DESIGNANDCOMMISSIONINGOFA16.1MHZMULTIHARMONICBUNCHERFORTHEREACCELERATORATNSCLByDanielMaloneyAltADISSERTATIONSubmittedtoMichiganStateUniversityinpartialentoftherequirementsforthedegreeofPhysics-DoctorofPhilosophy2016ABSTRACTDESIGNANDCOMMISSIONINGOFA16.1MHZMULTIHARMONICBUNCHERFORTHEREACCELERATORATNSCLByDanielMaloneyAltTheReAccelerator(ReA)linearacceleratorfacilityattheNationalSuperconductingCy-clotronLaboratoryisauniqueresourceforthenuclearphysicscommunity.Theparticlefragmentationbeamproductiontechnique,combinedwiththeabilitytostopandthenreac-celeratethebeamtoenergiesofastrophysicalinterest,giveexperimentersanunprecedentedrangeofrareisotopesatenergiesofnuclearandastrophysicalinterest.TheReAcceleratoralsofunctionsasatestbedfortechnologytobeincorporatedintheupcomingFacilityforRareIsotopeBeamslinearaccelerator,whichwilleventuallyinturnbecomethebeamsourceforReA.ThisprototypenatureoftheReAccelerator,however,dictatedsomedesignchoiceswhichhaveresultedinabeamwithatimestructurethatislessthanidealforcertainclassesofexperiments.ThecavitiesandRFQusedinReAhaveanoperatingfrequencyof80.5MHz,whichcorrespondstoaseparationbetweenparticlebunchesatthedetectorsof12.4ns.Whilethisseparationisacceptableformanyexperiments,sensitivetimeoftmeasurementsrequireagreaterseparationbetweenpulses.Asnuclearphysicsexperimentsrelyonstatistics,asolutiontoincreasingbunchseparationwithoutsimplydiscardingalargefractionofthebeamparticleswasdesired.Thisdocumentdescribesthedesignandconstructionofsuchadevice,a16.1MHzmul-tiharmonicbuncher.ThechapterprovidesbackgoundinformationontheNSCLandReA,andsomebasicconceptsinacceleratorphysicstolaythegroundworkfortheproject.Next,morespareprovidedonthetimestructureofacceleratedbeams,andtheexper-imentalmotivationforgreaterseparation.Thethirdchapteroutlinesthebasicprinciplesofmultiharmonicbunching.Inordertoevaluatethefeasibilityofanybuncherdesign,theexactacceptanceoftheRadiofrequencyQuadrupole(RFQ)oftheReAcceleratorneededtobeempiricallymeasured.Chapter4describestheresultsofthatmeasurement.Chapter5outlinesthesimulationsandcalculationsthatwentintothedesignchoicesforthisparticularbuncher,incorporatingtheresultsoftheRFQmeasurements.Thenexttwochaptersdescribetheconstruction,installation,andtestingofthedevice,andgiveexperimentalresults.Finally,Chapter8summarizestheprojectandthenalstepswhichneedtobeundertakentomakethedeviceasimpletouseassetforfutureexperimentalistsatReA.CopyrightbyDANIELMALONEYALT2016DedicatedtoLeighVanHandelforloremipsumandvariousotherphenomena.vACKNOWLEDGMENTSThedesignandconstructionofthisdevice,alongwiththewritingofthisdocument,repre-sentsanenormousamountofbyalargenumberofpeople.Thisisapartiallistonly,andthereareundoubtedlypeoplewhoIhaveforgottenthatdeserveaplacehere.Firstandforemost,myadviserMikeSyphersdeservesmyheartfeltandeternalthanks.Acceptinganon-traditionalstudentwithmyunusualbackgroundwasarisk,andIappreciatehisbeingwillingtotakeachanceonmeasastudent.Throughouttheentireprocessofdesign,approval,construction,andtestingofthebuncher,hewasasourceofexcellentadvice,anadvocate,andagoodfriend.Second,JohnBrandonandhiscolleaguesfromtheNSCL/FRIBRFgroup,DanMorris,NathanUsher,ShenZhaoandMikeHolcomb.Together,theytookmyabstractoptics,simulations,andplans,andtransformedthemintoadevicethatactuallyworks.Especiallyduringtesting,noneofthemhedfromlatenightstaystotryandpushthedevicethelastinchesovertheline.Iamdeeplyintheirdebt.TheadministratorsoftheReAcceleratorprojecthavealwaysbeensolidsupportersofthisdeviceanditssometimesbizarredemands.(Youwanttodrillaholeinourcleanroom?Well,OK!)FirstDaniellaLeitnerandWalterWittmer,andlaterAntonioVillari,wereallextremelysupportive,andvaluablesuggestionsandexperiencewhichcontributedtothesuccessoftheproject.IamparticularlygratefulforAntonio'swillingnesstorolluphissleevesandassistwithdebuggingthediagnosticsforthealtesting.SamNash.ItisimpossibletooverstatetheimportanceofSamNashtoallaspectsoftheReAcceleratorproject.Hisknowledgeoftheentirefacilityisastonishing,anditishardtoimaginehowitcouldcontinuetofunctionhalfaswellasitdoeswithouthisconstantviattentionanddedication.Hisassistanceandsupportinthisnewaspectofthefacilityhasbeenutterlyconsistentwithhissupporttoallotheraspectsofthefacility,whichistosay,simplyincredible.TheReA3operators,andinparticularShannonKrauseandRandyRencsok,haveshowngreatpatienceintheirsupportofthisdevice.ThecriticalmeasurementsoftheRFQaccep-tanceinparticularwouldnothavebeenpossiblewithouttheirskilledEugeneTanke's\Dynac"codewasabsolutelyindispensableinthesimulationsforthisproject.Iamespeciallygratefulforhiswillingnesstocontinuallyaddfunctionalityanddocumentationtothecodetosupportmyrequests.MyonlyregretinthisareaisthatIdidnothavethetimeorresourcestoportDynacGUItoanopensourceformat.OtherNSCL/FRIBpersonnelwhowereinstrumentalinthisendeavor:AlainLaPierre,fornotonlyprovidingmewithEBITbeamformyexperiments,butforhiswillingnesstoentertainthepossibilityofdoingstrangethingstohistimestructuresinthefuture,andhiswillingnesstorsomelatenightsduringthetesting.Wendstrom,fortheexcellentmechanicaldesignandadjustabilityofthebuncherelectrodes,theNSCLmachineshopfortheconstruction,andDaveSandersonforthealignmentofsame.PeterOstroumovandhisgroupatANLprovidedvaluablesuggestionsandtheuseoftheTRACKcodeforaspectsofthebuncherdesign.Mostimportantly,theexistenceoftheir12.125MHzbuncherwascontinuedproofpositivethatsuchadevicecouldbebuilt.Themembersofmycommittee:NormanBirge,FelixMarti,WolfgangMittig,andYoshishigeYamazaki,fortheirsupport,suggestions,andwillingnesstosubmittoendlessboutsofreschedulingonthedefensedate.SteveLund,forsteppinginasmylinemanagerforthelastyearoftheproject,andhiswillingnesstonavigatecountlesslayersofbureaucracyonmybehalf,afateIwouldwishonviinoone.MypredecessorsinacceleratorphysicsatNSCL,CarlaBenattiandJeremiahHolzbauer.Withouttheirsuggestionsonhowtoworkmoretlyandsurvivegraduateschool,Iwouldlikelystillbethere.Inasimilarvein,mymatesMikeJones,MikeBennet,VincentBader,andAmandaPrinkeallcontributedinvariouswaystohelpingmemaintainmysanity.AlsoinvaluableonthesanityfrontweremyfellowaswellastheskatersandcoachesoftheLansingDerbyVixens.Withouttheabilitytospendtimeonrollerskatesandblowwhistlesatpeople,Ihonestlydon'tknowhowotherpeoplemakeitthroughgraduateschool.Finally,andmostimportantly,mywife,LeighVanHandel.Goingbacktoschoolforaphysicsdoctorateatagethirty-sevenfromacareerasamiddleschoolmusicteacherisobjectivelyinsane.Notonlydidshesupportmychoice,butwithhersteadfastloveandencouragement,shesinglehandedlymadeitpossibleformetobelieveinmyownabilitytodothiscrazything.Icanneverthankherenough.viiiTABLEOFCONTENTSLISTOFTABLES....................................xiiLISTOFFIGURES...................................xivKEYTOABBREVIATIONS.............................xxChapter1Introduction...............................11.1OverviewofNSCLandReA...........................21.1.1IonSources................................31.1.2K500andK1200Cyclotrons.......................41.1.3TargetAreaandA1900FragmentSeparator..............51.1.4BeamStopping..............................71.1.5ElectronBeamIonTrapandQ/Aseparator..............81.1.6ReacceleratorReA............................111.1.7FuturePlans...............................121.1.7.1ReAExpansion.........................121.1.7.2FRIB..............................131.1.8ReATimeStructureIssues........................131.2OverviewofEssentialAcceleratorPhysics...................141.2.1Coordinates................................161.2.2TransverseDynamics...........................191.2.3TransverseEmittanceandCSparameters................231.2.4LongitudinalDynamics..........................271.2.5LongitudinalEmittance.........................30Chapter2TimeStructureofAcceleratedBeams...............312.1OriginalTimeStructureofReA.........................312.2MotivationfortTimeStructures....................342.3MethodsforAchievingGreaterBunchSeparation...............362.3.1MonofEBITTimeStructure..................362.3.2SubharmonicBunching..........................372.3.3OtherSolutions..............................37Chapter3PrinciplesofMultiharmonicBunching...............393.1IdealBunching..................................403.2SimulationofaSawtoothWaveUsingSineWaves...............423.2.1FourierSynthesis.............................423.2.2WindowFunctions............................443.2.3ConsequencesofaFiniteNumberofModes..............473.3OtherDeviationsfromtheIdealinaRealBuncher..............47ix3.3.1TransverseFieldFlatness.........................483.3.2TransitTimeFactor...........................493.4SatelliteBunches.................................503.5CaseStudies....................................553.5.180.5MHzMultiharmonicBuncheratReA...............553.5.212.4MHzMultiharmonicBuncheratATLAS(ANL).........56Chapter4MeasurementoftheLongitudinalAcceptanceoftheReARFQ584.1MeasurementMethodology............................594.1.1TotalTransmissionAsAFunctionofEnergy..............604.1.2TransmissionasaFunctionofPhaseandEnergy............624.2AnalysisandResults...............................634.2.1EnergyMeasurementOnly........................634.2.2CombinedEnergyandPhaseMeasurement...............664.2.3ErrorEstimates..............................734.2.4ImplicationsfortheBuncher.......................74Chapter5SimulationandSelectionofDesignParameters.........765.1ReABeamlineSimulation............................775.2BuncherFrequency................................795.3VoltageandFocalLength............................825.3.1IdealCase.................................825.3.2NumericalSimulation...........................845.4Beamline............................885.5ElectrodeGeometry................................915.6ontheBeamattheDetectors.......................955.7SatelliteBunches.................................965.7.1SimulationofSatelliteBuncheswithNoCleaning...........965.7.2SimulationofSatelliteBuncheswithCleaning.............975.8NumberofBuncherModes............................99Chapter6FabricationandInstallation......................1006.1MechanicalDesign................................1006.2RFDesign.....................................1036.2.1ResonatorsandTuners..........................1036.2.2LowLevelRF...............................1056.3ElectrodeInstallation...............................106Chapter7Commissioning:MethodologyandResults............1097.1TimingWireDetectors..............................1097.2TimingWireTesting...............................1127.3OpenLoopBunching...............................1177.3.1TestSetup.................................1177.3.2Results...................................1187.4ClosedLoopBunching..............................123x7.4.1Setup...................................1237.4.2SingleModeResults...........................1257.4.3MultipleModeResults..........................1297.5ComparisonwithSimulation...........................133Chapter8Conclusions................................1368.1Summary.....................................1368.2FuturePlans....................................1388.3SatelliteBunches.................................1408.3.1IntegerRatioCavities..........................1418.3.2BeamChopper..............................1428.3.3EBITSwitching..............................144APPENDICES......................................146AppendixAComparisonofAcceleratorCodes..................147AppendixBDynacGUI................................179BIBLIOGRAPHY....................................189xiLISTOFTABLESTable1.1:NSCLPrimaryBeamListasofDecember,2014...........6Table1.2:BeamfractionsforseveralofemittanceasafunctionofRMSbeamsize˙[1]...........................27Table4.1:SummaryofbeamtransmissionthroughtheReARFQasafunctionofdeviationfromthereferenceenergy..................63Table4.2:WidthofphaseacceptanceatvariousenergiesfortheReARFQ,alongwiththemeasuredphase.................68Table4.3:Calculatedtofand˚valuesfromtheMHBtotheRFQrelativetothereferenceparticle.........................71Table5.1:Windowfunctionswiththehighestbunchingbyfrequencyandinitialbeamenergyspread.....................87Table5.2:Predictedminimumtimeandenergyspreadattargetforbeamener-giesfrom0.3-3MeVand0.25-0.5Q/A.................95Table6.1:Lengthsoftheresonatorsandtunersforthe16.1MHzbuncher...105Table7.1:Openlooptestingresultsforthe(16.1MHz)modeofthebuncher.120Table7.2:Openlooptestingresultsforthesecond(32.2MHz)modeofthebuncher..................................121Table7.3:Openlooptestingresultsforthethird(48.3MHz)modeofthebuncher.122Table7.4:Closedlooptestingresultsforthe(16.1MHz)modeofthebuncher.126Table7.5:Closedlooptestingresultsforthesecond(32.2MHz)modeofthebuncher.Nopowerwasobservedatanyofthechosenvoltagesettings..................................126Table7.6:Cavitysettingsfortestingofthebuncherwithacceleratedbeam.Allofthecavitiesinthethirdcryomodulewereset..........131xiiTable7.7:Summaryofbunchedbeamproperties.\Transmission"givestheper-centageofthebeamcurrentmeasuredafterthelinacrelativetothebeamcurrentmeasuredjustbeforethebuncher.\Bunchingciency"givesthepercentageofthetotalbeamdetectedatL110inthemainpulse..............................133TableA.1:ComparisonofUnitsUsedinSeveralAcceleratorCodes.......178xiiiLISTOFFIGURESFigure1.1:LayoutoftheNSCL.ImageCredit:ErinO'Donnell..........3Figure1.2:CutawayviewoftheElectronBeamIonTrap.............9Figure1.3:LayoutoftheReAcceleratorfromtheEBITtothedetectorhall...11Figure1.4:Thecoordinateframeusedtodescribeparticlesrelativetoamovingreferenceparticle.............................15Figure1.5:Theparaxialapproximationmeansthatx0canbeapproximatedasforsmallvaluesof............................16Figure1.6:Pathsofthreeparticleswithidenticalenergies,buttinitialdisplacementsthroughadipole.....................22Figure1.7:Pathsofthreeparticleswithenergiesbutidenticalstartingtrajectoriesthroughadipole.......................22Figure1.8:ThephasespaceellipsedescribedbytheCourant-Snyderparameters.24Figure2.1:SimulatedlongitudinalstructureoftheReA3beamatvariouspoints.Fromlefttoright:theexitoftheEBIT,immediatelyafterthe80MHzMHB,thestartoftheRFQ,theexitoftheRFQ,theexitofthelinac,andthetarget............................33Figure2.2:Theuncertaintyinthetimeofttforasinglezero-widthpulseisdeterminedonlybythepulsespreadt.................34Figure2.3:Whenmultiplepulsesarelaunched˝secondsapart,themeasurementofthetimeoftbecomesuncertainbyanintegermultipleof˝.Iftislargerthan˝,themeasuredtimeoftcantakeanyvalueandbecomescompletelyuncertain....................35Figure3.1:Comparisonoftheofanidealbuncherwitharealisticbunchingwaverform.Theupperplotsshowthebeambunchedbyaperfectsawtoothwavewithzeroresettime.Thelowerplotsshowabunchingwaveformmadeupoffoursinewaves..................41Figure3.2:Asawtoothwavesynthesizedusingthe2,5,and100componentsoftheFourierseries............................43xivFigure3.3:Windowfunctionamplitudevs.normalizedcomponentforseveralwindowfunctions.Normalizedcomponent=(componentnumber-1)/(numberofcomponents-1)Plottedhereforn=10components.45Figure3.4:SideviewofapairofbuncherelectrodeswithaconicalThearrowindicatesthedirectionofbeamtravel..............48Figure3.5:Aplotofthetimeandenergydistributionofasimulatedbeambunchedat16MHz.Thedashedlinesindicatethe2nsacceptancewindowsforadeviceoperatingat80.5MHz..............51Figure3.6:TheofshorteningtheinitialEBITpulse.Atleft,theshortenedpulseafterinteractionwiththebunch.Atright,thebeamatthebuncherfocus.Notailsarepresentbecausetheshorterinitialpulsefallsentirelywithinthelinearportionofthebunchingwaveform...52Figure3.7:Bunchcleaningbyanfrequencycavity.Theredlineisata4:5frequencyratiowiththeblueone.Blackdotsrepresentbeamparticlesatathezerophaseofbothfrequencies.................53Figure4.1:Asimpleillustrationofalongitudinalacceptancewindow.......59Figure4.2:WiththeMHBturnedthetransmissionthroughtheRFQwasmeasuredatanumberofenergiestogiveapictureoftherelativetransmissionateachlevel........................61Figure4.3:WiththeMHBturnedon,thetransmissionthroughtheRFQwasmeasuredatanumberenergiesandthroughafull360degreesofphase,givingaseriesoftransmissioncurves..............62Figure4.4:RFQbeamtransmissionvs.inputenergyforReARFQ........64Figure4.5:NaiveRFQacceptancewindowwithnophasemeasurementortime-tcorrection............................65Figure4.6:Threephasescansattenergies.................65Figure4.7:ThesimulatedacceptanceoftheReARFQ.ThewhiteareaatthecenterrepresentsparticleswhichareacceleratedbytheRFQ,andtheredareashowsparticleswhicharenottransported...........66Figure4.8:Allphasemeasurmentssuperimposed.Eachcurveisnormalizedtoamaxofone,andphaseunitsareunadjusted..............68xvFigure4.9:Thephasecurvesin4.8withthemaximumtransmissionforeachenergyalignedatzerophase....................69Figure4.10:Phasecurveswithzeroesalignedandscaledbyoveralltransmissionateachenergy.Thesecondisaninterpolatedsurfacegeneratedfromthedatapointsinthe................69Figure4.11:AcontourplotofthemeasuredacceptancesurfacefromFigure4.10,withthe50%transmissioncontouremphasized,overlaidonthesim-ulatedacceptance.............................70Figure4.12:Measuredandpredictedphaseadvancesrelativetothereferenceen-ergyforthephasemeasurements....................72Figure4.13:Foreachenergy,thefromthepredictedrelativephaseadvance.73Figure4.14:Thecontourplotofthemeasuredacceptancesurfacewiththetime-tcorrectionapplied,overlaidonthesimulatedacceptance...74Figure5.1:AsamplelongitudinalmodelofReAfromtheEBITtothedetectorhall,showingxandyenvelopes,particlecount,referenceparticleenergy,andthelocationsofbeamlineelements.............78Figure5.2:Schematicillustrationofbunchingatseveraltsubharmonics.Eachplotshowsenergyvs.time.Thecolumnshowstheinitialbeam,thesecondcolumnthebeamimmediatelyafterbunching,andthethirdcolumnshowsthebeamatthefocus.............80Figure5.3:Simulatedlongitudinalbeamphasespacefortwotvaluesofinitialenergyspread...........................85Figure5.4:Peakbunchingvoltagevs.focallengthforaMonteCarlomodelofa16.1MHzbuncher............................86Figure5.5:oftheReALEBTsection.Thedoublewidthdiag-nosticbox(L052)afterthestableionsourcehasbeenmoveddown-streamofthequadrupoledoublet,anddividedintoasingledi-agnosticboxandthe16.1MHzbuncher................89Figure5.6:AbeforeandaftercomparisonofthesimulatedbeamenvelopefortheoftheReALEBTline.Thetopshowsthesimulatedenvelopefortheoriginalandthelowerretheenvelopeafterthequadrupolemove.Seetextforfurtherexplanations................................90xviFigure5.7:Electrodedesignforthe16.1MHzMHB................91Figure5.8:Crosssectionofthe16.1MHzMHBelectrodesmodeledincststu-dio,showingtheacceleratinginthex=0plane.........92Figure5.9:OnesimulationoftheLEBTportionoftheReAbeamlineusinga3Dmodelforthe16MHzbuncher...................93Figure5.10:Peakvoltageforeachmodeforarangeofelectrodegeometries....94Figure5.11:SimulationofthecentralbunchandsatellitebunchesatthedetectorpositionforthemiddleReAbeamline.Thissimulationwasofa2H+beamat3MeV/u.............................97Figure5.12:Normalizedhistogramshowingparticlesinsatellitebunchesrelativetothemainbunchwhencleanedwithtwo96MHzcavitieslocatedatthepositionofthepresentCM1.Timeaxisisinns..........98Figure6.1:Thecompletedelectrodeassembly,showingtheadjustmentscrewsforthexandyaxesandthealignmentmonuments.Thecenterplatecanalsorotatetoensurethecenterlineoftheelectrodesisparalleltothebeamaxis...............................101Figure6.2:AschematicdrawingoftheconnectionsfortheRFsystemforthe16.1MHzbuncher............................105Figure6.3:ThecontrolscreenfortheLLRFmodule,showingthecontrolsforeachofthethreemodes.........................106Figure6.4:Theelectrodeassemblyinstalledinthebeamline,withtheresonatorsvisible...................................108Figure7.1:Twoviewsofthetimingwiredetector.TheMCPisindicatedbynumber16,andthewireitselfby18.Intherighthandview,thedirectionofbeamtravelisintothepage,strikingthewirebeforeexitingonthefarsideofthe\can."..................110Figure7.2:Thedataacquisitionpathforthetimingwiremeasurements.....111Figure7.3:AexampleofahistogramfromtheTAC.Thisexampleisforbeambunchedwiththesecond(161.0MHz)modeofthe80.5MHzMHBatacontrolsystemsettingof11.....................112xviiFigure7.4:Themeanwidthofthebunchedbeamatarangeofcontrolsystemsettingsusingthe80.5MHzbuncher.The80.5MHzmodeisshownatleftandthe161.0MHzmodeatright................115Figure7.5:ComparisonoftheFWHMcurveforsimulatedbunchedbeamswitharangeofinitialenergyspreadsforthemodeofthe80.5MHzmultiharmonicbuncher..........................116Figure7.6:MeasuredbeamFWHMfromFigure7.4overlaidonsimulatedbunchwidths.TheX-axisofthemeasureddatahasbeenscaledtomatchthesimulatedbeamvoltage.......................116Figure7.7:Thedrivepowersetupforopenlooptestingofthe16.1MHzbuncher.117Figure7.8:MeasuredFWHMforthe(16.1MHz)modeofthebuncherover-laidonasimulatedcurve,withthex-axisscaledtomatch......120Figure7.9:MeasuredFWHMforthesecond(32.2MHz)modeofthebuncheroverlaidonasimulatedcurve,withthex-axisscaledtomatch....121Figure7.10:MeasuredFWHMforthethird(48.3MHz)modeofthebuncheroverlaidonasimulatedcurve,withthex-axisscaledtomatch....122Figure7.11:Fittedpeaksformanuallytunedopenloopbunchingusingmodes1and2....................................123Figure7.12:MeasuredFWHMforthe(16.1MHz)modeofthebuncherinclosedloopmode,overlaidonasetofsimulatedcurves,withthex-axisscaledtomatch..........................127Figure7.13:MeasuredFWHMforthesecond(32.2MHz)modeofthebuncherinclosedloopmode,overlaidonasetofsimulatedcurves,withthex-axisscaledtomatch..........................127Figure7.14:Anillustrationofanoverfocusedbeam,showingtheexpecteddoublepeakedstructureofthehistogram....................128Figure7.15:InitialbeamtimestructuremeasurementtakenatL110withnophaseadjustment................................132Figure7.16:BestcasebunchingachievedatL110withamplitudes335Vand35V,andphases22and202degrees....................132xviiiFigure7.17:Side-by-sidecomparisonofthetimestructureofthebeamatL110.Thelefthandimageistheactualhistogrammeasuredonthetimingwire,andtherighthandimageisasimulationofthesameconditions.135Figure8.1:AsimulatedtimedistributionusingallthreebunchingmodesatL110.Thecalculatedis92.96%...................139FigureA.1:Asampleemittanceplotproducedusingdynac...........151FigureA.2:Anexampleofalongitudinalplotproducedwithcosy.......156FigureA.3:Anexampleoftrack'soutputscreen.