/2"thickaluminumframes.TheseframesusesingleO-rings,with1/4"diameter. ThelargerO-ringwaschosensincethesewindowsaredesignedtoberemovedandre-installed frequently.TheO-ringgroovesforallwindowsaremadeasdovetailgrooves,whichholdthe O-ringscaptiveduringremovalandinstallation. 60 Figure2.43:TPCenclosuredesign,withouttopplate. 2.11Shipping TheTPCwasshippedfromtheNSCLtoRIKEN,wheretheSAMURAISpectrometeris located,inFebruaryof2014.Acustomcratewithvibrationdampeningandtemperature controlwasusedtoshiptheTPC.ThejourneyinvolvedtransportbytrucktoChicago,from ChicagotoNaritainternationalairport(NRT)byairplane,withalayoverinDallas.Upon clearingcustomsatNRT,theTPCwastransportedtoRIKENonaside-loadedtruck,where itwasloweredintotheRIBFbuildingandunpacked.Thetrucksusedandtheairplanecargo holdwerepartiallytemperaturecontrolled. ThecrateusedtoshiptheTPCwascustomfabricatedbyDeltaPackagingInterna- tional[36],ofLansing,Michigan,withguidancefromDennisYoungoftheMSUPackaging Department.Thecratewaspre-fabricatedandshippedtotheNSCL.Thecratewasbuilton aninsulatedbase,whichcouldbeliftedbyforkliftfromanyside.Aplatformwasmounted onthebaseusingStratocellSfoam,dampeningvibrationsaround70Hz,neartheresonant 61 Figure2.44:Thecratebaseandplatform.Abedofphasechangematerialissecuredtothe platformwithsteelstraps. frequenciesofthewireplanes,asdeterminedbytheirtensionandlength.Thecratebase andplatformareshowninFigure2.44.Thesidesoftheplatformareisolatedfromthewalls usingtheStratocellSfoam,andtheplatformhasabedofPCM22Pphasechangematerial fromRGEES[37],seeninwhitecontainersontheplatform. TheTPCwasmountedtotheplatformusingthemotionchassisandtwoI-beamsas shownintheleftpanelofFigure2.45.Thecratewalls,whichmustberemovedtoput theTPContheplatform,arevisibleinthepicturebackground.TheTPCcouldnotbe airtightduringshipment,toaccommodatechangesinairpressure.During˛ight,theair pressurecandropfrom14psitoapproximately3-4psiifthecargoholdisnotpressurized, orlosespressure.Anair-tightTPCwouldhavetocontain 2 : 25 m 3 ofairata10psipressure di˙erential,potentiallydamagingtheTPC.AsetofupstreamwindowswithHEPA˝lters 62 (a) (b) Figure2.45:TheTPCinstalledonthecrateplatform.Thebedofphasechangematerialis visiblein(a),andthesidepro˝leshownin(b)showsoneoftheHEPAwindow˝lters. wereproducedspeci˝callyforshipment.Oneofthesewindowsisseenintherightpanelof Figure2.45.TheHEPA˝ltersallowtheTPCtobreathe,whilekeepingitcleaninside.In principle,thegas˝ttingsoftheTPCcouldbe˝ttedwith˝lterstoprovidebreathability; however,thelimitedsizeofthegas˝ttingswouldrestrictair˛ow.Toensurefreeexchangeof airbetweenthe˝eldcageandenclosure,thedownstreamwindowwasinstalledwithwashers betweenthewindowframeand˝eldcage,sothatthe˝eldcagewasnotisolatedfromthe enclosurevolume. TheTPCismadeofdi˙erentmaterials,manyofwhichareepoxiedtoeachother.Of particularconcern,the4padplanesectionsaremadeofG10circuitboardandareepoxied tothealuminumtopplate.Thethermalexpansion(orcontraction)ofthesematerialscould causethepadplanetoseparatefromthetopplate,ortodamagetheG10boardinsucha waythattheplanarityofthepadplaneiscompromised.Tomaintainaconstanttemperature whileshipping,theshippingcratewaslinedwithfoaminsulation,andtheplatformhada bedofphasechangematerial(showninFigure2.45).CalculationsdonebyGaryBurgess oftheMSUPackagingDepartmentveri˝edthequantityof85kgofPCM22Precommended 63 Figure2.46:TheTPCinsidethecratewiththecratewallsinstalled. byRGEES.Thefoam-linedwallsareinstalledaftertheTPChasbeensecuredtothecrate platform,withtheinstalledwallsshowninFigure2.46.Thephasechangematerialhasavery highenthalpyoffusion,withameltingpointjustaboveroomtemperature.Temperature monitorswereinstalledontheinteriorandexterioroftheshippingcrate,torecordthe minimumandmaximumtemperaturestheTPCwassubjectedtoduringthejourney. Withthewallsandlidofthecrateinstalled,thecratewasfullypackedandhadto beweighedforshipment.TheTPChadbeenpreviouslyweighedatabout1000lbs,and themotionchassisat294lbs.Thefullypackedcrateweighedapproximately3200lbs.In additiontotheoverallweight,thecratewasweighedfromeachsidetodeterminethecenter ofgravity(COG),whichwasthenmarkedonthecrateexterior.Figure2.47showsthecrate beingweighed(leftpanel),andoneoftheCOGmarkingsonthecrateexterior(rightpanel). TheleftpanelofFigure2.47alsoshowsoneoftheNTELL Š "indicatorswhichwere 64 (a) (b) Figure2.47:Weighingthepackedcrate.Inadditiontotheoverallweight,thecratewas measuredfromeachend(a)allowingustodetermineandmarkthecenterofgravity(marked withorangepaintin(b)). placedonthecrate,andthetemperaturedisplay,whichislinkedtotheinteriortemperature monitors.Havingtheseindicatorsontheoutsideofthecrateallowsinspectionofthecrate withoutunpacking,whichisveryimportantforliabilitypurposes. Loadingandunloadingthecrateontotrucksrequiredthatthecratecouldbeliftedby forkliftfromanyside.Whenmovingthecratewithaforklift,itisnecessarytostrapthe cratetotheforklift,asaprecautionagainsttipping.ThestrapsarevisibleinFigure2.48, priortotightening.Thestrapswereusedregardlessofifthecratewasforkedfromthefront orside,asisvisibleinFigure2.49a,whichshowsunloadingthecratefromtheside-loaded truckatRIKEN. UponarrivalatRIKEN,theTPCwasloweredtotheB2FleveloftheRIBFbuilding, approximately22mbelowgroundlevel.Thecratewasallowedtoacclimatefor24hours beforeitwasunpacked.TheNTELL Š "indicatorsdidnothaveanysignoftipping, andthetemperaturewithintheshippingcratehadvariedbyonlyonedegreecentigrade duringshipping.Eachwireplanewascheckedforshorting,andbiasedtocheckleakage 65 Figure2.48:StrappingthecratetotheforkliftattheNSCL.Twoliftingstraps(yellow)are securedtotheforkliftwithachain,visibleonthetopofthecrate. (a) (b) Figure2.49:MovingtheTPCcrateatRIKEN.(a)removingthecratefromtheside-loaded truckwithaforklift,and(b)loweringthecratetotheB2FareaofRIBFusingacrane. 66 current.TheTPCwascheckedforleaksbypressurizingwithP10andcheckingallseams andscrewholeswithacombustiblegasdetector. 2.12DisassemblyandReassemblyofTPC ItissometimesnecessarytodisassembletheTPCtoperformrepairs,orinstallupgrades. Structurally,theTPCisformedbytwohalves:theenclosure,withbottomandsideplates attached,andthetopplate,withpadplane,wireplanes,and˝eldcageattached.Towork oncomponentsoutsidethe˝eldcage,sidewindowsoftheenclosurecanberemovedbyhand foraccess.Toworkoncomponentswithinthe˝eldcage,thetopplatemustberemoved fromtheenclosure,andthe˝eldcageremovedfromthetopplate.Toworkonthewire planes,thetopplateshouldthenberotatedtothetablecon˝guration. TodisassembletheTPC,caremustbetakentoavoiddamaginganysensitivecomponents. Priortoremovingthetopplate,gasconnections,electricalconnections,andtargetmotion peripheralsmustberemoved.Ifthetopplateistoberotated,theGETelectronicsmustbe removed,aswellasthegatinggriddriver.Thetopplateshouldbeinspectedforanyloose materialssuchasscrewsortoolsbeforeremoval. Whenitisdesiredtoputthetopplateinthetablecon˝guration,themotionchassis willbeinstalledtothetopplatepriortoremoval,asshowninFigure2.50.Twolifting strapsconnectthemotionchassistoanI-beamspreaderforliftingthetopplate,andtwo liftingstrapsconnectasideofthetopplatetoamanualchainhoist,tocontroltherotation. Thetopplateisliftedfromtheenclosureusingacrane,whileatleastonepersonwatches fromeachsideoftheTPC,toensurethetopplateand˝eldcageslidesmoothlyoutofthe enclosure.Whenthe˝eldcageissafelyabovetheenclosuresurface,theenclosurecanbe 67 Figure2.50:Liftingthetopplateand˝eldcageoutoftheenclosure. rolledaway.Thechainhoististhenusedtoliftonesideofthetopplate,rotatingtothe doorwaycon˝guration.Figure2.51ashowstherotationinprogress.Withthetopplatein thedoorwaycon˝guration,itisloweredsothatthemotionchassiswheelsareplacedonthe ˛oor.Leadbricksareplacedonthemotionchassisascounterweights,topreventtipping. Withthetopplateindoorwaycon˝guration,theliftingstrapsareremovedandthedetector ismovedintoacleantentforfurtherdisassembly,asshowninFigure2.51b. The˝eldcageisremovedwiththetopplateinthedoorwaycon˝guration.Thegasand electricalconnectionstothetopplatemustbedisconnected.Alternatingscrewsareremoved fromthe˝eldcage,andreplacedwithsetscrewsandwingnuts.Theremainingscrewsare thenremoved.Withthewingnutsloosened,sheetmetalclips,coveredwithacrylictape,are insertedaroundthetopperimeter,toholdtheO-ringscaptive.Afterremovingthewing nuts,the˝eldcagecanberemovedbythreepeople,leavingtheLexanringinplace,asshown inFigure2.52a.The˝eldcageshouldremaininthecleanenvironment,withthespringson 68 (a) (b) Figure2.51:Rotatingthetopplateand˝eldcage(a),andmovingthetopplateand˝eld cageindoorwaycon˝guration(b). thecathodeandthewindowsprotected.Aprotectivecovercanthenbeplacedoverthewire planes,incorporatingtheLexanring.ThiscoverisshowninFigure2.52b.Therotation procedureisthenrepeatedtobringthetopplatetothetablecon˝guration.Thereassembly followsthesameprocedureinreverse. (a) (b) Figure2.52:Removingthe˝eldcagefromthetopplate(b),androtatingthetopplate without˝eldcage(b). Analternativedisassemblyprocedure,whichdidnotrequirerotation,wasdeveloped 69 (a) (b) (c) (d) Figure2.53:Alternativeprocedureforremoving˝eldcagewithoutrotation:liftingtopplate (a),stabilizedtopplate(b),purpose-builtcartfor˝eldcageremoval(c),slidingthe˝eld cageawayfromtopplate(d). forupgradestothe˝eldcage.ThisprocedurewasperformedinacleantentatRIKEN. Althoughtheelectricalandgasconnectionshadtobedisconnected,theGETelectronicsdid notneedtoberemoved(asigni˝cantadvantage).A1000kghoistisused,withliftingstrap con˝gurationshowninFigure2.53a.Sincetheweightofthetargetmechanismdisplacesthe centerofgravity,counterweightsareplacedonthecornersofthetopplatetokeepitlevel duringtheliftingprocess.Thetopplateand˝eldcageareliftedabovetheenclosure,and theenclosureispulledawayonwheels.Thetopplateisloweredontotwoelectricalracks 70 Figure2.54:Illustrationofelectronleakagepriortorepair. forstability,asshowninFigure2.53b.The˝eldcageisloweredawayfromthetopplate usingacartwith4labjacks(showninFigure2.53c).Aluminumtabswiththreadedholes areusedtosecuretheLexanringpriortofullyremovingthe˝eldcage.The˝eldcageis thenfullyremovedfromthetopplate.Figure2.53dshowsthe˝eldcagebeingpulledaway. 2.13TPCUpgrades AftertheS ˇ RITexperiment,speci˝careasforimprovementwereidenti˝ed.Twoissueswere determinedtobecritical,andsolutionsweredevelopedandimplementedinearly2018.The ˝rstissueinvolvedthespeci˝cgeometryofthe˝eldcage,whichalloweddriftelectronsto passaroundthegatinggrid,enteringtheavalancheregiononthedownstreamendofthewire planes.Thustheampli˝cationinanodeplane14occurredforallbeamparticlesentering theTPC,potentiallyinducingspacechargee˙ectsanddetectoraging.Further,duetothe feedthroughsharingdescribedinSection2.7,thiselectronleakageinducedextracurrent onanodeplanes12and14.Thesecondissuewasdi˚cultyandreliabilityoftargetmotion. ThebrassleadscrewforX-motioncreatedfrictioninthemotion,asdidthemotioncarriage platform,whichtiltedwhenpushedintheZ-direction,causingtheX-motiontoseize. 71 Figure2.55:Upgradetopreventleakagearoundgatinggrid. Thewireplanesdonotextendtheentirelengthofthe˝eldcage.Thegapoflessthan4 cmbetweenthewireplanesandtopperimeterisshownintheleftsideofFigure2.55.The problemcanbesolvedbyextendingthetopperimetertocoverthegap,removingtheleakage pathfordriftelectrons.ThedesignedupgradeisshownintherightsideofFigure2.55,with analuminumplateclampedontothetopperimeterofthe˝eldcage. The˝eldcageisremovedasdescribedinSection2.12.Theinstalledaluminumblocking plateisshowninstalledinFigure2.56.Thepolycarbonateplateisscrewedtothetop perimeter,andusedasareferencepointforclampingthealuminumblockingplate.The plateiselectricallyconnectedtothetopperimeter,matchingtheelectricpotential. Theupgradestothetargetmotionfocusedontwoprinciples:reducingmotionresistance, andmakingthemotiontransferstructuremoresturdy.MotionintheX-axisiscontrolled usingaleadscrewandnut,whichisshowninFigure2.57,withtheupgradeddesigninstalled. Thewarpedbrassleadscrewincreasedresistance,astheconstrainedmotionofthemotion carriagerequiresbendingtheleadscrew.Figure2.58showstheoriginal˝xednutdesign,and theupdateddesign,wherethenutisfreetotravelintheYandZaxis.Byaccommodating thewarpingoftheleadscrew,theresistanceisgreatlyreduced.Althoughareplacement 72 Figure2.56:Theinstalled˝eldcageupgrade(April2018). Figure2.57:Theinstalledtargetmotionnut,whichaccommodatesawarpedleadscrew (April2018). 73 Figure2.58:Floatingleadnutdesigntoaccommodatewarpingofleadscrew. leadscrewcouldbemade,itiscostliertoproduceanewleadscrew,andthereplacement couldalsobewarpedfromthemachiningprocess. TotraversetheZ-axis,themotioncarriageplatformmovesontworailsonthemotion carriage.Whentheplatformispushedfromano˙-centerpoint,theplatformtwistson therails,greatlyincreasingmotionresistance.Thisproblemalsoa˙ectstheX-motion: thetwistingcinchesarodandbearing,causingfrictionduringX-motion.Thisissuewas addressedbycreatingamotionlinkingsystem(designshowninFigure2.59a),whichforces theplatformtomoveequallyalongitsrails.Theredbarsformatwohalvesofarhombus linkage,andthepurplebarconnectsthemtoformamodi˝edrhombuslinkage.Theinstalled upgradeisshowninFigure2.59b. Finally,tomaketheentiredesignmoresturdy,largebrassgearswereusedforevery corner,replacinggearboxesentirely.Themotionwastestedafterupgradesandobservedto besigni˝cantlyimproved. 74 (a) (b) Figure2.59:Motionlinkingsystem(a)designand(b)installed. 75 Chapter3 ExperimentalSetupandTrigger Selection 3.1S ˇ RITTPCinsidetheSAMURAISpectrometer TheS ˇ RITTPCwaspreviouslydescribedinChapter2.Duringtheexperiment,theTPC wasinstalledinsidetheSAMURAISpectrometeratRIKEN.Thefacilitylayoutwillbe discussedinChapter4.TheexperimentallayoutwithintheSAMURAIareaisillustrated inFigure3.1,withdimensionsinmm,andtheoriginoftheSAMURAIcoordinatesystem shownnearthecenterofthe˝gure.Itisconvenienttousetwoseparatecoordinatesystems todescribetheexperimentallayout:theSAMURAIcoordinatesystemandtheS ˇ RITTPC coordinatesystem.Therelativepositionandorientationofthesecoordinatesystemsmust beknowntoproperlyanalyzetheexperimentaldata. IntheSAMURAIcoordinatesystem,the z -axisisorientedalongthebeamlineaxis(not tobeconfusedwiththebeamaxis,whichbendsinsidethemagnet),the y -axisorientedanti- paralleltogravity,andthe x -axisde˝nedtoformaCartesiansystem,whichsetsthe x -axis tothebeamleftsideofthebeamlineaxis.TheoriginliesinthecenteroftheSAMURAI magnet.TheS ˇ RITTPCcoordinatesystemisde˝nedrelativetothepadplane,andis illustratedinFigure2.1.ThecoordinatesystemoftheS ˇ RITTPCisnominallyaligned 76 Figure3.1:Schematicviewofexperimentallayout. withtheSAMURAIcoordinatesystemwithsomeo˙set;however,somedi˙erenceinthe actualalignmentofcoordinatesystemswillbediscussedinthefollowingsection.The x - z planeoftheTPCcoordinatesystemliesonthepadplane,withthe y -axisextendingabove thepadplane,anti-parallelwithgravity.The z -axispointstowardsthedownstreamsideof thepadplane,andthe x -axispointstothebeamleftdirectionofthepadplane.Theorigin issettothecenterofthepadplanein x ,andtheupstreamedgeofthepadsin z . 