(Phasevs.zplotnotshown)160FigureA.4:Anexampleofageneratedwithmad..............164FigureA.5:Themainscreenoftrace3Dshowingagraphandbeforeandafteremittanceplots...........................168FigureA.6:Asampleplotgeneratedbythegraphictransportframeworkinterfacetotransport.........................172FigureA.7:ImageCredit:xkcd.com.UsedunderCreativeCommonsAttribution-Noncommercial2.5License[2].....................177FigureB.1:dynacguiMainControlPanel.....................183FigureB.2:dynacguiMainZ-AxisPlot......................183FigureB.3:dynacguiEmittancePlot.......................185FigureB.4:dynacgui'stoolscreen......................187xixKEYTOABBREVIATIONS‹ANL-ArgonneNationalLaboratory(ArgonneIL,USA)‹ARTEMIS-AdvancedRoomTemperatureIonSource‹ATLAS-ArgonneTandemLinearAcceleratorSystem(ANL)‹AT-TPC-ActiveTimeTargetProjectionChamber‹CCF-CoupledCyclotronFacility‹CERN-EuropeanOrganizationforNuclearResearch‹CSParameters-CourantSnyder(Twiss)Parameters‹CSS-ControlSystemStudio‹EBIT-ElectronBeamIonTrap‹ECR-ElectronCyclotronResonance‹FRIB-FacilityforRareIsotopeBeams(EastLansingMI,USA)‹FWHM-FullWidthHalfMaximum‹GUI-GraphicalUserInterface‹JENSA-JetExperimentforNuclearStructureandStellarAstrophysics‹LEBT-LowEnergyBeamTransport‹LEP-LargeElectronPositronCollider(Geneva,Switzerland)‹LHC-LargeHadronCollider(Geneva,Swizterland)‹Linac-LinearAccelerator‹LLRF-LowLevelRadioFrequency‹MCP-Micro-channelPlate‹MEBT-MediumEnergyBeamTransport‹MCA-Multi-channelAnalyzer‹MHB-MultiharmonicBuncher‹MSU-MichiganStateUniversity(EastLansingMI,USA)‹NSCL-NationalSuperconductingCyclotronLaboratory(EastLansingMI,USA)xx‹PSI-PaulScherrerInstitute(Villigen,Switzerland)‹Q/A-Chargetomassratio‹ReA-Reaccelerator‹RF-RadioFrequency‹RMS-RootMeanSquare‹ROCS-ReAOperationsandControlSoftware‹SG-SignalGenerator‹SuSI-SuperconductingSourceforIons‹TAC-Time-to-AmplitudeConverter‹TTF-TransitTimeFactorxxiChapter1IntroductionAcceleratororbeamphysicsisconcernedwithproducingbeamsofparticleswithnecessarycharacteristicsforbasicresearch,medicine,industrial,andotherapplications.Whilethecharacteristicsofeachacceleratoraret,thegoaloftheacceleratorphysicistisalwaystoprovideabeamwhichmostcloselymatchestheneedsoftheuser,withthehighestreliabilityandthelowestcost.Itissometimesthecasethatoverthecourseofthedesign,construction,oroperationofanacceleratorthattheremaybeademandforanadditionalcapabilitynotoriginallyenvisionedbythedesignersofthemachine.Inthatinstance,itisincumbentonthebeamphysicisttodetermineifthisrequestisfeasible,andifsohowbesttomeetit.Thisdissertationdocumentsonesuchinstance.Asoutlinedbelow,theReAccelera-tor(ReA)atMichiganStateUniversity'sNationalSuperconductingCyclotronLaboratory(NSCL)wasoriginallydesignedwithapulserepetitionrateatthetargetof80.5MHz.Evenwhilethefacilitywasstillunderconstruction,anumberofnuclearscientistsexpressedreser-vationsaboutthisrate,andadesirewasarticulatedforbeamswithgreatertimeseparation.Thisdocumentwilloutlinethedesignandconstructionofadevicetoaccommodatethatrequest.TheremainderofthischapterwillprovidebackgroundinformationabouttheNSCLandReAandanintroductiontobasicbeamphysicsconcepts.Chapter2willdiscussgeneralprin-ciplesofbeamtimestructure,andthenexplorethespofthetimestructuresavailable1atReA.InChapter3,thebasicprinciplesofmultiharmonicbunchingwillbedocumented.Chapter4describesapreliminarymeasurementwhichwasessentialtotheprocessofselect-ingdesignparametersfortheconstructedbuncher,whichprocessisdocumentedinChapter5.Chapters6and7describetheconstructionandtestingofthedevice,andChapter8presentstheconclusionswhichcanbedrawnfromtheproject.1.1OverviewofNSCLandReATheNationalSuperconductingCyclotronLaboratoryatMichiganStateUniversity(MSU)isaresearchfacilityexploringbasicquestionsinnuclearscienceusingbeamsofradioactiveisotopes.Stablebeamsfromanionsourceareacceleratedtohighenergiesinapairofcoupledcyclotronsandthenimpingedonathintarget.Theresultingcollisionproductsincludeunstableisotopesofexperimentalinterest.Abeamofthedesiredisotopesisfromthecollisionproductsinafragmentseparatorandthensenttooneofanumberoftargetareas.Sincethisprojectilefragmentationmethodforproducingradioactivebeamsresultsinradioactivebeamswithcomparableenergytotheoriginalstablebeam,forexperimentalapplicationswhichrequirelowerenergybeamstheparticlesarethermalizedinagasstopperorareversecyclotronstopper.Ifanenergygreaterthanthermalbutlowerthantheproductionenergyisrequired,thebeamisstoppedandthenacceleratedtothedesiredvelocityinasecondarylinearaccelerator,theReAccelerator.2Figure1.1:LayoutoftheNSCL.ImageCredit:ErinO'Donnell.1.1.1IonSourcesThestageinproducingtherareisotopebeamatNSCListheestablishmentofabeamofstableions.NSCLhastwoprimaryionsources,theAdvancedRoomTemperatureIonSource(ARTEMIS)[3],andtheSuperconductingSourceforIons(SuSI)[4][5].BothoftheseareElectronCyclotronResonance(ECR)typeionsources.InanECRionsource,alowpressuregasofthedesiredioniscontainedinamagneticThegasisthenexcitedbymicrowavesatafrequencycorrespondingtothecyclotronfrequencyofelectronsinthe!c=eBm(1.1)whereeisthechargeontheelectron,Bisthemagnitudeoftheandmisthemassoftheelectron.3Thisresonantexcitationincreasestheenergyofthefreeelectronsinthegas,whichcollisionallyionizeatomsofthesourcegas,leadingtomorefreeelectronsinapositivefeedbackcycle.RadialtisprovidedbyahexapolemagneticandaxialtbyasolenoidalWhileSUSIisthemoretsourceatNSCL,andiscapableofproducingmuchhigherchargestates,inthecurrentcoupledcyclotronoperationmode,eithersourceiscapableofdeliveringmostbeamstothecyclotron.Assuch,thesourcesaregenerallyusedinalternation,withthesourcenotcurrentlyprovidingbeamtothecyclotronsusedforfuturebeamdevelopment.1.1.2K500andK1200CyclotronsThestableionbeamisacceleratedbyapairofcoupledsuperconductingcyclotrons,theK500andtheK1200.TheK500Cyclotronwascompletedin1982,andwasthesu-perconductingcyclotronintheworld[6].TheK1200Cyclotronwascompletedin1988andwasatthetimethemostpowerfulcyclotronintheworld.In2001thetwocyclotronsbeganoperationinacoupledmode,wherebeamsfromtheionsourceareacceleratedintheK500andthenfurtherchargestrippedbeforeinjectionintotheK1200foracceleration[7].ThepairofcyclotronsarenowcollectivelyreferredtoastheCoupledCyclotronFacility.(CCF)The\K"numberofacyclotronisameasureofitstotalacceleratingstrength.Itrepre-sentsthekineticenergyinMeVaprotonwouldachieveifacceleratedatthemaximumofthecyclotron:K=e22ma(Bˆ)2ˇ48MeV(Tm)2(Bˆ)2:(1.2)Hereeistheelectroncharge,maisanatomicmassunit,Bisthemaximummagnetic4ofthecyclotronandˆisthemaximumradiusofthecyclotron.1TypicalextractionenergiesfromtheK500cyclotroninthecoupledmodeareontheorderof10-20MeV/u(pernucleon)[8].FinalproductionbeamsfromtheK1200cyclotronhaveenergiesontheorderof150MeV/u.Table1.1showstheavailableprimarybeamsfromthecoupledcyclotronsasofDecember,2014[9].1.1.3TargetAreaandA1900FragmentSeparatorOncethedesiredprimarybeamhasbeenbroughttoitsenergy,itisimpingedonaproductiontarget.Thistargetisusually,butnotalways,athinfoilofberyllium.Whilemostionsintheprimarybeamwillnotbealteredbythetarget,somewillstrikeatargetnucleusdirectly,leadingtofragmentation.Thebeamaftertheproductiontargetisthereforeacombinationofthestableinputbeam,andamixofstableandunstablefragmentationproducts[10].SeparatingthedesiredreactionproductfromtheotherfragmentsandtheunreactedbeamisthetaskoftheA1900fragmentseparator.Thisseparatorconsistsoffoursupercon-ductingdipolemagnetsand24superconductingquadrupolemagnetswithlargetransverseacceptances(8millisteradian)[11].Betweenthetwodipoles,thebeamisdispersedinhorizontalspaceaccordingtoitsrigidity,andthedesired(ˆ)canbeselectedwiththeinsertionofaslit.Thedesiredmassisfromtheremainingbeamwitha\wedge"en-ergydegraderplacedbetweenthesecondandthirdmagnet.Finally,asecondslitisinsertedbetweenthethirdandfourthmagnetstoforonlythedesiredisotope.Thepurityofthebeamdependsonthedistributionofnearbyreactionproductswithsimilarcharge1Whileinmostacceleratorcontexts,theparenthesizedquantity(Bˆ)representsmagneticrigidity(mo-mentumtochargeratio),andisapropertyofthebeam,inthisequationBandˆareseparate,andarepropertiesoftheaccelerator.5ParticleEnergy(MeV/nucleon)Intensity(pnA)16O15017518O12015020Ne1708022Ne1208022Ne15010024Mg1706036Ar1507540Ar1407540Ca1405048Ca901548Ca1408058Ni1602064Ni140776Ge1302582Se1403578Kr1502586Kr1001586Kr1402596Zr1201.5112Sn1204118Sn1201.5124Sn1201.5124Xe14010136Xe1202208Pb851.5209Bi801238U450.1238U800.2Table1.1:NSCLPrimaryBeamListasofDecember,20146tomassratios[12].1.1.4BeamStoppingBythenatureoftheparticlefragmentationprocessforrareisotopebeamproduction,thebeamofrareisotopeshasnearlytheenergyoftheprimarybeamwhenitwasimpingedonthetarget.AttheNSCL,thiscanbeupto170MeV/u(SeeTable1.1).Whilethisisacceptableforanumberofexperimentalmethodswhichrelyonsecondarycollisions,therearealsomanyexperimentswhichrequirebeamsofradioactiveisotopesatlowerenergies.Thestepinproducinganylowerenergybeamisthermalizationinsometypeofstoppingdevice,followedifnecessarybyreaccelerationtotherequiredenegy.(Slowingthebeamdirectlytoanintermediateenergywouldbeverytoaccomplishwithoutunacceptableemittancegrowth.)TheNSCLhastwoprimarybeamstoppingdevices,alineargascellcompletedin2004[13],andareversecyclotronstopperwithaprojectedinstallationdatein2016[14].TheNSCLlineargasstopperconsistsofa50cmlonggaschamberwithapureheliumgas.Theincomingradioactivebeamispassedthroughasetofdegradersandwedgesandentersthechamberviaathinberylliumwindow.Withinthegaschamber,whichisheldatapressureof1bar,collisionalinteractionwiththegasslowsthebeamwhilesimultaneouslyreducingitschargestatebackto1+.Thestoppedionsareguidedtotheexitnozzleofthecylinderusingacombinationofelectrostaticproducedbyaseriesofringelectrodesandgaspressurefromthesupersonicexitofgasthroughthenozzle.Thedrawbackofthegasstoppermethodisthatastheincomingbeamcurrentincreases,theheliumbgasbecomesionized,andspacechargebegintolimittheciencyofthedevice.Asanalternative,theNSCLhasdevelopedareversecyclotrongasstopper7whichisscheduledtobeinstalledin2016.Asthenameimplies,thedeviceessentiallyoperatesequivalentlytotheacceleratingcyclotrons-amagnetictheincomingionstocircularpaths.Insteadofbeingacceleratedbyanappliedelectricthebeamsaredeceleratedbyheliumgascontainedwithinthestopper.Bycontrasttothelineargascell,sincetheionsinthisdevicetakeamuchlongerpathlengthtoextraction,thegaspressurecanbemuchlower,thuslimitingspacechargeinthegas.Astheionsslow,theyspiraltothecenterofthedevice,wheretheyareextractedbyacombinationofstaticandRFelectricOnceextracted,thebeamscanbedirectedtothelowenergyexperimentalareasoftheNSCL,ortransferredtothereacceleratorforfurtheracceleration.Itisimportanttonotethatduetointeractionwiththegas,thechargestateoftheextractedbeamisdecreasedto1+,justasinthelineargascell.1.1.5ElectronBeamIonTrapandQ/AseparatorOncethethermalizedbeamisextractedfromthestopper,itmustbechargebredbackuptothedesiredlevelofionizationbeforeitcanbereaccelerated.ThisisaccomplishedintheElectronBeamIonTrap(EBIT)[15].(Figure1.2)Radialtwithinthetrapisprovidedbyacombinationoftwosuperconduct-ingmagnetstructures-apairofHelmholtzcoilsandalongersolenoidmagnetwhichcanbeadjustedindependently.Axialtisprovidedbyaseriesof22ringshapedelectrodes.The1+chargestatebeamfromthegasstopperisinjectedintothetrapwhereitinteractswithacoaxialbeamofelectronsproducedfromagunatthefarendofthetrap.Interactionwiththeelectronbeamincreasestheionizationstateoftheincomingions,increasingtheir8Figure1.2:CutawayviewoftheElectronBeamIonTrap.leveloftwithinthetrap,andpreventingtheirescape.Duetothisbeamcanbeinjectedcontinuouslyintothetrapfromthestoppingarea.Theparticleswithinthetrapcontinuetoincreaseinionizationuntilthedesiredchargestateisreached.Oncetheionsareattherequiredchargetomassratio,theelectrodepotentialattheexitofthetrapisloweredandthebeamisdirectedtowardsthereaccelerator.Thetrapisbiasedatthevoltagerequiredtoachieveabeamenergyof12keV/u.Thisenergycanbeachievedforionswithchargetomass(Q/A)ratiosfrom1:2to1:5.ThetimeandenergystructureofthebeaminjectedintoReAisthuscriticallydeterminedbytheparametersoftheEBIT:thethermaldistributionofthebeaminthetrap,andthetimestructureoftheloweringofthetrappingpotential.Typicalenergyspreadsareontheorderof0.3%[16].Ifthetrapissimplyopenedandallowedtoempty,thetypicaltimestructureisontheorderoftensofmicroseconds.Therehasbeenexplorationofusingalternatemodesofquickly9openingandclosingthetrapelectrodestocreateshorterpulsestructures,withsuccessfulextractiondowntopulsesof2s.However,thecapacitanceofthesystem,combinedwiththesizeofthetrappingpotential(ontheorderofhundredsofvolts),placesapracticallimitonthespeedwithwhichtheelectrodescanbeswitchedopenandclosed.AfterthebeamofradioactiveionshasbeenextractedfromtheEBIT,itispassedthroughaQ/Aanalyzertoensurecontaminantsfromthestoppingandchargebreedingprocessareminimized.Thissectionconsistsofa90degreeelectrostaticbendfollowedbya90degreemagneticbend.Betweenthetwobends,thebeamisbroughttoatransversefocuswithahorizontalspreaddominatedbyenergydispersion,andaslitisinsertedinthebeamtoselectthedesiredbeamenergy.Asecondslitisinsertedafterthemagneticbendingsectionwherethetransversebeamspreadisdominatedbymomentumdispersion.Takentogether,thesetwobendsandslitsconstituteamassseparator[17].TwoimportantofmeritforsuchamassseparatorarethemassresolutionRandtheachromaticity.ThemassresolutionisdasR=MM(1.3)whereMisthemassofthedesiredparticleandMistheminimumdinMatwhichacontaminantbeamcanbesuccessfullyseparated.Theachromaticityistheamountbywhichdesiredparticlescandeviatefromthereferenceenergyandstillbereturnedtoacommonfocusattheendoftheseparator.ThischaracteristicwasofparticularinterestfortheReAseparatorgiventherelativelywide(0:2%)predictedenergyspreadofthebeamfromtheEBIT.ThedesignoftheQ/AsectionwascalculatedtohaveanRof100andachromaticitywithin1.5%ofthenominalbeamenergy[18].10Figure1.3:LayoutoftheReAcceleratorfromtheEBITtothedetectorhall.1.1.6ReacceleratorReAThelayoutofReA,includingtheEBITandQ/AseparatorisshowninFigure1.3.ThebeamofradioactiveionsemergingfromtheQ/AseparatoristransportedthroughtheLowEnergyBeamTransport(LEBT)linepriortoinjectionintotheacceleratoritself.Inadditiontoelectrostaticquadrupolesusedforfocusing,theLEBTasdesignedcontainsan80.5MHzMultiharmonicBuncher(MHB)usedtobunchthebeampriortoinjectionandafocusingroomtemperaturesolenoid.Thisareaisalsowherethestableionsourceusedforcommissioningandtestingconnectstothebeamline,andiswherethe16.1MHzbuncherwhichisthetopicofthisdocumentwasinserted.TheMHBwillbediscussedingreaterdetailinthefollowingchapters.TheacceleratingstageofReAisafourvane,roomtemperatureRadioFrequencyQuadrupole(RFQ)structure.TheRFQisdesignedtoacceleratethebeamfrom12keV/uupto600keV/uforallQ/AvalueswithinthedesignspnofReA[19].Following11theRFQareaseriesofthreecryomodules,containingatotalof15superconductingniobiumquarterwavecavities.Thesevenofthesecavitiesareoptimizedfor=0.041,andthelasteightfor=0.085,whereistheparticlevelocityrelativetothespeedoflight.TheRFfrequencyfortheMHB,theRFQ,andthecavitiesis80.5MHzineachcase,meaningthatgroupsofparticles(\bunches")emergefromtheacceleratoratthatfrequency.Themaximumdesignenergyofthebeamfollowingthethirdcryomoduleis3MeV/uforuranium(A=238).Afterthethirdcryomodule,thebeamistransportedviaaMediumEnergyBeamTransport(MEBT)linetotheexperimentalhall.Thislineisapproximately30metersinlength.Asoriginallyinstalled,thislinecontainsnofurtherelementsforlongitudinalcorrectionofthebeam,butonepotentialupgradetothislinewouldbeoneortworebunchingcavitiestocompressthelongitudinalstructureofthebeampriortoreachingtheexperiments.Asof2016therewerethreemainexperimentallinesattheendoftheMEBT.TheconnectstotheActiveTargetTimeProjectionChamber(AT-TPC)experiment,thesecondtotheJetExperimentinNuclearStructureandAstrophysics(JENSA)andthethirdisautilitybeamlinewhichcanbeconnectedtoavarietyofdetectorsasneeded.1.1.7FuturePlans1.1.7.1ReAExpansionTheinitialconstructionofReAwascompletedin2014withtheinstallationandcommis-sioningofthethirdcryomodule.Thisincarnationoftheacceleratoriscommonlyreferredtoas\ReA3",afterthemaximumdesignenergyfortheheaviestisotopes.Plansareunderdevelopmentforadditionalcryomoduleswhichwillbringtheenergyto6or12MeV/u,12andthesefuturestagesarereferredtoas\ReA6"and\ReA12".OtherpossibleimprovementstoReAincludetheadditionofanECRionsourceforinjec-tionofstablebeams,andtheadditionofrebunchingcavitiesbetweenthethirdcryomoduleandthedetectorstationstoprovidegreatercontroloverthetimeandenergyspreadofthebeamatthedetectors.1.1.7.2FRIBIn2008,theU.S.DeparmentofEnergyapprovedtheconstructionoftheFacilityforRareIsotopeBeams(FRIB)asasuccessortothecyclotronsatNSCL.FRIBwillconsistofasuperconducinglinactoproducehighintensitybeamsofrareisotopesatintensitiesupto400kW[20].TheFRIBbeamlinewillconnecttotheexistingNSCLexperimenthalls,includingReA,thusallowingtheexistingdetectorstobeusedwiththenew,moreintensebeams.1.1.8ReATimeStructureIssuesTheReAcceleratorwasspdesignedtomakeuseof80.5MHzprototypecavitiesbuiltaspartoftheplanninganddevelopmentprocessforFRIB.Sincethefacilitywasconceivedtomakeuseofexistinghardware,ratherthanbeingdesignedfromthegroundup,notallpotentialuserneedswerenecessarilyanticipated.Theselectionofabunchingfrequencyequaltotheacceleratorfrequencywasalogicalchoice.Forreasonsthatwillbeoutlinedinthefollowingchapters,thisbuncherrequiresrelativelylittlepowerandphysicalspace,andnoprovisionsneededtobemadefordealingwith\satellite"bunches.However,thecostofthisbunchingmethodwasarelativelyshortrepetitionperiodof1312.4nsbetweenbunches.Inparticular,htmeasurementsinvolvingreacceler-atedbeamsaremadeextremelywiththisshortperiod[21].FutureplansforanIsochronousLargeApertureSpectrometer(ISLA)willalsobeadverselybythistimeseparation[22].Chapter2willexpandonthetimestructureoftheReAcceleratorasconstructed,andthereasonsfordesiringtheoptionofalongertimeseparation.Beforethisexplanationisgiven,somebasicsofacceleratorphysicsareoutlinedhere.1.2OverviewofEssentialAcceleratorPhysicsAtthemostfundamental,acceleratorphysicsissimplytheapplicationoftheLorentzforcelaw:~F=q(~E+~v~B)(1.4)Thereare,ofcourse,anumberofothercomplexwhichcancomeintoplay,includ-ingspacecharge,wakmisalignments,andsoforth.Manysophisticatedandpowerfultoolshavebeendevelopedforanalysisofbeamdynamics(seeAppendixA).However,itisusefultobearinmindthatthissimpleequationisstillattheheartofanyanalysisofthebehaviorofanaccelerator.Withthatinmind,theremainderofthischapterwillexploresomeofthefundamentalprinciplesofacceleratorphysicsthatareusedinthisdocument.Asweareconcernedherewithalinearaccelerator,littletonomentionwillbemadeofissuesthatareprimarilyofinterestincircularmachines,suchasstabilityofclosedorbitsorresonances.Additionally,sinceReAwillalmostentirelytransportbeamswithlowchargecurrents,evenwhenoperatedinconjunctionwithFRIB,therewillbenodiscussionofissuesassociatedwithhighcurrentbeamssuchasspacecharge14Figure1.4:Thecoordinateframeusedtodescribeparticlesrelativetoamovingreferenceparticle.Inordertodescribethemotionofaparticleinanaccelerator,itisnecessarytothecoordinatesysteminwhichthismotionwillbeanalyzed.Particlecoordinatesinanacceleratorareusuallydescribedrelativetoareferencetrajectory.Thereferencetrajectoryisthepathfollowedbyareferenceparticlewhichenterstheacceleratorwithnodeviationfromthedesiredenergy,transverseposition,ortransverseangle.Inaddition,foracceleratorswithtime-varyingthereferenceparticlealsodtheidealtimeofentryintotheacceleratorrelativetothephaseoftheWiththereferencetrajectorythusanorthogonalsetofplanarx,y,andzcoordinatescanbeateachpointonthebeamline.Thevariablezpointsalongthereferencetrajectoryinthedirectionoftravel,andxandyarecoplanarintheplanenormaltozwiththeiroriginonthereferencetrajectory(Figure1.4).Whilexandycanbeselectedtomeettheconditionsofagivenbeamline,theusualpracticeistochoosexandyrighthandedwithxinthehorizontalplaneandyvertical.Itisimportanttonotethattheorientationofthesecoordinatevectorscanchangerelativeto3DCartesianspaceastheoriginismovedalongthebeamline.15Figure1.5:Theparaxialapproximationmeansthatx0canbeapproximatedasforsmallvaluesof.1.2.1CoordinatesThereareanumberofpossibleofthezcoordinateforanindividualparticle.Whilethexandycoordinatesarealwaysmeasuredindistancefromthereferencetrajec-tory,zmaybemeasuredeitherrelativetoanabsolutepointonthebeamline,suchasthestartingpoint,oritmaybemeasuredrelativetothepositionofareferenceparticlealongthebeamline.Whetherzismeasuredrelativetoapointorrelativetoamovingreference,itmaystillbeexpressedeitherasanabsolutedistance,atimeoft(foragivenparticlevelocity),oraphase(foragivenreferenceparticlevelocityandsystemfrequency).Inadditiontox,y,andz,afulldescriptionofeachparticlemustalsoincludetheinstantaneousrateofchangeofeachofthesequantities.Forthetransversecoordinatesxandy,wedesignatetheratesofchangeasx0andy0.(Notethatsomesourcesrefertothesequantitiesasaandb.)Herewemakeuseofthe\paraxialapproximation",whichapplieswhentheparticle'strajectoryisnearlyparalleltothereferencetrajectory(Figure1.5).Inthiscase,thesmallangleapproximationmaybeusedtoreplacetan()with,andexpressx0andy0asangles.Further,inthecasethatanymagneticpresentisperpendiculartothebeamdirection,x0canalsobeexpressedastheratioofthetransversemomentumtothe16longitudinalmomentum.x0=dxdz=ˇ(1.5)ˇpxpz(1.6)Therateofchangeofzhasevenmorepossiblevariantsthanzitself,startingwiththesymboltobeused,whichcanbeeitherz0or.Conceptually,itisimportanttorememberthatthisquantityissimplyanexpressionoftherateofchangeoftheparticle'spositionalongthedirectionoftravel-inotherwords,thevelocityoftheparticle.Lesssimpleishowthisvalueistobeexpressed.Asbefore,thisquantitycanbedescribedeitherinabsoluteterms,orrelativetoareferenceparticle.Inabsoluteterms,thevelocitymaybegivendirectly,orthekineticenergy,totalenergy,ormomentumoftheparticlesp(foragivenparticlemass.)Ifthevelocityisrathertobesprelativetoareferenceparticle,thatmaybespasanabsolutedeviationinvelocityv),energyE),kineticenergyW),ormomentump)fromthatofthereferenceparticle.Alternately,therelativedeviationinvelocity(vv),energy(EE),kineticenergy(WW),ormomentum(pp)fromthereferenceparticlemaybespAsapointofconfusion,someacceleratorcodes,notablycosy[23],normalizethelongitudinalcoordinatebyafactorof1+,whichmustbeborneinmindwhenattemptinganapples-to-applescomparisonbetweentheseandothercodes.(Thisnormalizationcorrespondstoaconversionfromrelativekineticenergytorelativemomentum[24].)Thisdocumentwill,unlessspotherwise,expresszandz0relativetoareferenceparticle.Thelongitudinalcoordinatezwillusuallybespeciinunitsoftime(typicallyns),andz0ineitherabsoluteW)orrelative(WW)kineticenergydeviationfromthe17reference.Onceasuitablesetofcoordinateshasbeendecidedupon,eachparticlecanbespasasixelementvectorinphasespace:~s=8>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>:xx0yy0zz09>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>;(1.7)Assumingtheequationsofmotioncanbelinearized,theofbeamlineelementsactingonthebeamcanbeexpressedasaseriesofmatricesmultiplyingthisphasespacevector.Forasimpleexample,aparticlemovingthroughadriftoflengthLexperiencesthefollowingchangesinthephasespacecoordinates(Continuingtoassumetheparaxialapproximation.):x=xo+Lx0x0=x0oy=yo+Ly0y0=y0oz=zo+Lz0z0=z0o(1.8)18Thiscanbeexpressedcompactlyinmatrixnotationas:~s=26666666666666666641L0000010000001L0000010000001L0000013777777777777777775~so(1.9)Itisimportanttoreiteratethatthechoiceofzandz0matrixelements(andbyextension,equationofmotioncots)dependsontheunitschosenforthesequantities.Caremustalwaysbetakenthatunitsareunderstoodandconsistentwhendealingwithlongitudinaldynamics.1.2.2TransverseDynamicsIfbeamlineelementswhichtheenergyofthebeamarenotconsidered,thematrixapproachoutlinedaboveallowsforarelativelysimplecalculationoftheofagivensetofelementsonaparticle.Thelinearnatureoftheequationsofmotionmeansthatthematricesforeachelementonabeamlinecanbecombinedtogiveasingletransfermatrixwhichdescribestheofthatlineonthephasespacecoordinatesofagivenparticle.Formanycommonbeamlineelements,thexandyequationsofmotionarenotcoupled-theinitialxandx0coordinatesdonottheyandy0components,andviceversa.Inmatrixterms,thismeansthattheonal2x2blockswithinthetransfermatrixare19zero:T=2666666666666666664000000003777777777777777775(1.10)Forelementswhicharenotbyparticleenergy,thismeansthattheequationsofmotioncanbereducedtotwosimple2x2matrices,oneforeachtransversedirectionxandy.Thesimplestsuchelementisaquadrupole,whichfocusesthebeaminonetransversedirectionwhiledefocusingintheother.ThematrixforaquadrupoleapproximatedasathinlensisT=264101f1375(1.11)wherefisthefocallengthofthequadrupole,andthesignofthelowerleftelementistobenegativeinthefocusingdirectionandpositiveinthedefocusingdirection.TheonlyotherpurelyfocusingelementusedintheReAbeamlineisthesolenoid.Sincethesolenoidrotatesthebeamaboutthebeamaxis,xandyarenolongerindependentafterpassingthroughasolenoid,andthediagonalelementsofthetransfermatrixarenonzero.20Thex/ytransfermatrixforasolenoidis[25]T=26666666664C21kSCSC1kS2kSCC2kS2SCSC1kS2C21kSCkS2SCkSCC237777777775(1.12)wherek=Bs2(Bˆ);(1.13)C=cos(kL);and(1.14)S=sin(kL):(1.15)Here,Listhelengthofthesolenoid,Bsisthemagneticofthesolenoid,and(Bˆ)istherigidityofthebeam.TheotherimportanttypeofelementintheReAbeamlineisthebendingelement,whichbendsthetrajectoryofthebeamusingelectricormagneticdsorthogonaltothebeam'sdirectionofmotion.Sincethereisnorotationofthetransversecoordinates,thediagonalblocksareonceagainzero.However,duetothecurvedpathofthereferenceparticlethroughthedipole,thetransversemotionoftheparticleintheplaneofthebendbecomescorrelatedwiththelongitudinalcoordinatesoftheparticle.Foradipolewhichbendsinthexzplane,aparticlewhichentersadipoleatthereferenceenergybutwithadisplacementfromthereferencetrajctoryinxwillseeeitherashorterorgreaterpathlengththroughthemagnet,andwillthereforeseeachangeinitslongitudinalpositionrelativetothereferenceparticle(Figure1.6).Similarly,aparticleenteringonthe21Figure1.6:Pathsofthreeparticleswithidenticalenergies,buttinitialdis-placementsthroughadipole.Figure1.7:Pathsofthreeparticleswithenergiesbutidenticalstartingtrajectoriesthroughadipole.referencetrajectorybutawayfromthereferenceenergywillitselftravelingawayfromthecentraltrajectoryforwhichthemagnetiscalibrated(Figure1.7).ThisisuseddeliberatelyinmassspectrographssuchastheA1900,whicharecalibratedtopreventthepassageofenergyparticles.ThiscorrelationbetweenthebendingplanecoordinatesandthezcoordinatecanbeseeninthenonzeroelementsintherowandsixthcolumnofthetransfermatrixforabendingmagneticdipolewithbendradiusˆandmagneticdintheydirectionBy[25]T=2666666666666666664Cx1kxSx000h1Cxk2xkxSxCx000hSxkx00Cy1kySy0000kySyCy00hSxkxh1Cxk2x0011ˆ2(kx2Sx)k3x+s2(11ˆ2k2x)0000013777777777777777775(1.16)22wheren=ˆBy@By@xx=0;y=0;(1.17)kx=q(1n)h2;and(1.18)ky=pnh2:(1.19)Hereisthebendangleofthedipole,kxandkyrelatetothestrengthofthedipole(kyiszeroforapureverticalwithnogradient),sisthepathlengthofthereferenceparticlethroughthedipole,his1ˆandCx=cos(kxs),etc.Additionalmatricescanalsobeappliedtoaccountforduetothecurvaturesandanglesoftheentrancefacesfordipoleelements.1.2.3TransverseEmittanceandCSparametersSinceacceleratorsarerarelytaskedwithacceleratingasingleparticleatatime,itisvaluabletoextendthedynamicsdevelopedintheprevioussectiontoadescriptionofthemotionsofensemblesofparticles.OfparticularvalueinthisanalysisisLiouville'stheorem,whichstatesthatforacanonicallyconjugatepairofcoordinates,theareaoccupiedbyasysteminthephasespacebythatpairisconserved.Classically,thecanonicalpairofvariablesineachdimensionispositionandmomentum.AsindicatedinSection1.2.1,insituationswheretheparaxialapproximationholdsandallmagneticcomponentsareperpendiculartothebeamaxis,x0maybeexpressedasaratioofpxtopzandmaythereforebeconsideredasconjugatetox.Inthelongitudinaldirection,aclassicallyconjugateformisz=vt),wheretisthetimeoftandz0==pp[26].23Figure1.8:ThephasespaceellipsedescribedbytheCourant-Snyderparameters.Withthesecoordinatepairs,x/x0,y/y0,andz/z0,chosentobecanonicallyconjugate,itiscustomarytoploteachpairandexaminethephasespacerepresented.Thetotalareaineachphasespaceoccupiedbythebeamisreferredtoasthe\emittance"ofthebeamforthataxis.Assumingthemotionoftheparticlesineachdimensionisuncorrelated,theseemittancesareideallyconservedbyLiouville'stheorem.Thisisonlystrictlytrueforunacceleratedmotion.Animportantcaveattotheconservationofemittanceisthatasthemomentumofthebeamparticlesincreases,thebeambecomesmore\rigid"andoscillationsreduceinampli-tude,thusreducingtheemittance.Iftheemittanceisnormalizedbythefollowingformula[1],n(vc)(1.20)theresultantnormalizedemittanceshouldideallyremainconstantinallcases.Theprimaryreasonswhyitstillmightnot,suchasspacechargeandbeam-beaminteraction,arenotofgreatconcerninReA,asmentionedabove.24Theequationsofmotionfortransverseoscillationinanacceleratorareoftheform:x00+K(s)x=0(1.21)wheresrepresentsthepositionofthereferenceparticlealongitstrajectory,andK(s)isapiecewisefunctionthatrepresentstheactionofthemagneticandelectricalongtheaccelerator.(Forafullderivation,seeEdwardsandSyphers[1].)ThistialequationisknownasHill'sequation,andthesolutioncanbewrittenas:x(s)=Ap(s)cos[˚(s)+]:(1.22)Here,(s)isafunctionofthearrangementofeldsintheaccelerator,˚(s)representsthetotalphaseadvancedoftheoscillatingparticleuptopoint(s)intheaccelerator,andAandareconstantsofintegration.Thiscanberearrangedtotheform:=x2+2xx0+x02(1.23)whichistheequationofanellipsewithanareaof(Figure1.8).(Notethatinthisequationisnotthesameasinequation1.22.)Collectively,thevalues,,andareknownasthetransverseCourant-Snyder(CS)parametersforthebeamonthexaxis,andiscalledtheemittance.Conservationofmomentumconstrainsindividualparticlestoremainonagivenphasespaceellipseastheymovealongthebeamline,however,theellipseitselfchangesshapeasntareapplied.Inadrift,theparticlesintheupperhalfwithpositivex0valueswillmovetotheleftandthosewithnegativex0totheright,causingthemajoraxisoftheellipsetosheerinacounterclockwisedirection.Inathinlensquadrupole,thex25valueswillremainunchangedwhilex0valuesarealtered,causingtheellipsetoscalealongtheverticalaxis,etc.Thus,theCSparametersofthebeamevolvealongtheacceleratorwiththechangingshapeoftheellipse.Intuitively,theseparameterscanhelpgiveaquickassessmentofthebeampropertiesatapoint-isrelatedtothexsizeofthebeam,isrelatedtothespreadintrajectoriesonthexaxis,andrelatestotheanglethemajoraxisoftheellipsemakeswiththeorigin.(Sincexisminimizedwhentheaxisisvertical,iszerowhenthebeamreachesawaist.)Ifischangedwithoutalteringtheotherparameters,theellipsescaleslargerorsmallerinsizebutmaintainsthesamebasicshape.Oftheparameters,,,and,onlytwoareindependent,withthethirdbeingdeterminedbytherelation2=1:(1.24)Animportantnoteaboutemittance:Whileitisuniversallyasaphasespacearea,therearemanytconventionsforactuallycalculatinganumberforthevalueoftheemittanceofthebeam.Theˇinequation1.23mayeitherbeincorporatedintotheunits(as10ˇ*mm*mrad)orexplicitlyincludedinthenumber(asin31.4mm*mrad).Anothercommonistotaketherootmeansquare(RMS)beamsize˙atalocationwherethevalueofisknown,andusethesequantitiestoafractionofthetotalbeam,asinTable1.2.Asaresult,itiscriticallyimportanttodeterminewhichofemittanceisinusewhenusingaspvaluefortheemittance,ratherthansimplyusingthegeneralprincipleofemittanceconservation.Oneothercaveat-treatingthexandyemittanceasseparateisonlyfullyvalidifthe26F(%)˙215ˇ˙2394ˇ˙2876ˇ˙295Table1.2:BeamfractionsforseveralofemittanceasafunctionofRMSbeamsize˙[1].beamneverpassesthroughelementswhichcorrelatethetwocoordinates,suchassolenoids.Afterpassingthroughasolenoid,itisstillpossibletoa4Dconservedphasespaceareainx/x0/y/y0space,butthisisafarmorecomplexprospect,andnoconsensusexistsonhowbesttosuchanemittanceorhowtoapplyit.1.2.4LongitudinalDynamicsInsomeways,longitudinaldynamics(dynamicsinthedirectionofbeamtravel)aretreatedsimilarlytotransversedynamics.Despitethewiderangeofpossiblechoicesforexpressingzandz0,thesearechosentobecanonicallyconjugatevariables,andthusdisplayphasespaceconservationexceptinacceleratingorinsituations(suchasdipoles)wherezandcanbecomecorrelatedtomotioninotherdimensions.However,therearesomeimportantdistinctions.AswillbediscussedinmoredetailinChapters2and3,therearetwoprimarytypesofparticleaccelerator,thosewhichusestaticelectricforacceleration,andthosewhichuseradiofrequency(RF)acceleratingThedynamicsforasimplestaticacceleratinggradientaresimple-theLorentzforcelawappliedoveradistancegivesthechangeinenergy.However,eventhissimplecasemeansthatthebeamlinecannolongerbemodeled27asasimpleseriesofmatrixmultiplications,asmanymatrixelementsaredependentonbeamenergy.Oncetheparticlehasbeenacceleratedbyastaticacceleratinggap,thematricesforsubsequentelementsmustberecalculatedforthenewenergy.TheproblembecomesevenmoreforRFacceleration.Thenecessaryphaseinformationcanbeextractedfromthezcoordinatesoftheparticledistribution,butsincetheischangingwithtime,evenannarrowacceleratinggapwillchangetheenergyofparticlesthatarriveatttimesbytamounts.Mostcommonly,beamlineswithacceleratingelementswillbemodeledbyacombinationoftransfermatricesforportionsofthebeamlinewhereenergyisnotchanging,anddirectcalculationofthechangeinenergyforeachparticlewhereitis.Thesimplestformoftheenergychangeforaparticletraversinganacceleratinggapisgivenby:E=Eo+qVosin(˚)(1.25)whereqisthechargeontheparticle,Voisthemaximumvoltageacrossthegapand˚isthephaseoftheRFatthetimeoftheparticle'sarrival,with˚=90degreesgivingthemaximumaccelerationand˚=0degreesgivingnoacceleration.Whilethiswouldseemtoberelativelystraightforwardtorepresentasamatrix,264zE375=26410qVosin(˚)1375264zoEo375(1.26)aproblemarisesbecause˚isnotaedvalue,butchangeswithtime.Assuch,theentiretransfermatrixforanRFgapbecomestimedependent.(Thissimpleexampleisalsoanoversimbecausewhilezanddpparecanonicallyconjugate,zandEarenot.)28ThestandardpracticewithRFacceleratingstructuresistothedesiredvalueof˚forthereferenceparticleandadjusttheacceleratorsothatthereferenceparticlepasseseachacceleratingstationatthesamephase,knownasthe\synchronousphase."Thisdoesmakethetransfermatrixabovetime-independent.However,theproblemreturnswhenwetrytodescribethemotionofanarbitraryparticlewithaphaseorenergytfromthereferenceparticle.Inthatcase,theequationsofmotionbecome(EEs)f=(EEs)i+qVo(sin˚sin˚s)(1.27)˚f=˚+C(EEs)f(1.28)whereEand˚aretheenergyandphaseoftheparticleinquestion,iandfrepresenttheinitialandstatesbeforeandafterthegap,andCisafactorwhichisrelatedtothegeometryoftheacceleratorandtheenergyofthereferenceparticle[1].Withthetimedependenceonthephasereintroduced,thissituationisonceagainnotrepresentablebyastaticmatrix.Afurthercomplicationisintroducedbythefactthateventhetransversematrixelementsformagneticelementsaredependentonparticlevelocities,duetothe~v~BdependenceoftheLorentzforcelaw.Assuch,asinglematrixrepresentationforanacceleratingstructureisn'teasilygenerated,sincethematricesforlaterbeamlineelementsdependonthepropertiesoftheparticlesinputtopriorelements.TheacceleratorsimulationcodesreferencedinthedocumentwhichDOtreatcomplexacceleratingstructuressuchasbunchers,dosobytransportingdistributionsofparticlesusingthematrixformalismthroughnon-acceleratingelements,andthenevaluatingequations1.27and1.28individuallyforeachparticleateachacceleratingelement.291.2.5LongitudinalEmittanceAsmentionedabove,zandz0arealwaysselectedascanonicallyconjugatevariables,sothebeamareainthisphasespaceisgenerallyconservedforunacceleratedbeams(exceptwhencorrelatedtoanotherdimension,suchasinadipole).However,inactualpractice,abeam'slongitudinalemittanceisoftennotwelldescribedbyanellipse,andassuchCSparametersarelessoftenusedinthezdirection.Forexample,thecontinuousbeamemittedbytheReA3EBITappearsasasimplerectangleonthephasespaceplotwithazwidthof360degreesandaz0heightcorrespondingtotheenergyspreadinthebeam.WhiletheCSapproachtodescribingthenon-ellipticalshapeofthez/z0phasespaceisnotalwaysuseful,Liouville'stheoremisnotdependentonanyparticulargeometryonthephaseplot,sotheareaoftheplot(andthusemittance)isstillconserved.Thiscanbeextremelyusefulinmakingsimpleestimatesoftheeofbunchingoracceleratingelementsonthebeamtimeandenergyspreads.Forexample,ifamolecularhydrogenbeam(A=2)hasalongitudinalemittanceof2.4eVnsperperiod,forthecaseofthecontinuousbeamwithperiod12nstheenergyspreadis2:4eVns12ns=0:2eV:(1.29)Ifthatbeamwerethencompressedtoalengthof1ns,thebeamenergywouldexpandtoaspreadof2:4eVns1ns=2:4eV:(1.30)30Chapter2TimeStructureofAcceleratedBeamsAllacceleratingstructurescanbedividedintotwobroadclasses:DCandAC.DCacceler-atorsarethesimplestconceptually-anelectrostaticisusedtoprovideaccelerationinaccordancewiththeLorentzforcelaw.Thesetypesofacceleratorerfromthedrawbackthattheyarelimitedtoacceleratingvoltagesontheorderofafewmegavolts[1],beyondwhichelectrostaticbreakdownoccurs,placingalimitontheenergyofsuchamachine.Abovethatlimit,radiofrequency(RF)electricmustbeused.TheadvantageofusingRFforaccelerationisthatbyusingresonantcavitiessig-tlyhigheracceleratinggradientscanbeproduced.Forexample,thecavitiesplannedforFRIBwillhavepeakelectricattheaverageacceleratingvoltagefrom26.5-30.8MV/m[27].Thedisadvantageisthattheacceleratedbeammustbebunchedinordertoavoiddecelerationduringthephaseoftheelectricwhenitsdirectionisnegative.2.1OriginalTimeStructureofReATherearethreesourcesofbeamaccelerationinReA:FirstistheEBIT,whichejectsthebeamat12keV/uviaaDCbias.Second,theRFQ,whichacceleratesthebeamto600keV/u.Finally,thelinearaccelerator(linac)itself,whichacceleratesthebeamtoaenergyupto3MeV/uforA=238.TheinitialaccelerationfromtheEBITiselectrostatic,whiletheRFQandlinacuseoscillatingelectriceldsforacceleration.TheRFfrequencyof31theRFQandlinacis80.5MHz.Inorderforthealternatingofthelinactoprovideaccelerationtomorethanhalfofthebeamparticles,theymustbebunchedbeforeacceleration[28].WhilethereareRFQdesignscapableofprovidingbunchingaswellasfocusing[29],ithasbeenfoundthatthelongitudinalemittanceofthebeamaftertheRFQcanbegreatlyimprovedwiththeadditionofanexternalbuncherbeforethebeamreachestheRFQ[30].Forthisreason,theLEBTsectionofReAincludesamultiharmonicbuncherdesignedtolongitudinallybunchthebeampriortoinjectionintotheRFQ.Inprinciple,anexternalbunchercanoperateeitherattheRFfrequencyoftheacceleratororatanyintegerdivisor(subharmonic)ofthatfrequency.BunchingdirectlyatthetheRFfrequencyisthesimplestcase,andthiswasimplementedforthedesignofReA.Usingthe80.5MHzMHB,thebeamisbunchedwithaperiodof12.4ns,andthereforeonebunchoccupieseachRF\bucket"oftheaccelerator.Withineachbunch,thelongitudinalstructureisdeterminedbyanumberoffactors.Inanidealperfectlymonoenergeticbeam,alltheparticlestravelatthesamespeed.However,inreality,thereisalwaysarangeofenergiesinthebeam.Thisleadstothebeamspreadingoutalongthebeamaxis,asthefasterparticlesmoveaheadandthesloweronesfallbehind.ThespcaseofReAisillustratedin2.1.WhenthebeamleavestheEBIT,thereisaninitialenergyspread(WW)ontheorderof0.3%[16].Thetimestructureoftheinitialbeamisdeterminedbytherateatwhichtheionsleavethetrap.However,sincethetrapemptiesonacharacteristictimescaleontheorderofmilli-ormicro-secondsdependingontheschemeused,thebeamcanbetreatedascontinuousintimefromtheperspectiveofabuncherwithaperiodoftensofnanoseconds.Whenthebeamleavesthebuncher,theenergyspreadofeachbunchhasbeenincreased,andthetimespreadbeginstodecrease,32Figure2.1:SimulatedlongitudinalstructureoftheReA3beamatvariouspoints.Fromlefttoright:theexitoftheEBIT,immediatelyafterthe80MHzMHB,thestartoftheRFQ,theexitoftheRFQ,theexitofthelinac,andthetarget.33Figure2.2:Theuncertaintyinthetimeofttforasinglezero-widthpulseisdeterminedonlybythepulsespreadt.reachingafocusattheentranceoftheRFQ.AsthetotalbeamenergyisincreasedintheRFQandlinac,thespreadrelativetothatenergydecreases.Finallythisspreadingcanbereducedfurtherbyusingthecavitiesofthelinacasrebunchers-thecavitiesarerunattheirnon-acceleratingphaseinanattempttoequalizetheparticleenergieswithineachbunchasmuchaspossible.However,thelongdistancefromtheendofthelinactotheexperimentalhalls(30meters)meansthatevenwiththelowestachievableenergyspreads,somebeamspreadingintimeisinevitable.Theismorepronouncedatlowerenergies,becausethelongertraveltimesmeanthatequivalentfractionalenergyshavelongertimestospreadoutthanathigherenergies.Theworstcasescenariooccurswhenthetimespreadofthebunchexceedsthebunchingperiod(12.4ns)anditbecomesimpossibletotemporallyresolveindividualbunchesatthedetectors.2.2MotivationforDtTimeStructuresManyexperimentalprotocolsusingreacceleratedbeamsinvolvemakingameasurementofthetimeoftoftheparticlefromthesourcetothedetector[21].Ifasinglebunchwithnotimespreadislaunchedfromtheaccelerator,thentheprimarysourceofuncertaintyinthetimeoft,t,ofaparticlewithinthebunchisthetimespreadingofthatbunch(duetoitsinitialvelocityspread)betweenthelaunchandthedetector(Figure2.2).Iftisthefulltimewidthofthebunchatthedetector,thentheuncertaintyinthemeasuredtimeof34Figure2.3:Whenmultiplepulsesarelaunched˝secondsapart,themeasurementofthetimeoftbecomesuncertainbyanintegermultipleof˝.Iftislargerthan˝,themeasuredtimeoftcantakeanyvalueandbecomescompletelyuncertain.tis:jtmeasuredtjt2(2.1)However,ifmultiplebunchesarelaunchedwithaseparationof˝,thenthetimeoftisalsouncertainbyanintegermultipleof˝,representingtheinabilitytodeterminetowhichinitialbunchthedetectedparticlebelongs.(Figure2.3)jtmeasuredtjn˝+t2(2.2)Tominimizethebetweentmeasuredandt,theperiodbetweensuccessivebunches,˝,mustbeincreasedtothepointthatthevalueofncanbedeterminedbasedonconsiderationsextrinsictotheimmediatemeasurement.Oncenisknown,thetimeoftcalculationreducestothecase.Atthesametime,tmustbemadeassmallaspossible,andcertainlysmallerthan˝.Avalueoftlargerthan˝,asmentionedabove,willmakeitimpossibletoresolveindividualbunchesatall.DiscussionsbynuclearscientistsatNSCLandelsewhereconcludedthatevenwithalowenoughvalueoftattheReAdetectorsfortemporalresolution,theoriginal12.4nsvalueof˝forthebunchseparationisnotenoughforanunambiguousdeterminationofn-whichlaunchedbunchcorrespondstoadetectedparticleattheendofthebeamline[31].35Finitedetectorresettimesbetweenbunchesalsocontributetothedesireforagreaterbunchseparation.2.3MethodsforAchievingGreaterBunchSeparationSeveralpossiblemethodsareconsideredhereforlengtheningthegapbetweenbunchesatthedetectorsofReA.Anidealsolutionwouldhavethesametransmissionasthe80.5MHzbunchercase,wouldhavenoparticlesinoutlyingbunchesbetweentheprimarybunches,andwouldminimizethetimeandenergyspreadontarget.Obviously,apreferredsolutionwouldalsonotconsumeundueresources,intermsofeithermoney(eitherforequipmentoroperationalcosts),installationtime,orphysicalspacerequired.2.3.1MoofEBITTimeStructureConceptually,thesimplestmethodforachievinggreaterbunchseparationwouldbetosimplyreleasethepulsesfromtheEBITatthedesiredtimeseparation.IfthetrappingpotentialontheEBITcouldbeopenedandclosedagainwithintheMHBperiodof12.4ns,withanacceptablylowrepetitionratebetweenopenings,thatwouldimmediatelyallowforanydesiredbunchseparationwithnoadditionallossofparticlesfromthebunchingmethod.However,thismethodturnsouttobeextremelytoachieveinpractice.Inordertoopenandclosethetrapquicklyenough,asquarepulsewouldneedtobeappliedtothetrappingelectrodeswithacombinedrise/sustain/falltimeunder12.4ns.Forcomparison,thefastestavailableswitchfromBehlkeatthetimeofwritinghadacombinedtimeof62nswithamaximumrepetitionrateof3MHzwhenoperatedinliquidcooledmode[32].AprototypedriverdevelopedatCERNbyMauroPaoluzzicould36potentiallyhaveaveryshortpulsetimeontheorderof2ns,withavoltageslewofupto650V[33].However,thedeviceoperateswitha1msburstatarepetitionrateof2Hz,givingita0.2%dutycycle,whichwasdeterminedtobeunacceptablylow.Duetothesetechnicallimitations,pureEBITswitchingisnotlikelytoprovideashorttermsolutiontothebunchspacingissue.However,someformofswitchingmaybeusedinthefuturetoproduceimprovedresultscombinedwithanotherdevice.2.3.2SubharmonicBunchingAsconstructed,ReAbunchesthecontinuousoutputbeamfromtheEBITintotheRFQusinga80.5MHzMHB.Thiseachaccelerating\bucket"oftheRFQandLinac.IfabuncherweretooperateinsteadatanintegerdivisornoftheRFfrequency,thenitcouldinprinciplebunchthebeamintoeverynthbucket,increasingthespacingbetweenbunchestontimestheRFperiodof12.4ns[34].Therearetwomaintosuchanapproach.Theisthatthismethodofbunchingnecessarilyincreasestheenergyspreadofthebeam.Thesecondisthatunlessthebunchingwaveformisaperfectsawtoothwave,someparticleswillendupinsatellitebunches.Despitethesepotentialdrawbacks,thisoptionwasdeterminedtobethemostpracticaloftheavailableoptions,andthedesignandconstructionofsuchadeviceforReAisthesubjectoftheremainderofthisdocument.2.3.3OtherSolutionsTwootherpossibleapproachestoincreasingthebunchspacingwereconsidered.Thewasabeamchopper.Achopperinitssimplestformsimplyunwantedbeamaway37fromthetransverseacceptanceoftheaccelerator.Regardlessofthespmechanismofthethisapproachwasdeemedtobeundesirablebecausechoppersbydereducebeamtransmissioninproportiontotheamountbywhichthespacingisincreased.Inotherwords,toincreasebeamspacingbyafactorof5,achopperwouldneedtodiscard4/5ofthebeam.Thislevelofdecreaseinbeamtransmissionwasdeemedtobeunacceptable.Amoreexoticsolutionwouldbetomodulatetheamplitudeoftheacceleratingcavitiesalongtheentirelengthofthelinacinsuchawayastobunchthebeamtoafocusatthedetectors.Whileintriguing,itisunclearthatthecavityamplitudescouldbemodulatedaccuratelyonthesesub-microsecondtimescales,andtheresultingenergyspreadwouldlikelybequitelarge.38Chapter3PrinciplesofMultiharmonicBunchingTheoldestandsimplesttypesofparticleacceleratorsaresimpleelectrostaticdevices.Parti-clesareemittedfromasourceandareacceleratedacrossastaticvoltagegap.However,thesetypesofacceleratorsarelimitedbyelectrostaticbreakdowntogapvoltagesontheorderof10MV.Formorepowerfulmachines,itisnecessarytousetimevarying(RF)electricforparticleacceleration.Sincethesetimedependentalternatebetweenacceleratinganddeceleratinggradi-entsoverthecourseofasingleperiod,itisnecessarytorstbunchthebeamlongitudinallybeforeinjectionintosuchadeviceforacceleration.(SomeRFQsareanexceptiontothisrule,providingbothbunchingandaccelerationinonedevice.TheRFQinReAisnotofthistype.)Inthesimplestcase,thecontinuousbeamisbunchedatthefrequencyoftheacceleratingdevice,andthebunchistimedtoarrivenearthepeakoftheacceleratinggradient.Aswillbediscussedbelow,itisalsopossibletobunchthebeamatanyintegerdivisoroftheacceleratingfrequency.ItisareasonablemetaphortothinkofeachacceleratingperiodofanRFacceleratorasa\bucket",carryingparticleswithinthatperiodforwardthroughtheaccelerator.Ifthebeamisbunchedathalfthefrequencyoftheacceleratingdevice,forexample,theneveryother\bucket"oftheacceleratorwillbeempty.Ofcriticalinterestinthedesignofanybuncheristheacceptanceofthesubsequentbeamline.Theacceptanceisastheregioninphasespacewithinwhichparticles39willbesuccessfullytransportedthroughtheaccelerator.Inparticular,thelongitudinalacceptanceintime/energyphasespaceiscritical;particlesmustbecompressedalongthetimedimensionfromtheirinitialcontinuousdistributionfarenoughtoenterthetimeacceptanceofthemachinewithoutbeinggivensomuchenergytheyexceedthewidthoftheenergyacceptance.3.1IdealBunchingThebasicideaofabuncherissimple:particleswhichwouldarriveearlierthantheoptimumphaseoftheacceleratingdeviceshouldbesloweddown,andparticleswhichwouldarrivelatershouldbespedup,toadegreeproportionatetotheirtimeseparationfromthecenteroftheperiod.