3.2TPCalignmentandMeasurement Theinitialplacementofthedetectorsisperformedusingalaseralignmentsystem.Rotating laserswereusedtoproducereferenceplanes,allowingustosetthelevelandheightofthe TPCtomatchthereportedbeamheight.FixedmarkersintheSAMURAIareawereused asreferencesforthebeamlineaxis.TheTPCwasalignedbyscribemarksontheenclosure. TheTPCenclosureiscenteredin x oftheSAMURAIframe,andliftedtothetopofthe magnetgap,withasmallclearance.Thetargetheightisadjustablewithintheenclosure,and 77 isalignedtobecenteredatthebeamheight( y =0intheSAMURAIframe).Thealignment ofthetargetheightisshowninFigure3.2.Inthepicture,apieceofgraphpaperwas temporarilymountedinthetargetladder,facilitatingalignmentwiththelaser. Figure3.2:Laseralignmentoftargetheight Afteralignment,the˝nalpositionofdetectorsystemswasdeterminedusingaPho- togrammetryMeasurement(PGM)systemcalledV-STARS,whichisproducedbyGeodetic Systems,Inc.[38].Thistechniqueuses˛ashphotographytolightretrore˛ectivemarkers whichareplacedonthepointstobemeasured.Figure3.3showstheSAMURAIareawhile themeasurementwasperformed.Twoyellowbarsnearthecenterofthephotohavemarkers atprecisedistances,allowingthescaletobedetermined.Manyphotographsaretakenusing acamerawhichstoresinformationaboutitsangularorientationwhiletakingaphoto.The proprietaryV-STARSsoftwareisusedtocombineinformationfromthephotographsinto anarrayof3dimensionalpoints.FixedreferencepointsintheSAMURAIareaareusedto transformthemeasurementintotheSAMURAIcoordinatesystem. 78 Figure3.3:Flashphotographhighlightingretrore˛ectivephotogrammetrymarkers ApreviousPGMmeasurementoftheTPC[39]providedreferencepointsontheTPC, whichareusedtodeterminetheTPCpositionintheSAMURAIframe.Eventhoughthe triggerdetectorsobscuredmostofthemarkersontheTPC,15oftheTPCmarkerswere foundinthemeasurementoftheTPCinSAMURAI.Anumericalanalysiswasusedto minimizetheresidualsbetweenthetwosetsofmeasuredpoints(TPCinSAMURAI,TPC standalone)usingsingularvaluedecomposition[40],implementedwithaPythonscript.This minimizestheresidualsbetweenthemeasuredpointsintheSAMURAIcoordinatesystem andthereferencepoints,producingabesttranslationandrotationbetweentheTPCand SAMURAIcoordinatesystems.Usingthisbesttranslationandrotation,theoriginofthe S ˇ RITTPCpadplaneisfoundtobe: ( x;y;z )=(1 : 794 ; 205 : 502 ; 580 : 526) mm(3.1) 79 intheSAMURAIcoordinates,de˝ningtherelativepositionofthetheoriginsofthetwo frames.Theerrorisevaluatedasthestandarddeviationbetweenthemeasuredpositions andreferencepositions,andwasfoundtobe ( x;y;z )=(0 : 276 ; 0 : 090 ; 0 : 443) mm : (3.2) Thenormalized( ~x;~y;~z )vectorpointingfromthepadplaneorigintothecenterofthe downstreamendofthepadplaneis ( ~x;~y;~z )=(3 : 3397 10 4 ; 5 : 946 10 5 ; 0 : 9999) ; (3.3) whichde˝nesthe z axisoftheTPC.Thenormalizedvectorpointingfromthepadplane origintotheupstream,beamleftcornerofthepadplaneis ( ~x;~y;~z )=(0 : 9999 ; 3 : 616 10 4 ; 3 : 3397 10 4 ) ; (3.4) whichde˝nesthe x axisoftheTPC.The y axisthusliesalongthenormalizedvector ( ~x;~y;~z )=(3 : 606 10 5 ; 0 : 9999 ; 5 : 968 10 5 ) : (3.5) TherotationmatrixfromSAMURAIframetoTPCframeisthen 0 B B B B B @ x 00 y 00 z 00 1 C C C C C A = 0 B B B B B @ 13 : 616 10 4 3 : 34 10 4 3 : 616 10 4 15 : 934 10 5 3 : 34 10 4 5 : 946 10 5 1 1 C C C C C A 0 B B B B B @ x y z 1 C C C C C A ; (3.6) 80 wheretheunprimedcoordinatesalignwiththeSAMURAIframe,andthedouble-primed coordinatesarealignedwiththeTPCframe. 3.3TriggerDetectors Figure3.4:PhotographoftheTPCandancillarydetectorsinstalledintheSAMURAI spectrometer. Tocreateaphysicstrigger,ancillarydetectorsystemsareused.Figure3.4showsthe TPCinstalledinsidetheSAMURAIspectrometerwiththetriggerdetectors.TheKATANA arrayscintillatorsarelocatedonthedownstreamendoftheTPCandarecoveredwitha re˛ectivewrapping,whiletheKyotoMultiplicityArrayscintillatorsarelocatedonthebeam leftandrightsidesoftheTPCandhaveanadditionalblackplasticwrapping.TheActive VetoArrayandScintillatingBeamTriggerarrayarenotvisibleinthe˝gure. 81 3.3.1ScintillatingBeamTrigger TheScintillatingBeamTrigger(SBT)arrayservesasastartcounter.TheSBTarray consistsoftwothickplasticscintillatorsmountedinparallel,asshowninFigure3.5.Each scintillatorisreadoutontheleftandrightbyPMTs.TheSBTismountedapproximately 4.5mupstreamofthetarget,transversethebeampipe,showninFigure3.5.Thelogical ORofthePMTsisusedtoprovideastartsignalforthetrigger. Figure3.5:SBTarray 3.3.2KyotoMultiplicityArray TheKyotoMultiplicityArray[41]consistsoftwoscintillatorarrays,eachcontaining30 plasticscintillatorbars.Figure3.6showstheschematicdrawingoftheTPCwiththeKyoto MultiplicityArrayinstalled.Onlyonesideisvisible,withtheKyotoMultiplicityArraybars 82 shadedgrayintheillustration.ThesecondarrayismountedontheoppositesideoftheTPC. The ˘ 1.5mmthickG10˝eldcagewallsand ˘ 0.8mmthickaluminumenclosurewindows allowchargedparticlesfromtheheavyioncollisionstobedetectedbythescintillating arrays.Eachscintillatorbaris450 50 10mm 3 ,with1mmdiameterlightguide˝ber placedinsidea1.5mmdiameterholerunningthroughthecenterofthebar.Eachbaris coatedwithoxidizedtitaniumforlightre˛ection.Thelightfromthelightguide˝beris detectedbya1.3mm 2 HamamatsuMultiPixelPhotonCounter(MPPC),which,unlike normalphotomultipliertubes,canfunctioninsidethemagnetic˝eld. Figure3.6:DesigndrawingoftheKyotoMultiplicityArraymountedontheTPC TheMPPCsignalsareshapedanddiscriminatedusingEASIROC[42]chips,ASICchips designedspeci˝callyforsiliconphotomultiplierdetectors.Toprocessthedigitaloutputs fromtheEASIROCchips,andtocontrolthechips,anFPGAchipisintegratedwitheach EASIROCchip.DiscriminatorswithintheEASIROCchipwillproduceadigitalsignalas- sociatedwitheachMPPCsignal,andtheFPGAchipwilldeterminethetotalnumberof signalsproducedineachevent,providingamultiplicitymeasurementfromtheKyotoMul- 83 tiplicityArray.TheFPGAisabletoachievethefastresponserequiredfortriggeringby determiningthemultiplicitythroughROMsettingsandaddercircuits[41].Additionally,a multi-hitTDCwith1nstimeresolutionwasimplementedwiththeFPGAchip,allowing moredetailedo˜ineanalysisofthehitsontheKyotoMultiplicityArray.FortheS ˇ RITex- periment,thetypicalmultiplicityrequirementwas4orgreaterwithintheKyotoMultiplicity Array. 3.3.3KrakowKATANAArray TheKATANAarray[43]consistsof12plasticscintillatingpaddles,each400 100 10mm 3 insize,and3thinplasticscintillatingpaddles,400 100 1mm 3 insize,placedatthe downstreamedgeoftheTPC.ThedesignoftheKATANAarrayisshowninFigure3.7, viewedfromthedownstreamperspective.Theleftsideshowstheentirearray,whilethe rightsideshowsthearraywithoutthickpaddles.Thethinvetopaddlesareinstalledinan overlappingfashiontomaximizedetectione˚ciency.Thereare7thickpaddlesonthebeam rightsideofthecentervetopaddle,and5onthebeamleftside.Thisasymmetryischosen sincemostparticlesproducedwillhavepositivecharge,andbendtowardsthebeamright side.Foreachbeam,thearraypositionisoptimizedsothatthecentervetopaddleintersects thepathoftheunreactedbeam. Thethresholdonthevetopaddlesischosentoprovideavetosignalwheneverabeam particleorfragmentwithchargeZ ˇ 20 orgreaterpassesthrough.Thelightsignalin eachscintillatoriscollectedusingMPPCs:onthethickpaddles,aHamamatsuS12572- 025PMPPCisplacedonthetopandbottomofeachpaddle,whileonthethinpaddles,a HamamatsuS12571-010PMPPCissplacedonallfourcornersofeachpaddle.TheMPPCs aremountedtoaprintedcircuitboardwithapreampli˝er,tominimizenoise. 84 Figure3.7:DesigndrawingoftheKATANAarray.Thickscintillatorsareshowninblueand vetoscintillatorsareshowninpurple.Theleftsideshowstheentirearray,andtherightside showsthearraywithvetopaddlesisolated TheanalogMPPCsignalsfromeachpaddlearesummedtoproduceasinglesignal, withanormalandaninvertedsignaloutput.Thenegativesignalsaresenttoa20-channel discriminatorboardwithleadingedgediscriminators,andcomparedtothresholdlevelswhich aresetremotely.Theresultinglogicsignalisanalyzedwithalogiccircuitmadewith anFPGAboard,whichanalyzesthe15signalsproducedfromKATANApaddles,aswell asotherlogicsignalsusedforthetrigger.Gate&Delay(G&D)modulesareprogrammed intotheFPGAboard,allowingpropersynchronizationofsignalsforlogicprocessing.The delaydurations,gatewidths,aswellastheKATANAmultiplicitythreshold,arecontrolled remotelywithaRaspberryPiboard[44].Thediscriminatorboard,FPGAboard,logicoutput bu˙ers,andtheRaspberryPicontrollerareintegratedintoasingleunit,referredtoasthe riggerBox".TheresultingriggerBox"triggerisincorporatedintoaseparatetrigger logic,describedinSection3.4.4.ForfurtherinformationontheKATANAarrayandthe TriggerBox,readersarereferredtoReference[43]. 85 3.3.4ActiveVetoArray TheActiveVetoArray[45]consistsoffourplasticscintillators,each90 50 6mm 3 insize, placedontheupstreamedgeoftheTPCentrancewindowtoremoveeventswherethebeam particleiso˙-target.EachscintillatorusesaHamamatsuS10931-100PMPPCtogenerate asignalwhenachargedparticlepassesthrough,withthesamepreampli˝erPCBswhich wereusedfortheKATANAarray.SignalsfromtheActiveVetoArraywerediscriminatedby theTriggerBox.Thescintillatorsarearrangedinanoverlappingfashion,formingapro˝le aroundthebeampath,withemptyspace.TheActiveVetoArrayassemblyisshownin Figure3.8,withanaluminumhousing˝xture.Thetopandbottomscintillatorsareplaced with38mmofseparation,andtheleftandrightareplacedwith26mmofseparation.The overallpositionoftheleftandrightwassettoallowdesiredbeamstopassthroughandhit thetargetwithoutadjustmentbetweensettings.Thepaddlepositionsarealladjustable,to accommodatedi˙erenttargetsizesaswellasdi˙erentbeamrigidities. Figure3.8:PhotographoftheActiveVetoArray. 86 TheActiveVetoArrayis˝xedtothefrontplateoftheTPC,asshowninFigure3.9with abreak-outview.Thealuminumhousingisshowninturquoisebluewhilethescintillators areshowninpurple.Inoursetup,thereis23.8cmbetweenthe˝eldcageentrancewindow andtheleft/rightscintillators,and22.2cmbetweenthe˝eldcageentrancewindowandthe up/downscintillators.Theinneredgeoftheleftscintillatorispositioned21mmtotheleft ofthecenteroftheTPC,andtheinneredgeoftherightscintillatorisplaced5mmtothe rightofthecenteroftheTPC.ThebeamenterstheTPCtotheleftoftargetcenter,andis curvedtotargetcenterbythemagnetic˝eld. Figure3.9:BreakoutviewoftheTPCwithActiveVetoArrayinstalled 3.4TriggerSelection Thetriggercontrolstheselectionofeventsandcontrolstheopeningandclosingofthe gatinggrid.Thetriggerisdesignedtomaximizetheselectionofcentral,on-targetreactions, whileminimizingtheselectionofperipheraloro˙-targetevents.TheActiveVetoArrayis usedtorejecto˙-targeteventsfromthetrigger,whiletheKATANAVetoisusedtoreject 87 eventswithunreactedbeamparticles.AminimummultiplicityrequirementfromtheKyoto MultiplicityArrayisimposed,toselectcentralevents.Apreliminarytrigger,orFastTrigger (Section3.4.1),isproducedwithrackelectronics.Thegatinggridisopeneduponreceiving afasttrigger,whichmustbevalidatedbyatriggerfromtheKATANATriggerBox.Ifthe latterisnotproduced,thetriggerisfast-cleared,closingthegatinggrid.Thetriggercan alsobevetoedbyaKATANAVetosignal,whichwouldindicatethepresenceofasecond beamparticleorheavyprojectileresidue.Abusycircuitpreventstheformationofatrigger whiletheDAQiswriting,orifthesystemisotherwiseunabletorecordanentireevent. 3.4.1FastTriggerandFastClear Thefasttriggerisnecessarytobeginopeningthegatinggridasquicklyaspossible.Thefast triggerismadewithrackelectronics,requiringaScintillatingBeamTrigger(SBT)signalin coincidencewiththeKyotomultiplicitysignal,withoutaKATANAVetosignalorabusy signal.ThegatefortheKATANAVetois4 µ swide.Thisintroducesadeadtimeof4 µ s, whichcorrespondstothetimeforthechargeinducedbyabeamparticletobesafelycollected bytheclosedgatinggrid.Thisisnecessarytopreventthechargeproducedbyanearlier beamparticlefrompassingthroughthegatinggridandreachingtheanodeplaneinthecase thatasubsequent,otherwisetrigger-satisfying,reactionoccursbeforethechargefromthe ˝rstbeamparticlehasdissipated. Onekeydi˙erenceshouldbenotedbetweenthetwoexperiments:forthe 124 Xeprimary beam(the˝rstexperimentalrun),theKATANAVetosignalsarediscriminatedintherack trigger,whileforthe 238 Uprimarybeam(thesecondexperimentalrun),theKATANAVeto signalsarediscriminatedintheKATANAtriggerbox.Thefasttriggerisdiagrammedin Figure3.10. 88 Figure3.10:Fasttriggerlogic IfafasttriggerisproducedwithoutaTriggerBoxtrigger,thesignalisfastcleared.The fastclearcircuitallowsthegatinggridtobequicklyclosedifaneventisnotrecorded,which preventsunnecessarychargeampli˝cation,andreducesthetriggerdeadtimebylimiting unnecessarybusytime.Thisoccurredontheorderofa2-10Hz,dependingonbeamrate. ThefastclearlogicisshowninFigure3.11,withtheKATANATriggerBoxabbreviatedas K-BoxTrigger. Figure3.11:Fastclearlogic 3.4.2GGDLogic TheopeningandclosingoftheGGDiscontrolledthroughTransistor-TransistorLogic(TTL) signals.ThecontrolcircuitwithinthetriggerwasformedusingtwoLeCroyModel222Dual GateGenerators,foratotalof4distinctG&Dmodules.Forclarity,thesewillbereferred 89 Figure3.12:GatingGridDriverLogic tobyG&D1-4.ThelogicisillustratedinFigure3.12.Itisperhapseasiesttounderstand byexaminingG&D2˝rst,whichisalatchcircuit.Whenthelatchisopen,aTTLsignal isprovidedtotheen"inputoftheGGD.Whenthelatchisclosed,theTTLsignalis removedfromtheGGDopen,andthedelaysignalissenttoG&D4,whichsendsa5 µ s widesignaltotheinputoftheGGD.TheforG&D2isprovidedbyG&D1, whichsendsasignalwhenafasttriggerismade.TheforG&D2isprovidedbythe GGDstopcircuit.Tosummarizethelogicsofar:afasttriggerwillstarttheopening process,andaGGDstopsignalwillremovetheen"signal,whilesendinga5 µ s wide"signaltotheGGD. TheGGDstopcircuitistriggeredbyanyofthreeconditions:(i)theG&D1delay, whichsendsasignal11 µ safterafasttriggerisreceived,(ii)afastclear,describedinthe previoussection,or(iii)bytheG&D3delay,whichistriggeredwhenaKATANAveto signalisprovided.TheG&D3delaywastunedto650nsduringthe 124 Xeprimarybeam experiment,and800nsforthe 238 Uprimarybeamexperiment.Anadditionaldi˙erence betweenthetwoprimarybeamswasthediscriminationoftheKATANAvetosignals:For 90 the 124 Xeprimarybeamexperiment,theKATANAVetosignalsarediscriminatedinthe racktrigger,whileforthe 238 Uprimarybeamexperiment,theKATANAVetosignalsare discriminatedintheKATANAtriggerbox.Thethresholdsfortherackandtriggerbox discriminatorsweresimilar,butthetriggerboxdiscriminatorsareremotelyadjustable,and areusedinthedeterminationofthetriggerfortheDAQ. 3.4.3BusyCircuit ThebusycircuitpreventsatriggerfrombeingformedwhentheDAQortheTPCisunable tohandleatrigger.TheDAQproducesitsownbusy,butthismustbecombinedwithbusy signalsfortheGGD.The11 µ sgatefromG&D1andthe5 µ sgatefromG&D4areboth includedinthebusycircuitwiththeDAQbusy.Thefasttriggerwillthenproducean11 µ sbusy,whileanyGGDstopR"signalwillproducea5 µ sbusy.Whenamastertrigger isproduced,itwillproduceabusysignal,bridginganydelaybetweentheformationofa triggerandtheDAQbusysignal. 3.4.4KATANATriggerBox TheKATANAtriggerboxcombinesa20-Channeldiscriminatorboard,anFPGAboard,logic outputbu˙ers,andaRaspberryPiboardtoformaremotelyprogrammablelogiccircuit[43]. AcomprehensivediagramofthetriggerboxarchitectureisshowninFigure3.13.This documentationfocusesontheriggerLogic"portionofthisdiagram.Thelogiccircuitused withinthetriggerboxissimilartothefasttrigger,withtheadditionoftheActiveVeto signal.ThetriggerlogicisshowninFigure3.14,withdelaysandgatewidths. 91 Figure3.13:KATANATriggerBoxarchitecture Figure3.14:KATANATriggerBoxlogic 3.4.5TriggerforDAQ TheMasterTrigger,orthetriggerrequiredforDAQreadout,closelyresemblesthefast triggercircuit,withtheadditionoftheKATANABoxTrigger,andwithoutthevetoorbusy asdirectinputs.ThevetoandbusysignalsareprocessedwithintheKATANAboxtrigger. Thelogicforthe 124 XeprimarybeamexperimentisshowninFigure3.15,andthelogicfor the 238 UprimarybeamexperimentisshowninFigure3.16.Theonlydi˙erenceisthatfor thesecondexperiment,theKyotoMultiplicityrequirementisremoved.Thereasonforthis di˙erenceisdiscussedinthefollowingsection.Forthefunctionofthetrigger,itissu˚cient 92 tonotethatthisdi˙erencedidnota˙ectthedatataken. Figure3.15:LogicforMasterTrigger,orDAQtrigger,duringthe 124 Xeprimarybeam experiment Figure3.16:LogicforMasterTrigger,orDAQtrigger,duringthe 238 Uprimarybeam experiment 3.4.6Di˙erencesBetweenPrimaryBeamTriggers Asdiscussedinthepreceedingsection,thetriggerhadsomedi˙erencesbetweenthetwo experiments.Asummaryofthedi˙erencesisprovidedhereforeaseincomparingthe twotriggers.Forbrevity,the 124 Xeprimarybeamexperimentwillbereferredtoasthe ˝rstexperiment,andthe 238 Uprimarybeamexperimentwillbereferredtoasthesecond experiment. The˝rstdi˙erenceisthediscriminationoftheKATANAVeto:inthe˝rstexperiment, theKATANAVetoisdiscriminatedintherackelectronicsforthefasttriggerandtheGGD closing,whileitisdiscriminatedinthetriggerboxforformationoftheMasterTrigger. Ifthediscriminationintherackelectronicsismoresensitivethaninthetriggerbox,a 93 MasterTriggercanbeformedwhilethegatinggridhasnotbeenopened.Ifthetriggerbox discriminationismoresensitivethantherackelectronics,thegatinggridmaybeopenedfor aneventwhichwillnotformaMasterTrigger.The˝rstcasecanresultintakingdatawhich isnotusable,whilethesecondcasewillincreasetherateofGGDopeningandclosing.Inthe secondexperiment,weaddressedthisissuebydiscriminatingtheKATANAVetosignalonly withinthetriggerbox,providingaconsistentconditionfortheGGDandMasterTrigger. Theseconddi˙erenceisthedelayfromtheKATANAVetoORtotheGGDstop:inthe secondexperiment,thisdelaywasreducedfrom800nsto650ns,toaccountforanyextra delayfromthetriggerboxdiscrimination.Thischangeisnotlikelytohaveamajorin˛uence onthedatataken,butlikelycausesasmalldi˙erenceinthetimerequiredforafastclosing. Finally,theKyotoMultiplicityrequirementwasdirectlyincludedintheMasterTrigger forthe˝rstexperiment,butwasremovedforthesecondexperiment.Duringthe˝rstex- periment,thisrequirementwasnecessaryduetoanissuewithintheKATANAtriggerbox, whichtheKATANAmultiplicityandKyotoMultiplicityrequirement.TheKATANA Multiplicityrequirementwasinitiallysetto 20,whichwouldtheoreticallypreventthere- quirementfrombeingsatis˝ed;however,themultiplicitywasstoredasa4-bitnumberinthe triggerbox.Thebinarynumber00010100=20wascuto˙tobe0100=4,resultingintrig- gersformultiplicity 4.ThisresultedinKATANAtriggerboxtriggerswithouttheKyoto Multiplicityrequirementbeingful˝lled.TheadditionoftheKyotoMultiplicityrequirement directlyintheMasterTriggercircuitwasnecessarybeforesolvingthisissue,buttheproblem wasunderstoodduringthe˝rstexperiment,allowingustoremovetherequirementfromthe MasterTriggercircuitforthesecondexperiment. 94 3.5OtherAncillaryDetectors 3.5.1BeamDriftChambers TwoBeamDriftChambers(BDCs)areemployedaroundfocalplaneF13,upstreamofthe SAMURAIspectrometer.ThedetectorsareWalenta-typewirechambers[46]with2.5mm driftlengths,allowingforhighbeamrates.Adetaileddescriptionoftechnicalpropertiesof theBDCscanbefoundinReference[28],alongwithschematic˝guresofthedetectors.Key detailsincludethee˙ectiveareaof8 8cm 2 ande˙ectiveresolutionofapproximately100 µ m(rms).BDC1andBDC2aredenotedinFigure3.1,aswellastheirpositions,measured relativetotheoriginoftheSAMURAIcoordinatesystem.ThecenterofBDC1is3159.7 mmupstreamoftheSAMURAIorigin,whilethecenterofBDC2is2158.7mmupstreamof theSAMURAIorigin.Theinformationfromthesedetectorsisusedtoreconstructthebeam trajectoryasitenterstheSAMURAIspectrometer.Thisinformation,alongwithbeam informationfromBigRIPSandthemagnetic˝eldmapforSAMURAI,isusedtodetermine thebeamtrajectoryatthetargetplane.TheBDCanalysisisdescribedinChapter4. 3.5.2NeuLANDArray ThepartialNewLarge-AreaNeutronDetector(NeuLAND)[47]waspositionedata30 angle relativetothebeamlineaxis,asshowninFigure3.1.Thesetuputilized400plasticscintil- latorbars[48].Figure3.17ashowsthepartialNeuLANDarray.Eachofthesescintillators haveacrosssectionof5cm 5cm,withalengthof250cm.Eachscintillatorisreadout withphotomultipliertubesatthefarends.Thereare8planesof50barseach,arranged withalternatinghorizontalandverticalorientations.Aplaneof8vetoscintillatorsfrom NEBULA[49],each1cmthick,is˝xedinfrontoftheNeuLANDarray,whichisusedto 95 identifyandremovesignalsfromchargedparticles.Thevetoscintillatorarrayisshownin Figure3.17b.TheminimumdistancefromthecenteroftheSAMURAIspectrometertothe NeuLANDneutronwallswasmeasuredtobe85.6cm,andthepreciseanglewasmeasured tobe29.6 ,providingangularcoveragefromapproximately22 to43 inthelaboratory frame. (a) (b) Figure3.17:ThepartialNeuLANDarrayisshownin(a),andthechargedparticleveto arrayborrowedfromNEBULAisshownin(b) 3.6DAQ TheDataAcQuisition(DAQ)fortheexperimentconsistedofthreeseparatesystems.The RIBFDAQsystemusingthebabirlDAQframework[50]collecteddataforBigRIPSdetectors, SAMURAIdetectors,theNeuLANDdetector,andtheKyotoMultiplicityArray.TheNAR- VAL[51]DAQframeworkisemployedtoreadouttheGETelectronicsfortheS ˇ RITTPC 96 (seeSection2.3).TheKATANAarrayandActiveVetoarrayarehandledbytheKATANA system.SynchronizationoftheseparateDAQswasachievedbysupplyingthesametrigger toeachsubsystemwiththeGeneralTriggerOperator(GTO)[52]eventhandlingmodule. ThebabirlDAQframeworkisusedfortheRIBFDAQ,whichhandledeventbuildingfor allbeamlinedetectors,aswellastheNeuLANDarrayandKyotoMultiplicityArray.When thecommontriggerisprovidedbytheGTOeventhandlingmodule,theRIBFDAQreads datafromallmodulesinparallel.Foreachmodule,aSlaveeventbuildercreatesasub-event whichissenttoaMastereventbuilder,whichwritesallinformationinanevent.Asystem busyisproducedfromthelogicalORofallmodulesinthesystem. TheTPCdataishandledwiththeNARVALDAQframework,whichcanhandlethelarge amountsofdataproducedbytheGETelectronics.Upto1.2GByte/sofdatafromtheGET electronicsissavedtolocalDAQserversusingtheNARVALsystem,andthedataiscopied fromtheDAQserverstotheRIKENHOKUSAI-GreatWavehighperformancecomputing clusterstoragethrougha10Gbpsnetworkforo˜ineanalysisandtapebackup. DatafromtheKATANAarrayandActiveVetoArrayaresavedbyaseparateDAQ, aftersignalprocessingbyaFlashADCboardwithintheKATANAtriggerbox.Foreach paddle,thesignalsfromallMPPCsforthatpaddleweresummedanddigitized,resultingin onedatapointforeachpaddle. 97 Chapter4 DataAnalysis Thedataanalysiscanbedividedintotwomaincategories:beamanalysisandTPCanal- ysis.ThebeamanalysisisnecessaryfortaggingthePIDofincomingbeamparticlesand determiningtheirenergyandangleofincidenceatthetarget.TheTPCanalysisisnecessary todeterminethePID,magneticrigidity,andangleofemissionforparticlesproducedinthe beam-targetreaction.TheTPCanalysisalsoprovidesaneventvertex,whichiscombined withthebeamanalysiswhendeterminingtheabsolutecrosssectionformeasuredreactions. 4.1RIBFFacilityandProductionofPrimaryBeam Theheavy-ionbeamsusedfortheexperimentalcampaignwiththeS ˇ RITTPCwerepro- ducedattheRadioactiveIsotopeBeamFactory(RIBF)attheRIKENNishinaCenterfor Accelerator-BasedScienceinWako,Japan.Thebeamsusedinthe˝rstS ˇ RITTPCex- perimentalcampaignaretabulatedinTable4.1.The 132 Snand 108 Snbeamsimpinged onisotopicSntargetsareusedtoprobeawiderangeofasymmetry, = N Z A ,withthe sameCoulombforcespresentineachsystem.The 124 Snand 112 Snbeamsareimpingedon 112 Snand 124 Snisotopictargets,respectively,toprovidedirectcomparisonsbetweenthe twoprimarybeams,andtoprovideaprobeatthemidrangeofasymmetryprobedbythe otherbeams.TheZ ˇ 1-3cocktailbeams(tunedfor particlesatspeci˝cmomenta)provide momentumandenergylosscalibrationsfortheTPC. 98 PrimaryBeamSecondaryBeam IsotopeDesiredEnergyatmidtargetIntensity Isotope(MeV/u)(kHz) 238 U 132 Sn269.29.5 238 U 124 Sn270.39.1 124 Xe 112 Sn270.47.6 124 Xe 108 Sn269.37.5 238 UZ ˇ 1 3 ˇ 3000.6 238 UZ ˇ 1 3 ˇ 1000.09 Table4.1:BeamsusedintheS ˇ RITTPCexperimentalcampaign Theprimarybeams 238 Uand 124 Xewereacceleratedusingmode1oftheRIBFheavy-ion acceleratorsystem,showninFigure4.1.The28GHzSuperconductingElectronCyclotron ResonanceIonSource(SC-ECRIS)[53]isusedtoprovideeither 238 Uor 124 Xeionsto theRILACIIlinearaccelerator[54],afterwhichtheyareacceleratedbytheRIKENRing Cyclotron(RRC)[55],theFixed-frequencyRingCyclotron(fRC)[56],theIntermediate- stageRingCyclotron(IRC)[57],and˝nallybytheSuperconductingRingCyclotron(SRC) [58].Usingthismodeofacceleration,theprimarybeamsareacceleratedtoa˝xedenergy of345MeV/u[59]. Figure4.1:Mode1oftheRIBFheavy-ionacceleratorsystem[8] 99 4.2BeamAnalysis Theproductionofsecondarybeamsisperformedusingtheprojectilefragmentationtech- nique[60].Afteritsacceleration,theprimarybeamisimpingedonarotating,3-mm-thick Beproductiontarget.Fragmentsfromthereactionofprimarybeamontheproductiontar- getare˝lteredin-˛ight,providingthedesiredsecondarybeam.Thein-˛ightproductionof rare-isotopebeamswasperformedbytheBigRIPStwo-stagefragmentseparator[61].The RIBFbeamlinelayoutisshowninFigure4.2startingafterthelasttwocyclotronstages, withtheBigRIPSarealabeled. Figure4.2:RIBFfacilityatRIKENcirca2012.Althoughthis˝gurewillnotrepresentthe latestupgrades,itwellrepresentstheBigRIPSandSAMURAIbeamlineduringtheS ˇ RIT experimentin2016.Figurefrom[9]. Asimpli˝edschematicofBigRIPSisshowninFigure4.3.Dipolemagnetsaredenoted asD1-D6,andfocalplanesF3,F5,andF7areshown.Thenamingconventionfollowsthat inFigure4.2.The˝rststageofBigRIPSselectsfragments,whilethesecondstageprovides beamidenti˝cation,withadditional˝lteringcapabilities.The˝rststageisperformedwith 100 dipolesD1andD2,withawedgeenergydegraderbetweenthetwodipoles.Separationis achievedinD1with˝lteringbymagneticrigidity Bˆ Bˆ = p Q ; (4.1) where B isamagnetic˝eldwhichresultsinaradiusofcurvature ˆ foraparticleofmomentum p andcharge Q = Ze (assumingafullyionizednucleus).Slitsbeforeandafterthedipole magnetsareusedtoselectaspeci˝cbendingradius,providinga˝lterofmagneticrigidity. AfterD1,mostunwantedparticlesarecollectedinabeamdump.Remainingbeamparticles passthroughthewedgedegrader,withthethicknessencountereddependenton Bˆ .This createsdispersionin B=rho betweendi˙erent A=Q ratios.Afterthewedgedegrader,an additional Bˆ selectionismadeusingD2.The˝rststageofseparationresultsinasecondary beamwiththedesiredisotope,aswellasavarietyofcontaminants,whichhaveamass-to- charge A=Q ratiosimilartothatofthedesiredisotope. Figure4.3:Simpli˝edschematicofBigRIPS.DipolemagnetsarelabeledD1-D6.Asingle energydegraderwasusedbetweenD1andD2.FocalplanesF3,F5,andF7areshownwith beamlinedetectors.Descriptionsofthesedetectorsaregiveninthetext. ThesecondstageofBigRIPSprovidesbeamidenti˝cation,withadditional˝lteringca- 101 pabilities.AsecondwedgedegraderissometimesinstalledatfocalplaneF5,butthiswas notusedfortheS ˇ RITexperiment,toachievemaximalenergy.Beamanalysisisrequired forbeamidenti˝cation,aswellastodeterminethebeamenergyandbeampositionontar- get.PlasticscintillatorsarelocatedinfocalplanesF3andF7,allowingtheTime-Of-Flight (TOF)tobemeasuredoveraknowndistance.TheF3andF7focalplanesarefullyachro- matic,andthebeamspotatthesefocalplanesissmall,allowingconsistentandprecise timemeasurements[62].Todeterminethebeamtrajectory,doubleParallelPlateAvalanche Counters(PPACs)[63]areusedatfocalplanesF3,F5,andF7.Thisinformationprovides thepositionandanglethatthebeamtakesthroughdipolepairsD3andD4,andD5and D6.Themagnetic˝eldofthesedipolesismeasuredusingNuclearMagneticResonance (NMR)probes.Withthetrajectoryofbeamparticlesandtheknowledgeofmagnetic˝elds ofthedipolemagnetsD3,D4,D5,andD6,themagneticrigidity Bˆ canbedetermined foreachbeamparticle[64,65,66].Energylossisdeterminedusingasegmentedgaseous ionchamber,calledtheMUlti-SamplingIonizationChamber(MUSIC)[11].TheTOFis usedwiththemagneticrigiditytodeterminethemass-to-chargeratioofeachbeamparticle, whiletheenergylossisusedtodeterminetheatomicnumberofeachbeamparticle(with slightcorrectionscomingfromvelocity).Finally,BeamDriftChambers(describedinSec- tion3.5.1,locatedafterBigRIPS)withhighpositionresolutionareusedtodeterminethe beamtrajectoryontarget. Theparticleidenti˝cationmethodisdescribedindetailinReference[62],usingthe TOF- Bˆ - E method.Thereonecan˝ndadditionaldetailsabouthowtheTime-Of-Flight (TOF) TOF = L c ; (4.2) 102 magneticrigidity( Bˆ ),andtheenergyloss( E )aremeasuredinBigRIPS[61],andhow theatomicnumberandmass-to-chargeratio( A=Q )aredeterminedfromthesequantities. Asummaryispresentedhere.FromtheTOF,thevelocity v = c canbedetermined,given thatthelength( L )ofthe˛ightpathisknown.With v = c and Bˆ (Equation4.1),one candeterminethemass-to-chargeratio A=Q A Q = Bˆ c m u ; (4.3) where =1 = p 1 2 and m u =931.494MeV/c 2 istheatomicmassunit.Finally,since hasbeendetermined,ameasurementofenergylosscanbeusedtodeterminethecharge Z usingtheBethe-Blochformula, dE dx = 4 ˇe 4 Z 2 m e v 2 Nz ln 2 m e v 2 I ln(1 2 ) 2 : (4.4) here e istheelementarycharge,and m e istheelectronmass.Thematerialthroughwhich thebeampassesisdescribedbyitsatomicdensity N ,atomicnumber z (nottobeconfused withbeamatomiccharge Z ),andmeanexcitationpotentialofthematerial I .With A=Q and Z determined,theparticleidenti˝cationiscomplete. Rawinformationfromthebeam-linedetectorsisstoredinRIBFDataFormat(RIDF) ˝lesforo˜ineanalysis.TheRIDF˝lesareanalyzedwiththeANAROOT[67]toolkit,which wasdevelopedatRIBFforbothonlineando˜ineanalysis.ANAROOTisusedtounpack therawdata,andbuilt-inlibrariesareusedtoperformtheparticleidenti˝cationmethods. Finally,ROOT˝lesareproducedfortheanalyzedbeamdata,facilitatingmergingwiththe TPCdata,indexedbyeventnumber(seeSection3.6forfurtherdetailsontheDAQ). 