(AsillustratedinFigure2.1.)Inthedistancefromthebunchertotheaccelerator,thebeamwillthencometoatimefocus,asthe(now)slowerparticlesatthefrontofthebunchandthefasterparticlesattherearconvergeontheparticleatthecenter.Thisspeedingupandslowingdownisaccomplishedbymeansofanoscillatingelectricdirectedparalleltothedirectionofbeamtravel.Anidealizedbuncherwouldhavethefollowingproperties:Theamplitudeofthelongi-tudinalelectricwouldfollowapure\sawtooth"waveformwithaperfectlylinearrampandaninstantaneousreturntothestartingvoltageatthestartofeachperiod.Thelon-gitudinalwouldbeperfectlyuniforminthetransversedirection;therewouldbenodeviationinstrengthawayfromthebeamaxis.Inaddition,theboostfromthewouldbeappliedoveraninshortdistance,sothateachparticlewouldseenochangeinintimetakentopassthroughthebuncher.Finally,thebuncherwouldbecompletelytransparenttoparticles.40Figure3.1:Comparisonoftheofanidealbuncherwitharealisticbunchingwaverform.Theupperplotsshowthebeambunchedbyaperfectsawtoothwavewithzeroresettime.Thelowerplotsshowabunchingwaveformmadeupoffoursinewaves.Therefore,theidealizedbuncherwouldbeapairofwideplatesclosetogetherapplyinganbunchingvoltage(tocounteractthezerobunchingdistance)viaapairofthinpermeableplanes,withanfastresettimefortheappliedvoltage.Thusfar,nosupplierhasbeenlocatedforsuchadevice.Thepuresawtoothwave,inparticular,isimportant.Ifthevoltagecouldbeappliedwithaninstantaneouschangeofdirectionatthestartofeachperiod,thenalloftheinitialbeamcouldinprinciplebebroughttoafocusinthebunchedpulse(Figure3.1).Thefactthatthisinstantaneouschangeindirectionisimpossibleinpracticeisthedirectcauseofthe\tails"oftheparticledistributioninlongitudinalphasespacevisibleinthesecondlineofplots.Theoftheseunwantedtailswillbediscussedbelow.413.2SimulationofaSawtoothWaveUsingSineWavesAtglance,itmayappearthatthesimplestwaytoapplythebunchingvoltagetothebeamwouldbetoconnectafunctiongeneratorproducingasawtoothwavetoanHowever,theexpectedpeak-to-peakvoltageforourapplicationisintherangeofseveralkilovolts,sopowerrequirementsrenderthisapproachimpractical.Instead,thewaveformistypicallyapproximatedusingacombinationofsinewaveswhichcanbeproducedviaaresonantcavityorresonantcircuit.3.2.1FourierSynthesisConstructingaperiodicfunctionusingaseriesofsinewavesisthewell-knowntechniqueofFouriersynthesis.Toproducethedesiredfunction,aseriesofsinusoidalwavesatintegermultiplesofthefundamentalfrequencyoftheoriginalfunctionareaddedtogetheratcalcu-latedamplitudestoproducethedesiredfunction.ThelistofamplitudesrequiredtoproduceagivenfunctionarereferredtoastheFourierseriesforthatfunction.Whilesomefunctionscanbecompletelyconstructedwithanumberofterms,theFourierseriesformanyperiodicfunctionsareAsanaside,Fourierseries,whichinvolveaddingtogetheronlysineandcosinewavesatintegermultiplesofafundamentalfrequency,cantechnicallyonlyreproducere-peatingperiodicsignals.Toexpressanon-periodicsignalintermsofsinusuoidalcomponentsrequiressinewavesoveracontinuousspectrumoffrequencies,withacontinuous,ratherthandiscrete,amplitudefunction.Theextensionofthetechniquefromasumoverdiscretefre-quenciestoanintegraloverafrequencyspectrumisreferredtoasaFouriertransform.Forthepurposesofthepresentdiscussion,thewaveformtoberepresentedwillbeassumedto42Figure3.2:Asawtoothwavesynthesizedusingthe2,5,and100componentsoftheFourierseries.besinceinpracticethetotallengthofthebunchingsignalismuchgreaterthantheperiodofanindividualrepetition.TheidealsawtoothbunchingwaveformdesiredforparticlebunchingisanexampleofafunctionwithanFourierseriesexpansion.Ifthezeropointofthebunchingwaveformistakentobethetimeorigin,theFourierseriescanbeexpressedsolelyintermsofsinewaves.Theamplitudesofeachmoderelativetothemodeare1,-1/2,1/3,-1/4,etc.Inordertoproduceacompletelyperfectversionofasawtoothwaveusingsinewaves,adevicewouldrequireanitenumberofresonatorswithamplitudessetaccordingtothisseries:f(t)=sin(!t)12sin(2!t)+13sin(3!t)14sin(4!t):::(3.1)=1Xk=1(1)k11ksin(k!t)(3.2)43TheofusingfewercomponentscanbeseeninFigure3.2.Withonlyafewsinewaves,thecentralregionisnotverylinear.Further,thetimeextentofthe\tail"area,wherethevalueofthefunctionisreturningfromtheextrematozero,islonger.Asmorecomponentsareadded,thelinearregionbecomesmorelinearandoccupiesmoreofthefunctionperiod.Evenwith100components,fastoscillationsareobservednearthediscontinuitiesattheendofthewaveform,anartifactknownasthe\GibbsPhenomenon"[35].3.2.2WindowFunctionsSincearealdevicecanonlyusealimitednumberofresonators,theFourierseriesmustbetruncated.Thisistheequivalentofapplyingalow-passtothebunchingwaveform.Thequestionarises:aretheidealamplitudesforatruncatedseriesthesameasthoseforthecompleteseries?Iftheyarenot,whatistheappropriatewaytoaltertheamplitudesforoptimumbunching?Letusrepresentthechangetoeachcomponentasaseriesofcotsak:1Xk=1ak(1)k11ksin(k!t)(3.3)Inthesimplestcase,ifwecompletelyeliminatealltruncatedmodeswhilekeepingtheremainingmodesattheirfullFourieramplitudes,thenakis:ak=8><>:1kn0k>n(3.4)wherenisthenumberofretainedmodes.ely,thisappliesarectangularlow-passtothesawtoothwaveform.Whilethisistheeasiestcasetounderstand,thereisno44Figure3.3:Windowfunctionamplitudevs.normalizedcomponentforseveralwindowfunc-tions.Normalizedcomponent=(componentnumber-1)/(numberofcomponents-1)Plottedhereforn=10components.requirementthatakbesuchasimplestepfunction,andotherfunctionsmayinfactgivebetterresults.Anyarbitrarydiscretefunctionakmaybeusedtodescribetheshapeoftheeappliedandthisfunctionisknownasa\windowfunction."(Inthecontinuouscase,akbecomesa(!).)Thewindowfunctionisalwaysnormalizedtoamaximumvalueof1andhasavalueofzerooutsidethefrequencydomainofinterest.Thereareanumberofpossiblewindowfunctionsdescribedinthesignalprocessinglit-erature[36].Selectionofanappropriatewindowfunctionismadebasedonthedesiredcharacteristicsoftheoutputsignal.Thestepwisefunctionshownaboveisknownasarect-angularwindowfunction,basedonitsshape.AnumberofwindowfunctionsareillustratedinFigure3.3.Atriangularwindowfunction,consistingofalineardecreaseintheweightofeachcom-45ponent,wouldbeexpressed:ak=8><>:n+1knkn0k>n(3.5)AnothercommonlyusedwindowfunctionistheLancoszwindow:ak=8>><>>:sin(ˇ(k1)n)ˇ(k1)nkn0k>n(3.6)Severalwindowfunctionshavetunableparameterswhichcanadjusttheshapeofthewindow.TheseincludetheGaussianwindow:ak=8><>:e(k1)2˙nkn0k>n(3.7)Thepolynomialwindow:ak=8><>:(nk+1n)˙kn0k>n(3.8)AndtheChebyshevwindow:ak=8>><>>:(1)k1cos[ncos1[cos(ˇ(k1)n)]]cosh[ncosh1()]kn0k>n(3.9)=cos[1ncosh1(10)](3.10)Byadjusting˙orinthesewindows,theexactsizeofthewindowcanbevariedwhile46keepingthefundamentalcharacteristicsofeachshape.Theselectionofawindowfunctioncanhaveatimpactonthecharacteristicsofthealsynthesizedwaveform.ThegoalinthepresentcaseistoselectawindowthatallowsthegreatestpercentageofthebeamtoenterthelongitudinalacceptanceoftheRFQafterthebuncher.erentwindowfunctionsresultinlongerorshorterlengthsofthelinearportionofthelbunchingwaveform,andinmoreorless\ringing"attheendsofthewaveform.Inaddition,thebestchoiceofwindowcanvarydependingontheenergyspreadoftheinitialbeam;abeamwithaverynarrowenergyspreadcantoleratemore\ringing"atthecornersbeforelosingbunchedbeamfromtheacceptancewindow.3.2.3ConsequencesofaFiniteNumberofModesRegardlessofthespwindowfunctionchosen,aconsequenceofusingnumberofmodestosimulatethesawtoothbunchingwaveformisthatthereisanonzerotransitiontimefromthemaximumbunchingvoltageattheendofoneperiodtotheminimumatthebeginningofthenext.Duringthattransitiontimewhiletheelectricisslewingbacktothestartingvalueforthenextperiod,thebeamparticlespassingthroughthebuncheraresmearedinto\tails"inphasespace,theconsequencesofwhichareexploredinSection3.4.3.3OtherDeviationsfromtheIdealinaRealBuncherTheprevioussectionexploredthesynthesisofthebunchingwaveform,thereasonswhyitwilldeviatefromtheideal,andtheconsequencesofthatdeviation.Inadditiontodeviatingfromaperfectsawtoothwaveform,arealbuncherdeviatesfromtheidealbuncherdescribedaboveinseveralotherimportantways.47Figure3.4:Sideviewofapairofbuncherelectrodeswithaconical.Thearrowindicatesthedirectionofbeamtravel3.3.1TransverseFieldFlatnessTheidealbuncherconsistsoftwoplanesoftransverseextent,transparenttoparticles.Thesetwoplanes,beingwillhaveaperfectlyuniformacceleratingatallpointsbetweenthem.Sinceanyrealmeansofapplyingvoltageinthedirectionofbeamtravelmustincludesomesortofaperturetoallowthebeamtopass,thisraisesthequestionofhowbesttoequalizetheinthelongitudinaldirectionacrosstheaperture.Sinceanelectricpotentialistobeappliedinthebeamdirection,bunchersgenerallyconsistofasymmetricpairofelectrodeswithanopeninginthecentertoallowforbeampassage,forexample,Figure3.4.Theseelectrodesaregenerallyconicalorcylindrical,andcanemployseveralstrategiesforequalizationacrosstheaperture,aswellasacrossthegapbetweenthem.Theaperturecanbewithgrids,bars,orotherconductingstructureswhichequalizetheappliedvoltage,atthecostofsomeimpedimenttothebeam.Alternately,theaperturecanbeleftopen,andthedeviationsfromhomogeneitywithdistancefromthebeamaxissimplytolerated.Whichapproachispreferabledependsonthecircumstancesoftheindividualdevice.483.3.2TransitTimeFactorAnotherdeviationfromidealityisthetimetakenbytheparticlestotraversetheacceleratingvoltageregion.Anidealbuncherwouldimpartthebunching\kick"toeachparticleinstantaneously,butarealelectricmustbeappliedacrossagap.Andsincetheacceleratingvoltageischangingintime,theactualofthebunchermustbemobyconsideringtheofthechangeofinthetimeittakestheparticletotraversethegap.Thisknownasthe\transittimefactor"(TTF)ismathematicallycalculatedasacotmultipliedtotheoverallenergygainoftheparticleacrossthegap.ATTFof1indicatesthattheparticleseesnochangeinvoltageacrossthegap,andisthereforeonlypossibleforDCATTFofzeroindicatesthattheparticleseesnonetaccelerationacrossthegap,andoccurswhenthetimetakenbytheparticletocrosstheisequaltoanintegernumberofperiods.TheformulafortheTTFis:TTF=sin(!d2v)!d2v(3.11)wherewisthefrequencyoftheappliedvisthespeedoftheparticle,anddisthelengthofthegap.Thisassumesahardedgeddwithnooutsidethegap,andvsmallenoughthatitcanbeneglectedduringthetimetheparticleistraversingthegap.Forthebuncherwhichisthetopicofthisdocument,visontheorderof4%.Physically,theTTFisdirectlyrelatedtoseveralfactors:Astheparticletravelsfaster,thehaslesstimetocycle,andtheTTFgoesup.Asthephysicallengthofthe(determinedbythegapbetweentheelectrodes)increases,theparticletakeslongertocross49thegap,allowingthetocyclefurther,loweringtheTTF.Forvelocitieswhicharehighcomparedto!d,ashere,theTTFdecreasesmonotonicallyasthefrequencyincreases.Assuch,lowerfrequencymodeshavebetterTTFsthanhigherones.Selectionofelectrodephysicalparameterssuchasaperturesizeandgapwidthismostdirectlybythisparameter.3.4SatelliteBunchesWhenparticlesarebunchedatthesamefrequencyastheacceleratorintowhichtheyarebe-inginjected,anyparticleswhicharenotsuccessfullymovedintothetime/energyacceptanceoftheacceleratorwillnotbetransportedthroughtheaccelerator.However,ifthebuncherisoperatingatasubharmonicoftheacceleratorfrequency,thereisapotentialforparticlestoenteranacceptancewindowotherthanthedesiredone.Forexample,anacceleratorwithafrequencyof60MHzbeinginjectedwitha12MHzbuncherhaselongitudinalacceptancewindowsforeachperiodofthebuncher.Figure3.5illustratesthecaseofbunchingatthe5thsubharmonic.Whilethemajorityoftheparticleswillbebunchedintothedesiredacceptancewindow,andmostoftherestwillfalloutsideofanyacceptancewindowandbelost,someparticleswillenteroneoftheundesiredacceptancewindowsandbetransportedthroughtheremainderoftheaccelerator.Theseparticlesformbuncheswhichwillbereferredtoas\satellitebunches."Sincethepointofasubharmonicbuncheristoincreaseseparationbetweenbunchestransportedthroughthelinac,thesesatellitebunchesarepotentiallyproblematiciftheirparticlecountistoohighrelativetothemainbunch.Whatconstitutes\toohigh"isdeterminedonacase-by-casebasis.50Figure3.5:Aplotofthetimeandenergydistributionofasimulatedbeambunchedat16MHz.Thedashedlinesindicatethe2nsacceptancewindowsforadeviceoperatingat80.5MHz.Thereareanumberofpotentialstrategiesforeliminatingsatellitebunches.WhilethedetaileddesignandconstructionofabunchcleanerforReAisbeyondthescopeofthisdissertation,presentedhereareafewpossibleapproachestosuchadevice.‹MoofSourceBeamThemostdirectwaytoeliminatesatellitebuncheswouldbetosimplyshortentheinitialpulsedeliveredtothebuncher(Figure3.6).ThisapproachwouldcombinethesubharmonicbuncherwiththetrapswitchingdescribedinSection2.3.1.InsteadofaconstantDCbeam,ifthebuncherwereinsteadfedwithapulsedbeamshorterinextentthanthelinearportionofthebunchingwaveform,therewouldbenoparticlespassingthebuncherwhilethesawtoothwavewastransitioningfrommaximumtominimum.Assuch,noparticleswouldbepresenttobesmearedintotails.‹requencyCavitiesAbuncherwithagivenfrequencywillcreateabeamstructureatthatfrequency.51Figure3.6:TheofshorteningtheinitialEBITpulse.Atleft,theshortenedpulseafterinteractionwiththebunch.Atright,thebeamatthebuncherfocus.Notailsarepresentbecausetheshorterinitialpulsefallsentirelywithinthelinearportionofthebunchingwaveform.Suchabeamcanonlybetransportedbysubsequentdeviceswithfrequencieswhichareintegermultiplesofthebuncherfrequency.Forexample,theReARFQfrequencyisetimesthefrequencyofthebuncherdescribedinthisdocument.Thisprincipleholdstrueforallsubsequentdevicesaswell-allmustbeintegermultiplesoftheoriginalfrequencytotransportthebunchedbeam.Thiscanbeexploitedbyutilizingdevicesinthebeamlineattwoentintegermultiplesoftheoriginalfrequency.AnexampleisillustratedinFigure3.7.Inthisillustration,thecirclesrepre-sentparticlesatthefundamentalfrequencyofthebuncherandzeroamplitudeistakentobethedesiredpointontheacceleratingwave.Ifthebluelinerepresentsadevicewhichisata5:1frequencyratiowiththebuncher,andtheredlineaseconddeviceata4:1frequencyratio,thebeamstructurefromthebuncherwouldbesuccessfullytransportedthrougheitheroneinisolation.Thisisillustratedbythecirclesfallingatthezeroamplitudepointofbothwaves.Thehollowcirclesintheillustrationrepresentsatellitebunchesproducedinthedevice.Sincetheyareatthezeroamplitudepointofthedevice(blueline),theywouldbetransportedsuccessfullybythatdevicealone.However,theseconddevice52Figure3.7:Bunchcleaningbyanfrequencycavity.Theredlineisata4:5frequencyratiowiththeblueone.Blackdotsrepresentbeamparticlesatathezerophaseofbothfrequencies.hasa4:5frequencyratiowiththeone.Thismeansthat,assumingtheacceptancewindowsarealignedinphasefortheprimarybunchtotransitbothdevices,theywillbeoutofphaseforthesatellitebunches.Particleswhicharriveateitherdeviceoutofphasewillnotreceivethesameamountofaccelerationastheprimarybunch.Sincethesebunchesareunwanted,thisaccomplishesthegoalofcleaningsatellitebunchesbymovingunwantedbunchesawayfromthetargetenergyoftheprimarybunch.Thesebunches,now,willfailtotraversesubsequentbendingelementswhicharetunedforthereferenceenergy.ThisisthebunchcleaningstrategyemployedbytheATLASacceleratorcomplexatANL(See3.5.2below).‹BeamChoppersAmoredirectapproachistosimplypushtheundesiredbunchesaxisusinganelectricSuchadevicegenerallyconsistsofapairofparallelplatesapplying53avoltagethatvariesfromzeroatthemainbunchtoamaximumattheundesiredbunches.Thebunchesarethenstoppedbyaslitinsertedfartherdownthebeamline.Thedevicemustbeabletoapplytvoltagetoresolvethesatelliteandmainbunchesatthelocationoftheslit,andmustbeabletocyclequicklyenoughtoleavethemainbunchuntouchedwhilethesatellites.Thesimplestchoppingwaveformconceptuallywouldbeaconstantvolt-agethatturnswithasquarepulseforthebunchtobetransmitted.Duetothefastrisetimesitisoftenmorepracticaltouseasinusoidalchoppingwaveformandaccepttheadditionalbunchingandconcomitantenergygrowthofthemainbunch.Amorecomplicatedformofthetransversechopperisthe\striplinechopper"[37],whichallowsthesquarepulsetobeappliedoveralongerdistance,thusloweringtherequiredvoltage.‹StorageRingsThemostcomplicatedapproachtobementionedhereisastoragering.Asmallstorageringinsertedintothebeamlinewouldallowtrainsofionsfromtheionsourcetobestoredandcompressedintimebeforebeingsenttothebuncher.Thishasthesameadvantageofthemoofthesourcebeamapproachabove,inthatthebuncherwouldnotreceiveanyparticlesoutsideofthelinearportionofthebunchingwaveform.Italsoallowsforalongerspacingofbunches,sincetheringcanreleasethestoredparticlesatasubharmonicofthebuncheritself.Ithasthedisadvantageofbeinglogisticallyverycomplex.543.5CaseStudiesDescriptionsoftwoexistingmultiharmonicbunchersarepresentedhereasillustrations.3.5.180.5MHzMultiharmonicBuncheratReATheReAcceleratoratNSCLisdescribedinSection1.1.6above.ThesourcebeamisprovidedbyeitherviaanElectronBeamIonTrap(EBIT)orateststableionsource.Inparticular,theEBITisusedtostoreandchargebreedradioactiveionbeamsfromthecoupledcyclotronfacilityatNSCL,andinthefuturefromthelinearacceleratorofFRIB.Ineithercase,theinputbeamhasanenergyof12keVpernucleon(keV/u).Thebeamisacceleratedbya4-rodtypeRFQandtheninasuperconductingRFlinearaccelerator,bothatafrequencyof80.5MHz.TheinputbeampulsefromeitherthetestsourceortheEBITistlylongthatitmaybeconsideredcontinuouscomparedtothe12.4nsperiodoftheacceleratorRF.PriortoinjectionintotheRFQ,thebeamisbunchedbyamultiharmonicbuncheratthe80.5MHzfrequencyoftheaccelerator.TheMHBsynthesizesitsbunchingwaveformfromthefundamentalfrequencyandtheharmonic(161MHz)oftheacceleratorfrequency.Eachmodeisproducedina4modecoaxialresonatingcavity.Asinitiallydesigned,the80.5MHzcavitywasalsointendedtobeexcitedinthe34modetoproduceasecondovertone(241.5MHz),butthismodeprovedtotuneproperly,andisnolongerused.Theelectrodesusedtoapplythevoltagetothebeamhavealsoundergoneseveralchangesfromtheoriginaldesign.Asoriginallyconceived,theelectrodeswereapairofcoppercylin-derswithawiremeshacrossthefacestoequalizetheThewiremeshproved55susceptibletodamagefromthebeam,andin2013theelectrodeswerereplacedwithcylin-derswithsolidfacesanda1cmapertureinthecenterofeach.Theseaperturescontainedverynarrowbarsalignededgeontothebeam,intendedtoequalizetheelectricacrosstheaperture.Astherequiredvoltageforbeambunchingdidnotchangeafterthereplace-mentoftheelectrodes,itcanbeinferredthatthebarsareindeedprovidinganequivalentHowever,thesmallerapertureandphysicaldimensionsofthebarsdidposeamoresubstantialchallengeforbeamtuning.SincetheMHBisattheRFfrequency,thisbuncherhasnoissueswithsatellitebunches-12.4nsofinputbeamarebunchedintoeachRFQperiod,or\bucket."Thesmallportion(ˇ15%)ofthebeamwhichseesthebunchingwaveformwhileitisresettingfromhightolowformsatailwhichislargelynottransportedbytheRFQ.3.5.212.4MHzMultiharmonicBuncheratATLAS(ANL)TheATLASacceleratoratArgonneNationalLaboratoryisalsoaheavyionaccelerator,fedbyeitheranECRstableionsourceorbytheCARIBUradioactiveionsource.Ineithercase,theinputbeamhasanenergyof30.5keV/uandiselyDC.Theacceleratorconsistsofa60MHzRFQ,aseriesofsplit-ringtypeSRFcavitiesat72.75MHzand97MHz,andthencryomodulescontaininganumberof4SRFresonatingcavitiesat72.75MHzand109.125MHz[38].BeforetheRFQ,thebeamisbunchedbyaMHBwithafrequencyof12.125MHz[39].Unlikethe80.5MHzMHBinReA,thisbuncherisatthesubharmonicoftheRFQ.Thelowerfrequencyallowsthebunchingvoltagetobegeneratedusingaresonanttankcircuit,ratherthanacoaxialcavity.Thisbuncheremploysthethreeharmonicsofthebunchingfrequencyinadditiontothefundamental(12.125,24.25,36.375,and48.5MHz)tosynthesize56thebunchingwaveform.SincethebunchingperiodislongerthantheRFperiodfortheRFQ,somebeamdoesentertheacceptancewindowforadjacentbucketstothemainbucket,andthusformssatellitebunches.However,sincethe15acceleratingcavitiesareateithera6:5or8:5frequencyratiowiththeRFQ,theoutofphasebunchesarestronglyfromtheenergyofthecentralbunch,anddonottransportthroughthebendaftertheacceleratingsection.TheelectrodesoftheATLASMHBhavebothanaperturewidthandanelectrode-to-electrodegapdistancewhichislargerthantheReA380.5MHzMHB.TheATLASelectrodesarealsocompletelyopen,withnogridsorbarstoequalizethePracticalexperiencewiththedevicehasshownthatgoodbunchingcanstillbeachievedwiththiselectrodedesigninthisfrequencyrange.57Chapter4MeasurementoftheLongitudinalAcceptanceoftheReARFQThemosttpotentiallimitationontheparametersofabeambuncheristheaccep-tanceofthedevicesdownstream.Aslongasthelongitudinalphasespaceareaisconserved,itispossibletocompressaportionofbeamtoanarbitrarilyshortduration,atthecostofanincreasedspreadinbeamenergyandincreasedbunchingvoltage.However,thelongitudinalacceptanceofatypicalacceleratingdeviceisnotsolelyone-dimensionalintime;thereisalsoanenergycomponent.ParticleswhichdeviatetoofarfromthereferencephaseORthereferenceenergywillnotbetransported.Thus,inordertodetermineacceptableparametersforabunchingdevice,itisessentialthatthefulltwo-dimensionallongitudinalacceptanceofdownstreamdevicesbewellunderstood.InthecaseofReA,thenextdevicewithalongitudinalacceptancewindowdownstreamfromtheproposedbuncherlocationistheroomtemperatureRadioFrequencyQuadrupole(RFQ)whichservesasaninjectortothesuperconductinglinac.WhiletheRFQhadbeenextensivelysimulatedpriortothiswork[19],theacceptancehadnotbeenempiricallymea-sured.AnimportantprerequisitetobuncherdesignwasthereforeadirectmeasurementoftheshapeoftheRFQacceptancewindowinlongitudinalphasespace.Sinceabuncherhasinprincipleverylittleonthetransversedynamicsofthebeam,directmeasurementof58Figure4.1:Asimpleillustrationofalongitudinalacceptancewindow.thetransverseacceptancewasnotperformed.Thus,theobjectiveofthismeasurementwastodeterminethelongitudinalacceptanceoftheRFQ;thatis,ifanincomingparticlehasphase˚relativetotheacceleratingphaseoftheRFQandenergyE,forwhatvaluesofEand˚willitbesuccessfullyacceleratedbytheRFQ,andforwhichvalueswillitfailtobeaccelerated?Thiscanbevisualizedintermsofa\window"onaplotofenergyvs.phase.(Figure4.1)TheresultsofthismeasurementwerepresentedasaposterattheInternationalParticleAcceleratorConference2014inDresden,Germany[40].4.1MeasurementMethodologyMeasurementwasconductedusingastablebeamofH+2fromthetestsourcelocatedupstreamoftheRFQandtheexisting80.5MHzMHB.Whenunbunched,thisbeamhasaverylowenergyspread(˘18eVRMSforH+2),andanadjustablecentralenergy,makingitasensitiveprobeoftheenergywidthoftheacceptancewindowoftheRFQ.Withthebuncheractive,thebuncheshaveanarrowtimespreadattheentranceoftheRFQ,making59themgoodprobesforthephasewidthoftheacceptance.4.1.1TotalTransmissionAsAFunctionofEnergyThephaseofthemeasurementusedthisbeamasaprobefortheoveralltransmissionoftheRFQasafunctionofbeamenergy.Tominimizetheenergyspreadofthebeam,theMHBwasturnedforthisportionofthemeasurement.Thiswouldneverbedoneundernormalconditions,asmuchoftheunbunchedbeamfallsoutsideofthephaseacceptanceoftheRFQandthereforeisnotaccelerated.Inthiscase,however,amplebeamcurrentwasavailablefromthetestsourceandthenarrowenergyspreadwasessentialforaprecisemeasurementoftheenergyacceptance.Thebeamwassettothedesignenergyof12keV/uandtheRFQ,linac,andsub-sequentbeamlinetunedformaximumtransmission.Thebeamlinebetweentheendofthelinacandthemeasurementpointincludedtwomagneticdipoles.Thispointisimportant,becauseitallowedthedipolestobeusedtooutunacceleratedbeamparticles.Thedipolesweretunedforabeamwitharigiditycorrespondingtoanenergyof600keV/u,thedesignoutputenergyoftheRFQ.ThebeamcurrentwasthenmeasuredonaFaradaycupdesignated\L130".Theacceleratingcavitiesinthelinacwereturnedfortheentiretyofthismeasurement,althoughthesolenoidswereusedforfocusingthebeam.Atthetimeofthemeasurement,thethirdcryomoduleoftheReAcceleratorhadnotyetbeeninstalled.Thesemeasurementswerethenrepeatedatanumberofotherbeamenergies(Figure4.2).Ateachenergy,thebeamlinewasretunedformaximumtransmissiontoL130.Bymeasuringtotaltransmissionfortheunbunchedbeamateachenergy,apictureofthephasewidthofthelongitudinalacceptanceatvariousenergieswasbuiltup.Whilethebeamlinewastunedforeachenergy,thephasemeasurementdescribedin4.1.2belowwasalsoperformed.60Figure4.2:WiththeMHBturnedthetransmissionthroughtheRFQwasmeasuredatanumberofenergiestogiveapictureoftherelativetransmissionateachlevel.Onthedayofmeasurements,afterthereferencecurrentat24keV/uwasestablished,theinputbeamwasadjusteduntilthemeasuredtransmissionontheL130Faradaycupreachedadesiredfractionoftheoriginalbeam,suchas50%.Sinceadjustingtheenergyoftheinputsourcealsotherigidityofthebeam,andthusthetuningoftheaccelerator,thiswasactuallyaniterativeprocesstoreachthedesiredleveloftransmission-thesourceenergywaschanged,thebeamlineretuned,thesourceenergychanged,etc.untiltheoperatorwastthatthelowestpossiblebeamenergywith50%transmissionhadbeenreached.Oncegoodtuneswereestablishedfortheacceleratoratarangeofenergiesusingthisprocess,moremeasurementsweretakenbysimplyscalingthebeamlineandinputsourcevoltageupanddown.Whilenotiterativelyretuningforeachmeasurementmayhaveresultedinsomebeamloss,periodicchecksweremadetoseeifincreasedtransmissioncouldbeachievedbeyondsimplescaling,andnotincreasewasfound.61Figure4.3:WiththeMHBturnedon,thetransmissionthroughtheRFQwasmeasuredatanumberenergiesandthroughafull360degreesofphase,givingaseriesoftransmissioncurves.4.1.2TransmissionasaFunctionofPhaseandEnergyAfterthebeamwastunedforeachenergyandthetotaltransmissionmeasured,theMHBwasturnedbackon.Thisalteredthebeamfromonewithacontinuousphasedistributionandnarrowenergyspreadtoonewithamuchwiderenergydistributionandanarrowtimespread.TherelativephasebetweentheMHBandtheRFQwasthensweptthroughafull2ˇofphase.