103 4.2.1AnalysisofPPACsignals TrajectoryreconstructionwithinBigRIPSisperformedwithParallelPlateAvalancheCounter (PPAC)[10]detectorslocatedatthefocalplanesF3,F5,andF7.Ion-opticaltransfermaps, deducedexperimentally[9],areusedalongwiththetrajectoryinformationtocalculatethe valueof Bˆ atthethreespeci˝edfocalplanes.Additionally,correctionstothe˛ightpath lengthcanbedeterminedfromthetrajectoryinformation.Atotalof12PPACdetectors wereusedinthebeamlineduringtheS ˇ RITcampaign,with4PPACslocatedineachof thefocalplanesF3,F5,andF7(seeFigure4.3).PPACsaredoubledtogetherfore˚ciency, makingPPACs",attheforeandaftofthefocalplanes. Figure4.4:StructuralschematicofBigRIPS240 150mm 2 PPAC,fromReference[10] ThefollowingdescriptionofthePPACdetectorsissummarizedfromReference[63].As seeninFigure4.4,thePPACdetectorismadebyananodeplate,sandwichedbetweentwo cathodeplates.Thecathodeplatesaremadeof1.5 µ mthickMylarfoil,with0.30nm stripsofeitherAuorAlevaporatedonthesurface.Thesestripsare2.4mmwidewitha pitchof2.55mm,andareconnectedtoadelaylinereadout.Thereare40stripsoneach cathodeplane,withonecathodeplanecontainingstripsseparatedinthe x direction,and 104 theothercathodeplanecontainingstripsseparatedinthe y direction.Thedetectoris˝lled withisobutane(C 4 H 10 )gas.Theoperatingvoltagedi˙erencebetweenanodeandcathode isvariable,butistypicallylessthan2000V.Throughouttheexperiment,theoperating voltageofPPACdetectorswassometimesloweredtopreventelectricaltrips.EachPPAC layeroutputs5timesignals: T X 1 , T X 2 , T Y 1 , T Y 2 ,and T A .Calibrationofthesesignalsis performedtoconvertfromTDCchannelstons,andwewillonlyconsidercalibratedsignals inthiswork.Thestripsarereadoutwithalumped-constantdelayline,whichenablesthe high-ratereadoutcapabilitiesofthePPACs.Thedelayofa100mmdelaylinewith40steps wasmeasuredtobe81.6ns,consistentwithadelaytimeofonestepbeing2.04ns. ThetimesignalsfromthePPAClayersarerecordedusingaCAENV1190multi-hit Time-to-DigitalConversion(TDC)module[68],whichrecordstimesignalsformultiplehits. ThisTDCmoduledoesnothaveasharpcorrelationbetweenitsgateandtheTDCvalue foragivensignal:thereisabetweenthegateandtheTDCvalue,whichvaries event-by-event.Thisisdonedeliberatelytocorrectfordi˙erentialnon-linearitiesinthe TDCreadout.Althoughthisintroducesinaccuracyinabsolutemeasurementsofasingle channel,therelativetimebetweenTDCchannelsprovidesanaccuratemeasurement[68]. Thismethodisreferredtoasasynchronoustimeintervalmeasurement,asopposedtosyn- chronoustimeintervalmeasurement[69].Withsynchronoustimeintervalmeasurement, TDCsignaltimesarecomparedtoareferenceclock,whichhassomejitter,causingrandom, potentiallynon-Gaussian,measurementerror.Thus,allmeasurementsmadewithPPACs usethedi˙erenceoftwosignals. Sincethemulti-hitTDCmodulesrecordhitsoverarangeoftime,thehitassociatedwith theeventmustbedistinguishedfromotherhits.ATDCover˛owparameterissetforeach PPAC,whichisappliedtothedimensionaltimesignals( T X 1 , T X 2 , T Y 1 ,and T Y 2 ).Inour 105 analysis,anyhitsattimesgreaterthantheTDCover˛owareignored.Thelastsignalbelow theTDCover˛owlimitisconsideredtobetherealsignal. Thedi˙erencebetweendelaylinesignalsisusedtodetermineposition.Asanexample, weconsiderpositiondeterminationinthe X dimension.Threesignalswillbeused: T X 1 , T X 2 ,and T A ,with T A beingtheanodetimesignal.Asidefroma˝xeddelayassociatedwith thesignalgenerationandcabledelay, T A isequaltothearrivaltimeofthebeamparticlein thePPAC. T X 1 and T X 2 haveadditionaldelays,astheyarereadoutthroughadelayline. Thedi˙erencebetweenthetwodimensionaltimesignals, T di˙ = T X 1 T X 2 ,isbasically equaltothedi˙erenceinthedelaysofthetwosignalsgoingoutofthetwoendsofthedelay line.Thisdi˙erenceisproportionaltothe X displacementofthetrackrelativetothecenter ofthePPACandisusedtodeterminetheposition,givenas x = K x T di˙ = 2+ x o˙ ; (4.5) withano˙setcorrection x o˙ inmmandapositioncoe˚cient K x ,inmm/ns.Weused previouslydeterminedvaluesfortheseconstants,witheachPPACindividuallycalibrated. Wecanalsoseethat ( T X 1 + T X 2 ) = 2 isinsensitiveto X andisequalto T A uptoanadditive constant. TovalidatesignalsfromthePPAC,wede˝nethequantity T sum : T sum = T X 1 + T X 2 2 T A : (4.6) Since T X 1 + T X 2 =2 T A withinanadditiveconstant,weexpect T sum toremainconstant, withsomevariationduetothetimingresolutionofthePPAC.Ifthevalueof T sum iswell 106 established,wecanuseanytwoofthethreesignals( T X 1 , T X 2 ,and T A )todeterminethe third.ThiswillbeexploitedinSection4.2.1.1forsignalrecovery.Weshowanexample T sum spectrainFigure4.5,˝ttedwithaGaussianfunction.Itcanbeseenthatthedistribution hasatailforlowervaluesof T sum . Figure4.5:Anexample T sum spectra.Thedistributionis˝ttedwithaGaussianfunction, showninred. Twoe˙ectstypicallycontributetotheasymmetrictailofthe T sum distribution: -ray productionwithinthePPAC(anelectronwhichisliberatedfromthePPACgaswithsuf- ˝cientenergytoproduceasignalonthedelayline),ormultiplehits(pile-uptypeevents). Thesee˙ectscauseerroneouspositionmeasurements,asoneofthetimingsignalsistoo small.Wecanidentifytheseeventsbyrequiringaminimumvalueof T sum .We˝ttheGaus- sianportionofthe T sum distribution,usingthemeantode˝netheexpectedvalue h T sum i , andde˝ningtheupperandlowerboundsof T sum tobeat h T sum i 2 ˙ .Eventsoutsidethese boundswilloftenhavecompromisedpositioninformation,andweattemptpositionrecovery 107 forsucheventsinthefollowingsection. Oneadditionalcauseofinformationlossshouldbenoted:thePPACscanexperience electricaldischargebetweentheanodeandcathodes,especiallywithhighbeamintensity. ThiscausesthehighvoltagemoduleforaPPACtotrip,causingtotallossofinformation forthatPPACuntilitisresetmanually.Suchtrippingoccurredwithvaryingfrequency throughouttheexperiment. 4.2.1.1Positiondeterminationwithpartialinformation Inprinciple,asingledimensionalsignalfromoneendofthePPACdelaylinecanbecombined withtheanodetimetoreconstructtheposition.Withtheexpectedvalue h T sum i determined previously,weconstruct T di˙ forthecaseofanerroneous T X 1 : T di˙ = h T sum i +2 T A 2 T X 2 ; (4.7) orif T X 2 iserroneous, T di˙ =2 T X 1 h T sum i 2 T A : (4.8) Foreventswhichdonotsatisfythe T sum condition,wetakethegreaterof T X 1 and T X 2 , andcheckifitsatis˝esthefollowing: h T sum i 4 ˙ 2 ( T X T A ) h T sum i +4 ˙; (4.9) where T X iseither T X 1 or T X 2 ,and h T sum i and ˙ areextractedfromthe˝ton T sum describedpreviously.Whentheseconditionsaresatis˝ed,thePPACinformationcanbe safelyreconstructedusingtheavailabletiminginformation. 108 IssueswiththePPACsignalsaremadeevidentbyinspectingtherelationshipbetween T X 1 T A and T X 2 T A .Sincethesumofthesequantitiesshouldbeconstantinprinciple, weexpecttoobserveananti-proportionalitybetweenthem.TheleftpanelofFigure4.6 showsthebehaviorfortheF7-1BPPAC,whichexhibitstheexpectedbehavior.Theright panelofthesame˝gureshowstheF7-2BPPAC,whichexhibitsnon-standardbehavior. Figure4.6:CorrelationplotforPPACsignalsfortheF7-1B(left)andF7-2B(right)PPACs. SignalissuesareevidentfortheF7-2BPPAC. ThedistinctgroupingsseenintheF7-2BPPACsuggestthatthedatahasbeena˙ectedin asystematicfashion.Alikelycauseiscrosstalkbetweenthecableswhichrunfromthefocal planedetectorstotheDAQroom.TheF3andF7focalplaneshouseplasticscintillators aswellasthePPACs,withtheF7focalplanealsohousingtheionchamber.Theregularly timedsignalswithinthecablesforthesedetectorscancauseregularlytimedcrosstalkinthe datacablesforthePPACs,corruptingtherecordeddata.Byusingproper T sum gatesin conjunctionwithpartialinformationpositionrecovery,wecanestimatepositioninformation forsomeofthea˙ectedevents. Toensurethatdependentquantitiessuchas A=Q andprojectionontargetarenotad- verselya˙ectedbyusingthepartialinformationpositionrecovery,wecomparetherecon- 109 structionofarunusingthepositionrecoverytothereconstructionwithoutpositionrecovery. Asinglerunfromthe 132 Snbeamwillbeusedforthiscomparison.Forsimplicity,wewill refertothereconstructionwithoutpositionrecoveryasmethod1,andthereconstruction withpositionrecoveryasmethod2.Therunisreconstructedusingbothmethods,and 132 Sn isotopesareselectedwithanellipticalcutforbothreconstructions: ( A=Q 2 : 64) 2 (0 : 005) 2 + ( Z 50) 2 (0 : 6) 2 < 1 : (4.10) ThePIDforbothmethodsareshowninFigure4.7,withtheellipticalcutoverlaid.Method 2showsnearlya50%increaseovermethod1of 132 SnisotopesreconstructedwithinthePID cut.ThenumbersarelistedinTable4.2. Figure4.7:BeamPIDfromreconstructionwithout(a)andwith(b)positionrecovery.Refer toTable4.2fornumericalcomparisonofthesetwoplots. The A=Q distributionoftheselected 132 Snisotopesis˝twithaGaussianfunctionfor bothmethods.TheFullWidthatHalfMaximum(FWHM)ofthedistributionsarereported inTable4.2.ThePIDisrequiredtoprojectthebeampathtotarget(thisprojectionis describedinSection4.2.8).Thenumberof 132 Snisotopessuccessfullyprojectedontarget ishigherformethod2,sincemore 132 Snisotopesarefoundbymethod2.TheFWHMof 110 projected x positionandyawangleontargetarelistedinTable4.2.Themeanofthe x distributionsfoundbythetwomethodsagreewithin0.05mm,andthemeanoftheyaw distributionsagreewithin0.2mrad. ObservableMethod1Method2 132 Sn2171931436 FWHM A=Q 0.003360.00350 132 Snontarget1849027020 FWHM x ontarget(mm)9.3279.367 FWHMyawontarget(mrad)4.784.72 Table4.2:ResultingquantitiesforPPACreconstructionwithout(method1)andwith (method2)PPACpositionrecovery 4.2.1.2BeamRateCalculationwithPPAC Thetypicalscalerestimationofbeamrateprovidesatime-averagedrate,whichdoesnotac- countfor˛uctuationsinthebeamintensity.Analternativeestimateofthebeamratecomes fromthemulti-hitinformationofthePPACs.Afteraneventistriggered,theprobability thatanadditionalbeamparticlewillpassthroughisdirectlyrelatedtothebeamrate.We cansetawindowoftimewithwidth W after aftertheTDCover˛owlimitandtaketheratio ofhitswithinthiswindow( N after )tothenumberoftriggeredevents( N events ) tocalculate thebeamrate Rate beam = N after N events W after : (4.11) ThisrateiscalculatedusingtheF7-2PPACS,andcanbecomparedtothescalerratefor theF7plastic.TherelativeratescanbeusedtocorrectthescalerratefortheSBTstart counter(describedinChapter3). 111 4.2.2AnalysisofBeamTimeofFlight Todeterminethevelocity, ,andmass-to-chargeratio, A=Q ,ofthebeamparticles,an accurateandprecisemeasurementoftheTOFmustbeperformed.TheTOFwasmeasured usingplasticscintillatorslocatedatfocalplanesF3andF7.Anexamplerawspectrais shownintheleftpanelofFigure4.8,andthesamespectraaftercalibrationintheright panelofFigure4.8.TherawspectramustbeconvertedfromTDCchannelstons,and correctedwithano˙settoproducetheactualTOF.AmesytecMTDC-32modulewasused torecordthescintillatorsignals,andtheconversionfactorfromTDCtonsforthesetup was64TDC=1ns.ThecalibratedTOFvalueisestimatedusingthebeamenergyand distancebetweenfocalplanesF3andF7(roughly46.6m)[9],andis˝ne-tunedbyadjusting theo˙settoproducecorrect A=Q values.TheTOFisrecordedbetweenfocalplanesF3and F7,astheF5scintillatorwasremovedtoachievehigherbeamenergies.Wecanestimate theexpectedTOFusingtheexpectedbeamvelocitywithEquation4.2. Figure4.8:Theuncalibrated(a)andcalibrated(b)time-of-˛ightspectrafromrun2894. TheconversionofTOFtovelocity isperformedusingANAROOT,whichusesPPAC informationtocorrectforthe˛ightpath.Theion-opticaltransfermapsthatareusedto determine Bˆ arealsousedtodetermineaparticle'strajectory,producingsmallcorrections 112 tothe˛ightlength.ANAROOTscales toaccountforenergylossbetweenF3andF7, providinganestimatefor atF7.With and Bˆ determined,the A=Q ratioiscalculated usingEquation4.3. Atimeo˙setisrequiredtocalibratethetimesignalsbetweentheF3andF7plastic detectors.AnestimateismadeusingtheexpectedTOF,whichistheniterativelycorrected toreproducetheexpected A=Q ratioforthemainSnisotope.Anexampleisshownin Figure4.9,withthereconstructed A=Q ratioplottedasafunctionoftheTOFo˙set. Figure4.9:RelationshipbetweenTOFo˙setusedandreconstructed A=Q ratioof 132 Sn. Radiationfromtheheavy-ionbeamdamagestheplasticscintillators,changingthelight outputovertime.ThescintillatoratF3issubjectedtoahigherbeamintensitythanthe scintillatoratF7,causingthedamagetooccurunevenly.Inadditiontotheslowdegradation, thephysicalpositionofthescintillatorswereperiodicallyadjustedtoplacethebeamspot onanundamagedsection.AslewingcorrectionsimilartothatdescribedinReference[62] 113 isperformed,withslightdi˙erences.Weperformtheslewingcorrectionwithtwoequations, ˝ = t + t slew (4.12) and t slew = c 1 p q ; (4.13) where ˝ istheactualtime, t istheobservedtime,and q istheintegratedchargesignal. Theslewinge˙ect t slew isafunctionofparameter c 1 ,whichisdeterminedempiricallyfor eachrun.Thee˙ectoftheslewingcorrectioncanbeobservedinFigure4.10,whichshows a 112 SnPIDreconstructedwithandwithouttheslewingcorrection. Figure4.10:PIDreconstructedwithout(left)andwith(right)plasticslewingcorrection. Resolutionin A=Q isvisiblyimprovedbyusingtheslewingcorrection. 4.2.3DeterminationofChargewiththeIonChamber ThechargeofeachbeamparticleisdeterminedusingenergylossinformationfromtheMulti- SamplingIonizationChamber(MUSIC)[11],andfromthebeamvelocity.Thecombined energylossandbeamvelocityinformationisusedinthechformula(Equation4.4) 114 todeterminecharge.AschematicviewofMUSICisshowninFigure4.11.Thechamberis ˝lledwithP10gasatapproximately760Torr(thispressuredi˙ersslightlyfromthepressure usedinReference[11]).Aseriesof4 µ mthickaluminizedMylarfoilsarealternatedas anodeandcathodeplates,withthecathodesettogroundpotential,andpairsofanode signalslinkedtogether,withatotalof25aluminizedMylarplanes.Atotalof6ADCsignals arereadoutfromanodeplanes,providingthemulti-samplingcapabilities.EachADCsignal isproportionaltotheamountofenergylostin4Mylarplanesand80mmofcountergas. MUSICislocatedinfocalplaneF7,betweentwoPPACsandpriortotheplasticscintillator atF7. Figure4.11:MUSICside-viewschematic,fromReference[11] TheenergylosswithinMUSICistabulatedasageometricmean,toreducestatistical ˛uctuation.Thegeometricalmeanfor6ADCchannelsisgivenas ADC = 6 v u u t i =5 Y i =0 ADC i : (4.14) Ananalysisprogram,LISE++[70],wasusedtocalculatetheexpectedenergylossofthe 115 majorparticlespeciespresentintheisotopicSnbeams.Thegeometricalmeanoftheob- servedenergylossinADCisplottedagainstthegeometricalmeanofsimulatedenergyloss inMeVinFigure4.12,foranarrayofselectedisotopes.Alinearrelationshipisobserved betweenthesevalues,withthesloperepresentingthegain. Figure4.12:GeometricalmeanofADCresponsecomparedtosimulatedenergyloss Itiscommonthatadetectorwillregisteranon-zerosignal,evenifthereisnoparticle present.Thetypicalsignalsizeforanon-eventiscalledthepedestal,abaselinevalue whichcorrespondstonosignal.ThepedestalforeachADCchannelisdeterminedusingthe gain.Foreachchannel,themeasuredADCsignalandsimulatedenergylossarecomparedfor severalisotopes.ThecombinedresultsareplottedinFigure4.13,withtheleftpanelshowing resultsbeforepedestalsubtraction.Foreachchannel,thepedestalcanbecalculatedas pedestal = MeasuredEnergy(ADC) E Loss gain : (4.15) Foreachchannel,theaveragepedestaliscalculatedusinganarrayofisotopes.Afterapplying pedestalsubtraction,therelationshipbetweenpedestal-subtractedmeasuredADCsignaland 116 simulatedenergylossisshownintherightpanelofFigure4.13.Alinear˝tisappliedto thisdistributiontodeterminethe˝nalcalibrationbetweenADCchannelsandenergyloss inMeV. Figure4.13:Ionchambersignalandsimulatedenergylossbefore(leftpanel)andafter(right panel)pedestalsubtraction. The˝nalstepistodetermineparticlechargefromenergylossandbeamvelocity.This isdoneinANAROOTwiththeequation Z = slope s E Loss ln(4866 2 ) ln (1 2 ) 2 + o˙set ; (4.16) where4866correspondsto 2 m e = ( I c 2 ) ,with m e themassofanelectron, c thespeedof light,and I asthemeanexcitationpotentialofthecombinedMylarandionchambergas. Theenergyloss, E Loss ,isdeterminedusingthegeometricalmeanofall˝redADCchannels, withtheconversionfromADCtoMeVdetailedearlierinthissection.Theslopeando˙set arecalibratedby˝ttingdataforselectedisotopes. Forthe 108 Snand 112 Snbeams,ADCchannels1,3,and4(ofthe6totalchannels)had driftinggains.Toperformrun-by-runcalibrationinanautomatedmanner,therunswere 117 Figure4.14: 112 SnbeamPIDplotforrun2580,using3ADCchannels(left),andall6ADC channels(right). ˝rstreconstructedusingionchamberADCchannels0,2,and5only,producing PIDplots,asshownintheleftpanelofFigure4.14.Thesecanbeproducedusingasingle calibration,astheselectedADCchannelsexhibitedstablebehavior.TheADCresponsefor asinglerunisdeterminedbyselectingisotopesusingthefuzzyPIDplot,andperformingthe standardcalibrationwithascriptthatcollectstheADCresponseforeachchannel,sorted byisotope,andperformsthecalibrationasdescribedpreviouslywithinthissection. ThebeamPIDplotsshowninFigure4.14alsoindicatethepresenceofbeampileup:beam particlespassingthroughtheionchamberinclosesuccessionaltertheionchamberresponse, causingthesmeared,seeminglyhigh- Z distributionabovethemainisotopicpeaks.Theion chamberresponseforatypicaldatarunwiththe 124 SnbeamisshowninFigure4.15.The mainpeak,whichisassociatedwithproperlyidenti˝edcharge,canbeseenatapproximately 4000ADCchannels.ThetailingfunctionathigherADCvaluesiscausedbybeampileup. Othersourcesforaberrantionchambersignalscouldbereactionswithintheionchamber, orcrosstalkintheionchamberdatacables. 118 Figure4.15:Ionchambersignalfor 124 Snbeam 4.2.4BeamPileupandBackground Twobeamparticlesincloseproximitywillcausealargeionchamberresponse,resultingin anon-physicalreconstructedvalueof Z .ThepileupcanbeseeninthebeamPIDplots asasmeareddistributionabovetheproperlyreconstructedisotopepeaks.Thesetailscan overlapwithotherisotopes,alteringthestatistics.Anadditionalindicatorofpileupcomes fromthemulti-hitTDCmodulesusedforthePPACs.AnexampleTDCspectrumisshownin Figure4.16,withthemainpeakatapproximately32,500TDCchannels,whichisconstrained bytriggertiming.Eachhitinthisspectrumismadefromaparticlepassingthroughthe PPAC,sohitsbeforeorafterthemainpeakareassociatedwithpileupevents.Thepileup occursforallbeams,butthissectionwillfocusonanalysisofthe 132 Snbeam. Forthe 124 Snand 132 Snbeams,theextrahitsbeforethemainpeakaresuppressedby thetrigger,whileforthe 108 Snand 112 Snbeams,therateofextrahitsisthesamebefore andafterthemainpeak.Thiswasduetodi˙erencesinthediscriminationofsignalsforthe KATANAVetoarray,andisexplainedinthetriggerdescriptioninChapter3. 119 Figure4.16:Multi-hitTDCspectra,fromaPPACattheF7focalplane,for 132 Snbeam Themulti-hitinformationfromtheF7PPACsisusedtoidentifypileup,asmultiplehit eventsinF3andF5canbecausedbyparticleswhichare˝lteredoutbyBigRIPS.Wegate onmultiplehitsinatleast2PPACs,toprevent -rayproductionfromcausinganeventto beidenti˝edaspileup.Theionchamberresponseisrelatedtothetimedi˙erencebetween themainparticleandapileupparticle,ascanbeseenintheleftpanelofFigure4.17.Pileup particleswhicharrivewithin3 µ sbeforeoraftertheinitialparticlesaturatetheionchamber, andresultinnon-physical A=Q reconstruction.Forpileupeventsseparatedfromthemain peakbymorethan3 µ s,theionchamberresponseconvergestoavaluejustabovethetypical responseforanon-pileupevent.TheresultingPIDspectrumfromtheseeventsisshownin therightpanelofFigure4.17.Thedistributionissmearedinreconstructed Z forpileup whichoccurswithin6 µ softheinitialparticle,andapeakjustabovetheexpected Z is formedfrompileupattimeslaterthan6 µ s. Pileupwhichoccursbeforethemainparticleisalsopresent,butmoredi˚culttoidentify. Figure4.16showsaTDCspectrumforthe 132 Snbeam,withcountsbeforethemainpeak 120 Figure4.17:(Left)Ionchamberresponseplottedagainstpile-uptimeaftermainparticle, for 132 Snbeam.(Right)ResultingPIDspectrumfortheseevents.Bothplotsarerestricted toeventswithtimedi˙erencegreaterthan3 µ s. correspondingtopileupbeforethemainparticle.Thepileupratebeforethemainpeakis partiallysuppressedbythetrigger.Thelimitedmulti-hitTDCwindowdoesnotprovide informationlessthan3 µ sbeforethemainpeak.Pileupwithin6 µ softhemainpeakcan beidenti˝eddirectlybytheionchamberresponse,whilepileupseparatedbymorethan6 µ s cannoteasilybeseparatedfromthemainionchamberresponse.Thepileupwhichcannot beidenti˝edbythemulti-hitTDCinformationandwhichisnotclearlydistinguishablefrom thebeamPIDmustbeestimated. Othersourcesofbackgroundcanbecausedbypoorreconstruction.Thebackground duetopoorreconstructionisestimatedbyinspectingthefocalplanereconstructionandthe reconstructedbeamvelocity.Thereconstructedeventmustpassthrougha100 100mm 2 areaformedaroundthefocusofeachofthefocalplanesF3,F5,andF7.Reconstruction outsidethesetlimitcorrespondstoanon-physicalposition,indicatingthereconstructionis compromised,andcannotbetrusted.Eventswhicharepoorlyreconstructedcanresultina non-physicalvalueof A=Q ,providingaclearindicationofmis-reconstruction. 121 4.2.5ReconstructedBeamPIDplots Figure4.18:Fromtoptobottom,lefttoright,beamPIDplotsfor 108 Sn(TL), 112 Sn(TR), 124 Sn(BL),and 132 Sn(BR). ThereconstructedbeamPIDplotsofthe4mainbeams( 108 Sn, 112 Sn, 124 Sn,and 132 Sn) areshowninFigure4.18.Pileupisevidentinallofthesystems,with 132 Snexhibiting anadditionalpileuppeakinadditiontothesmearedpileupdistribution.Low- Z ( Z< 45) contaminantsareevidentinFigure4.19,whichshowsthebeamPIDplotsoverawide rangeof Z and A=Q values.Thewidthofthe Z and A=Q plottingrangesisconsistentfor allsubplotsinFigure4.19,andwaschosentoshowallcontaminantsinthe 124 Snbeam. Althoughlow- Z beamparticlesarepresentinallsystems,theydonotcontributemorethan 1%tothestatisticsofanysystem,althoughduringsomeminimumbiasrunsof 124 Sn,low- Z 122 particlesaccountedformorethan10%ofparticles. Figure4.19:Fromtoptobottom,lefttoright,wideperspectivebeamPIDplotsshowing lighterbeamparticlesfor 108 Sn(TL), 112 Sn(TR), 124 Sn(BL),and 132 Sn(BR). 4.2.6BeamPurity Thebeampuritymustbemeasuredforeachrun.Thetriggersettingscana˙ectthepurity, ascantheslitsettingsorotherchangestothebeamsettings.Webeginbyidentifying isotopesusingthereconstructedPID.Sincethereconstructione˚ciencyvariesbyrun,we de˝netherelativepurityofanisotope A Snas: Purity A Sn = N A Sn N found (4.17) 123 where N found isthetotalnumberofisotopesfoundwithinisotopegates.Thisissmaller thanthenumberofcollectedtriggers,duetoreconstructionine˚ciencies. Todeterminethemainisotopespresent,arunwithlowbeamrateischosentomitigate pileup.Foreachparticleinthisrun,thereconstructed A=Q ratioandcharge Z arechecked againstpossibleisotopecombinationsnearby.Ifagoodagreementisfound( Z 0 : 1 , A=Q 0 : 002 ),thematchingisotopeisaddedtoalistofmainisotopes.Anexampleisshown inFigure4.20,for 124 Sn.Ellipsesaredrawnrepresentingthesamplingrangeforisotope.A graphicalcutforlow- Z particlesisusedtocollectisotopeswhicharereconstructed,butmay notbereconstructedwellenoughtobetaggedautomatically. Figure4.20:BeamPIDfromlow-intensity 124 Snruns,usedtodeterminemaincontaminants. Foreachoftheidenti˝edisotopes,a2DGaussian˝tisdeterminedusingtheaccumulated statisticsofalldataruns.Ellipticalcutsaredeterminedindividuallyforeachisotopeusing these˝ts,withwidthsupto7 ˙ ,butnotexceedinghalfthedistancetoanyneighboring isotopes,preventingoverlappingcuts.Thelargecutsarenecessarytocompensateforaccu- mulateddi˙erencesinreconstructionfordi˙erentruns.Foreachbeam,aloosegraphicalcut 124 isusedtocounttheoverallsumoflow- Z particles,ratherthanapplyingindividualisotope cuts.InFigure4.21,thebeamPIDfor 124 Snisplottedwithnon-identi˝edeventsinblack, andidenti˝edisotopesincolor. Figure4.21:BeamPIDfor 124 Sn,withfoundisotopeshighlightedincolor Themeasuredpurityfor 132 Snisshownrun-by-runinFigure4.22.Sharpchangesin beampuritycorrespondtobreakswherethebeamwaslostandrecovered,oftenduetoion sourceissues.Fromrun3015,minimumbiasrunsintroducedchangestothetriggerandslit conditions,causingchangestothepurity. Thepurityselectedbythetriggermaynotbethesameastheincidentbeampurity, sincethecrosssectionofcontaminantsisnotnecessarilythesameasthedesiredisotope. Forcrosssectiondetermination,therelativepurityofgatedtriggerstoincidentbeamshould beestablished.Somerunsweretakenwithabeamtrigger,whichcanbeusedtocompareto runswiththedatatrigger.TherelativepuritiesarelistedinTable4.3,andtheseareused forthedeterminationoftheabsolutecrosssection. 125 Figure4.22:Beampurityfor 132 Snbyrun PrimaryBeamSecondaryBeamPurityBeam(%)PurityData(%) 238 U 132 Sn53.556.9 238 U 124 Sn9.7810.97 124 Xe 112 Sn47.846.9 124 Xe 108 Sn51.550.8 Table4.3:Beampuritiesandtriggeredpuritiesforthesecondarybeams 4.2.7ReconstructionE˚ciency Thereconstructione˚ciencyisde˝nedbythenumberofisotopesthatcanbeidenti˝ed. Thisisa˙ectedmainlybypileupandbeam-linedetectorperformance.Thee˚ciencyis tabulatedinTable4.4.Duringthe 108 Snbeamsetting,theF3PPACHVsettingswere lowered,reducingthereconstructione˚ciency.Duringthe 124 Snbeamsetting,theF7 plasticandF5PPACswerereplaced,increasingreconstructione˚ciency.Therefore,two distinctreconstructione˚cienciesarereportedforboththe 108 Snand 124 Snsettings.A reconstructione˚ciencyof100%wouldindicateproperreconstructionofeachevent. 126 BeamReconstructionE˚ciency(%) 132 Sn62.2 124 Sn20.5,30.4 112 Sn73.5 108 Sn85.6,66.4 Table4.4:Eventreconstructione˚ciencyforeachbeam, 108 Snand 112 Snbothhadtwo distinctreconstructione˚ciencies,describedinthetext. 4.2.8BeamDriftChambersandProjectiontoTarget AftertheproductionofthebeamatBigRIPS,thebeamissenttotheSAMURAImagnetand experimentalsetup.ApairofWalenta-typedetectors,calledBeamDriftChambers(BDCs) wereemployedfortrajectoryreconstructionpriortothemagnet.InFigure3.1,thesedetec- torsarelabeledBDC1andBDC2.IntheSAMURAIcoordinatesystem,BDC1islocatedat ( x 1 ;y 1 ;z 1 )=( 0 : 72 ; 0 ; 3159 : 28) andBDC2islocatedat ( x 2 ;y 2 ;z 2 )=( 0 : 52 ; 0 ; 2158 : 7) . The x and z positionsaremeasuredusingphotogrammetry(PGM)[38],butthe y positions couldnotbedeterminedfromthemeasurements,sothenominalheight(centeredat y =0 ) isassumed. TheBDCdetectorsmeasurethe x y positionofabeamparticlewithprecisionof120 µ m[71]asitpassesthrough8wireplanes(4planesin x ,and4planesin y .)Thebeam positionaswellasanglecanbedeterminedindividuallyfromeachBDCdetector,butfor ourpurposes,weonlyusethebeampositionsatthemid-planesofthetwoBDCs.The BDCsaresituatedwelloutsidetheSAMURAImagnetic˝eld,soitisreasonabletoassume thebeamtakesastraightpathbetweentheBDCs.Todescribethebeamlocationand momentumvector,asystemsimilartotheTait-Bryanconventionused:theoriginisthe beamparticlelocation,therollaxisisparalleltotheSAMURAI z -axis,thepitchaxisis paralleltotheSAMURAI x -axis,andtheyawaxisisparalleltotheSAMURAI y -axis.The 127 yawangleisdenotedas ,andthepitchangleisdenotedas p ,withbothanglesillustrated inFigure4.23.Intermsofmomentum,theseanglesarede˝nedas =tan 1 p x p z (4.18) p =tan 1 p y p z : (4.19) IfthemeasuredpositionsatBDC1andBDC2arewrittenas ( x 1 ;y 1 ;z 1 ) and ( x 2 ;y 2 ;z 2 ) , respectively,thestartingpositionoftheprojectionwillbe ( x 2 ;y 2 ;z 2 ) andthestartingangles 0 and p 0 willbe 0 = x 2 x 1 z 2 z 1 (4.20) p 0 = y 2 y 1 z 2 z 1 ; (4.21) wherewehavetakenadvantageoftheaccuracyofthesmallangleapproximationforthese calculations. Figure4.23:Yaw( )andpitch( p )anglesusedfortheBDCprojection Sincewearedealingwithanon-uniformmagnetic˝eld,weperformastep-wiseprojection. For˝xedstepsin z ,thelocalmagnetic˝eld,particleenergy,startingpositionandangleare 128 usedtodeterminetheposition,angle,andenergyattheendofthestep.Themagnetic˝eld isorientedmostlyalong y ,andsonon- y componentswereignored.The˝nalpositionwill beexpressedas( x f , y f , z f ),where z f ischosenasthenominaltargetposition. Overasmallstep z ,thelocalmagnetic˝eldcanbeapproximatedasconstantand combinedwiththeparticlemagneticrigiditytodeterminetheradiusofcurvature ˆ inthe x z plane.Givenstartingyawangle 1 ,theendingyawangle 2 isgivengeometricallyas 2 =sin 1 z + ˆ 1 ) ˆ : (4.22) Thecorrespondingchangein X , x ,isgivenas: x = ˆ 2 ) 1 )) : (4.23) Thechangein Y , y ,isfoundthroughalinearprojectionusingpitchangle p y = z tan( p ) : (4.24) Thepitchangle p remainsconstantthroughtheprojection,asthesmallnon- y components ofthemagnetic˝eldcanbesafelyignored. Afterupdatingtheposition,theenergylossisestimated.Foreachbeam,theenergy lossisestimatedfortheisotopeofinterestusingLISE++[70].Theenergylossthrough eachmaterialisstoredinarray,asapercentofenergyremaining.Thestartingandending coordinatesforeachmaterialarealsostoredinarrays.Foreachstep z ,theenergyis updatedbasedontheenergylosstables. TheprojectedpositioncanthenbecomparedtothevertexreconstructedbyS ˇ RITROOT. 129 Figure4.24:Di˙erencesbetweenBDCprojectionandTPCvertexfor x (left)and y (right). Weperformthiscomparisonwith 132 Snevents,limitedtoeventswithidenti˝ed 132 Sn,with vertexlocatednearthetarget.Thedi˙erencesTPC x -BDC x andTPC x -BDC x areshown inFigure4.26.Foreachsystemwedeterminethetypicalo˙setbetweentheTPCand SAMURAIcoordinatesystems: TPC x = SAMURAI x + x o˙set ; (4.25) TPC y = SAMURAI y + y o˙set : (4.26) ThecorrelationbetweenTPCandBDCisplottedinFigure4.25for x and y ,applyingo˙sets to x and y oftheTPCvertexsothattheyareinSAMURAIcoordinates. Figure4.25:CorrelationsbetweenBDCprojectionandTPCvertexfor x (left)and y (right). 130 Thecalculatedo˙setsaredi˙erentforeachsystem:di˙erencesin y o˙set aremostlikely causedbyslightlydi˙erentdelaysinthetrigger.Di˙erencesin x o˙set aremostlikelycaused byanerrorintheBDCprojection.Theaverage x and y o˙setforeachsystemislistedin Table4.5,andthe x o˙set isplottedforeachsystem,witherrorbarsof 1standarddeviation inFigure4.26.Althoughtheresultsareconsistentwithin2standarddeviations,itappears thatsystematicdi˙erencesarea˙ecting x o˙set . Beam x o˙set (mm) y o˙set (mm) 132 Sn-0.299-227.29 124 Sn-0.609-227.1 112 Sn-0.757-228.4 108 Sn-0.706-228.7 Table4.5:Average x and y o˙setsbetweenTPCvertexandBDCprojectedposition,for eachbeam.Theseo˙setsalsore˛ectthefactthattheBDCandTPCverticesarede˝nedin di˙erentcoordinateframes. Figure4.26:Foreachbeam,typical x o˙set witherrorbarsof 1standarddeviation Tochecktheexpectedresolution,weperformananalyticalerrorcalculation.TheBDCs havemeasurementresolutionof m ˇ 120 µ m[71],andcombiningwithuncertaintyinthe physicalpositions,theuncertaintyofmeasurementsbyBDC1andBDC2is:( x ; y ; z )= 131 (0.32,0.12,0.32)mm,withtheuncertaintyin y reportedasafunctionofmeasurement resolution,sincesystematicpositiondi˙erencecanbecalibratedawayforthe y projection. Theerrorfor x and y straight-lineprojectionscanbeapproximatelyfoundas x f ˇ q 2 x 1 + 2 x 2 z f z 2 z 2 z 1 =0 : 708 mm ; (4.27) y f ˇ q 2 y 1 + 2 y 2 z f z 2 z 2 z 1 =0 : 265 mm : (4.28) Thedi˙erencesin x o˙set fallwithinthiserror,andthedi˙erencesin y o˙set withinaprimary beamsettingalsofallwithinthiserror. Theerrorforprojectedanglesfollowstheerroroftheinitialangledetermination 0 = j 0 j s x 2 x 1 x 2 x 1 2 + z 2 z 1 z 2 z 1 2 =0 : 639 mrad(4.29) pf ˇ p 0 = j p 0 j s y 2 y 1 y 2 y 1 2 + z 2 z 1 z 2 z 1 2 =0 : 240 mrad ; (4.30) where pf ˇ p 0 since pf = p 0 .Tocalculate f anapproximationismade:theerror iscalculatedforthecaseofaprojectionthroughconstantmagnetic˝eldof0.5T.Further, beamtypeandmomentumareheldconstantforthisapproximation.Theradiusofcurvature ˆ andassociatederror ˆ iscalculatedassuming Z =50 and B =0 : 5 Texactly.Inthis approximation, f isgivenby f =sin 1 z + ˆ 0 ) ˆ ; (4.31) with z ˇ 0 : 642 msettoreproducethetypical f =45 mradfoundbythestep-wise 132 projectionforthe 132 Snbeam.Using =0 : 6565 and =2 : 597 10 4 ,we˝ndmomentum p =106 : 945 GeV/c, p =0 : 07435 GeV/c, ˆ =14 : 269 m,and ˆ =0 : 00248 m.Taking 0 =0 ,wecan˝nd f =45 mrad,and f =0 : 6397 10 4 mrad.Withthesevalues,the errorinyawangleisdominatedbytheerrorin 0 f = f ) s z ˆ 2 ˆ 2 + 0 ) 0 2 =0 : 6397 mrad : (4.32) 4.3AbsoluteCrossSection Determiningtheabsolutecrosssectionforeachsystemisnecessarytonormalizecomparisons betweensystems.Forsimplicity,westartwiththecrosssectionforcollisionsthatsatisfythe trigger.Thecrosssectioncanbedeterminedstatisticallyfromtheratioofthenumberof nuclearreactionsthatsatisfythetriggertothenumberofincidentparticlesbytherelation N reactions N incident = ˆ A ˙ m ; (4.33) where ˆ A istargetareadensitying/cm 2 , ˙ isthecrosssectionincm 2 ,and m isthemass ofthetargetnucleusing.ThetwotargetsusedintheS ˇ RITcampaignwereisotopically enriched 112 Snand 124 Sn,withmeasuredthicknessesof0.836mmand0.828mm,respec- tively.Theareadensitiesofthe 112 Snand 124 Sntargetsweremeasuredat0.561g/cm 2 and 0.608g/cm 2 ,respectively.Tocalculatethecrosssection,wemustdetermine N reactions and N incident . 133 4.3.1MeasurementofReactedSn Thesimplestmeasureof N reactions forarunisprovidedbycorrectingthenumberofgated triggers, N gated ,forpurityando˙-targetreactions N reactions = N gated Purity ( data ) R ( ontarget ) : (4.34) ThevaluePurity ( data ) wasdeterminedpreviouslyinSection4.2.6.Theaverageratioof eventsontarget R ( ontarget ) = N gated ( ontarget ) N gated (4.35) wasmeasuredforeachsystemusingreconstructedvertexinformationfromS ˇ RITROOT. The Z positionofreconstructedverticesfor 132 SnisshowninFigure4.27,alongwitha Gaussian˝ttothepeakatthetargetposition.Eventswithina5 ˙ cutofthetargetpeak arecountedason-target.Theaveragevalueisused,ratherthantherun-by-runvalue.The vertexreconstructionforallofthefoursystemsisdiscussedlaterinSection4.5. 4.3.2MeasurementofIncidentSn Themeasurementof N incident ismadeusingthecountsfromtheSBTscaler,butcorrection forActiveVetoArrayhits,theerate",reactionsupstreamoftarget,beampurity,anda normalizationbetweenthetwoprimarybeamsisrequired.Thebeampurity,Purity ( beam ) , istabulatedinSection4.2.6.ThebeamparticleswhichhittheActiveVetoArrayproducea scalercountAVAwhichissubtractedfromtheSBTcounts.Theliverateiscalculatedusing 134 Figure4.27:Vertex Z probabilitydistributionfor 132 Sndata.A˝tonthetargetpeakis showninred. theSBTscalerandtheSBT&BUSYscaler liverate = SBT SBT&BUSY SBT : (4.36) Reactionsupstreamoftargetwereestimatedusingthetotalabsorptioncrosssection.,which isdeterminedgeometricallybytreatingeachnucleusasahardspherewithsetinteraction radii R B and R T forbeamandtarget.Itisassumedthatwhentheimpactparameteris lessthanorequalto R B + R T ,areactionwilloccur.Interactionradiusisestimatedas R =1 : 2 A 1 = 3 fm,andcrosssectionforreactionisgivenas ˙ = ˇ ( R B + R T ) 2 .The probabilityforcollisionisthengivenby P rxn = ˙N A ˆ A =A T : (4.37) 135 ThereactionprobabilitiesaretabulatedinTable4.6,withthebackgroundrateestimate comingfrom P bkgd betweentheSBTandthetarget(TGT).Thisprobabilityismultiplied bythenumberofSBThitstodeterminethenumberofupstreamreactions. P bkgd (%)P bkgd (%)P bkgd (%)P bkgd (%) StartEnd 108 Sn 112 Sn 124 Sn 132 Sn SBTTGT1.121.301.361.40 TGTTGT1.251.281.311.36 TGTFC exit 0.2930.2980.3120.322 SBTFC exit (noTGT)1.411.591.671.72 Table4.6:TotalabsorptioncrosssectionsfortheSnbeamsusedintheS ˇ RITexperiment Thenormalizationbetweenthetwoprimarybeamsisrequiredtoaccountfortrigger di˙erences.AsdescribedinChapter3,thediscriminationoftheKATANAvetowasper- formeddi˙erentlybetweenthetwoprimarybeams.Forthe 108 Snand 112 Snbeams,pileup beforethetriggerisnotsuppressed,whereasforthe 124 Snand 132 Snbeams,pileupbefore thetriggerwaspartiallysuppressed.Thepileupsuppressionreducesthenumberofcandi- dateincidentSn.Todeterminethesuppression,thepileuprateisdeterminedbeforeand afterthetriggerusingtheF7PPACinformationasdescribedinSection4.2.4.Thisrateis usedtodeterminetheprobabilitythatasuppressedpileupeventoccurs.Withthetriggered pileupratebeforeas R before andtriggeredpileuprateafteras R after ,thesuppressedrate R suppressed isgivenas R suppressed = R after R before : (4.38) TheprobabilitythatanincidentSnissuppressedduetopileupcanbecalculatedusing Poissonstatistics.Thevetowindowis4 µ swide,sotheprobabilitythatasuppression occursisgivenas: P suppression = e 2 2! ; (4.39) 136 where iscalculatedas: = R suppressed 4 µ s : (4.40) Withtheaccumulatedcorrections,thenumberofcandidateSncanbedeterminedas N incident =( SBT AVA ) (1 P suppression P bkgd ) Purity ( beam ) liverate ; (4.41) givingthe˝nalvalueforcrosssectiondetermination. 4.3.3MeasuredCrossSection With N reactions and N incident determined,thecrosssectioncanbedeterminedusingEqua- tion4.33.Theaverageofthedeterminedabsolutecrosssectionsforalldatarunsareshown inFigure4.28asafunctionofsystemmass,witherrorbarscorrespondingtothestandard deviationofdeterminedabsolutecrosssectionsforeachbeam.Thevaluesaretabulatedin Table4.7,alongwiththestandarddeviation. BeamTarget ˙ (barn)stddev(barn) 132 Sn 124 Sn1.7750.012 124 Sn 112 Sn1.6790.013 112 Sn 124 Sn1.6870.009 108 Sn 112 Sn1.5980.010 Table4.7:Averageabsolutecrosssection, ˙ ,withstandarddeviationofthecrosssection measuredforthedataruns. 137 Figure4.28:Calculatedcrosssectionforeachsystem,organizedbytotalsystemmass 4.4ImpactParameterSelection Themeasuredcrosssectionrelatestotherangeofimpactparametermeasured.Inthe following,weusethenumberofchargedparticlesmeasuredinanevent(i.e.,themultiplicity) asameasureoftheimpactparameter.Generally,theaveragechargedparticlemultiplicity ofeventsatagivenimpactparameterdecreaseswithincreasingimpactparameter.For simplicity,weassumethisrelationshipiscorrectforindividualeventsanddiscussthevalidity ofthisapproximationlater.Inthisapproximation,thecrosssectionforeventswitha multiplicitygreaterthanagivenvalueisrelatedgeometricallytothemaximumimpact parameter b max ˙ b max = ˇ b 2 max : (4.42) Theuncertaintyassociatedwithdeterminingcrosssection ˙ b max causesanuncertaintyin b max ,discussedlater. 138 Thedetectedchargedparticlemultiplicityprovidesabasic˝lteroftheimpactparameter. Areactionwithasmallimpactparameterwillingeneralproduceahigherchargedparticle multiplicitythananotherwisesimilarreactionwithalargerimpactparameter.However,this relationshipisnotexactformanyreasons.First,thechargedparticlemultiplicitydepends onwhethertheemittedparticlesemergeasnucleonsorasboundclusterswith Z> 1 .At hightemperatures,andhighentropies/nucleon,theemissionofindividualnucleonsanda highmultiplicityarefavoredwhileatlowtemperaturesandlowentropies,theemissionof clusterswith Z> 1 andalowmultiplicityarefavored.Theamountofheatingisincreased withthenumberofhardcollisionsperevent,butthenumberhardcollisionsvariesrandomly fromeventtoevent,evenwhenalleventsareatthesameimpactparameter.Second, wedonotdetectallchargedparticles;thisintroducesanotheruncertaintythatcanbe assessedbysimulatingtheevent.Third,itisobviousthatwecannotperfectlyconstrainthe continuousimpactparameterdistributionwithadiscretemultiplicitydistribution.These uncertainties,however,canallbeexploredandaddressedbysimulatingtheimpactparameter ˝ltertheoreticallyanddeterminingtheuncertaintiesintheimpactparameterforeachchoice ofimpactparameter˝lter.Wereturntothisissuelater. Thenormalizedchargedparticlemultiplicitydistributionsforallsystemsareshownin Figure4.29,withP[N C ]theprobabilityofdetectingagivennumberofchargedparticles.In contrasttoaminimumbiastriggerforwhichthemostprobablemultiplicityisverylow,the triggersuppresseslowmultiplicities.Therequirementofmultiplicitygreaterthanorequal to4intheKyotoMultiplicityArrayisthemoste˙ectiveatsuppressingperipheralcollisions withlowchargedparticlemultiplicities.Theeventsareselectedwiththesame˝lterused todeterminecrosssection:a5 ˙ cutaroundthevertexpeak,andthebeamPIDcutused forparticleselection.TrackscontributingtothemultiplicitycountmusthaveaPointOf 139 Figure4.29:Chargedparticlemultiplicitydistributionforthefourbeamsystems ClosestApproach(POCA)of20mmtotheeventvertex.Thedistributionsarenormalized bythenumberofentries. Assumingamonotonicrelationshipbetweenimpactparameterandchargedparticlemul- tiplicity N C ,withasmallerimpactparameterassociatedwithalargerchargedparticle multiplicity,wecancalculatethecrosssectionforagivenmultiplicity N N C : ˙ N = N N C N total : (4.43) Itiscommontode˝neareducedimpactparameteras ^ b = b ( N C ) b max = 8 < : 1 X N C dP ( N C ) dN C 9 = ; 1 = 2 ; (4.44) where b max isthemaximumimpactparameterdeterminedbytheabsolutecrosssectionin 140 Section4.3,and dP ( N C ) =dN C isthenormalizedprobabilitydistributionfor N C .Values of ^ b rangefrom0forthemostcentraleventsto1fortheleastcentralevents.Valuesof ^ b aremultipliedby b max toextract b ( N C ) .Therelationshipbetween b and N C isshownin Figure4.30forallfoursystems.Theshadedregionsrepresenterror,whichisdiscussednext. Figure4.30:Relationshipbetween b and N C forthefourbeamsystems,witherrorshown byshadedregions Therearetwomainsourcesoferrorthatcontributetothedeterminationof ^ b :theerror indetermining b max ,andtherangeofvaluesof b whichcanresultinmeasured N C .Asignif- icantcontributiontoerrorindetermining b max comesfromtheuncertaintyofthemeasured absolutecrosssection.Thiscontributionisdeterminedusingstandarderrorpropagation, b max = s @b max @˙ tot ˙ tot 2 = ˙ tot 2 p ˇ˙ : (4.45) Thecalculatederrorof b max islistedforeachsysteminTable4.8,usingonestandard deviationof ˙ tot for ˙ tot . 141 BeamTarget b max (fm) b max 132 Sn 124 Sn7.520.0254 124 Sn 112 Sn7.310.0283 112 Sn 124 Sn7.330.0195 108 Sn 112 Sn7.130.0223 Table4.8:Averageabsolutecrosssection, ˙ ,withstandarddeviationofthecrosssection measuredforthedataruns. Aneventatgivenimpactparameter b doesnotproduceadeterministicvalueof N C .We assumethatthevaluesof N C fromagiven b followaPoissondistribution.Amultinomial distributionislikelyabetterdescriptionof N C ,butthiswillrequirefurtheranalysisto model.Theaveragevalueof N C isdeterminedusingtherelationshipinEquation4.44,and thestandarddeviationisthen p N C bystandardPoissonstatistics.Thisallowsustoset errorbarsfor b from b N C p N C to b N C + p N C .Theerrorfor b max isincludedby adding ^ b b max . 4.5TPCAnalysis ThedataproducedbytheGETelectronicsisstoredashardware-speci˝cbinary-encoded ˝les,whichareunpackedtoROOT˝lesusingtheGETDecodersoftware[12,72].Each CoBoboardproducesarawdata˝le,andtheunpackedROOT˝lesaremaintainedas˝les foreachCoBo,resultingin12˝lesforeachdataset.TheseunpackedROOT˝lesarethen analyzedusingS ˇ RITROOT[73],apackagebasedontheFairRootframework[74].The analysis˛owisshowninFigure4.31,withtwobranches:oneforsimulation,andonefor analysisofexperimentaldata.Afterdigitizationofasimulatedevent,theanalysisfollows thesame˛owasthatofthedata. 142 Figure4.31:Analysis˛owfortheS ˇ RITROOTsoftwarepackage,showingbranchesfor experimentaldataaswellassimulation Thereconstructionstagestartswiththepulse˝ndingtask.Thedataforeachpadconsists ofanamplitudeovertimespectra,dividedintodiscretebinsoftime.Anexampleofthedata fromasinglepadinasingleeventisshowninFigure4.32.FortheS ˇ RITexperiment,the AsAdsamplingfrequencyof25MHzresultedintimebins,ortimebuckets,of40nswidth. SincethedrifttimeforelectronsintheTPCisroughly9 µ s,only270timebucketswereused, whichleavesafewtimebucketsforpedestalsubtraction.The˝rsttaskforreconstructionof aneventistoanalyzethehitsonallpads.ThePadResponseFunction(PRF)describesthe amplitudeonapadresultingfromcollectedcharge.Areferencepulsewasgeneratedfrom experimentaldatawhichwasusedto˝tthesignalsfromeachpad.Eachpadisscanned fromtheearliesttimetothelatesttime,searchingforpeaks.Whenapeakisfound,itis ˝tusingthereferencepulseshape.The˝ttedpulseshapeissubtractedfromthespectra, andthepeak˝ndingcontinuesthescanforadditionalpeaks.Each˝ttedpulseisstoredasa withpositionandamplitudeinformation.InFigure4.32,theindividual˝tsareshown inred,theoverall˝t(sumofallindividual˝ts)isshowninblack,andtherawspectrais showningray. Sincethechargefromanavalancheisspreadoutovermultiplepads,asinglehitdoes notcontainthecompleteinformationforanavalanche.Whenanavalancheoccursovera 143 Figure4.32:ExampleADCspectraforapad.SignalheightisinADCchannels,andeach timebucketcorrespondsto40ns.Figurefrom[12]. pad,theneighboringpadswillhaveasignalproportionaltotheirrelativeproximitytothe avalanche.Neighboringhitsaregroupedintowhichcollectivelyprovidemore completeinformationaboutpositionandcharge.Thetotalcharge Q foraclusterisdeter- minedbysummingthecharge q i fromallcontributinghits, Q = P i q i .Theposition X is determinedusingthecharge-weightedpositionsofeachpad, X = P i q i x i P i q i . Thecreationofclustersandthetrack˝ndingprocessareintertwined.Clustersare ideallyformedperpendiculartothetrack,sotheclusterformationisintegratedwiththe track˝ndingtask.HitsaremappedtoaRiemannsphere,withradius R R equaltotwicethe varianceofhitsinthepadplane.Thesphereiscenteredwith x 0 atthelocationoftheaverage x hitposition, h x hit i , y 0 at R R ,and z 0 atthecenterofthepadplane.Themappingofhits ontotheReimannspheregroupshitsassociatedwithatrackneareachother,allowingthe formationoftrackcandidates,whichareparametrizedwithahelicalequation.Remaining hitsarecomparedagainstthetrackcandidates,andareassociatedwiththetrackbasedon theirpoint-of-closest-approach(POCA)tothetrack'shelicalequation.Withhitsassociated toatrack,clusterscanbeformedfromthehits.Clustersareideallyformedasagroupofhits 144 perpendiculartoatrack.Sincethepadsruninrow(alongthe x direction)andlayers(along the z direction),clustersmustbeformedalongthesedirections.Thedecisionofwhetherto clusteralongaroworlayerisdeterminedbythetrack'scrossingangle:ifthetrack'syaw angleatagivenpointisgreaterthan45 ,itisclusteredalongthatrow.Otherwise,itis clusteredalongthelayer. The˝nal˝toftracksisperformedusingtheGENFITpackage[75].GENFITusesthe leastsquareKalman˝lteringalgorithmwiththegaspropertiesandmagnetic˝eldmapas inputparametersto˝tthetrackmomentum.Initialparametersareprovidedfromthehelix parametrizationdiscussedabove.Wehavetheoptiontore˝tthetrackmomentaincludinga pointfromtheBDCvertex,butforthiswork,theinitialmomentumprovidedbyGENFIT isusedtodetermineparticlemomenta. TheRAVEtoolkit[76]wasimplementedforvertex˝nding.RAVEwasdesignedforthe CMSexperiment[77],whichutilizesalargesolenoidalmagnet.RAVEperformsbestwith themagnetic˝eldalignedalongthez-axis,asisthecaseforCMS.Thus,acyclicalchangeof coordinatesystem,(x,y,z) ! (z,x,y),wasmadewhenprovidingtrackstoRAVE,sothatthe magnetic˝eldwasalignedalongthez-axisinthe˝ttingenvironment.Thereconstructed x and y positionscanbecomparedtotheBDCprojection,aswasshownearlierinSection4.2.8. Thedistributionofreactionpositionin z isshowninFigure4.33,forallfoursystems.A sharppeakcorrespondstoreactionsontarget.Thepositionandwidthofthepeakforeach systemarelistedinTable4.9,alongwiththemeasuredphysicalpositionofthetarget.The eventvertexfoundfromtheTPCisusedtodetermineifthereactionoccurredontarget. 145 Figure4.33:Normalizeddistributionof z positionofreconstructedvertex,forallsystems. BeamTargetTargetcenterReactionPeakSigma (measured)(mm)(RAVE)(mm)(mm) 132 Sn 124 Sn-13.12-13.101.83 124 Sn 112 Sn-13.27-13.131.44 112 Sn 124 Sn-13.12-12.861.27 108 Sn 112 Sn-13.19-13.351.70 Table4.9:Comparisonofmeasuredtargetpositionandreconstructedreactionvertex.Di- mensionsareintheTPCframe. 4.5.1TrackValidation Toremovebackground,wemustremovetracksthatarenotassociatedwithoureventor cannotbereconstructedwell.TheGENFITresultprovidesatrack˝tthatcanbecompared totheRAVEvertextoobtainthepointofclosestapproach(POCA).Trackswhichhave POCA > 20mmareinvalidated,astheyarelikelyeitherade˛ectedparticle,afalserecon- struction,oranupstreamreactionproduct.Trackswithfewclusterscanbecausedbyfalse reconstruction,orbyshorttracksforwhichthemomentumandenergylosscannotbewell resolved.Aminimumof15clustersisrequiredfortrackstobevalidated. 146 Figure4.34showsatypicaleventfortheTPC,from(toppanel)aboveand(bottom panel)theside.Theregionbytheentrancewindowhasahighoccupancyprobability. Theclusteringdoesnothandlechargesharing,resultinginarti˝ciallyhighdE/dxvalues forclustersinthisregion.Also,padsforthishighdensityregionareoftensaturated.An ellipsoidcut,drawnonFigure4.34witharedline,isusedtoexcludeclustersinthishigh densityregionassuchclusterstendtomakethetrackreconstructionlessaccurate. Figure4.34:AtypicaleventintheTPCviewedfrom(toppanel)aboveand(bottompanel) theside.Thehighdensityregionoutlinedinredisexcludedfromdataanalysis. Inadditiontotrackcuts,eventcutsareappliedtothedata.Isotopiccuts,described earlierinthischapter,areappliedtoselectonlyreactionswiththedesiredisotopes.The RAVEvertexisusedtoselectreactionsontarget,excludingupstreamandactivetarget reactions.Eventswithreactionvertexwithin3 ˙ ofthevertex z peakareconsideredtobe ontarget.Additionallythe x and y vertexpositionisrequiredtobewithinthephysical targetlocation. 147 Todemonstratethee˙ectofthetrackvalidation,thePIDplotafterdetermining Bˆ and dE/dxisshownintheleftpanelofFigure4.35,for 124 Snbeamimpingedona 112 Sntarget. AlthoughPIDlinesareclearlyevident,theyarenotclearlyresolved,withpionlinesalmost impossibletodiscern.ThePIDplotafterremovingbackgroundwiththe˝ltersde˝nedabove isshownintherightpanelofFigure4.35,forthesamesetofevents.ThePIDshowsdrastic improvementintheresolutionofparticles,withpionlinesclearlyevident. Figure4.35:ThePIDfor 124 Snevents,(left)withoutcuts,and(right)withcuts. 4.5.2DetectionE˚ciencyfromEmbeddingStudies Thedatacontainshightrackmultiplicityevents,whicharedi˚culttoaccuratelyrepro- ducewithsimulations.Todeterminereconstructione˚ciency,anembeddingsimulationwas developed.ThismethodisusedbytheSTARcollaboration[78],andinvolvesembeddingsim- ulatedparticlesintorealdataevents.SinglepiontracksweregeneratedusingGEANT4[79] overarangeofanglesandmomenta,andembeddedintodataeventsfromthe 132 Sn+ 124 Sn system.AsshowninFigure4.31,theelectrondriftandpadresponseforeachsimulated trackisdeterminedinthesimulationbranch.Afterthesimulatedtrackisembeddedinthe realdataevent,theeventisanalyzedusingthereconstructionsoftware.ThePOCA < 20 148 mmconditionandminimumof15clustersconditionareappliedtotracks(includingthe embeddedtrack),andiftheembeddedtrackisreconstructedandmeetstheseconditions,it canbeclassi˝edasThereconstructione˚ciencyisdeterminedasafunctionof trackangle,momentum,andeventmultiplicitybydeterminingtheproportionofdetected tototaltracksembeddedwithsimilarproperties. 4.6CalibrationwithCocktailBeam The 238 Uprimarybeamwasusedtoproducetwo Z ˇ cocktailbeamsforcalibration oftheTPC.Thebeamenergiesweretunedforalphaparticles:thehigherenergycocktail beamproducedalphaparticlesat300MeV/u,whilethelowerenergycocktailbeamproduced alphaparticlesat100MeV/u.Bothofthesebeamsweremeasuredwithanemptytargetin theTPC,andthe100MeV/ubeamwasalsomeasuredwitha21mmthickaluminumtarget, whichservedasanenergydegrader.Thecombinationofthesesetupsprovides3distinct energycalibrationpointsfortheTPC.TheTPCisusedtoconstructthePIDofincoming particles,astheionchamberenergylossistoolowtoproduceabeamPID. 4.6.1CocktailBeamSettings Forthecocktailbeam,plasticscintillatorswereusedinfocalplanesF3,F8,andF13.The F8plasticscintillatorwasusedtotriggerdataacquisition.The˝nalquadrupole,STQ25, istunedtomaximizeacceptanceoftheexpectedrigidity.Forthe E ˇ 300MeV/ubeam, STQ25wastunedtomaximizeacceptancearound5.3759T m,andforthe E ˇ 100MeV/u beam,STQ25wastunedtomaximizeacceptancearound2.9239T m,correspondingto300.11 MeV/uand97.93MeV/ualphaparticles,respectively. 149 Sincetheparticlesarelowcharge,theplasticscintillatorsdonothave100%detection e˚ciency,althougheverytriggeredeventwillhaveasignalintheF8plastic.Wearenot abletoreconstructabeamPID,butwecandeterminePIDusingtheTPC,andexaminethe correspondingTOFfromF3toF8,andF8toF13scintillators.TheseTOFmeasurements areuncalibrated,buttheo˙setshouldbethesameregardlessofisotope.Using 2 Hand 4 He astestisotopes,theTOFo˙setbetweenF8andF13istunedtoreproducetheexpected Bˆ value.TheTOFo˙setissetto477.6nsforthe300MeV/ubeam,and479.4nsforthe100 MeV/ubeam.Theseo˙setsareexpectedtobedi˙erent,astheplastictimingwasadjusted foreachsetting.Theaverage Bˆ valueforeachisotopeislistedinTable4.10.Theparticle rigiditiesarewithin+0.7%/-1.7%oftheexpected Bˆ . Particle Bˆ (T m)(100MeV/usetting) Bˆ (T m)(300MeV/usetting) p2.9345.358 d2.9445.402 t2.8905.366 3 He2.9255.366 4 He2.9035.394 6 LiN/A5.322 7 LiN/A5.287 Table4.10:Magneticrigidityforeachparticleincocktailbeams 4.6.2RigiditywithinTPC TheTPCprovidesameasurementofmagneticrigidity,whichcanbecomparedtotheex- pectedrigidity.ThemeasuredmagneticrigidityintheTPCappearstobecorrectifweonly analyzetracksoverthe˝rst90layersoftheTPC,correspondingto108cmalongthelength ofthepadplane.Moreprecisevaluesfortherigiditycanbeobtainedbyutilizingthefull112 layers(134.4cm)oftheTPC,buttherigidityobtainedusingthefull112layersbecamesys- 150 tematicallyhigherthantheexpectedrigidity.Thisdiscrepancyoriginatesfromthemagnetic ˝eld,whichhasnon-negligiblehorizontalcomponents,andareduced,non-uniformvertical componentasitapproachestheedgeofthepoleface.FortheTPCanalysisinthisbody ofwork,thisdiscrepancywaspatchedbyshiftingthemagnetic˝eldcenter22cmupstream, e˙ectivelyreducingthemagnetic˝eldstrengthfortrack˝tting.TheoriginalPIDisshown intheleftpanelofFigure4.36,andthePIDwhichresultsfromusingashiftedmagnetic˝eld isshownintherightpanel.Thedi˙erencesarenotsubstantial,butshiftingthemagnetic ˝eldbetteralignsthereconstructedmomentumwiththeexpectedmomentum. Figure4.36:CocktailPIDusing(left)propergeometryand(right)shiftedmagnetic˝eld Adetailedanalysisoftheelectrondriftinthisregionrevealsthatnon-negligible x and z componentsofthemagnetic˝eldintheoriginal(correct)˝eldmapchangethedriftof electronsinthe˝nal24.4cmofthe˝eldcage.Thisshiftsandstraightenstheimageofthe trackonthepadplaneandincreasestherigidityvaluesextractedfromthetrack.Anew correctionthattakestheresulting E B componentoftheelectronicdriftvelocityhasbeen obtainedandwillbeappliedtoallfutureanalyses,althoughitwasnotreadytobeapplied totheanalysisinthiswork. 151 4.7Mixed 124 Sn-likebeam Becausethestatisticsofthe 124 Snbeamarelimited,itisnecessarytoincludeadditional beamparticlesintheanalysis.Theselectionofisotopesisperformedtomatchtheaverage charge,mass,andasymmetryofthe 124 Sn+ 112 Snsystem,withasymmetry de˝nedas: = N Z N + Z : (4.46) Forexample,ifanequalnumberof 123 In, 123 Sn, 125 Sn,and 125 Sbbeamparticlesareim- pingedonthe 112 Sntarget,thebeam-targetsystem'saveragecharge,averagemass,and averageasymmetrywillbethesameasthatofthe 124 Sn+ 112 Snsystem. Theselectedisotopes,andrelativeproportions,arelistedinTable4.11.Fortheduration ofthiswork,themixedbeamconsistingoftheseisotopeswillbedenotedasthe 124* Snbeam. BeamRelativeBeamRelative IsotopeComposition(%)IsotopeComposition(%) 121 Ag1.3 124 Sn16.71 122 Ag1.43 125 Sn4.41 121 Cd1.08 124 Sb7.19 122 Cd5.44 125 Sb22.48 123 Cd2.93 125 Te0.07 122 In3.3 126 Te5.67 123 In13.1 127 Te4.01 124 In5.78 127 I0.77 123 Sn4.35 Table4.11:Beamisotopesincludedformixed 124* Snbeam Tocheckthattheseadditionsarereasonable,weplotthereducedimpactparameter ^ b (Seesection4.4)spectraforthe 124 Snbeamandthe 124* Snbeam.Thereducedimpact parameterisingoodagreementforallbeamtypes.Whenmeasuringthepionspectrainthe 152 followingsection,the 124 Snand 124* Snspectraareevaluatedforconsistency. Figure4.37: ^ b spectrafor 124* Snmixedbeam. 4.8 112 Sn+ 124 Snand 124* Sn+ 112 Snpionproduction The 112 Sn+ 124 Snand 124* Sn+ 112 Snsystemsprovidecriticalcomparisonsofthetwo primarybeams,andthepionproductionfromthesesystemsispredictedtobesensitiveto thesymmetryenergy.Sincethesystemsareapproximatelymirrorreactions,weexpectthat thephysicswillbesimilarandmainlya˙ectedbytheinterplayofeachsystem'skinematics withtheexperimentalsetup.Incompletestoppingandincompleteequilibrationmaya˙ect thereactions,thatis,thebeamnucleonsmaynotfullymixwiththetargetnucleons.This wouldcausethe 124* Snreactiontobemorerepresentativeofemissionfromasystemthatis moreneutronrich,andcausethe 112 Snsystemtobemorerepresentativeofasystemthatis moreneutronde˝cient.Thisdi˙erenceshouldbemoremanifestathighparticlerapidities, whichmoveatrapiditiesconsistentwiththebeamvelocity,andlesssoatparticlerapidities 153 consistentwithemissionfromanequilibratedsystem,whichmoveatrapiditiesconsistent withthecenter-of-momentumoftheprojectileplustargetsystem.Suche˙ectswouldalsobe moreevidentinperipheralcollisions,consistentwithahigherdegreeofstoppingincentral collisions.UsingtheimpactparameterdescribedinSection4.4,eventsareselectedfromthe 112 Snsystemand 124* Snwithimpactparameterupto3.1fm.Thepionspectraforthetwo systemsareproducedandexaminedinthissection. 4.8.1PID˝ttingandpionselection Theparticleidenti˝cationdependsonmeasuringeachparticle'smomentumandenergyloss. Theenergylossisafunctionofaparticle'srelativisticvelocity andcharge q .TheTPC measuresmagneticrigidity,or p=q .Ifthechargeandmassofaparticleareknown,the momentumandvelocitycanbedetermined.Themomentumisrelatedto by = p p p 2 + m 2 c 2 : (4.47) Theenergyloss dE=dx ( Z; ) isapproximatedfollowingtheformusedbyBlumetal.[30]: dE=dx = Z 2 p 1 p 4 ˆ p 2 p 4 ln p 3 + 1 p 5 ; (4.48) where p 1 p 5 arefreeparameters.Theenergylosscurvewasfoundtovarybypitchand yaw,soitis˝tseparatelyfordi˙erentregionsofangularemission,with6equaldivisions ofyawand12equaldivisionsofpitch.This˝tprovidesafunctiontodescribeenergyloss dE=dx (typ.)ofatypicalpion,asafunctionofmomentuminthelabframe.Figure4.38 154 showsthequantity ln dE=dx ( track ) dE=dx ( typ. ) (4.49) forpionsasafunctionoftrackmomentuminlabframe,where dE=dx (track)isthemeasured energylossforagiventrack,and dE=dx (typ.)isthetypicalvalueofenergylossdetermined fromthe˝tsdiscussedabove.TheprojectiontotheY-axisisshownontheleftfor ˇ ,and ontherightfor ˇ + .Alargecontributionfromprotonsisvisibleinthetop-rightcornerof theplotof ˇ + .Thetoppanelsshowthe 124* Snsystem,andthebottompanelsshowthe 112 Snsystem.Electron( e )andpositron( e + )linescanbeseenunderneaththepionlines. Pionsareselectedfromthesespectrausinggraphicalcuts. Figure4.38:Comparisonofenergylosstotypicalenergylossfor(top) 124* Snsystemand (bottom) 112 Snsystem.Y-projectionsareshowntotheleftfor ˇ ,andtotherightfor ˇ + . 4.8.2BackgroundEstimation Figure4.38showsthepositronandelectronlinesintersectingwiththepionline,aswellasthe protonlineoverlappingwiththe ˇ + line,indicatingthatthepionlinescontainbackground fromotherparticles.Thisbackgroundisestimatedasafunctionofmomentum,usingthe 155 ˇ + asanexample.Slicesofthe˛attenedPIDaremadeevery20MeV/c,andprojectedto they-axis.Figure4.39showsthisprojectionfor 124* Sn+ 112 Snbetween380and400MeV/c. Thepeaksfrom ˇ + andprotonsareclearlyvisibleandoverlapping.Thespectrais˝twith thesumoftwoGaussianfunctions,showninredinthe˝gure.Thedeconvolutionofthese GaussiansprovidesGaussianestimatesfor ˇ + (˝tshowningreen)andprotons(˝tshown inblue).These˝tsareusedtoestimatetherelativecontributionfrompionsandprotons. Figure4.39:Projectionof˛attenedPIDbetween380and400MeV/c.The ˇ + (green)and proton(blue)peaksare˝tsimultaneously,withthetotal˝t(red)andseparatecontributions shown. Withinthissection,welet x be x =ln dE=dx ( track ) dE=dx ( typ. ) ; (4.50) therebygivingavariablenametothequantityde˝nedbyEquation4.49.Forthemomentum rangeshowninFigure4.39,aparticleatagiven x willhavesomeprobabilityofbeingapion andsomeprobabilityofbeingaproton.IfwewritetheGaussian˝tforapionas G ˇ ( x )= A ˇ e ( x ˇ ) 2 2 ˙ 2 ˇ ; (4.51) 156 andforaprotonas: G p ( x )= A p e ( x p ) 2 2 ˙ 2 p ; (4.52) thentheprobabilitythataparticleisapioncanbefoundas P ( ˇ )= 0 B @ 1+ A p A ˇ e ( x p ) 2 2 ˙ 2 p + ( x ˇ ) 2 2 ˙ 2 ˇ 1 C A 1 : (4.53) Theerrorisestimatedbypropogatingthe˝terrorforeachparameter: P ( ˇ ) P ( ˇ ) 2 = @P ( ˇ ) @A p A p 2 + @P ( ˇ ) @ p p 2 + @P ( ˇ ) @˙ p ˙ p 2 + @P ( ˇ ) @A ˇ A ˇ 2 + @P ( ˇ ) @ ˇ ˇ 2 + @P ( ˇ ) @˙ ˇ ˙ ˇ 2 (4.54) Figure4.40showstheaveragebackgroundasafunctionofmomentumbin,fortracksselected withagraphicalcut.Thebackgroundcontributionislessthan5%formostofthemomentum regionsweinvestigate.Near100MeV/c,thebackgroundcontributionrisestoabout8%: thisiswherethepositronlineintersectsthepionline. 4.8.3PionMultiplicities Withpionsselected,wecreatethemomentumspectraforpionsinthelabframeandenergy spectraintheCOMframe,normalizedbythenumberofcandidateevents(selectedas describedinSection4.5.1).ThepionsaretranslatedtotheCOMframeusingaLorentz boost,oppositethebeamdirection,withmagnitude COM .Thebeamangleisdetermined usingtheBDCinformation(SeeSection4.2.8),andthebeamvelocityisdeterminedusing 157 Figure4.40:Averagebackground/signalratiosfor ˇ + ,asafunctionofmomentum.The e˙ectsofpositronandprotoncontaminationareevident. theTOFinformation(seeSection4.2.2),withanenergylosscorrection,whichiscalculated withLISE++.Themassofthetargetisaddedtothebeamenergy,andthetotalenergyand massofthesystemusedtodetermine COM .Aratherrestrictivecutisused,implemented intheCOMframe,allowingustocomparethetwosystemsinregionsofsimilaracceptance andreconstructione˚ciency: 40 ˚ COM 20 ; 150 ˚ COM 220 ; (4.55) 0 COM 90 : (4.56) Sincethesolidanglecoverageisnotcomplete,wemustscaletheresultsbyacorrection factor.Wecalculatethesolidangleoftheangularrangeselected, selected = 130 360 2 ˇ Z 90 0 sin( ) = 13 2 ˇ 36 (4.57) 158 wherethefactor 130 = 360 comesfromthe ˚ COM selection,whichcutsoutpartofthesolid angle.Toobtainthecorrectionfactor,wedivide selected by4 ˇ toobtain selected total = 13 2 ˇ 36 4 ˇ ˇ 0 : 18056 : (4.58) BeamEvents ˇ ˇ + ˇ ˇ + (Raw)(Raw)(E˙.Corr.)(E˙.Corr.) 124* Sn74168532118333656712736 124 Sn911263720143661397 112 Sn115543856127575922019198 Table4.12:E˚ciencycorrected(E˙.Corr.)pionyieldsforthiswork. Figure4.41:PionkineticenergyspectrainCOMframe. ˇ aredrawnontheleftside, ˇ + ontheright.Thetoppanelsareforthe 124* Snsystem,whilethebottompanelsareforthe 112 Snsystem. TheCOMkineticenergyspectraforpionsareshowninFigure4.41,with ˇ onthe leftside, ˇ + ontheright,fromthe 124* Snsystemontop,andfromthe 112 Snsystemon thebottom.Therawspectraisdrawnwithblackhistograms,andthee˚ciencycorrected 159 spectraisdrawnwithgreencrosses.Thee˚ciencycorrectionincorporatesthesolidangle correction,backgroundcorrection,andtheembeddede˚ciencycorrection.Thestatisticsare particularlylimitedfor ˇ + above200MeV.Adirectcomparisonbetweenthetwosystemsis showninFigure4.42,for ˇ (left)and ˇ + (right).Itisapparentthattheratioiscloseto 1,althoughthereisnotperfectagreementbetweenthesystems. divergingforkineticenergyover150MeVforboth ˇ and ˇ + . Figure4.42:Relativepionproductionforthe 124* Snsystemandthe 112 Snsystem,for ˇ (left)and ˇ + (right) Therapidities y beam , y COM ,and y ˇCOM areallcalculated,alongwithtransversemomen- tum p t ,allowingustoplotthe p t - y 0 phasespacedistributionsforthepions.Wenormalize thepionrapidity, y 0 = y ˇCOM y beam y COM ; (4.59) todeterminerapidityrelativetobeamrapidity.Thisnotationisconsistentwith y 0 asde˝ned inReference[80].Inthisnormalization,arapidityof1correspondstoaparticlemovingat thebeamrapidity.Thetransversemomentumindicatesmomentumdirectedawayfromthe beamaxis.Figure4.43showsthe p t - y 0 spectrafor ˇ (left)and ˇ + (right)for 124* Sn(top panels)and 112 Sn(bottompanels)beams.Notethattheseplotsincludedatafromalarger 160 Figure4.43: p t - y 0 distributions,withrapiditynormalizedtobeamrapidity. ˇ aredrawn ontheleftside, ˇ + ontheright.Thetoppanelsareforthe 124* Snsystem,whilethebottom panelsareforthe 112 Snsystem. cutin COM ,upto100 ,inordertodemonstrateacceptanceissuesfor y 0 < 0 .Dataused forother˝guresexcludestrackswith y 0 < 0 . 4.8.4ComparisonofPionSpectrafor 124 Sn-likebeamsand 124 Sn beam Tocheckthattheresultsusingthe 124* Snsystemarerepresentativeofthe 124 Snsystem,we comparethepionspectraforbothsystems.Figure4.44showsthenormalizedpionKE COM spectra,withthetoppanelshowingthee˚ciencycorrectedspectra,andthebottomshowing therawspectra.Themixedbeam, 124* Sn,isplottedwithblackcircles,andthe 124 Snbeam isplottedwithmagentadiamonds.Withinstatisticaluncertainties,thedistributionshapes forbothsystemsmatchwell. 161 Figure4.44:PionKE COM spectrafor 124* Snand 124 Snbeams.Thetoppanelise˚ciency corrected,andthebottomistherawspectra. 4.8.5ErrorinPionSpectra Weneedtocombinetheerrorassociatedwithbackgroundande˚ciencycorrectionswith thestatisticalerrorforthepionspectra.Thebackgroundande˚ciencycorrectionsare calculatedforeachtrack,andsavedasfractionalerror.Wedenotetheprobabilitythattrack i isbackgroundas b i ,andtheembeddinge˚ciencycorrectionas e i .Forapionwithweight n i = b i e i ,thesquareofthefractionalerroris n i n i 2 = b i b i 2 + e i e i 2 : (4.60) Aswe˝llthepionspectra,theweightofeachtrackisadded,andthesquareofthefractional errorissaved.Forbin j ofthespectra,thepioncountis N j N j = X i n ij : (4.61) 162 Wemustalsoincludethevariance ˙ N j = p N j ofthepioncount,sothe˝nalerrorofthe pioncountis: ( N j ) 2 =( ˙ N j ) 2 + X i ( n i ) 2 : (4.62) Wescaleourspectrabythenumberofevents N events ,andthesolidangleacceptance, producingforeachbintheprobability p j thatapionisproducedinthatbin: p j = N j N events total selected : (4.63) Wetakeoureventnumberandsolidanglecorrectiontobeknownexactly,thereforetheerror for p j is p j = N j N events total selected : (4.64) Thisisassumingthatthetriggerselectsauniformazimuthaldistributionofthereaction plane,andthatthereactionissymmetricforwardsversusbackwards.Thecorrectionfor solidanglere˛ectsthelimitedacceptanceoftheTPC. 4.8.6PionRatios Figure4.45showsthe ˇ =ˇ + spectralratioasafunctionofKE COM for 124* Snand 112 Sn beams.Thee˚ciencycorrectedspectraisshownwithgreencrosses,andtherawspectra withablackhistogram.Bothrawande˚ciencycorrectedspectramatchwell.Thisratio isexpectedtoprovidestrongsensitivitytothesymmetryenergyforthemostasymmetric system, 132 Sn+ 124 Sn.Forcollisionsbetween 124 Snand 112 Sn,thesensitivitywillbemuch less.Ifthecollisionmixesprojectileandtargetnucleonswell,weexpectspectralratiosfor the 112 Sn+ 124 Sncollisionstobeessentiallythesameasforthe 124 Sn+ 112 Sncollisions. 163 Twodi˙erencesmaya˙ectthespectralratiocomparisons:theinclusionofadditional 124 Sn- likebeamnucleons,andthedi˙erenceintheCOMframeforthetwosystems,relativeto thedetector. Figure4.45:The ˇ =ˇ + spectralratiofor(left)the 124* Snsystemand(right)the 112 Sn system Wewishtoreduceoreliminateasmanysystematicuncertaintiesaspossible.Inparticu- lar,theacceptanceanddetectione˚cienciesareingeneraldi˙erentfor ˇ and ˇ + .Without knowingandcorrectingforthesee˚ciencies,physicsinterpretationswillbeinaccurate.One methodtomitigatethisistoconstructwhatiscalledthedoubleratio.Ifwedenotethe ˇ and ˇ + detectione˚ciencyas " ˇ and " ˇ + ,thedoubleratiois DR = Y ( ˇ ) " ˇ Y ( ˇ + ) " ˇ + 124 Sn Y ( ˇ ) " ˇ Y ( ˇ + ) " ˇ + 112 Sn : (4.65) Ifthee˚cienciesandacceptancesaresimilarbetweenthetwosystems,theywillcancelout, 164 leavingthedoubleratioas DR = Y ( ˇ ) =Y ( ˇ + ) 124 Sn Y ( ˇ ) =Y ( ˇ + ) 112 Sn : (4.66) ThedoubleratioisplottedinFigure4.46asafunctionofKE COM .Thee˚ciencycorrected spectraisshownwithgreencrosses,andtherawspectrawithablackhistogram.Thedouble ratiomeasuredisconsistentwithadoubleratioof1for7ofthe10bins. Figure4.46:ThedoubleratioasafunctionofKE COM for 124* Sn+ 112 Snand 112 Sn+ 124 Sn. TheleftpanelofFigure4.47showsthe ˇ =ˇ + spectralratioplottedasafunctionof y 0 (Equation4.59),forthe 124* Snbeamsystemwithblackcircles,andthe 112 Snbeamsystem withgreensquares.Therightpanelshowsthemeasureddoubleratioofthetwosystems, whichisconsistentwitharatioof1for4ofthe5bins.Adoubleratioof1isconsistentwith completemixingofthenucleonsforthesecentralcollisions. Basedonasymmetryargument,weexpectthatthe ˇ =ˇ + spectralratioatpositive rapidityforthe 112 Snbeamshouldbeequaltothe ˇ =ˇ + spectralratioatnegativerapidity 165 Figure4.47:The ˇ =ˇ + spectralratioasafunctionofrapidity(left)andthedoubleratio asafunctionofrapidity(right). forthe 124* Snbeam.Inprinciple,wecancombinethemtogetthe ˇ =ˇ + spectralratioat allrapidities.ThisisshowninFigure4.48.Aswecanseeinthe˝gure,thegeneraltrend isthatthe ˇ =ˇ + ratioislargerat0rapidity,anddecreasesmonotonicallywithincreasing j y 0 j .BothsystemsaregenerallyconsistentwithaCoulombshiftinthe ˇ and ˇ + spectra wherebythe ˇ + areshiftedtohigherrapiditybytheCoulombforceandthe ˇ areshifted tolower j y 0 j becauseoftheirnegativecharge. Figure4.48:The ˇ =ˇ + spectralratio,withtherapidityofthe 112 Snbeamreversed. 166 Weshowtheindividual ˇ and ˇ + p t - y 0 spectrainFigure4.49,combiningthe 124* Sn systemwiththerapidity-reversed 112 Snsystem.Redlinesaredrawncorrespondingtopion kineticenergyof50and200MeVintheCOMframe(calculatedseparatelyforthe 112 Sn and 124* Snsystems).Wecanclearlyseethee˙ectoftheCoulombforce:atlow p t and y 0 , correspondingtotheregionofbeamandtargetnucleonmixing,the ˇ areabundant,and the ˇ + arede˝cient. Figure4.49:The ˇ (left)and ˇ + (right) p t - y 0 spectra,withtherapidityofthe 112 Snbeam reversedandaddedtothe 124* Snbeamtoformacompletespectra.Redlinescorrespondto kineticenergiesof50(bottom)and200(top)MeVintheCOMframe. Evaluatingthespectrashowninthissectionindicatessomedi˙erencesandsimilarities betweenthepionratiosbetweenthetwosystems.Thepionratiosareverysimilarwhen examinedasafunctionofrapidity,evidentinFigure4.47.Thisindicatescompletemixing forcentralevents.Anexaminationofthedoubleratioasafunctionofkineticenergyin theCOMframe(Figure4.46)showsdi˙erencesbetweenthetwosystems.Thedoubleratio di˙ersfrom1forkineticenergyjustbelow200MeV,whichcorrespondstojustbelowthetop redlinesinFigure4.49,andjustabove50MeV,whichcorrespondstojustabovethebottom redlines.Wecanseethataround200MeV,ourstatisticsarebecominglimited.Thedouble ratiodi˙eringfrom1isinteresting,butitisnotimmediatelyevidentwhatthestatistical 167 relevanceis,sothesedi˙erencesbearfurtherstudy.Thedeviationfrom1atjustabove50 MeVmayindicatethatthekineticenergydeterminationisnot˝neenough:between5075 MeV,thedoubleratiotrendsbelow1,whilebetween75100MeV,thedoubleratiotrends above1. 4.8.7Examinationoflesscentralcollisions Wecanexaminetheemissionofpionsforlesscentralcollisions(5fm 5fm)collisions,the 112 Sn+ 124 Snsystemproducesfewer ˇ + and ˇ + thanforthe 124* Sn+ 112 Snsystem.Thepionratio( ˇ =ˇ + )isalsolowerfor the 112 Sn+ 124 Snsystem.Thisisapuzzlingresult:weexpectthatformoreperipheral collisions,particlesdetectedintheTPCshouldbea˙ectedmorebythebeamcomposition thanthetarget.Asthebeamnucleonsenterthecollisionwithvelocitydirectedintothe TPC,they,andtheparticlesproducedbytheirinteractions,aremorelikelytoachieveor 174 maintaintherequiredvelocitytoentertheTPC.Bythisreasoning,peripheralreactions fromthe 124* Snbeamshouldbere˛ectiveofamoreneutronrichreaction,whileperipheral reactionsfromthe 112 Snbeamshouldbemorere˛ectiveofaneutronde˝cientsystem.This apparentcontradictionislikelyduetoeithertheimpactparameterselectionorabiasfrom thetriggerforthesemoreperipheralreactions,asevidencedbythereducedpionproduction forthe 112 Sn+ 124 Snsystem.Furtherstudyofthisconundrumshouldbedone,using t= 3 He ratiostoprovideanadditionalindicatoroftherelativeneutron-richorneutron-de˝cient behaviorofthesemoreperipheralreactions. Overall,this˝rstanalysisoftheS ˇ RITexperimentindicatesthattheTPCandexperi- mentalsetupworkedwell,andweareabletomeasuretherequisitepionspectra,although someworkremainstoobtainaccuratespectraforlargervaluesofkineticenergy.Theanal- ysisshouldincorporatealargersolidangleintheCOMframe,whichcanbeachievedwith thedataavailablebutwillrequirecarefulanalysisoftheacceptanceande˚ciencyforeach system,inthelabandCOMframes.E˙ectsoftheimpactparameterarenotcurrentlywell understood,andadetailedstudyshouldbedone,includinganalysisofminimumbiasruns. Thepionspectraandratiosshouldbecomparedtoafullsuiteoftransportcodes,asis beingdevelopedbyacollaborativegroupe˙ort[27],toplacesatisfactoryconstraintsonthe symmetryenergyattwicesaturationdensity.Otherobservables,suchasanisotropic˛ow, n=p ratios,and t= 3 Heratios,shouldbeextractedfromthisexperimenttoprovidethebest constraintsonthesymmetryenergy. 175 APPENDIX 176 AppendixA A.1Clebsch-GordanCoe˚cientsforPionProductionfrom DeltaResonanceDecay A.1.1Productionof baryons Toinvestigatetheproductionanddecayofpions,itisnecessarytoassumetheproduction ofthe baryons(orresonances)accountsforthemajorityofourpionproduction.Inour system,theenergyisjustreachingthethresholdforpionproductionthroughthe resonance model,butathigherenergies,thisanalysismaynotbeavalidrepresentationofthewhole system. Mostofourpionsshouldbeproducedthroughnucleon-nucleoncollisions,soweexamine the productionfromp-p,n-n,andn-preactionsusingtheisospin t andisospinprojection t 3 asourquantumnumberstodetermineallowedreactionsandresultingreactionrates.The isospinandisospinprojectionvaluesfor baryons, ˇ particles,andnucleonsaretabulated below(usingtheparticlephysicsconventionforthesignof t 3 ). 177 particlet t 3 p 1 = 21 = 2 n 1 = 2 1 = 2 ++ 3 = 23 = 2 + 3 = 21 = 2 0 3 = 2 1 = 2 3 = 2 3 = 2 ˇ + 11 ˇ 0 10 ˇ 1 1 First,weexaminethe statesthatageneralizednucleon-nucleoncollisioncanproduce. Thegeneralizedreactionis 1 2 ; 1 t 3 ˛ 1 2 ; 2 t 3 ˛ !j T;T 3 i : (A.1) Fromtheinitialvaluesof i t ,wedeterminefromthetriangleruletheallowed˝nalstatesof T , 1 2 1 2 T 1 2 + 1 2 ; (A.2) whichallowsstates T =0 ; 1 .Theisospinprojectionmustequalthesumoftheinitialisospin projections,whichmustequalthesumoftheisospinprojectionsinthe˝nalstate,sowe have T 3 = 1 t 3 + 2 t 3 .Ifthereactionresultsintwoparticles,wecanwritethismoreexplicitly as: 1 2 ; 1 t 3 ˛ 1 2 ; 2 t 3 ˛ ! 3 2 ; 3 t 3 ˛ 1 2 ; 4 t 3 ˛ : (A.3) 178 Weexaminetheallowedstatesresultingfromthenucleon/ state, 3 2 ; 3 t 3 ˛ 1 2 ; 4 t 3 ˛ !j T;T 3 i ; (A.4) whichallows T =1 ; 2 and T 3 = 3 t 3 + 3 t 3 .Thuswewanttoinvestigatethecaseof T =1 as itistheonlycasesharedinbothdirections.Thisalsoprovidestheconstraint 1 T 3 1 . Decomposingthepossible -nucleonstatesusingClebsch-Gordancoe˚cientsgivesus 3 2 ; 3 2 ˛ 1 2 ; 1 2 ˛ ! r 1 4 j 2 ; 1 i + r 3 4 j 1 ; 1 i 3 2 ; 1 2 ˛ 1 2 ; 1 2 ˛ ! r 3 4 j 2 ; 1 i r 1 4 j 1 ; 1 i 3 2 ; 1 2 ˛ 1 2 ; 1 2 ˛ ! r 1 2 j 2 ; 0 i + r 1 2 j 1 ; 0 i 3 2 ; 1 2 ˛ 1 2 ; 1 2 ˛ ! r 1 2 j 2 ; 0 i r 1 2 j 1 ; 0 i 3 2 ; 1 2 ˛ 1 2 ; 1 2 ˛ ! r 1 4 j 2 ; 1 i + r 3 4 j 1 ; 1 i 3 2 ; 3 2 ˛ 1 2 ; 1 2 ˛ ! r 1 4 j 2 ; 1 i r 3 4 j 1 ; 1 i : (A.5) UsingtheWigner-Eckarttheorem,wecandeducethebranchingfractionsofthe j T;T 3 i , j 1 ; 1 i! r 3 4 3 2 ; 3 2 ˛ 1 2 ; 1 2 r 1 4 3 2 ; 1 2 ˛ 1 2 ; 1 2 j 1 ; 0 i! r 1 2 3 2 ; 1 2 ˛ 1 2 ; 1 2 r 1 2 3 2 ; 1 2 ˛ 1 2 ; 1 2 j 1 ; 1 i! r 1 4 3 2 ; 1 2 ˛ 1 2 ; 1 2 r 3 4 3 2 ; 3 2 ˛ 1 2 ; 1 2 ; (A.6) the T 3 valuesdetermineuniquelywhichnucleonsarepresentwithinthesystem,although the j 1 ; 0 i systemincludesbothp-nandn-psystems. 179 A.1.2 BaryonDecayBranching Themeanlifetimeforallvarietiesof baryonsisabout 5 : 63 10 24 s.The ++ and baryonshaveonemaindecaychanneleach.The + and 0 baryonscandecaythrough tworoutes.ThebranchingratiosforthesedecaysaredeterminedusingClebsch-Gordan coe˚cients.The˝nalresultforthedecaysis 3 2 ; 3 2 ˛ !j 1 ; 1 i 1 2 ; 1 2 ˛ 3 2 ; 1 2 ˛ ! r 1 3 j 1 ; 1 i 1 2 ; 1 2 + r 2 3 j 1 ; 0 i 1 2 ; 1 2 3 2 ; 1 2 ˛ ! r 2 3 j 1 ; 0 i 1 2 ; 1 2 + r 1 3 j 1 ; 1 i 1 2 ; 1 2 3 2 ; 3 2 ˛ !j 1 ; 1 i 1 2 ; 1 2 ˛ : (A.7) A.1.3Nucleon-NucleonCollisions Summarizingusingparticlenotation,wehavetheproductionof baryonsfromnucleon- nucleoncollisions: p + p ! r 3 4 ++ + n r 1 4 + + p n + p ! r 1 2 + + n r 1 2 0 + p n + n ! r 1 4 0 + n r 3 4 + p : (A.8) 180 Wehavetheresultof baryondecays: ++ ! ˇ + + p + ! r 1 3 ( ˇ + + n )+ r 2 3 ( ˇ 0 + p ) 0 ! r 2 3 ( ˇ 0 + n )+ r 1 3 ( ˇ + p ) ! ˇ + n: (A.9) Puttingthistogether,wehavethepionproductionfromnucleon-nucleoncollisions: p + p ! r 3 4 ˇ + + p + n r 1 4 r 1 3 ( ˇ + + n + p )+ r 2 3 ( ˇ 0 + p + p ) ! n + p ! r 1 2 r 1 3 ( ˇ + + n + n )+ r 2 3 ( ˇ 0 + p + n ) ! r 1 2 r 2 3 ( ˇ 0 + n + p )+ r 1 3 ( ˇ + p + p ) ! n + n ! r 1 4 r 2 3 ( ˇ 0 + n + n )+ r 1 3 ( ˇ + p + n ) ! r 3 4 ˇ + n + p ; (A.10) whichsimpli˝esto p + p ! r 5 6 ˇ + + p + n r 1 6 ( ˇ 0 + p + p ) n + p ! r 1 6 ( ˇ + + n + n )+ r 2 3 ( ˇ 0 + n + p )+ r 1 6 ( ˇ + p + p ) n + n ! r 1 6 ( ˇ 0 + n + n ) r 5 6 ˇ + n + p : (A.11) 181 A.1.4PionDecayBranchingRatios Thepartialdecaywidthsforchargedandneutralpiondecayscanbecalculatedusingthe branchingratiosandtotaldecaywidthforeachpion˛avor.Therelevantequationsinvolve therelationbetweendecaywidthandpartialdecaywidths = h ˝ = 1 + 2 + :::; (A.12) andthede˝nitionofbranchingratios, BR i = i : (A.13) Startingwith ˇ ,thedecayinto + and leptonsarerespectively: ˇ + ! + + ˇ ! + (A.14) withabranchingratioof0.999877.Theothermodeofdecayis: ˇ + ! e + + e ˇ ! e + e (A.15) 182 withabranchingratioof0.000123.Withchargedpionshavingameanlifetimeof 2 : 6 10 8 s, thepartialdecaywidths, = h ˝ and e h ˝ e arefoundtobe = h 2 : 6003 10 8 s e = h 2 : 114 10 4 s : (A.16) Theneutralpion( ˇ 0 )hasameanlifetimeofabout 8 : 4 10 17 s.Examiningthethree largestdecaymodesoftheneutralpiondecay, 1) ˇ 0 ! 2 2) ˇ 0 ! + e + e + 3) ˇ 0 ! e + e + + e + e + ; (A.17) thepartialdecaywidthsarefoundtobe 1 = h 8 : 5 10 17 s 2 = h 7 : 16 10 15 s 3 = h 2 : 8 10 12 s : (A.18) 183 BIBLIOGRAPHY 184 BIBLIOGRAPHY [1] https://www.nndc.bnl.gov/nudat2/ .AccessedJuly3,2019. 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