(Inpractice,itprovedeasiertoadjustthephaseoftheRFQthantheMHB,butsincetherewerenootherRFelementsinvolvedinthemeasurement,thisdistinctionisirrelevant.)ThebunchingamplitudeoftheMHBwasnotalteredformeasurementsattenergies.ThetransmissiontotheL130Faradaycupwasmeasuredasafunctionofthisrelativephase(Figure4.3).Thisgavetheshapeofthetransmissionasafunctionofphaseforthatenergylevel.ItisimportanttonotethatwhiletheenergyprobewasextremelynarrowE=Eˇ0:001),thetimeprobewasnotasfocused.˚=2ˇˇ0:16)Theexactshapeofthebunchedbeaminlongitudinalphasespacewasalsolikelynotapureverticalrectangle.62E=Eo(%)Transmission(%)-11.525-8.850-6.870-4.590-4.0102-2.099.801001.9999.93.9998.95.87909.196612.475015.5925Table4.1:SummaryofbeamtransmissionthroughtheReARFQasafunctionofdeviationfromthereferenceenergy.Despitetheselimitations,areasonablyclearpictureoftherelativetransmissionasafunctionofphaseforeachenergylevelwasobtained.4.2AnalysisandResults4.2.1EnergyMeasurementOnlyThestageofbuildingapictureofthewindowusesonlythemeasurementsoftheunbunchedbeam.ThetransmissionpercentageateachenergyisshowninTable4.1andFigure4.4.Thispercentageisnormalizedto100%transmissionatthereferenceenergy.Withjustthesemeasurements,itispossibletoconstructaapproximationoftheacceptancewindow.Sincenophaseinformationisyetbeingincorporated,thismodelmustassumethatthetransmissionasafunctionofphaseisperfectlysquare.Inotherwords,if50%oftheparticlesaretransmitted,themodelassumesthatthephasewindowis180degreeswide,andsymmetricaboutzerophase.Italsoassumesahardedge-allparticles63Figure4.4:RFQbeamtransmissionvs.inputenergyforReARFQ.withinthephasewindowtransmitted,andnoneoutsidethewindow.Forexample,atthereferenceenergyof12keV/u,theratioofbeamcurrentatL130totheinjectedcurrentwasmeasuredtobe0.4.Therefore,theequivalentwidthofthetransmissionwindowatthereferenceenergyistakentobe360°0:4=144°or4.96ns.Theerroronthetransmissionisestimatedasfollows:Thedominantsourceoferrorinthetransmissionateachenergyisassumedtobetuning.Whilethebeamlinewasbeingtunedbyanexperiencedoperator,duetotimerestrictions,oncethetransmissionappearedtobenearamaximumforeachenergy,tuningwashaltedandameasurementwastaken.Areasonablyconservativeestimateforthefurthertpossibleateachlevelisanincreaseofupto5%intransmission.Sincethiserrorwasalsopresentfortheoriginalmeasurementagainstwhichtheothersarecompared,anerrorof+/-10%isassumedinthetransmissionamount.(Thisalsoexplainshowarelativetransmissionpercentagegreaterthan100%canbecomputedforameasurementawayfromthereferenceenergy.)ThisnaiveacceptancewindowisshowninFigure4.5.64Figure4.5:NaiveRFQacceptancewindowwithnophasemeasurementortcorrection.Figure4.6:Threephasescansattenergies.65Figure4.7:ThesimulatedacceptanceoftheReARFQ.Thewhiteareaatthecenterrep-resentsparticleswhichareacceleratedbytheRFQ,andtheredareashowsparticleswhicharenottransported.4.2.2CombinedEnergyandPhaseMeasurementPlottingtheacceptancewindowbasedentirelyontotaltransmissiongivesareasonableapproximationoftheenergywindow,butthephasedependentdatagatheredateachenergylevelallowsforasomewhatmoredetailedpicture.Asthebunchedbeamateachenergywassweptinrelativephase,thebeamtransmissionwasmeasuredasafunctionofthatphase.Figure4.6showsseveralmeasurementsofthetransmissionduringaphasesweep.Thetransmissioncurveforeachenergyisnormalizedtoamaximumof1.Oneinterestingfeaturethatisapparentinthehighestenergycurveissecondpeakinthephasedistribution.ThisadditionalpeakispredictedbythedynacsimulatedacceptancewindowshowninFigure4.7,buthadnotpreviouslybeendirectlyobservedforthismachine.Thereareanumberofimperfectionsinthismeasurementthatarenotpresentintheenergymeasurement.Aperfectversionofthismeasurementwouldrequirebeambuncheswithbothverynarrowenergyandtimespreadstogivethebestpossibleresolutiontothe66measureddata.Whenthebeamisbunched,thetimedistributionofthebeamisanapprox-imatelyGaussianshapewithawidthofˇ2ns.Assuch,eveniftheRFQphaseacceptanceforagivenenergywereaperfectstepfunction,wewouldstillexpecttoseeagradualriseandfallintransmissionasthebeamphasewassweptacrosstheacceptance.Further,thebunchedbeamhasacomputedenergyspreadontheorderofˇ2%.Sincethephaseacceptancewidthnarrowsfartherfromthereferenceenergy,themeasuredtransmissionwillseeagreatercontributionfromtheportionofthebunchwithenergyclosertothereference.Bothofthesedeviationsfromtheidealmeasurementcouldinprincipleberesolvedgivenaperfectknowledgeoftheexactlongitudinalphasespaceshapeoftheprobebeam.SuchashapecouldtheninprinciplebedeconvolvedwiththemeasuredtransmissiontogiveafullyaccuratepoftheRFQwindow.However,nosimplewaytomeasurethefull2Dofthebeaminlongitudinalphasespacewasavailable.Instead,thephaseacceptancewidthwillbehereasthefullwidthofthetransmis-sioncurveatwhichthetransmissionisonehalfofthemaximumtransmissionatthedesignenergy.Inotherwords,ifthemaximumcurrentreadontheFaradaycupatthedesignenergyis500pA,thenthephaseacceptancewidth˚istobethebetweenthephases˚and˚+wherethecurrentreadis250pA.Thisvalueofcurrentisappliedateveryenergylevel,sothat˚=˚+˚becomessmallerasthebeamenergyismovedawayfromthedesignenergy,andeventuallyreacheszerowhenthemaximummeasuredcurrentdropsbelowhalfofthevaluemeasuredatthedesignenergy.ThemeasuredphasewidthsbyenergyareshowninTable4.2.Thefollowingparagraphsareavisualillustrationofthesameinformation.Usingthisinformation,afull2Dmodeloftheacceptancecanbeconstructed.First,thephasecurvesaresuperimposed(Figure4.8).Then,thephasesareadjustedsothatthe67E=Eo(%)PhaseWidth(°)PhaseWidth(ns)Phase(ns)-11.5000.739-8.8401.4-0.284-6.8752.60.325-4.51053.6-0.16501404.8-5.87953.3-0.8759.19702.4-0.45612.47501.7-1.1615.600-0.291Table4.2:WidthofphaseacceptanceatvariousenergiesfortheReARFQ,alongwiththemeasuredphasesets.maximumtransmissionofeachcurveisalignedatzero(Figure4.9).Figure4.8:Allphasemeasurmentssuperimposed.Eachcurveisnormalizedtoamaxofone,andphaseunitsareunadjusted.Next,eachindividualcurveisscaleddownbytherelativetransmissionatthatenergylevelfromFigure4.4,asshowninFigure4.10.Finally,the50%transmissioncontouroftheinterpolatedsurfaceinFigure4.10canbeextracted.ThisallowsFigure4.5tobeupdatedtoshowmeasureddeviationsfromzerophase,insteadofassumingasymmetric,hard-edgedtranmissionTheresultisshown68Figure4.9:Thephasecurvesin4.8withthemaximumtransmissionforeachenergyalignedatzerophase.Figure4.10:Phasecurveswithzeroesalignedandscaledbyoveralltransmissionateachenergy.ThesecondisaninterpolatedsurfacegeneratedfromthedatapointsintheinFigure4.11,overlaidonthesimulatedRFQacceptancewindowfromdynacwhichwasusedintheremainderofthisproject.ThiscontouristheequivalentofinterpolatingbetweenthedatapointslistedinTable4.2.Onefurthercorrectioncanbeapplied.Beamparticlesattenergiesarenaturallytravelingatdtvelocities,meaningthattheirarrivaltimesattheRFQarealsot.69Figure4.11:AcontourplotofthemeasuredacceptancesurfacefromFigure4.10,withthe50%transmissioncontouremphasized,overlaidonthesimulatedacceptance.TheactualtimeoftfromthebunchertotheentranceoftheRFQforeachenergycanbecalculatedfrombasicdynamics.Assuch,foreachenergyawayfromthereferenceenergy,apredictedenceintimeoft,tof,canbecalculatedbasedsolelyontheinenergy.ThisisthenconvertedtoapredicteddinRFphase(indegrees),˚˚=toff360:(4.1)wherefistheRFfrequencyoftheaccelerator.tofisfoundbytof=LvoLv:(4.2)HereListhedistancefromthebunchertotheRFQ,voisthevelocityofthereference70dE/E(%)v(m/s)MHB-RFQtoftof(ns)˚(°)-11.51.0000114021431618508.306-30.094-872.127-8.81.0000117461453032500.815-22.602-655.034-6.81.0000120051468975495.38-17.167-497.522-4.51.0000122991486865489.419-11.207-324.786-4.01.0000123661490877488.102-9.890-286.617-2.01.0000126231506327483.096-4.883-141.53701.0000128831521711478.212002.01.0000131391536760473.5294.683135.71514.01.0000133961551753468.9549.258268.30365.91.0000136381565715464.77213.440389.49579.21.0000140661590073457.65220.559595.821612.51.0000144891613776450.9327.281790.62415.61.000014891636004444.80333.408968.1759Table4.3:Calculatedtofand˚valuesfromtheMHBtotheRFQrelativetothereferenceparticle.particle,andvistheparticlevelocity.ThesevaluesaresummarizedinTable4.3,whererepresentstherelativisticgammaoftheparticlegivenby=Emc2+1:(4.3)(Asareminder,Erepresentskineticenergythroughoutthisdocument.)Thesecalculatedphaseatvariousenergylevelscannowbecomparedwiththemeasureddata.WhilenoinformationisavailableontheabsolutetimeoftfromtheMHBtotheRFQ,wecancomparetherelativephasesbetweenthepeakphaseofeachmeasurement,andthepeakphaseatthereferenceenergy.TheserelativephasescanthenbecomparedwiththepredictedphaseshowninTable4.3.Sinceourobservedphasesareallintherangeof0-360,wecaneithercomparerelativephasesmodulo360oraddorsubtractintegermultiplesof360tocorrespondtothevaryingvelocities.Figure4.12comparesthepredictedversusobservedphaseadvancesinthelattermannerforeaseof71Figure4.12:Measuredandpredictedphaseadvancesrelativetothereferenceenergyforthephasemeasurements.visualization.Foranidealmeasurement,allofthebetweenthecalculatedandmeasuredphaseadvancescanbeattributedtoa\tilting"oftheacceptancewindowonthephaseplot.Ifthepeaktransmissionphaseisobservedtoarriveearlierthanpredicted,thewindowisshiftedearlierforthatenergy.Ifthepeaktransmissionphaseisobservedlater,thewindowisshiftedlater.Foraperfectmeasurementwithawindowfollowinganlinear\tilt"theinphaseadvanceswouldbeexpectedtofollowalineartrendwithenergy.Unfortunately,whilethistrendissomewhatvisibleintheactualdata,thereisagreatdealofdivergencefromasmoothlinearincrease,asseeninFigure4.13.Thereareanumberofpossibleexplanationsforthisdivergencefromideality:theshapeoftheprobebeamiscertainlynotaperfectverticalrectangle,andneitheristheacceptancewindow.Further,theMHBwasnotreoptimizedforbesttransmissionatthevariousenergylevels.IftheshowninFigure4.13areappliedtothephasesofthemeasuredtransmissioncurvesdespitethenoise,theresultingacceptancewindowisshowninFigure4.14.Comparing72Figure4.13:Foreachenergy,thefromthepredictedrelativephaseadvance.thiswiththeuncorrectedcontourplotinFigure4.11thewindowdoesdisplayatiltonthesameorderasthepredictedtiltfromsimulation.4.2.3ErrorEstimatesForthemeasurementoftransmissionusingtheunbunchedbeam,itisunlikelythattherewasterrorinthebeamenergy.Thepowersupplyregulatingtheionsourcehasbeenmeasuredtovarybylessthanˇ0.1%.Alargersourceoferrorinthetransmissionrateresultsfromthetuningofthebeam.Whilethebeamlinewasretunedformaximumtransmissionateachenergylevelbyanexperiencedoperator,thereisnonethelessapossibilitythatgreatertransmissionwouldhavebeenpossiblegivenfurthertuning.Thereforethemeasuredtransmissionateachenergylevelshouldberegardedasaminimum.Areasonableestimatewouldbethatthetransmissionachievedateachlevelwaswithin5%ofthemaximumachievable.Duringthephasescans,thephaseoftheRFQrelativetotheMHBwasincreasedinincrementsofedegreeseverytwoseconds.Theerrorin73Figure4.14:Thecontourplotofthemeasuredacceptancesurfacewiththetcorrectionapplied,overlaidonthesimulatedacceptance.phaseforeachmeasurementwasthusestimatedasonephaseincrementor5degrees.However,ashasalreadybeennoted,thiserrordoesnotincludetheirregularshapeoftheprobebeam,andisalmostcertainlyalowerbound.4.2.4ImplicationsfortheBuncherWhileitisdisappointingthatthetimeshapeofthebunchercouldnotbemeasuredmoreprecisely,theactualresultsofthemeasurementforthisprojectweredeemedtobehighlyencouraging.Boththetimeofightcorrectedanduncorrectedmeasurementsshowedanacceptancewindowsomewhatlargerthanthehard-edgedwindowofthesimulation.Inaddition,thepureenergymeasurementshowedatleastthepossibilityfor100%transmissionrelativetothereferenceenergyoutto5%awayfrom12keV/u,givenanappropriatetimestructureoftheinjectedbeam.Asthedynacsimulatedacceptancewindowshownintheaboveissmallerthanthemeasuredacceptancewindow,thesemeasurementsvalidatedusingthesimulationasa74conservativeconstraintonbuncherparametersgoingforward.Arealacceptancewindowdoesnothavethehardofthesimulation,butsincethehardedgeinthiscaseisdisplacedinwardfromthemeasuredtransmissioncontour,itseemssafetoconcludethatmostparticleswhichpassthroughthesimulationarealsolikelytopassthroughtherealmachine.75Chapter5SimulationandSelectionofDesignParametersFromabeamopticsstandpoint,abuncherisarelativelysimplydevice.Intheidealcase,ithasnotransverseonthebeamatall,andappliesasimplesawtoothaccelerat-ing/deceleratingvoltageinthelongitudinaldirection.Inthiscasetheonlyoutputparam-eterswhichmustbechosenaretheacceptabletimeandenergyspreadofthepulsesatthebuncherfocus,andthefrequencyofthebunchedbeam.Theonlyinputparameterswhichneedtobechosenforthisidealbuncherarethefocallengthandvoltageneededtoachievethedesiredoutput.Further,thosetwoparametersarenotindependent,asoutlinedbelowinSection5.3.Forarealisticbuncher,inadditiontothefocallengthandbunchingvoltage,additionalquestionsmustbeconsidered.Whatshapeshouldbechosenfortheelectrodesapplyingthebunchingvoltage?Whereisspaceavailableonthebeamlinetoinstallthedevice?Howcantheappropriatefrequenciesbeappliedtotheelectrodes?Whatamountofpowerispracticallyavailabletodrivetheelectrodes?Whatisthemaximumamountofbeamwhichcanbeallowedtofalloutsideoftheacceptanceoftheaccelerator?ThischapterwilldescribetheprocessbywhichthesedesigndecisionsweremadefortheReA16.1MHzbuncher.765.1ReABeamlineSimulationSincethepurposeofaparticleacceleratoristosupplybeamtousers,thejudgmentonthectivenessoftheacceleratorrestsonthequalityofthatbeamatthedetector.Therefore,inordertoevaluateanyproposedchangetoanaccelerator,itisimportanttobeabletoevaluatetheofthatchangeatthedetectorfocus.(Forsimplechanges,itwouldbettoshowonlythatthebeamcouldbereturnedtoitspriorstateatsomepointbeforetheendoftheline,butthatismanifestlynotthecasehere.)Inordertoensurethattheofthebuncheronthebeamatthedetectorswaswellunderstood,itwasnecessarytosimulatetheentireReAbeamlinefromtheinjectionofthebeamfromtheEBITtothedetectorsintheexperimentalhall.Thissimulationprovedchallengingforseveralreasons.First,thereareawiderangeofdevicesalongthisline,includingelectrostaticandmagneticquadrupolesanddipoles,anRFQ,15two-gapacceleratingcavities,aswellasthebuncheritself.TheRFQinparticularposedaparticularlythornysimulationchallenge,asitscomplicatedgeometryrequiresspecializedsoftwareforsimulation.Further,sincebunchersbyoperateinthetimedomain,anysimulationmustproperlyaccountforlongitudinaldynamicsatmultiplefrequencies.Finally,whilemanyofthesedevicescanbeapproximatedbysimpleanalyticalmodelssuchasthoseinSection1.2,amoredetailednumericaltreatmentisrequiredincertainareas,suchastheSRFcavitiesandforevaluatingspbuncherelectrodegeometries.Anumberofcodesareavailableforbeamlinesimulation,andseveralarecomparedindetailinAppendixA.Inordertolimitpotentialsourcesoferror(aswellastimeanditwaspreferabletouseasfewcodesaspossible.Wherenecessary,asimulatedparticledistributioncanbeextractedfromonecodeandinputtoanother,butonegoalwastokeep77Figure5.1:AsamplelongitudinalmodelofReAfromtheEBITtothedetectorhall,showingxandyenvelopes,particlecount,referenceparticleenergy,andthelocationsofbeamlineelements.thistypeofcodeswitchingtoaminimum.Forthisprojecttheprimarycodeselectedwasdynac[41].dynachastheadvantageofbeingabletosimulatetheentiretyofReA,includingallbeamlineelements,fromtheexitoftheEBITtothedetectors.Anend-to-endmodeloftheReAlinewascreatedusingdynac,andusedtotesttheresultofvariousbuncheratthedetector.AsamplelongitudinalplotofvariousbeamparametersproducedinthismodelisshowninFigure5.1.Overthecourseoftheproject,agraphicalfrontendtodynacwasalsodevelopedusingthematlabenvironment.Thisfrontend,dynacgui,isdescribedinAppendixB.Othercodeswereusedfortasksunsuitedforexecutionindynac.Thecodetrack,developedatArgonneNationalLaboratory[39],wasusedformodelingtheofspbuncherelectrodegeometries.trackhastheadvantageofbeingabletouse3Dnumericalmodelsforbeamlineelements,inadditiontobasicanalyticmodels.TheuseoftracktoselectelectrodegeometryisexploredinSection5.5.trackwasnotselectedastheoverallcodeofchoicebecausewhileitdoespossesstheabilitytosimulateRFQs,itprovedtoochallengingtotranslatetheRFQspfortheReARFQintotrack'sformat.Other78codeswereusedfortasksunsuitedforexecutionindynac.Thecodetrack,developedatArgonneNationalLaboratory[39],wasusedformodelingthectsofspbuncherelectrodegeometries.trackhastheadvantageofbeingabletouse3Dnumericaldmodelsforbeamlineelements,inadditiontobasicanalyticmodels.TheuseoftracktoselectelectrodegeometryisexploredinSection5.5.trackwasnotselectedastheoverallcodeofchoicebecausewhileitdoespossesstheabilitytosimulateRFQs,itprovedtoochallengingtotranslatetheRFQspfortheReARFQintotrack'sformat.Onetaskthatisoftencalledforinopticssimulationistheofcertainbeamlinesettingstoachieveadesiredresult,suchasminimumtransversefocusatadetector.dynachasnointernalcapability,sothecodecosy[23]wasusedinsomecasestomakepre-liminarycosyhasexcellentinternalcapabilities,butunfortunatelythepubliclyavailableversionsarenotideallysuitedtomultiplefrequencystructuresinthetime/energydomain.Whereneededtobedoneusingthedynacmodel,anextensiontodynacguiwasdevelopedusingmatlabtodoautomatedusingmatlab'sinternaltoolstocalldynacasanexternalfunction.Finally,otherprogramsweresometimesusedforspecializedtasks.Thesewillbemen-tionedintheappropriatesections.5.2BuncherFrequencyAsdiscussedin2.3.2,itispossibletobunchthebeamatanyintegerdivisorofthefrequencyofthesucceedingelements.Ifthereferencefrequencyoftheacceleratorisfrf,withacorrespondingperiodof˝rf,thenbunchingatsubharmonicnentailsafrequencyoffrf=n,andaperiodofn˝rf.Aapproachtofrequencychoicemightthenbetoselectthe79Figure5.2:Schematicillustrationofbunchingatseveralntsubharmonics.Eachplotshowsenergyvs.time.Thecolumnshowstheinitialbeam,thesecondcolumnthebeamimmediatelyafterbunching,andthethirdcolumnshowsthebeamatthefocus.desiredbunchseparation˝andcalculatethenearestappropriateintegern.However,thereareconstraintsonsuchaprocedure.Largervaluesofnand˝correspondtobunchinglongersegmentsofthecontinuousbeam.Thelongerthebeamsegmenttobebunched,thegreaterthepositiveandnegativevoltagesrequiredtobringthefore-andrearmostparticlestoafocusinagivendistance,correspondingtoagreaterenergyspreadinthebeam.Ifthevalueofnchosenistoohigh,itmaynotbepossibletobringtheentirebeamtoafocuswithintheenergyacceptanceoftheacceleratoratall.Thisisillustratedin5.2,whichshowsasimplemodelofenergyvs.timeforanoriginallycontinuousbeam.Thelineillustratesbunchingwithn=1,atafrequencyoffrf.Column1showsthebeambeforebunching.Column2illustratesthebeamimmediatelyafterbunchingatfrf.Theparticleswithpositivephase(i.e.,behindthecenterofthebunch)havebeenincreasedinenergy,andthosewithnegativephasehavebeendecreasedinenergy.Thecolumnshowsthebeamatthefocusofthebuncher,wherethetrailingparticleshavecaughtupwiththecenterofthebunch,andtheleadingparticleshavefallenbackto80thecenter.Thebunchseparationisthesameasthebunchingperiod,˝.Thesecondandthirdrowsshowbunchingatlowersubharmonics,n=2andn=5respectively.Inordertobunchmorebeaminthesamefocallength,theleadingandtrailingendsofthebunchmusthavetheirvelocityalteredbycorrespondinglylargeramounts,leadingtoalargerenergyspread.(Thephaseofthediagraminthethirdrowhasbeenshiftedby180°relativetotheothersinordertoshowtheseparationbetweenbunches.)Ineachcase,thebunchseparationatthefocusisn˝.Agoodwaytomakeasimpleestimateisviathelongitudinalemittance.Forasimplecontinuousbeam,thelongitudinalemittanceas=˝E,where˝isthetimeextentofthebeamtobebunched,andEistheenergyspreadofthebeam.If˝ischosensothatislargerthantheacceptancewindowoftheaccelerator,thereisbynowaytobunchtheentirebeamintotheacceptancewindow.Theconverse,however,isnotnecessarilytrue;itispossibletohaveabeamwithansmallerthantheacceptancewindowwhichnonethelesscannotbeeasilybunchedinitsentiretyintothewindow,duetotheparticularshapeofthewindow.Inordertominimizetherequiredbunchingvoltageandbeamenergyspread,itisneces-sarytochoosethelowestvalueofnwhichcanstillmeetexperimentaldemands,andthenthatabeambunchedatthisfrequencycanstillwithintheacceptanceoftheaccelerator(seeChapter4).Othertechnicalconstraints,suchasresonatorgeometry,mayalsomitigateagainsttheconstructionofabuncheratcertainfrequencies.ForthecaseofReA,apulseseparationof100nswasoriginallyrequestedbysomeexperimentalists.Thiswouldcorrespondtoannofabout8,andafrequencyofabout9MHz.Concernsabouttheenergyspreadandrequiredvoltageforbunchingthisamountofbeamleadtoacompromisechoiceofn=5,correspondingtoaperiodof62nsanda81bunchingfrequencyof16.1MHz.ItwasagreedthatthisfrequencywouldstillpresentasubstantialimprovementinthepotentialfortitmeasurementsatReA,withoutposinginsurmountabletechnicalchallenges.5.3VoltageandFocalLengthWiththeselectionof16.1MHzasthefundamentalfrequencyforthebuncher,thenextstepisthedeterminationofthelocationandbunchingvoltageforthedevice.Thetwoparametersarenotindependent-foragivenfocallength,thereis(toorder)onlyoneoptimalbunchingvoltage.5.3.1IdealCaseThesimplestapproximationistouseaninputbeamwithnoenergyspread.Lettheincomingbeamhavevelocityc,thedistancetothefocusbeL,andthetimeextentofbeamtobebunchedbe˝bunch,or62nsforthecaseathand.Thereferenceparticleislocatedatthecenterofthebunchwithanunchangedvelocity,andwillthereforereachthefocalpointattimet,wheret=0correspondstothefrontofthebunchreachingthebuncher:t=Lc+˝bunch2(5.1)Foranidealsawtoothbunchingwaveformwithnoresettime,anentirebuncherperiodoftheincomingbeamwillbebunchedatthefocus.Asaresult,boththeforemostandrearmostparticlesmustalsoreachthebuncherattimet.Theforemostparticlemusttravel82adistanceLintimet,andsomustbedeceleratedtovelocity:v=Lt=2c2L+c˝bunch(5.2)Correspondingly,therearmostparticlemusttraveladistanceofL+c˝bunchintimet,andsomustbeacceleratedtovelocity:v+=L+c˝buncht=2c2L+c˝bunch+2(c)2˝bunch2L+c˝bunch(5.3)Ifweusethenon-relativisticapproximation(appropriateinthecaseofthisbuncher,as=0:00508),thenthechangeinkineticenergyforeachoftheseparticlesissimplyKE=12m(v2(c)2);(5.4)andthevoltagerequiredtoproducethatchangeofenergycanbefoundsimplyfromtheLorentzforcelaw(whereSistheacceleratinggapsize):qE=F(5.5)qVS=F(5.6)qV=FS(5.7)qV=KE(5.8)V=12mq(v2(c)2)(5.9)Asanexample,ifweusetheoriginaloftheReA80.5MHzMHB,withL=0:73m,=0:00508,and˝bunch=12.4ns,foraheliumbeam(Q/A=1/4),wea83peakbunchingvoltageof1230V.Themostimportantfacttoobservefromthissimplemodelisthatforthelowcasewherethenonrelativisticapproximationisappropriate,thevelocityandhencethebunchingvoltageisinverselyproportionaltothefocallength.Thiscanalsobeunderstoodintuitivelyintermsofphasespacerotation;thelongerthedistanceinwhichtherotationmustoccur,thesloweritmusttakeplace,andthelowerthenecessaryvoltagetoaccomplishthatrotation.5.3.2NumericalSimulationOtherthanforthegeneralinsightsjustmentioned,thisidealcaseisoflittleuseevenforaapproximation,fortworeasons.Theisthatsincethesawtoothwaveisinpracticebuiltfromitssinusoidalcomponents,theidealderivedpeakvoltagewillbewellabovetheactualpeakvoltageappliedtoanyindividualmode.Ofmuchmorepracticalinterestisthepeakvoltagewhichwillneedtobeappliedtotheindividualsinusoidalcomponentsofthewave,asdescribedinSection3.2.Secondly,thissimplisticapproachfailstotakeintoaccountthefactthatthebeamhasanonzeroenergyspread.TherotationinphasespaceshowninFigure5.3meansthatthewiderthespreadinenergiesofbeamparticlesastheyreachthebuncher,thegreaterthetimespreadofthoseparticlesatthefocus.Assumingtheinitialenergyspreadhasnotimedependence,theenergyspreaddoesnottheleveloftheoptimumvoltage,butitdoesthewithwhichparticlescanbebunched.Thewidertheinitialenergyspread,thelesstightlycompresseditispossibletomakethebunchintime.Thiscanalsobeunderstoodsimplyintermsofconservationoflongitudinalemittance,andisillustratedinFigure5.3.Fortheactualdeterminationoftheoptimumbunchingvoltageandfocallength,anu-84Figure5.3:Simulatedlongitudinalbeamphasespacefortwotvaluesofinitialenergyspread.85Figure5.4:Peakbunchingvoltagevs.focallengthforaMonteCarlomodelofa16.1MHzbuncher.mericalMonteCarlosimulationwasmadeinthestatisticscoder[42].Alargenumberofsimulatedparticleswasgenerated.Theseparticleswereuniformlydistributedintimewithinthelengthofasingle16.1MHzbunchandinenergywithinEE=0:2%,thedesignspfortheenergyspreadfromtheEBIT.Theenergiesofthoseparticleswerethenadjustedbyapplyingabunchingwaveformconsistingofthesumofmultiplesinewaves.Fi-nally,theparticlesweretransportedthroughasimulateddriftspaceaccordingtotheirnewvelocities.Thisprocedurewasrepeatedforarangeofbunchingvoltagesandfocallengths.Usingthecalculatedtimespreadforthebeamineachcase,thealbunchingwasdetermined.Here,\bunchingisasthepercentageoftheoriginalparticlesthatreachthefocalpointwithinsomeacceptancetimewindow.Nopar-86E=0:02%E=0:2%E=0:5%frf=16.1MHzTriangleTriangleTriangle,Lancosz,Gaussianfrf=80.5MHzLancoszGaussian,Lancosz,TriangleLancosz,GaussianTable5.1:Windowfunctionswiththehighestbunchingcybyfrequencyandinitialbeamenergyspread.ticlesarerejectedforenergiestoofarfromthereferenceenergy,butwedotakenoteoftheresultingenergyspreadforfuturereference.Aplotofthebunchingvs.focallengthandpeakvoltageonthebunchingmodeisshowninFigure5.4.Asthebuncherismovedclosertothefocalpoint,thebunchingincreases,butsodoestherequiredvoltage.Thissuggeststhatamethodfordeterminingtheoptimalbuncherplacementistoselectthemaximumpracticalbunchingvoltage,andlocatethebuncheratthecorrespondingdistanceupstreamfromthefocalpoint.Inprinciple,themaximumacceptableenergyspreadwouldputahardlimitonthemaximumvoltage,butinthiscasethevoltagebecomesalimitingfactorwellbeforetheenergyacceptancemeasuredinChapter4isreached.Anumberoftwindowfunctions(see3.2.2)weretestedatthesametime.Theresultswerefoundtobesensitivetoboththeenergyspreadoftheinitialbeamandthebunchingfrequency.Asthesimulatedbeamenergyspreadincreased,thesbetweenthevariouswindowfunctionsdecreased,asthelargeroveralllongitudinalemittanceofthebeambecamedominantoverthesmallchangesinbunchingshape.FortypicalinitialenergyspreadsforReA,thebestbunchingwereobservedusingtheGaussian,Lancsoz,andtriangularwindowfunctions,withonlysmall(seeTable5.1).Inpractice,theseamplitudeswouldlikelybeusedasstartingpointsfortheempiricaltuningofarealbuncher.875.4BeamlineAtthispoint,practicalphysicalconsiderationscomeintoplay.Thepresentprojectinvolvesanupgradetoanexistingfacility,notsimplydeterminingtheoptimalfocallengthaspartofanewdesign.Itwasdeterminedthatbunchingvoltagesontheorderof1.5-2kVwouldrequirepowerontheorderof300-500W,whichwasseenasareasonableupperlimit.Assuch,theideallocationforthebuncherwasfoundtobesomewherebetween1.7and2.5metersupstreamfromthefocalpointattheentrancetotheRFQ.AfterconsultationwiththemechanicaldesignatNSCLandtheoperatorsandengineersofReA,alocationwasselected1.96mupstreamoftheRFQentrance.Inordertolimitcosts,ratherthanfabricatinganewhousingforthedevice,anexistingdiagnosticbox(\L052")wasdesignatedtoreceivethebuncher.Asoriginallyinstalled,theboxwaslocatedfartherthan2mupstreamfromthefocalpoint.Additionally,theboxwaslocatedafterarelativelylong1mdriftspacecorrespondingtotheinsertionboxfortheionsource,whichcouldhavemadefocusingthebeamthroughtheelectrodespotentiallyproblematic.Toputthebuncherintheappropriatelocation,whilereducingthedistancethebeammusttravelwithoutfocusing,theL052boxwasexchangedwiththeimmediatelyfollowingelectrostaticquadrupoledoublet.ThischangeisshowninFigure5.5.Inthisschematicdrawing,thebeamistravelingfromlefttoright.Theabbreviationsintheschematicrep-resentthefollowingelements:\L052",doublewidthdiagnosticbox,\EQD",electrostaticquadrupoledoublet,\80",80.5MHzmultiharmonicbuncher,\Box",singlewidthdiagnosticbox,\Sol",roomtemperaturesolenoid,\16",16.1MHzmultiharmonicbuncher.Thisexchangeofpositionsinprinciplesolvesmultipleissues;thebunchercanbeinstalledatapositionthatallowsforgoodfocusingncy,thebeamhastotravelashorterdistance88Figure5.5:noftheReALEBTsection.Thedoublewidthdiagnosticbox(L052)afterthestableionsourcehasbeenmoveddownstreamofthequadrupoledoublet,anddividedintoasinglediagnosticboxandthe16.1MHzbuncher.withoutfocusing,andfocusingelementsareplacedimmediatelyupstreamofthe16.1MHzbuncherelectrodestoallowforthebeamtobefocusedatthebunchingregion.Beforethismovewascarriedout,however,simulationsneededtobeconductedtoverifythatgoodbeamfocusingcouldbeachieved,boththroughtheelectrodesofthe16.1MHzbuncheraswellasthroughtheevennarrowerapertureofthe80.5MHzbuncher.Inthenewonlytwoquadrupoleswereavailablebetweenthedesiredfocuspointsatthetwobunchers,andsotherewasnotaguaranteeofafocalmatchbetweenthecenterpoints.Usingdynac,simulationsweremadeofboththeoldbeamlineandtheproposednewonetodetermineifacceptablebeamsizescouldbeachievedwiththeproposedSomeresultsofthesesimulationsareshownininFigure5.6.Thexbeamhalfwidth(1RMS)isshowninredandtheywidthingreen.Thegreenbarsindicatethepositionsofquadrupoles.Thetopgraphisasimulationoftheoriginalbeamlineandthebottomshowstheofmovingonesetofquadrupolesupstreamandthenretuningfortheminimumbeamsizeatthetwobunchers(withapriorityassignedtothesecondbuncher,sinceithasthenarroweraperture).Alsovisibleintheisthemoveofthe80.5MHzbuncher30cmfartherfromtheRFQ,whichwascarriedoutforunrelatedreasonsatthesametimeastheforthe16.1MHzbuncher.Thesimulationsshowedthatwiththemoveofthequadrupoledoubletupstream,itwas89Figure5.6:AbeforeandaftercomparisonofthesimulatedbeamenvelopeforthereurationoftheReALEBTline.Thetopshowsthesimulatedenvelopefortheoriginalandtheloweretheenvelopeafterthequadrupolemove.Seetextforfurtherexplanations.90Figure5.7:Electrodedesignforthe16.1MHzMHBinprinciplepossibletobringthebeamtoatightfocusatthe80.5MHzbuncherandstillachievearelativelygoodfocusatthe16.1MHzbuncher.Thesimulationpredictedacircularbeamwitharoughly1mmwidthatthe80.5MHzbuncher,andasomewhatmorespreadoutbeamwitha4mmhorizontalwidthanda2mmverticalwidthatthe16.1MHzbuncher.(Allarewidthsgivenas1RMSfullwidthvaluesforthesimulatedparticledistribution.)5.5ElectrodeGeometryAsdiscussedinSection3.3,whileanidealbeambuncherwouldhaveaperfectlyuniformacceleratinginpracticethisisnotachievablebecauseofthesimplefactthattheremustbeanopeningforthebeamtopassthrough.Choosinganelectrodedesignwiththeofapairofcones(Figure5.7)allowsforthemajorityoftheacceleratingtobeconcentratedatthegap[43].Withthisdesign,therearetwomainparametersofinterest,theseparationbetweentheelectrodes,andthewidthoftheaperture.Eachoftheseparametersrepresentsatensionbetweencompetinggoals.Awideapertureradiusmakesfocusingthebeamthroughtheapertureeasier.Theofanarrowerapertureontheeaseofbeamtuningwasseeninthebeamtransmissionratesobservedat91Figure5.8:Crosssectionofthe16.1MHzMHBelectrodesmodeledincststudio,showingtheacceleratinginthex=0plane.ReAaftertheoriginalelectrodesforthe80.5MHzMHBwerereplacedwithanarrowerradiusopening.Ontheotherhand,thewidertheaperture,themoretheacceleratingwillvarywithradialdistance,leadingtoundesiredspreadingTheseparationbetweentheelectrodesmustalsobebalancedbetweentwopriorities.ArguingforanarrowerseparationistheTransitTimeFactordescribedinSection3.3.2.TheTTFwillfallastheelectrodesaremovedapart,requiringhigherappliedvoltageforthesameacceleratingThisbecomesmorepronouncedathigherfrequencies.Balancingthedesireforasnarrowaseparationaspossibleisthecapacitancebetweentheelectrodes,whichincreaseswithdecreasingseparationandincreasestheneededpowertoachieveadesiredacceleratingvoltage.Toselecttheoptimumelectrodegeometryinthiscase,athreedimensionalmodeloftheelectrodegeometrywascreatedincstemstudio(Figure5.8).Forarangeofvaluesoftheapertureradiusandelectrodeseparationathreedimensionalmapofthestaticelectricwasgeneratedforapotentialofonevoltbetweentheelectrodes.Thesewerethenimportedtotheparticletrackingcodetrack.Withintrackthe3Dmapcould92Figure5.9:OnesimulationoftheLEBTportionoftheReAbeamlineusinga3Dmodelforthe16MHzbuncher.thenbescaledupbythedesiredvoltageappliedtoeachmodeonthebuncher.Todeterminethenecessaryper-modevoltageforeachelectrodegeometrythefollowingprocedurewasused:First,usingtheMonteCarlosimulationdescribedin5.3.2combinedwiththebuncherlocationdeterminedin5.4,theoptimumbunchingwaveformwasfoundfortheidealbunchercasemodeledwiththissimulation.(Toreiterate,thisidealcasedoesNOTconsidertransittimeorradialess.)Oncethisoptimumwaveformwasfound,thevoltagerequiredforeachmodewasrecorded.Next,eachmodewiththisidealvoltagewasappliedtothebeamoneatatime,andtheresultantpermodeenergyspreadofthebeamafterbunchingwasdetermined.Todeterminetheactualappliedvoltagesneededforeach3Dmodelintrack,thisprocesswasreversed.Thebeamwastransportedthroughthesimulatedandthevoltageoneachmodeadjustedindividuallyuntiltheenergyspreadforthatmodematchedtheenergyspreadforthatmodeinsimulation.Oncethecorrectvoltageforeachmodewasdetermined,allfourmodesweresimulatedusingthecalculatedvoltages,andcorrectfocusingwasv93Figure5.10:Peakvoltageforeachmodeforarangeofelectrodegeometries.Figure5.9showsasimulatedpassagethroughthebuncherforaQ/A=1/4beamusingtrack.Thisprocedurewasrepeatedforarangeofsimulatedelectrodegeometries.Theresults,showninFigure5.10,indicatethatwhilethevoltagerequiredforbunchingisrelativelyinsensitivetothegapbetweentheelectrodes,itismuchmoresensitivetothewidthoftheaperture.However,evenwitharelativelywideapertureradiusof1cm,thepeakvoltagerequiredforbunchingstillresultedinapowerrequirementunderthe500Wlimitestablishedasareasonablevaluefortheproject.Thedesignvaluesselectedwere1cmfortheapertureradiusand6mmforthegapbetweentheelectrodes.Itisworthnotingthatthegapforthe80.5MHzMHBisonly4mm,andcouldnotbepracticallymadewider.Thereasonforthenarrowergapinthiscaseisthemuchhigherfrequencies.Theoriginaldesignofthebunchercalledforathirdbunchingmodeatafrequencyof321.5MHz.Thedistancetraveledbythebeam()inoneRFperiodforthismodeisonly6.4mm,givinganalreadylowTTFof0.45.Bycomparison,forthehighestproposedfrequency64.4MHzmodeforthepresentbuncheris22mm,meaningthatforthecaseofthe6mmgap,theTTFisamuchhigher0.86.94BeamEnergy[MeV/u]:0.3530.353Freq.[MHz]Rebunchersdt[ns]dE/E(3˙)(3˙)16.1yes6.80.60.5%0.2%no12.81.70.9%0.3%80.5yes3.20.50.2%0.06%no8.31.30.4%0.2%Table5.2:Predictedminimumtimeandenergyspreadattargetforbeamenergiesfrom0.3-3MeVand0.25-0.5Q/A.5.6ontheBeamattheDetectorsOncethebuncherlocationwasdetermined,end-to-endsimulationsoftheacceleratorwererunforanumberofscenariostoestimatetheonthebeamatthedetector.Thesimulatedbeamlinewastunedforthetwomostcommonlyrequestedexperimentalscenarios-minimumtimespreadontarget,andminimumenergyspreadontarget.Goodtransversefocusingisalsorequired,andwasincludedinthesimulation,butisnotdiscussedhere.ThefundamentalchallengeinachievinganarrowtimeorenergyfocusatthedetectorsisthattherearenolongitudinallyfocusingelementsintheReAlineafterthecryomoduleofthelinac,whichis30mupstreamfromthetargetpoint.Dependingonthebeamenergy,oneormorecavitiesinthesecondorthirdcryomodulewereusedtorebunchthebeampriortotransport,butespeciallyatlowenergies,minimizingthelongitudinaldefocusingatthetargetprovedextremelyAsmentionedinSection1.1.7.1,onepossiblefutureadditiontoReAwouldbeoneortworebunchingcavitiesaddedjustafterthevertical\S"bendinthebeamline.Theadditionofthesecavitiestothesimulationresultedinasubstantialimprovementinthetimeandenergyfocusofthebeamatthedetector,especiallyatlowerenergies.TheresultsofthesesimulationsareshowninTable5.2.Ineachcase,thetimeandenergyspreadiscalculatedasa3˙deviationfromthereferenceparticle.95Forthetimespread,theresultswithoutrebunchingcavitiesrangedfrom6.8nsforthelowestenergycase,350keV/u,to0.6nsforthe3MeV/ucase.Theenergyspreadwithoutrebunchersrangedfrom0.9%forthelowenergycaseto0.3%forthe3MeV/ucase.Itisworthnotingthatthe350keV/uscenariowasnotenvisionedwhenthelinacwasdesigned,asitactuallyentailsrunningthecavitiesatadeceleratingphasetolowerthebeamenergyfromtheRFQexitenergyof600keV/u.Atthemorelikely3MeV/ulevel,theseenergyspreadsshouldbelowenoughtoallowreasonabletmeasurementstobemade,incaseswherethesatellitebunches(see5.7below)arenotanundueburden.5.7SatelliteBunches5.7.1SimulationofSatelliteBuncheswithNoCleaningThesamesimulationwasalsousedtoestimatethenumberofparticleswhichwouldremainintheundesiredacceleratorbucketsandbetransportedallthewaytothedetectorinthesebuckets.Simulatingthisquestionwasnotasimplematterusingeithertrackordynac.Forinternalreasons,bothcodescanonlytransportparticleswithphases180°awayfromthereferenceparticlethroughasimulatedRFQ.Particlesoutsideofthatphaserangeareeitherdiscarded,orshiftedinphasemodulo360untiltheyarewithinoneperiod.ThisisacceptablewhenthesimulatedbunchingfrequencyisthesameastheRFfrequencyoftheaccelerator-anyparticleswhicharemovedinphasecanbeassumedtobeequivalenttoparticlesfromadjacentbuckets.However,forthesubharmoniccase,asolutionwasdevelopedusingdynacguitotransportaparticledistributionlongerthanasingleRFperiodthroughanRFQ.ThelongerdistributionwasgeneratedandtransportedtotheentranceoftheRFQ,whereitwasdumpedtoanexternalandthendividedintoanumberofdistributions,96Figure5.11:SimulationofthecentralbunchandsatellitebunchesatthedetectorpositionforthemiddleReAbeamline.Thissimulationwasofa2H+beamat3MeV/u.eachoneperiodinwidth.Thosesub-distributionsweretransportedthroughthesimulatedRFQoneatatime.Theoutputdistributionswererejoinedintoonelargedistribution,whichwasthentransportedthroughtheremainderofthesimulation.ForthecaseoftheunmoReA3withnobunchcleaningsimulated,oftheparticlesreachingthedetectorposition,roughly96%wereinthemainbunch,leaving4%insatellitebunches(Figure5.11).Thisisnotideal,butshouldallowatleastpreliminaryexperimentstobeginwithhighercurrentbeams.5.7.2SimulationofSatelliteBuncheswithCleaningWhilethedevelopmentofacomprehensivebunchcleaningsolutionwasdeterminedtobebeyondthescopeofthisproject,afewsimulationswereruntodeterminetheectivenessofseveralmethodsofcleaningsatellitebunches.Themosteprovedtobereplacing97Figure5.12:Normalizedhistogramshowingparticlesinsatellitebunchesrelativetothemainbunchwhencleanedwithtwo96MHzcavitieslocatedatthepositionofthepresentCM1.Timeaxisisinns.the80.5Mhzacceleratingcavityinthecryomodulewithtwoacceleratingcavitiesat96.6MHz,whichwereabletoreducetherelativesizesofthesatellitebunchesbyafactorof104comparedtothemainbunch(SeeFigure5.12).ThesefrequencycavitieswouldonlyagreeinphasewiththeRFQand16MHzbuncheratthezerophaseofboth.AnyparticlesatthezerophaseoftheRFQnotinthemainbunchwouldseeanon-zerophaseforthe96MHzcavityandbefurtherinenergyfromthereferenceparticle.Theseparticleswouldthenbedispersedintransversepositionafterbendingelementsandcouldbeusingaslit.985.8NumberofBuncherModesForthethepresentchapter,allcalculationsweremadewiththeassumptionthatthebuncherwouldbeconstructedtosynthesizeitswaveformusingfourbunchingmodes.ThisassumptionwasmadebasedonthefourmodebuncherinuseatANL,andasareasonablechoicegivenmitigationofsomeoftheissuesthatwerefacedwiththehighestmodeintheexisting80.5MHzMHBbytheloweroverallfrequencyofthisbuncher.Someconsiderationwasgiventothepotentialectsifthebuncherwaseventuallyconstructedusingonlythreemodes.Withfewerbunchingmodes,thelinearportionofthebunchingwaveformwouldbeshorter,resultinginalowerbunching.Theestimateddropinbunchingciencyfor3vs.4modeswasapproximately4%.However,theloweredisbalancedbylowerpowerrequirements-withthreemodes,thevoltageforallmodesislowerthaninthefourmodecase.99Chapter6FabricationandInstallationAprojectofthisscoperequirescontributionsfromanumberofspecialties.Theexpertiserequiredtodesigneveryelementofthisdevice,fromthelowlevelradiofrequency(LLRF)moduletothephysicalelectrodes,islikelybeyondthecapabilitiesofanyoneperson.Sim-ilarly,anexhaustivedescriptionofthedesignandoperationofeachsusbsystemisbeyondthescopeofthisdocument.Thissectionwillprovideanoverviewofthedesignandconstructionofallthemajorsub-systemsofthisprojectinareasonableamountofdetail,butwillnotattempttoencompassallofthedesignchoicesinthesamelevelofspeyasChapter5.Thebroadareasad-dressedare:theelectrodesandelectrodemountingassembly,theRFtunersandresonators,andtheLLRFandelectronics.6.1MechanicalDesignOncethephysicaldimensionsofthebuncherelectrodesweredetermined,(asoutlinedin5.5)thesespweretransmittedtotheNSCL/FRIBmechanicaldesigndepartment.Inadditiontoprovidingtheappropriateelectrodegeometryasdescribedabove,anumberofotherrequirementsalsoneededtobemet.ThedesignoftheelectrodeassemblyisshowninFigure6.1.First,afterinstallationthecenterlineoftheinstalledelectrodesmustpreciselymatchthe100Figure6.1:Thecompletedelectrodeassembly,showingtheadjustmentscrewsforthexandyaxesandthealignmentmonuments.Thecenterplatecanalsorotatetoensurethecenterlineoftheelectrodesisparalleltothebeamaxis.101referenceaxisofthebeamlinetoavoidsteeringorfocusingonthebeam.Thetwopossibleapproachestothisconstraintweretoeitherpreciselydesigntheelectrodemounttoexactlymatchtheboxintowhichitwouldbemounted,orelsetomaketheelectrodemountingadjustable.Thesecondoptionwasdeterminedtobemoredesirable,bothbecausetheexactdimensionsoftheL052boxwerenotpreciselyknown,butmoreimportantlytoprovideyshouldtheelectrodesbemovedtoanotherlocationinthefuture.Threeaxesofadjustmentwereincorporatedinthedesign-horizontaladjustmentalongthexaxis,verticaladjustmentalongtheyaxis,androtationaladjustmentaroundthecenterofthemountingNoadjustmentwasincorporatedinthezaxistoreducetheexpenseandcomplexityofthedesign,aftersimulationshowedminimalonthebeamparametersfromsmallchanges(<1cm)tothezpositionoftheelectrodes.Toallowforadjustmentofelectrodepositionrelativetothebeamlineafterinstallationintothebox,theelectrodeswererigidlyattachedtoa6"vacuumwhichwasthenconnectedviaabellowstothe8"ontheoutsideoftheL052box.Smallchangestoelectrodepositionwillthereforebeabsorbedintotheshapeofthebellows.The6"wasmountedtoa\collar"whichmatestoasecondcollarsupportedbythreadedrodsconnectedtothe8"onthebox.Theheightofthecollarconnectedtothe8"isadjustableusingnutsoneithersideofthiscollar.Thesenutsprovidethehorizontal(xaxis)adjustmentfortheelectrodes.Thetwocollarscanslideagainstoneanother,allowingtheirpreciserelativepositiontobeadjustedbyroundedscrewsandthenlockedinplacewiththreescrewsonthesides.Thismechanismprovidesthevertical(yaxis)adjustment.Finally,the6"isitselfrotatablewithinthemountingwhichallowstherotationalorientationoftheelectrodestobeadjusted.Tofacilitatealignmentoncetheassemblyismountedinthebeamline,asetofthreemonumentswereinstalledon102theoutsideofthe6"t.Secondly,theelectrodesneededtobeheldatapreciserelativealignmentwhilebeingelectricallyseparated.Thisissuewasresolvedbymountingtheelectrodesonapreciselymachinedceramicblock.AstheNSCLmachineshopdoesnothavethetoolsnecessaryforsuchmachining,thisblockwastheonlycustomizedcomponentofthedesignwhichhadtobefabricatedsite.Thethirdmajorrequirementwastoprovideapathtotransfertheelectricalpowerfromtheexteriorofthebeamlinetotheelectrodes.Tothisend,apairofceramicfeedthroughsweremountedin1"ontheouter6"Theconnectionfromtheinsideofthefeedthroughstothecopperelectrodesincludedalengthofecopperstrap,allowingforasmallamountofmechanicaltoleranceduringassembly.6.2RFDesign6.2.1ResonatorsandTunersToapplytheRFpowertotheelectrodes,someformofresonatorisrequired.ThetankcircuitdesignusedattheANLbuncheranddescribedinSection3.5.2wasnotselectedinthiscase.Theexisting80.5MHzMHBusesrigidcoaxialstructuresasresonators,butthisisnotfeasibleatthelowerwavelengthsofthepresentdevice.Toorder,therequiredresonatorlengthissimplygivenby:L=4=c4f(6.1)(Thefactorof4isduetothefactthatthisisaquarterwaveresonator.)Assuch,foran80.5103MHzmode,theresonatormustbeapproximately93cmlong.Bycontrast,fora16.1MHzmode,therequiredlengthfora4resonatorisapproximately4.66m,whichisimpracticalforarigidresonatingstructure.Instead,twolengthsof1"diameterair-corecoaxialcablewithadielectricinsertwereusedasresonators.Thelongercableactsasaquarterwaveresonatorforthelowest,16.1MHzmode,andtheshorteroneactsinquarterwavemodeforthesecond,32.2MHzmode.Inaddition,eachresonatorcanbeexcitedinthe34modetoprovidethe48.3MHzand64.4MHzmodesrespectively.Thechosencableshaveadielectricmaterial(HDPE)separatingtheinnerandouterconductors,whichaltersthecapacitanceofthecable.Thislowersthepropagationspeedoftheelectromagneticwaveinthecableby7%,whichinturnshortenstherequiredresonatorlengthbythesameamount.Theactuallengthofcableusedisstillshorter,however,becausepartoftheresonatorlengthisprovidedbyarigidcopperstructurewithaslidingshortwhichisusedforprecisetuningoftheresonatorfrequency.Thisrigidstructureis80cmlong(with70cmofusablelength)forthelongerresonatorand70cm(with50cmusable)fortheshorterone.AlloftheselengthsaresummarizedinTable6.1.ThecablelengthisnotsimplytheHDPE4lengthminusthetunerlengthbecausethereisnodielectricmaterialinthetuneritself.Tofacilitateeaseofadjustment,thetunerswerelocatedontheroofoftheReA3clean-roomenclosurewiththeresonatingcablespassingthroughasealedholeintherooftoconnecttothefeedthroughsfortheelectrodes.Thisallowsthetunerstobeadjustedwithoutthefullgowningrequiredtoenterthecleanroomitself.Additionally,sinceapproachingthebuncherfeedtrhoughsrequiresturningthebeamtothecleanroom,placingthetunersontheroofallowsforadjustmentofthebunchingfrequencywithoutdisablingthebeam.104Frequency[MHz]4(vacuum)[m]4(w/HDPE)[m]TunerLength[m]CableLength[m]16.14.664.330.703.6832.22.332.170.501.70Table6.1:Lengthsoftheresonatorsandtunersforthe16.1MHzbuncher.Figure6.2:AschematicdrawingoftheconnectionsfortheRFsystemforthe16.1MHzbuncher.6.2.2LowLevelRFThelowlevelradiofrequency(LLRF)moduleusedtodrivethesystemrequiresanumberofinterconnections,showninFigure6.2.TheLLRFmodulereceivesatimingsignalfromthemasterclockcircuitforReA.Itthensendsadrivesignaltothewhichisfedtothetuner/resonatorassemblyviaadirectionalcoupler.ThereturnsignalfromthedirectionalcouplerisusedbytheLLRFmoduletoactivelyadjustthequalityofthetransmittedwave.TheLLRFmoduleusesactivecancellationtechniquestoproduceapuresignalateachmodeusingonlyoneandcontrolmodulewhenoperatedinclosedloopmode.ThismoduleisthetimetheseactivecancellationtechniqueshavebeenusedintheReAcceleratorproject.TheoperationoftheLLRFmoduleisdescribedinmoredetailin105Figure6.3:ThecontrolscreenfortheLLRFmodule,showingthecontrolsforeachofthethreemodes.Section7.4.ThemoduleiscontrolledviaEthernet,andisconnectedtothelaboratorycontrolsystemthroughagigabitEthernetswitchlocatedinthesamerackwiththeLLRFmodule.Duringnormaloperations,allcontrolofthesystemisviatheLLRFmodule.AControlSystemStudio(CSS)[44]applicationcanbeusedtosettheamplitudeandpowerforeachmode,andmonitortheforwardandpowerforeach.TheoperatingscreenforthisapplicationisshowninFigure6.3.6.3ElectrodeInstallationAsastep,a\dirty"(i.e.,notundercleanroomconditions)assemblyoftheelectrodeswasperformedtoverifythepresenceofallnecessaryparts,correctetc.Severalsmall106changeswererequiredatthispoint,includingshorteningseveralscrews,addingspacernutstothebarrelconnectorsforthefeedthroughs,etc.Oncethedirtyassemblywascomplete,theelectrodesweredisassembledandthepartscleanedinpreparationfortheassembly.Finalassemblywasmadeincleanroomconditions,andtheelectrodeswerebytheNSCL/FRIBalignmentgroupwithrespecttothemonumentsontheoutsideofthe6"toallowforalignmentoftheelectrodesfromoutsidethevacuumchamberafterinstallation.TheelectrodesasinstalledinthebeamlineareshowninFigure6.4.Inthisimage,theresonatorscanbeseenpassingthroughtheholeinthecleanroomroof.Theconnectionsfromtheresonatorstothefeedthroughsweremadewithcopperstraps.Theentireassemblywasthenshieldedwithaprotectivecover,astheconnectingstrapssupportahighvoltageconnectionduringdeviceoperation.107Figure6.4:Theelectrodeassemblyinstalledinthebeamline,withtheresonatorsvisible.108Chapter7Commissioning:MethodologyandResultsTestingtheoutputofthe16.1MHzmultiharmonicbuncherposedveryspchallenges.OnlyonetypeofdiagnosticavailableatReA,thetimingwire,operatesinthetimedomainonthescalerequiredformeasuringtheamountofbunchingproducedbythedevice.AnindirectbunchingmeasurementwasalsopossiblebymeasuringthetransmittedbeamcurrentaftertheRFQandlinac,sincelessoftheunbunchedbeamisacceleratedtothefullvelocityofthereferenceparticle.Thischapteroutlinesthediagnosticequipment,testingmethodology,andresultsfromthecommissioningofthebuncher.7.1TimingWireDetectorsTheprimarydiagnosticdeviceusedformeasuringthetimedistributionofthebeamwasatimingwiredetector.ThedesignofthetimingwiresusedatReAiscomparabletothedevicedescribedbyVerzilov[45]foruseattheheavyionLinacatTRIUMF.Thedetectorconsistsofathinwirestretchedalongtheaxisofametalcylinder,coupledtoamulti-channelplate(MCP).ItisshowninFigure7.1.Whilethecylinderisheldatgroundpotential,thewireischargedtoapotentialonthe109Figure7.1:Twoviewsofthetimingwiredetector.TheMCPisindicatedbynumber16,andthewireitselfby18.Intherighthandview,thedirectionofbeamtravelisintothepage,strikingthewirebeforeexitingonthefarsideofthe\can."orderofafewkilovolts,thuscreatingaradialelectricWhenthebeamstrikesthewire,secondaryelectronsemittedfromthewireareacceleratedbytheradialAholeinthecylinderpermitssomeofthesesecondaryelectronstopassthroughandstrikeaHamamatsumicro-channelplatedetector(modelF4655-12).ThedataacquisitionpathisshowninFigure7.2.ThecenterofthedataacquisitionisanOrtec566Time-to-AmplitudeConverter(TAC).Thisdevice\listens"forsignalsonitsstartandstopterminals,andgeneratesanoutputpulsewithamplitudeproportionaltothetimedelaybetweenthosesignals.TheStartinputisconnectedviaaconstantfractiondiscriminatortotheoutputofthetimingwire.Eachdetectedsecondaryelectronpulsefromthetimingwirethustriggersthestartinput.Thestopinputrequiresaconstantfrequencysignalsynchronizedwiththebunchingsignaltobeanalyzed.Forclosedloopmeasurements,wherethebuncherissynchronizedto110Figure7.2:Thedataacquisitionpathforthetimingwiremeasurements.theReAmasterclocksignal,thisclocksignalispassedthroughatimingdiscriminatortotransformthesinusoidalreferencetoasquarepulse.Foropenloopmeasurementswherethebuncherisdrivenbyasignalgenerator,thestopsignalistakenfromthesyncoutputofthesignalgeneratordrivingthebuncher,andthenpassedthroughaleveltranslatortoprovidethecorrectvoltage.SincethisgivesamaximumstarttostopdelayofoneRFperiodineithercase,thesignalisthenpassedthrougharatedivider[46].Thislowersthefrequencyofthestopsignalbyanintegerdivisor,andallowsformultiplepulsestobevisibleatonceinthedata.Finally,theoutputfromtheTACispassedtoaMultiChannelAnalyzer(MCA)fordisplayandanalysisonalaptopcomputerusingthemaestrosoftwarefromOrtec[47].TherecordedspectrumconsistsofahistogramshowingtotalcountsforeachpossibletimeseparationbetweenthestartandstopsignalsdetectedattheTAC.Thishistogramisthenextractedforanalysisinmatlaboranothercode.Anexamplehistogramisshownin111Figure7.3:AexampleofahistogramfromtheTAC.Thisexampleisforbeambunchedwiththesecond(161.0MHz)modeofthe80.5MHzMHBatacontrolsystemsettingof11.Figure7.3.Itisimportanttonotethatinthesehistograms,timeisincreasingtotheleft.ThereasonforthisisthatthestopsignalfortheTACiscomingfromaclock,whilethestartsignalcomesatavariabletime.Earliersignalshavehighertimeseparationfromthereferenceclockthanlaterones.SinceahighertimeseparationcorrespondstoahigheramplitudepulsefromtheTAC,suchpulsesaregraphedfarthertotheright.Conversely,latersignalshaveshorterseparationsandlowerTACpulseamplitudes,andarethusplottedatleft.Sotheprogressionfromearliertolaterpulsesinthehistogramsisfromrighttoleft.7.2TimingWireTestingPriortotestingthe16.1MHzbuncher,thetimingwiredetectorlocatedjustbeforetheRFQ(designated\L061")wastestedusingbeambunchedbytheexisting80.5MHzbuncher.Forthistest,abeamof14N5+wassuppliedbytheEBIT.TheEBITwasusedtoensure112asmallertransversebeamatthelocationsofthebuncherandthetimingwirethancouldbeachievedwiththetestsourceusedforthemeasurementsdescribedinSection4.1.Sincethebeamfromthetestsourceisbentataninetydegreeanglejustbeforethe16.1MHzbuncher,itstransverseextentisrelativelylargeatthatpoint.ThebeamfromtheEBITtravelsinastraightlineforfourmetersbeforethebuncher,makingiteasiertoachieveasmallertransversesizeatbothbunchersandatthetimingwire.Forthesemeasurements,thebeamenergywas12.9keV/u.ThisisnotthereferenceinjectionenergyforReA,astheEBITwaskeptatthesamevoltagelevelfromapriorexperiment,whichusedabeamwithaslightlytmasstochargeratio.WiththeEBITheldtothehighervoltage,thebendingdipoleintheQ/Aseparatorwasadjustedtoselectfora14N5+beam.ForallmeasurementsusingtheL061timingwire,theroomtemperaturesolenoidlocatedjustupstreamofthedetectorwasturnedtoavoidinterferencebetweenthesolenoidfringeandthepathsofelectronsfromthewiretotheMCPofthedetector.However,withouttheadditionalfocusingprovidedbythesolenoid,thebeamlinemustberetunedtobringthebeamtoastightasfocusaspossibleonthewirewithouttheuseofthesolenoid.Oncethebeamwastunedtoprovideadequatecurrentonthetimingwire,theamplitudeofeachmodeofthe80.5MHzbuncherwasindividuallyramped,andthetimingwiredataforeachpowersettingwasrecorded.Theprimarypurposeofthesemeasurementswastotestthedataacquisitionsysteminpreparationforthemeasurementsofthe16.1MHzbuncher.Fortuitously,itisalsopossibletogainadditionalinformationaboutthebeamandtheexistingbuncherbycomparingtheoverallresultsofthesemeasurementswiththepredictionsoftheory.Inparticular,basedsolelyonthesemeasurements,itispossibletoestimateboththeenergyspreadoftheincipient113beam,andtheappliedvoltageatthebuncher.Sincethecontrolsystemforthe80.5MHzbuncherwasnotwellcalibrated,thisinformationispotentiallyuseful.Atthetimeofthesemeasurements,theamplitudesettingforthetwomodesofthebuncherscouldbesetfrom0to80inthecontrolsystem.However,whiletheunitsonthedisplayaremarkedas\MV/m",thesenumberswereessentiallyuncalibrated,althoughtheywereadjustedtoscalelinearlywithelectrodevoltage,ratherthanpower.Toanalyzethedata,eachhistogramwasusingthepeakfit.mcurvemoduleformatlabdevelopedbyO'Haver[48].Foreachcontrolsystemsetting,themeanfullwidthathalfmaximum(FWHM)ofthecurvesandthemeanseparationbetweenthepeakswastabulated.Sincethefrequencyofthebuncherisknown,theseparationbetweenthepeaksisjustasingleperiodofthemodeundermeasurement.Thisallowsthewidthofthehistogrambinstobecalibrated:˝bin=103fmodenbins(7.1)where˝binisthelengthofthebininns,fmodeistheRFfrequencyinMHz,andnbinsisthemeannumberofbinsbetweenpeaks.Giventhiscalibration,theFWHMcanalsobeconvertedtoanequivalentwidthinns.Figure7.4showstheFWHMplottedagainstthecontrolsystemsettingforeachmode.Theapproximatelyparabolicshaperepresentsthetransitionfromanunderfocusedbeamtooptimumfocusing,andthentooverfocusing.Inordertocomparethesemeasurementswiththeory,aseriesofsimulatedbunchedbeamparticledistributionsweregeneratedinmatlabusingtheprocedureoutlinedin5.3.2.Foreachmode,themeanFWHMofthebunchedpeakswascalculatedforarangeofappliedvoltagesandinitialbeamenergyspreads.Theresultofthesesimulationsforthemodeof114Figure7.4:Themeanwidthofthebunchedbeamatarangeofcontrolsystemsettingsusingthe80.5MHzbuncher.The80.5MHzmodeisshownatleftandthe161.0MHzmodeatright.the80.5MHzbuncherisshowninFigure7.5.Theminimumpossiblemeanwidthisrelatedtotheenergyspreadbysimpleconservationofemittance;thegreatertheinitiallongitudinalemittance,thelessitispossibletocompressthebeambyrotationinphasespace.InthethisisapparentintheincreasingheightoftheportionoftheFWHMcurveswithinitialenergy-thegreatertheinitialenergyspread,thehigherthis\plateau."ComparingthesesimulatedcurvestothedatafromFigure7.4allowsforanimmediateestimateoftheinitialenergyspreadofthebeam-theFWHMofthe\plateau"inthemeasuredcurvecorrespondstoasimulatedinitialenergyspreadof0:1%.Adjustingthescalingofx-axisuntilthemeasureddataalignswithsimulationalsoallowsforanestimatedcorrespondencebetweenthevoltageseenbythebeamandthecontrolsystemsetting.Figure7.6showstheresultsofcombiningthesimulatedwidthmeasurementswiththemeasureddatafortheandsecondmodeofthe80.5MHzbuncher.Themeasureddataismultipliedbyascalingfactortogivetheestimatedon-axisbunchervoltagethatcorrespondstotheobservedbunchwidths.Theestimatedscalingfactorforthemodeis115Figure7.5:ComparisonoftheFWHMcurveforsimulatedbunchedbeamswitharangeofinitialenergyspreadsforthemodeofthe80.5MHzmultiharmonicbuncher.Figure7.6:MeasuredbeamFWHMfromFigure7.4overlaidonsimulatedbunchwidths.TheX-axisofthemeasureddatahasbeenscaledtomatchthesimulatedbeamvoltage.116Figure7.7:Thedrivepowersetupforopenlooptestingofthe16.1MHzbuncher.approximately18,andforthesecondmodeisapproximately10.Inbothcases,theminimumobservedFWHMcorrespondstoasimulatedbeamwithinitialenergyspreadof0:1%.7.3OpenLoopBunching7.3.1TestSetupForthetestsofthe16.1MHzbuncher,thedevicewasrunin\openloop"modebelow).ThedrivepowerrationforthesetestsisshowninFigure7.7.AsinusoidaldrivesignalwasgeneratedbyaRigolDG4162signalgeneratoratthefrequencytobetested,andfedtoa100wattEmpower2160(Thepowerofthiswaspredictedtobetforbestbunchingofthehighestrigiditybeams,butadequatefortestingwiththe14N5+beamusedhere.)Thesignalwasthenfedthroughtwothree-portcouplersasseeninFigure7.7.(Theincidentterminalofthecouplerwasnotusedforthistest.)Thepowerfromthesecondcouplerwasfedtotheelectrodesviathetunersandresonators.TheforwardpowerwasmonitoredviaaRigolDSA815SpectrumAnalyzerconnectedtotheincidentterminalofthesecondcoupler.CavitypowerwasmonitoredviaanAgilentN9913ARFAnalyzerconnectedtothetunerpickups.117Openloopinthiscasereferstothefactthatthereisnofeedbackbetweenthesignalgeneratorandtheortheresonators.Withoutsuchfeedback,adjustingthephaseoramplitudeofanyofthethreemodescanhaveanimpactontheotherphasesandamplitudes.Assuch,anyattempttotuneallthreemodestogetherinthismodeisandunlikelytoproduceconsistentlyreproducibleresults.Openloopmodeissuitableforstudyingtheofthemodesindividually.Asdescribedbelow,abriefattemptwasmadetocombinemodesoneandtwoasaproofofconcept.Thesamebeamandtuning(withminorretouching)wereusedforthesetestsasforthe80.5MHztimingwiretestsdescribedinSection7.2:abeamof14N5+withenergy12.9keV/uwasgeneratedbytheEBITandtransportedtotheL061timingwirewiththeL060solenoidturned.Thedataacquisitionforthistestwasviathe\OpenLoop"pathshowninFigure7.2.ThesyncoutputofthesignalgeneratorwasusedforthestopinputoftheTAC,viaaleveltranslatorandaratedivider.TheratedividerandTACweresettosampleamaximumlengthof200ns,meaningthatifastopsignaldidnotarrivewithin200nsofthesignalfromthetimingwire,nooutputpulsewouldbesentbytheTAC.Thislimitedthemaximumnumberofpeaksvisibleforthemodetoatmostfour.7.3.2ResultsTherawdataforthesinglemodescansforthethreemodesofthe16.1MHzbuncherareshowninTables7.1,7.2,and7.3.Fromlefttoright,eachtableshowsthedisplayedamplitudeoftheinputsignalonthesignalgeneratorindBm,theforwardpowerreadfromthespectrumanalyzerinbothdBmandwatts,thecavitypowerreadfromtheRFanalyzerindBm,themeanwidthsofthepeaksinns,andtheestimatedon-axispeakvoltageforthatinputpowerinvolts.TheFWHMwerecalculatedwithmatlabusingthe118sameprocedureoutlinedinSection7.2above.Sincethesamebeamwasusedforthistestasforthepriortests,theenergyspreadwasassumedtobethesameasthespreaddtothe80.5MHzmultiharmonicbuncherdata,0:1%.Asimulatedpeakwidthvs.bunchervoltagecurvewasgeneratedforeachmodeusingthisenergyspread,thistimeusingthefrequencyandfocallengthforthe16.1MHzbuncher.ThepeakvoltageforeachmodewasthenestimatedbyoverlayingthemeasuredFWHMcurveoverthesimulateddata.Inthiscase,sincethemeasuredinputvaluewaspower,thescalingfactorwasrelativetothesquarerootoftheforwardpowerinwatts(sincepowerscalesasvoltagesquared).Onaxispeakvoltageisthusgivenbytheequation:VpˇsppP[W](7.2)Thevaluesofthescalingfactorspwerefoundtobe195,70,and50formodes1,2and3respectively.TheseresultsareshowninFigures7.8,7.9,and7.10.Inadditiontothesinglemoderesultstabulatedhere,anattemptwasmadetocombinethetwomodestoproduceimprovedbunchingoverthemodeindividually.Thesignalgeneratorwassetto\harmonic"mode,whichallowedittoproduceasynthesizedwaveformcombiningsinewavesofvaryingphaseandamplitude.However,althoughtherelativephasesandamplitudesatthesignalgeneratoramplitudewerewellcontrolled,withoutfeedback,thesynthesizedwaveformattheelectrodeswaslesspredictableduetotheexcitationofhigherharmonicsintheresonators.Inparticular,shiftingthephaseoramplitudeofeithermodecouldresultinunpredictableshiftsintheotherparameters.Thiswasvbyviewingthepickupsignalfromthetunersonanoscilloscope.Furthercomplicatingtheattempttoproduceatwo-modebunchingsignalonthebeam119SGAmplitudeForwardPowerCavityPowerMeanFWHMEst.VpdBmdBmWdBmnsV5-12.24.265795188-6.83.206705103.26900786-11.35.248074602-5.72.297505114.54338267-10.36.60693448-4.72.075214128.51978918-9.38.317637711-3.71.609026144.20157529-8.2510.59253725-2.651.507151162.730891710-7.213.48962883-1.61.304313183.641150210-7.4412.76438809-21.426882178.636419110.4-714.12537545-1.531.364091187.918702111-617.7827941-0.41.231745210.848251711-6.416.21810097-11.301527201.358517211.9-5.420.4173794501.209429225.927972212-4.922.908676530.661.235012239.315046212.2-522.387211390.481.199475236.575629512.6-4.4525.4097270611.243016252.040309613-428.183829311.471.509026265.442222114-3.2533.496543922.21.593702289.380994215-2.539.810717062.962.46934315.478672216-1.7447.424198533.653.183149344.3261482Table7.1:Openlooptestingresultsforthe(16.1MHz)modeofthebuncher.Figure7.8:MeasuredFWHMforthe(16.1MHz)modeofthebuncheroverlaidonasimulatedcurve,withthex-axisscaledtomatch.120SGAmplitudeForwardPowerCavityPowerMeanFWHMEst.VpdBmdBmWdBmnsV3-11.759.66050879-3.663.738695147.84-10.5512.73503081-2.452.560171101.215-9.615.84893192-1.531.86418773.6966-8.9518.40772001-0.881.23164548.696.1-9.117.7827941-1.051.50271359.4066.7-8.619.95262315-0.511.24651849.2787-8.3521.1348904-0.281.18176246.7187.5-8.0722.542392120.011.22949448.6058-7.724.547089160.361.15064845.4888.4-7.4725.882129150.611.19648447.38.7-7.2727.101916320.781.21279947.9459-7.0728.379190280.991.22281648.3419.6-6.7730.408850261.291.35809753.68910-6.5232.210687911.541.42136256.1911-5.6339.536662012.42.12928684.17612-4.5251.05053.493.322329131.3413-3.958.884365544.14.003288158.26Table7.2:Openlooptestingresultsforthesecond(32.2MHz)modeofthebuncher.Figure7.9:MeasuredFWHMforthesecond(32.2MHz)modeofthebuncheroverlaidonasimulatedcurve,withthex-axisscaledtomatch.121SGAmplitudeForwardPowerCavityPowerMeanFWHMEst.VpdBmdBmWdBmnsV5-18.656.99841996-84.1306067.9996-17.778.570378452-7.12.2570196.0526.7-17.49.332543008-6.81.8421625.5987-1710.23292992-6.371.3926665.0317-1710.23292992-6.481.5997654.5427.6-16.611.22018454-61.3706274.2048-16.1512.44514612-5.51.2324513.7758-16.312.02264435-5.71.3137483.8888.6-15.913.18256739-5.281.2267084.1889-15.414.79108388-4.772.0689464.9879-15.6314.02813705-51.3380133.73110-14.219.498446-3.553.0674028.69511-13.6522.1309471-34.2017056.6512-12.8926.36331386-2.255.003036.889Table7.3:Openlooptestingresultsforthethird(48.3MHz)modeofthebuncher.Figure7.10:MeasuredFWHMforthethird(48.3MHz)modeofthebuncheroverlaidonasimulatedcurve,withthex-axisscaledtomatch.122Figure7.11:Fittedpeaksformanuallytunedopenloopbunchingusingmodes1and2.weredelaysinherentinthesignalgenerator,whichrequiredseveralsecondstoreadjusteachtimeawaveformwaschanged,andthedataacquisitionsystem,whichrequired30-60secondstodisplaytheresultsofeachnewsetting.Givenalloftheseissues,nosystematicattemptwasmadetoexploretheparameterspace,butratheranempiricaltuningwasattemptedasproof-of-concept.TheresultsofthisattemptareshowninFigure7.11.Whiletheresultantpeakswerenotparticularlysymmetrical,makingthesomewhatsuspect,theroutineestimatedameanFWHMforthepeaksof2.47ns.Thisisofthesameorderofmagnitudeasthebunchingachievedwiththemodealone,andindicatesthatthesecondmodecanatleastinprinciplebecombinedattheappropriaterelativephasewiththemode.7.4ClosedLoopBunching7.4.1SetupTheoperationalmodeofthe16.1MHzbuncheris\closedloop."Asopposedtoopenloopbunching,closedloopbunchingusesthefeedbackfromtheresonatorsandthedirec-tionalcouplerstoanalyzetheamountofpowerintheundesiredupperharmonicsforeach123bunchingmode.Itthenactivelyadjuststhetransmittedpoweratthosefrequenciestocan-celtheunwantedharmonics.Thisrequiresmorepowerthanopenloopmode,becausethecancellationisactivelydrivenbythesameIthastheadvantageofprovidingaverystablesignalwithpreciselycontrollableamplitudeandphaseforeachmode.ThisactivecontrolisprovidedbyalowlevelRF(LLRF)moduledesignedandbuiltbytheNSCL/FRIBRFdepartment.Fortheclosedloopmeasurements,a12.0keV/ubeamof40Ar13+wasused.Thiswasselectedinplaceofthepreviouslyusednitrogenbeamonthetheorythatsincetheacceleratorhadbeentunedforthisbeamfortheimmediatelypriorexperiment,itwouldthereforerequireminimalretuning.Thisassumptionprovedsomewhatoptimistic,asthelowerbeamcurrentavailablemeantthatmorecarefultuningwasneededtoplacetbeamontotherelativelysmallareaofthetimingwire.Twotimingwireswereused,thewireat\L061"describedabove,locatedimmediatelybeforetheRFQ,andthe\L110"timingwire,locatedattheendofthelinac.Unliketheopenloopmeasurements,whichweredirectlycontrolledfromasignalgenera-torlocatednearthedevice,oncetheLLRFmodulewasinplacetheclosedloopmeasurementscouldbecontrolledandmonitoredfromtheReAcontrolroomareausingtheControlSystemStudioapplicationdescribedinChapter6.TheothermajorinthetestsetupfortheclosedloopmeasurementswasthesourceofthesynchronizationsignalfortheTACconnectedtothetimingwiredetector.Inthecaseoftheopenlooptests,the16.1MHzsynchronizationsignalwastakendirectlyfromthesignalgeneratordrivingthebuncher.Intheclosedloopcase,theclocksignaldrivingtheLLRFmodulewasan80.5MHzfeedfromtheReAmasterclock,dividedinternallyto16.1MHzwithintheLLRFmodule.Unfortunately,theLLRFmodulehasnooutputfor124thisdividedsignal.Additionally,noratedividerwasavailablewhichwassptoworkatthe80.5MHzclockfrequency.Sinceasynchronized,lowerfrequencysignalisarequirementofthisdataacquisitionmethod,asynchronizationsignalwasinsteadtakenfromthe10MHzoutputoftheReAclockmodule.ThisoutputwasoriginallyintendedforRFtestequipment,butseemsnevertohavebeenuseduntilthisexperiment.Thissignalwasusedtophaselocka16.1MHzsignalfromaRhode&SchwartzSML03SignalGenerator,whichwasthenfedtothesameratedividerasintheopenloopcase.Forthesetofmeasurements,acapacitorwasaddedbetweenthelongerresonatorandthefeedthroughinanattempttohelpstabilizethefrequencyofthethirdmode.Whileinitialmeasurementsshowedthatthethirdmodewasstableinthisithadthedrawbackofincreasingtherequiredpowerforthemodetothepointthatthebeamcouldnotbebroughttoalongitudinalfocusatthedetector.Asaresult,forthetesting,thiscapacitorwasremoved,andthebuncherwasoperatedwithtwomodesonly.Finally,the100wattwhichwasusedduringtheopenlooptestingwasreplacedwitha300watt(E&ImodelA-300)toprovideadditionalheadroomandlongtermsupportforhigherrigiditybeams.7.4.2SingleModeResultsSincelimitedtimewasavailablefortesting,fewerdatapointsweretakenfortheclosedloopmeasurementsthanfortheopenloopcase.Fortheandsecondmodeindividually,arangeofvoltagesweresetinthecontrolsystem,andthepowerconsumptionrecordedandahistogramcapturedfromthetimingwire.Atalaterdate,thehistogramswereanalyzedtodeterminetheaverageFWHMperpeakateachbunchingpower.125CSSSettingForwardPowerPowerMeanFWHMEst.VpVWWns1˙V1001.40.420.80.717015030.717.01.22552005.51.414.60.63402508.329.60.342530012.133.20.151035016.54.11.90.159540021.45.32.40.04680Table7.4:Closedlooptestingresultsforthe(16.1MHz)modeofthebuncher.CSSSettingForwardPowerPowerMeanFWHMEst.VpVWWns1˙V500.18-11.93.7601000.75-10.51.31201501.7-9.11.01801752.3-3.90.92102003-3.70.92402253.8-2.70.62702504.7-2.20.43003006.8-2.00.6360Table7.5:Closedlooptestingresultsforthesecond(32.2MHz)modeofthebuncher.Nopowerwasobservedatanyofthechosenvoltagesettings.TherawdataisshowninTables7.4and7.5.Nopowerwasobservedduringthemode2observations,indicatingthecavityresonantfrequencywastunedquiteaccuratelytothedesired32.2MHzresonantfrequency.TheerrorsintheFWHMarederivedfromthe\bootstrap"methodusedinthepeakroutine[49],andarereportedattheonesigmalevel.ItcanbeseenfromFigures7.12and7.13thatthesinglemodedatatakeninclosedloopmodeisnotascomprehensiveasthatinopenloopmode.Thisisunfortunate,butisaresultoftwomainfactors.Thewassimplytimepressuretothemeasurementsinthetimeallotted.Theotherwasthatatthehighendofthevoltagerangethatwasscannedforeach126Figure7.12:MeasuredFWHMforthe(16.1MHz)modeofthebuncherinclosedloopmode,overlaidonasetofsimulatedcurves,withthex-axisscaledtomatch.Figure7.13:MeasuredFWHMforthesecond(32.2MHz)modeofthebuncherinclosedloopmode,overlaidonasetofsimulatedcurves,withthex-axisscaledtomatch.127Figure7.14:Anillustrationofanoverfocusedbeam,showingtheexpecteddoublepeakedstructureofthehistogram.mode,thepeakinthetimingwirehistogramwasseentobifurcate.Abifurcationathighervoltagesisanexpectedconsequenceofthemechanicsofbunching.Whileanunderfocusedbeamappearsasawidepeak,anoverfocusedbeamwillappearastwoseparatepeaks,asthemostacceleratedandretardedportionsofthebunchedbeamareoverlaidonthetailsofthelongitudinaldistribution.ThisisillustratedinFigure7.14.Unfortunately,afteranalysisofthesizesofthepeaks,itwouldappearthatthebifurcationinthiscasewaslikelynottheresultofoverfocusing,butrathertheresultofasecond,narrowpeakwhichwashiddenbynoiseatthelowerbunchingenergies.Themostlikelyexplanationforthispeakisthatsomesmallfractionofthebeamwashittingthe\can"ofthetimingwiredetector,resultinginatimesignalslightlyfromthedesiredsignalfromthewireitself.Theshowninthetablesandforclosedloopbunchingaremadetothelargerofthetwopeaks,andcontinuetomatchthesimulatedshapeofthebunchingcurvereasonablywell.Thiswouldalsotendtosupportthetheorythatthesecondpeakwasnottheresultofoverfocusing.Onamorepositivenote,however,thedatathatwascollectedstillindicatesareasonablygoodforthesimulatedcurvesshown,andthetwomodesgiveconsistentresultsfortheinitialbeamenergyspread,inthiscaseabout0:15%.Sincethecontrolsystemwas128calibratedforvoltage,notpower,therelationshipbetweenthecontrolsystemsetting(Vcs)andtheactualpeakcenterlinevoltage(Vp)isthesimplelinearrelation:VpˇsvVcs(7.3)Theconstantssvrelatingthecontrolsystemsettingtotheactualonaxisbeamvoltageareestimatedat1.7formode1and1.2formode2.Sincethemaximumpowerusedforeithermodewaslessthan30watts,therewouldseemtobeplentyofleewayavailabletoreachfocusing,evenatthehigherrequirementsimposedbymulti-modebunchingandhigherrigiditybeams.7.4.3MultipleModeResultsThemostcriticalresultfortheperformanceofthebuncherwastothecharacteristicsofthebeamaftertheRFQandlinac.Thesestructureshavethegreatestimpactonthelongitudinalstructureofthebeam,andtheentiremotivationforthisprojectwastohaveanimpactonthosecharacteristics.OncetheapproximateshapeoftheFWHMtovoltagecurveshadbeenplotted,thisinformationwasusedtomakearoughestimateofthebunchingvoltageneededwhenthetwomodeswerecombined.Usingthisestimateasastartingpoint,bothmodesofthebuncherwereturnedonandthebeamobservedatL061again.Thetwomodeswerethenadjustedempiricallytoproducethebestpossiblefocusinareasonableamountoftime.Thecontrolsystemsettingsusedwere305voltsforthemodeand55forthesecond.Basedonthemorethoroughcalibrationperformedafterthefact,thiswaslikelyslightlyunderfocused.Thesevalueswerethenscaleddown(bytheratioofthefocallengths)to129movethefocus25cmforwardtotheentranceoftheRFQ.TheexperimentwasthenpausedtoallowtheRFQtowarmuptoitsstableoperatingtemperature.Inprinciple,oncethebeamhasbeenbroughttoalongitudinalfocusattheRFQ,thereisonlyoneremainingbuncherparametertooptimize-therelativephasebetweenthebuncherandtheRFQ.TherelativephasesbetweenthemodeswereexpectedtobecorrectwithintheLLRFmoduleandtheCSScontrolapplication-i.e.iftheandsecondmodephaseswerebothsetto\0",bothwouldhavetheirascendingzerocrossingsatthesametime.However,therelativephasebetweenthe16.1MHzbuncherandtheRFQisdeterminedbythecablelengthsbetweeneachdeviceandthemasterclock,aswellastimeoftforparticlesfromonetotheother,andanydelaysduetoelectronics.Whilethesecouldallinprinciplebecalculated,itwouldseemtobefareasiertosimplythecorrectrelativephaseempirically.Inordertoaccomplishthis,theL110timingwire,locatedattheendofthelinacwasused.ThecontrolsystemsettingsusedforthecavitiesinthersttwocryomodulesaregiveninTable7.6.Noneofthecavitiesinthethirdcryomodulewereusedforthistune.Asareminder,thechoiceof40Ar13+forthesemeasurementswasspmotivatedbythefactthatthelinachadalreadybeentunedforthisbeam,sominimalretuningwasneeded,otherthansomeadjustmentofthefocusingsolenoidstorefocusthebeamatthelocationofthetimingwire.Oncethebeamwasacceleratedtotheendofthelinacandbroughttoafocus,theL110timingwirewasinsertedandthelongitudinalbeamobserved.Evenwithnoadjustmentwhatsoever,thepredictedlargepeaksseparatedbyfoursatellitebuncheswereimmediatelyapparentonthehistogram,asseeninFigure7.15.ThiswasattributablelargelytoluckasitwaspossiblethatthebulkofthebeamcouldhavebeenbunchedentirelyoutsideoftheacceptanceoftheRFQ,butwasapromisingsignthatthebuncherwashavingits130CavityNameControlSystemSettingL0773.3L08215.78L08423.17L08522.68L08822.62L08927.61L0910Table7.6:Cavitysettingsfortestingofthebuncherwithacceleratedbeam.AllofthecavitiesinthethirdcryomoduleweresetdesiredNext,thetwomodesofthebuncherweregraduallymovedupwardsinphaseuntilthemaximumamountofcountswerepresentinthemainpeaks,correspondingtothebuncherfocusbeingalignedinphasewiththeRFQacceptancewindow.Finally,someexperimenta-tionwasperformedtoseeifthebunchingperformancecouldbeimprovedstillfurtherwithtamplitudesettingsonthetwomodes.GiventhattheRFQacceptanceisnotaperfectlyuprightrectangle,asoutlinedinChapter4,itwouldnothavebeensurprisingifothershapesthanperfectlyverticallongitudinalfocusingattheRFQentrancecouldproduceimprovedbunchingresults.Indeed,someimprovementwasseen.ThebestresultachievedisshowninFigure7.16.Thebunchersettingsusedforthiscasewereamplitudesof335Vand35Vformodesoneandtworespectively,andphasesof22and202.Onenoteaboutphases-thephaseofthesecondmodewasactuallyseterroneouslyonceitwasmovedawayfromitsstartingvalue.Itwasdeterminedaftertheconclusionoftheexperimentthattheunitsforthephaseofthesecond(andthird)modearedegreesrelativetothefrequencyofthatmode.Soifthezerocrossingsofmode1andmode2arealigned,andthephaseofmode1isshiftedbytwentydegrees,inordertokeepthetwocrossingsaligned,thesecondmodemustbeshiftedbyfortydegrees.Sincethesecondmodewasshiftedduring131Figure7.15:InitialbeamtimestructuremeasurementtakenatL110withnophaseadjust-ment.Figure7.16:BestcasebunchingachievedatL110withamplitudes335Vand35V,andphases22and202degrees.theactualobservationsbyhalfoftherequiredamount,butthatamountwasrelativelysmall,someimprovementinbunchingisconceivablypossiblejustfromcorrectingthaterror.Oncethetimingwiremeasurementswereconcluded,twoothermeasurementsweremade.First,thebeamwassteeredthroughthedipolejustafterthelinacandthedipolemeasuredtogiveanempiricalmeasurementofthebeamenergy.Secondly,thebeamcurrentwasmeasuredbeforeandaftertheRFQandlinactogiveameasurementoftotaltransmissionintheunbunched,80.5MHzbunched,and16.1MHzbunchedcases.ThisdataissummarizedinTable7.7.Approximately30%ofthebeamwasacceleratedtotheendofthelinacevenwithnobunchingbeforetheRFQatall.Thisisconsistentwiththevaluesobservedduring132SummaryBeam40Ar13+EnergyInitial:12keV/uAfterAcceleration:1.6MeV/uTransmissionNobunching:30%16.1MHzbunching:50%80.5MHzbunching:75%Bunching85%Table7.7:Summaryofbunchedbeamproperties.\Transmission"givesthepercentageofthebeamcurrentmeasuredafterthelinacrelativetothebeamcurrentmeasuredjustbeforethebuncher.\BunchinggivesthepercentageofthetotalbeamdetectedatL110inthemainpulse.theRFQacceptancemeasurements.7.5ComparisonwithSimulationAsavaftertheconclusionoftheexperiment,adynacsimulationwasrunusingthetunesettingsusedforboththe80.5MHzbunchingcaseandthe16.1MHzbunchingcase.Thisalsoallowsinferencestobemadeaboutbeamcharacteristicsthatwerenotdirectlyobservedduringthemeasurement.Thissimulationwasrunforaperiodsubstantiallylongerthanthe62nstoensurethatthesimulatedsatellitebunchesincludedanyparticlesfrommainpeaksoneitherside.Forclarity,onlythesatellitesfromasinglebuncherperiodareshownintheTheaspectsofthesimulationwhichcanbereasonablyassumedtobeinexcellentagree-mentwiththerealityofthebeamlineare:thephysicalgeometryandplacementofthebeamlineelementsandtheamplitudeoftheappliedvoltagetotheRFQandtheelectro-staticelementsinthelowenergysectionofthebeamline.Somewhatlesscertain,butstillconsistentwithobservation,arethecurrencurvesforthemagneticelementsandthe133acceleratingsofthesuperconductingcavities.Thelargestuncertaintiesinthesimula-tioncomefromtheinitialconditionsoutoftheEBITandtheexactbehaviorofthebeamthroughtheRFQ.Additionally,thesettingsforthebuncheritselfaretunedinsimulationtoprovidemaximumtransmissionthroughtheRFQ,buttherealbuncherwasonlytunedempirically,sotherearelikelysomediscrepanciesbetweenthesimulatedandactualbuncherDespitethesesourcesoferror,thesimulatedandmeasuredbunchedbeamswerequitesimilarincharacteristics.Themeasuredbeamenergyfromthedipoleafterthelinacwas1.60MeV/u.Thesimulationpredictedabeamenergyof1.64MeV/u(65.55MeVtotalforthisbeam),aofonly2.5%.AsidebysidecomparisonofthetimestructureoftheobservedbeamwiththesimulationatL110isshowninFigure7.17.Ineachcase,thenumberofcountsinthemainpeakwascomparedwiththoseofthesumofthecountsinthefournearestsatellitebunches(twobeforeandtwoafterthemainpeak).Thebestcasebunchingachievedinsimulationwas88%,slightlyhigherthanthe85%achievedwiththerealbeam.Itislikelythathadmoretimebeenavailablefortuningandcalibration,atleastsomeimprovementintherealcouldhavebeenachieved.Thesimulationalsoallowsfortheestimationofaquantitynotdirectlymeasuredduringtheexperiment,namelytheenergyspreadofthebeamafteraccelerationinthelinac.Whilethepredictedenergyspreadimmediatelyfollowingthebuncherisontheorderofseveralpercent,theaccelerationandlongitudinalfocusingoftheRFQandlinacreducethisrelativedeviation.Thepredictedabsoluteenergyspreadis0.71MeV(3˙),orarelativeofabout1%.134Figure7.17:Side-by-sidecomparisonofthetimestructureofthebeamatL110.Thelefthandimageistheactualhistogrammeasuredonthetimingwire,andtherighthandimageisasimulationofthesameconditions.135Chapter8ConclusionsBasedonthestatedneedsofanumberofexperimentalistsattheNationalSuperconductingCyclotronLaboratory,a16.1MHzmultiharmonicbuncherhasbeendesigned,installed,andtestedintheReAcceleratorlinac.Inaddition,valuabletoolshavebeendevelopedformodelingthebeamthroughtheReAccelerator,andimportantinformationgatheredabouttheexistingfacilitythatshouldinformfuturebeamdevelopment.8.1SummaryTherearetwocantresearchfocusesinthisdocument-theempiricalmeasurementofthelongitudinalacceptanceoftheReARFQ,andthedesignandconstructionofthe16.1MHzmultiharmonicbuncher.Whilethebuncherwilllikelyseemorewidespreaduse,theRFQmeasurementsalsohelpincreaseourunderstandingoftheperformanceofthiscomplexdevice.ThemeasurementsoftheRFQlongitudinalacceptancewerecarriedoutusingatestbeamwhichwasusedasaprobeoftheenergyandtimedimensionsofthephasespaceareainwhichparticleswillbesuccessfullyacceleratedthroughtheRFQ.Theprobebeamwasmadeasnarrowaspossibleinenergytoprobetherangesofenergywhichwouldbeaccepted,andthenasnarrowaspossibleintimetoprobethephaseacceptance.Asitispossibletomakethebeammuchnarrowerinenergythaninphase,thepredictedaccuracy136ofthemeasurementismuchbetterintheverticaldimensiononatimevs.energyplot.Theresultfoundthatthemeasuredacceptancewindowwasatleastaswide,ifnotwiderthanthepredictedwindow.Thisresulthastimplications,notjustforthebuncherconstructedthroughthisproject,butforanyfurthermototheReAbeamlineupstreamoftheRFQ.Themultiharmonicbuncherprovedtobeacomplexdesignproject,drawingontheexpertiseofalargenumberoffacultyandattheNSCL.OncetheacceptanceoftheRFQwasdetermined,studieswereconductedtodetermineappropriatevaluesforthelocationandpowerrequiredtobunchthebeam,andtheeventualonthelongitudinalbeampropertiesattheendofthelinac.Thesestudiesrequiredtheuseofanumberoftacceleratormodelingcodes,andthedevelopmentofanewsoftwarefrontend,dynacGUI.Thephysicalgeometryforthebunchingelectrodeswassimulatedusing3Dnumericalmodelingsoftware,andfurthersimulationsconductedtopredictthebehaviorofthebeamthroughvariouselectrodegeometries.Theselectionofelectrodegeometrywasbasedonbetweeneaseoftuningandpower,andbetweenelectrodecapacitanceandtransittimefactors.Onceselected,theelectrodeandRFspweregenerated,andthedevicewasconstructed,installed,andalignedutilizingappropriateNSCLtechnicalFinally,thebuncherwastestedinopenandclosedloopmodes,andwasfoundtoperforminamannerconsistentwithsimulation.Whilesatellitebunchesremainaseriousissue,thebeamistlybunchedevenwithonlytwomodestoallowfortimeoftmeasure-mentsforbeamswithreasonablyhighbeamcurrentsinsomecases.OneotheroutcomeofthisexperimentwhichmayproveusefulinthefuturewasthegaininexperienceofusingthetimingwiredetectorsintheReAcceleratorbeamline.Whilethese137detectorshadbeenusedinthepast,theTAC/MCAdataacquisitionpathusedherehasprovenfareasiertousethanthesomewhatchallengingsoftwareusedpreviously.8.2FuturePlansAtthetimeofthiswritingthe16.1MHzbuncherhasbeendemonstratedtoelybunchthebeamwitha62nsseparationbetweenprimarypulses.However,thereareanumberofareaswhichcouldbeimprovedandexploredtoimprovetheofthedeviceanditsusefulnesstoexperimentalists.‹StabilizationoftheThirdModeDuringtheopenlooptestingofthebuncher,the48.8MHzmodewasshowntofunctionproperlywhendrivenindependentlybyasignalgenerator.However,duringtheclosedlooptesting,itwasnotpossibleinthetimeallottedtobothstabilizethethirdmodeandkeepthepowerconsumptionofthemodetoareasonablelevel.Assuch,thethirdmodewasjettisonedforthemeasurements.Ifthethirdmodecanbestabilizedinclosedloopmode,itispredictedtoadduptoanother5%bunching,whichwillgreatlyreducethestatisticalnoisefacedbyexperimentalistsdoingtimeoftmeasurements.ThisisillustratedinFigure8.1whichshowsasimulatedbeamtimestructureatatL110usingthreebunchingmodes.Whilethisshowsthebestbunchingachievedsofarinsimulation,itispossiblethatthisrepresentsonlyalocalmaximuminparameterspace,andthatfurtherimprovementmaybepossible.‹ImprovedCalibrationMeasurements138Figure8.1:AsimulatedtimedistributionusingallthreebunchingmodesatL110.Thecalculatedis92.96%.Thesinglemodemeasurementsinclosedloopmodewereencouraginglyconsistent,butwerehamperedbythelowbeamcurrentoftheargonbeamandbytheundetectedpres-enceofasecondarypeakinthetimespectrum.Assuch,whiletheexistingcalibrationdataisagoodstart,improveddata,possiblycollectedwithahighercurrentbeam,couldimproveourunderstandingofthepowertovoltagerelationshipinthedevice.Inaddition,anyfutureactivationofthethirdmodewouldrequireasetofcalibrationmeasurementswhichhavenotyetbeentaken.FurtherpmeasurementscouldalsobemadeoftheperformanceofthebeamlaterinthebeamlinethantheL110timingwire.Inparticular,theevolutionofthetimestructureofthebeamtothetargetareawouldbevaluableinformationforex-perimentalistspotentiallywishingtousethisbunchstructure.Alsoremainingtobemeasuredaretheonthetimestructureofusinglatercavitiesinthelinacat139rebunchingphase.‹ControlApplicationImprovementsThecontrolapplicationprovedveryusefulduringtheclosedlooptesting,butatthetimeofthemeasurements,thephaserelativetothemasterclockhadtobesetmanuallyeachtimetheRFwasturnedon.Asthisprocessinvolvessimpleobservationsandcomputations,itcouldeasilybeautomated.ItalsoremainstobeseenwhethercontrolsforthisdevicecanorshouldbeintegrateddirectlyintotheexistingReAcontrolsystem,ROCS,(ReAcceleratorOperationsandControlSoftware)orintoapotentialfutureCSSbasedcontrolscheme.‹DocumentationForthegoalofmakingthisdeviceaccessibletousers,thebeamspmustbeproperlydocumentedinasimpleformandmadeavailableaspartoftheReAServiceLevelDescription[50].Atamoredetailedlevel,proceduresforoperatingandtuningthedeviceshouldbedocumentedandmadeavailabletotheReAcceleratoroperatorsforuseinoperatingthebuncherinaproductionenvironment.Whilethebuncherasitstandsatthetimeofthiswritingisalreadycapableofprovidingbeamswithawideraverageseparationtousers,theseadditionalstepswillmoveitfromanexperimentaldevicetoanotherreliabletoolinthehandsoftheNSCLusers.8.3SatelliteBunchesAspredictedinSections3.4and5.7,theresultsfromthebuncherdiddisplaysatellitebunchesasaresultofparticlesseeingthe\tails"ofthebunchingwaveform.Section3.4also140outlinedanumberofpossibleavenuesforcleaningthesesatellitebunches.ThissectionwillgiveabriefoutlineoftwopossibleapproachestoaddressingthesebunchesinthespcaseofReA.8.3.1IntegerRatioCavitiesAsdescribedinSection3.5.2,onewaytocleansatellitebunchesistouseasecondbuncher.Thisbunchershouldhaveafrequencywhichisatanintegerratiotothatofthemainaccelerator,suchthatitwillalsotransporttheprimarybunchesfromthesubharmonicbuncher,butnotthesatellitebunches.Thesatellitebuncheswillinsteadbeplacedatincorrectenergiestotransportthroughtherestoftheaccelerator.Inpractice,thiswouldactuallylikelymeanmorethanonecavity,asasinglesinusoidalbuncherwithenoughamplitudetothesatellitebunchesawayfromthereferenceenergywouldalsohaveatimpactonthestructureofthemainbunch,andamultiharmonicbuncherwouldbeimpracticalattherequiredvoltages.Aseriesofsuchcavitieswouldallowforthe\kicks"tobeappliedateachcavitypassagetothesatellitebuncheswithoutexcessivedistortionoftheprimarybunch.InthecaseofReA,thesecavitieswouldlikelyneedtobeateitherafrequencyof64.4MHzor96.6MHz,representingeithera4:5ora6:5ratiowiththemainRFfrequencyoftheaccelerator.Themostpromisinglocationforthesecavitieswouldbeinplaceoftheexistingcryomodule.Afterthelinac,thehigherbeamenergywouldrequiremuchmorevoltagetothesatellitebunchesectively.Atpresent,thecryomoduleconsistsoftwosuperconductingsolenoidsandaquarterwavesuperconductingcavity.Thecavityisusedexclusivelyasabuncher,tolongitudinallyfocusthebeamformoretaccelerationthroughthelinac.Becausetherequiredvoltage141forthisbunchingisverylow,thecavityoperatesatasubstantiallylowervoltagethanotherdevicesintheline,withintherangeofwhatcouldreasonablybeaccomplishedwithanormallyconductingcavity[51].The600keV/ubeamenergyatthispointisalsoinaregimewherethebeamcouldbefocusedusingnormallyconductingquadrupoles.Therearetwotdrawbackstothisapproach.Therstisthelargeexpenseofremovingthestcryomoduleandreplacingit.Inadditiontothetwocleaningcavities,thefocusingcapabilitiesofthetwosuperconductingsolenoidslocatedinthethatcryomodulewouldneedtobereplaced.Whileneitherthecavitiesnorthenewfocusingelementswouldneedtobesuperconducting,thiswouldstillrepresentasubstantialinvestmentofresourcesandSincetheseproposedintegerratiocavitieswouldonlyaligninphasewiththeRFQandthelinacwhenoperatedin16.1MHzmode,theywouldneedtobeturnedwhenReAwasoperatedinnormal80.5MHzmode.Assuch,thecavityofthesecondcryomodulewouldhavetobededicatedtolongitudinallyfocusingthebeam.Thisnewrebunchinglocationwouldgivethebeammoretimetospreadoutbeforebeingrebunched,andlesstimetocometoafocusbeforeenteringtheacceleratingcavities,bothofwhichwouldrequireanincreaseinthebeamenergyspreadforelongitudinalfocusing.Secondly,dedicatingthiscavitytorebunchingwouldreducebyonethenumberofcavitiesavailableforacceleration,loweringthemaximumpossibleenergyofthebeam.Thiswouldbepermanent,evenforbeamsoperatedin80.5MHzmode.8.3.2BeamChopperThemoreconventionalapproachtoremovingunwantedbunchesisabeamchopper,alsodescribedinSection3.4.Apairofplatesapplyanelectricinorderto142\kick"unwantedbeamtotheside.Thevoltageontheplatesismodulatedsothatthevoltageiszeroforthedesiredportionsofthebeam.Thetransverseoftheunwantedparticlesmustbecientsuchthatdownstreamofthechopper,theandbeamsdonotoverlap.Thisallowsaslittobeinsertedtoallowpassageofthedesiredbeamparticlesandblockthesatellites.InthespcaseofReA,thelimitationonthismethodistheneedforakickerwhichcancyclefastenoughtoeitherectalltheparticlesdestinedforthetailsbeforetheyreachthebuncher,orelsekickalloftheunwantedparticlesasideafterward.Bothofthesewouldrequireasquarepulsewithapproximately12-15nsofcombinedrise,hold,andfalltime,witharepetitionfrequencyof16.1MHz,acapabilitywhichisnotoutsideoftherealmofpossibility,butquitetoachievewiththeshelfequipment[52].TheotherspconsiderationforReAwouldbethelocationofthechopperanditscorrespondingslit.Themorespaceallocatedforthechopper,thelongerthebeamwouldseetheeld,andthelessvoltagewouldberequiredforthekick.Correspondingly,thelongerthedistancebetweenthechopperandtheslit,thelessvoltagewouldberequired.Aslowavoltageaspossibleiscritical,giventheaforementionedspeedwithwhichitwouldneedtobeswitched.ThesplocationsinReAwhereachoppercouldbelocatedareupstreamofthebuncher,betweenthebuncherandtheRFQ,betweentheRFQandthelinac,orafterthelinac.LocationsimmediatelybeforeandaftertheRFQareproblematicforreasonsoflimitedspace-thedistancefromtheRFQtothecryomoduleisonly80cm,andthespacebetweenthe16.1MHzbuncherandtheRFQiscompletelyoccupiedbynecessaryfocusingandbunchingelements.Locatingthechopperafterthelinacwouldrequireaveryhighvoltage.Forexample,for143abeamwithanalenergyof4500keV/uandachargetomassratioof1/5,separatingtwobeamsby5mminachoppingdistanceof8mwouldrequireapproximately30kVappliedtoa7cmlongsinewavechopper,or2kVappliedtoa50cmtravelingwavechopper.Neitherofthesewouldseempracticalatafrequencyof16.1MHz.Theremaininglocationwouldbeupstreamofthe16.1MHzbuncher,andthiswouldappeartobethemostpromisingpossibility.Thebeamtherehasalowenergy,andthereareafewpotentiallocationsforachopperwhichcouldbeusedtoseparatethebeambeforeenteringthe16.1MHzbuncher.Althoughanumberofsubstantialengineeringhurdleswouldneedtobeovercome,thiswouldseemtobethebeststartingpointforproducingcompletelyclean16.1MHzbunchingforusers.8.3.3EBITSwitchingTheotherapproachoutlinedinsection3.4whichbearsconsiderationisfastswitchingofthetrapelectrodesontheEBIT.Theelectrodeswouldneedtobeswitchedwithasquarepulsewitha50nscombinedrise/hold/falltimewithavoltageshiftontheorderof500-1000V.However,itremainsatantalizingpossibility,giventheextremedesirabilityoftheresult.IftheemittedpulsefromtheEBITcouldbeshortenedto50nsorless,thatentirepulsecouldbecompressedbythe16.1MHzbuncherintoonebunch.Inthatcase,thebunchseparationatthedetectorwouldbedeterminednotbythefrequencyofthebuncher,butbythefrequencywithwhichthetrapwasopened,givingtheoperatorscompletecontroloftheseparationbetweenbunches.Inpractice,therewouldlikelybeaminimumratherthanamaximumseparation,basedonthemaximumswitchingspeedoftheelectrodes.Inthismode,nobeamwouldbelosttothesatellitebunchesorunaccelerated\tails"becauseallofthetransmittedbeamwouldbecompressedbythebuncher.144Thisapproachfacessubstantialhurdles-heatingofthesuperconductingEBITduetothefastswitchingbeingthemostobvious.However,becauseitneatlysolvessomanyproblems,itisstillworthyofseriousconsideration.145APPENDICES146AppendixAComparisonofAcceleratorCodesAtglance,simulatingthemotionofasingleparticleinalinearacceleratormayappeartobearelativelysimpletask.TheLorentzforcelawthatdeterminesthemotionofachargedparticleinanelectromagneticisasimpleequation,andtheproducedbyvarioussteeringandacceleratingdevicesarewellunderstood.Thismotionbecomesmorecomplicatedwhenhigherordersuchasparticleinteractionsareincluded,buttoorderthemotionofparticlesinelectromagneticwouldseemtobeasimplecalculation.Asalways,thedevilisinthedetails.Alargenumberofcodeshavebeenwrittentosimulateaccelerators,andeachhasadvantagesandlimitations.Thisoverviewofcodesisbynomeansexhaustive,coveringonlythecodesthatwereusedinthepreparationofthisdissertationandafewofthemajoralternativesthatwerenotused.Ingeneral,acceleratorsimulationcodescanbeintotwotypes:matrixcodesandnumericalmodels[53].Matrixcodescalculatetheanalyticaltransportmatrixforeachelementuptoasporderandcombinethemtoproduceanoverallmathematicaldescriptionoftheaccelerator,throughwhichparticlesmaythenoptionallybetracked.Nu-mericalcodessimulatethethreedimensionalelectromagneticofeachelementandnumericallytrackthemotionofparticlesthroughthosewithelementmodelling.Somecodesuseacombinationofbothapproaches,whichwillbenotedbelow.147A.1Dynac‹Authors:Lapostolle,Valero,andTanke‹Institution:CERN‹Type:Matrixcodewithparticletracking‹Website:http://dynac.web.cern.ch/dynac/dynac.html‹OpenSource:YesA.1.1Overviewdynacwastheprimarycodeusedforthisdissertation.ItwasselectedforitsabilitytomodeleachelementoftheReAbeamlineinasinglesimulationrun.ThisincludesthelowenergyelectrostaticelementsatthestartoftheReAline,theRFQ,theacceleratingcavities,aswellasthebuncheritself.Anotheradvantageofdynacisthatitisopensource,soitisrelativelystraightforwardtolookatthesourcecodetodeterminetheinnerworkingsofanelementorroutine,oraddneededfunctionality.(Likeanyprogramfork,thisshouldbedonewithcaution.)Itisalsowell-documented,andstillbeingactivelymaintainedandupdatedatthetimeofthiswriting.AppendixBofthisdissertationdescribesdynacgui,agraphicalfrontendfordynacwritteninthematlabenvironmentbytheauthor.A.1.2SimulationMethodandCapabilitiesdynacsimulatesabeamlinebycalculatingtheordertransportmatrixforeachelementandthentransportingtheparticledistributionthroughthematrixforthatelement.(Secondordermatricesmaybespforsome,butnotallelements.)148Certainelementsaretreatedquasi-numerically.Theelectricinanacceleratingcavitymaybespbyanexternalwhichgivestheon-axisacceleratingasa1Dfunctionofdistance,orbytheFouriercomponentsoftheon-axisThe3Dcomponentsarethenextrapolatedawayfromtheaxisandtheparticlestransportedthroughthisdistributionbasedonthesizeandlengthofthecavity.Solenoidsmaybetreatedeitherbyspecifyinganarbitrary1Ddistribution,orbyasimplehardedgemodel.RFQsarealsotreatedquasi-numericallyinamannersimilartotheRFQdesigncodeparmteq[54].ThegeometryoftheRFQisspbyanexternalwhichdividesthedeviceintoanumberofcells.The3Dcomponentsofeachcellarecalculatedbasedonthecelltypeandparameters,andtheparticlestransportedthrougheachcellindividually.Bunchersaretreatedaszerolengthelementswhichprovideaninstantaneouskicktothebeam.Eachindividualbunchingmodeisspasanindependentdevice.dynacprovidessupportforanumberofcapabilitiesnotutilizedinthisproject,in-cludingbeamsconsistingofmultiplechargestates,spacecharge,modelingofelectronguns,synchrotronradiation,andIHtypedevices.dynacalsoprovidesroutinesforthesimulationofmisalignments.A.1.3InputandOutputFilesTheacceleratorlatticefordynacisspbyaninputwhichgivestheparametersforeachdeviceonthebeamlineaswellasauxiliaryinformation,suchaschangesinthereferencefrequencyorthelocationstogenerateoutputgraphs.dynaccangenerateaninitialparticledistributionusingavarietyofmodels,orcanimportanarbitraryparticledistributionfromanexternalOptionalexternalinputcanalsobeusedtospecifydistributionsforacceleratingcavities,RFQs,andsolenoids.149Onexecution,dynacproducesanumberofoutputEachrunwillproduce:‹dynac.short-asummaryofbasicinformationforeachbeamlineelementandthenum-berofparticlesremainingatthatpoint.‹dynac.long-amoreverboseelement-by-elementdescriptionofthebeamline.‹dynac.print-atabularsummaryofthebeampropertiesateachelement.‹emit.plot-therawdataforallrequestedplots.(seeA.1.4)‹dynacinpr.dst-theinitialparticledistribution‹rfqlist.data,rfqlistmid.data,rfqlost.data,rfqcoef.data-variousdataabouttheRFQ.(ifused)Thesetakethesamenamesaftereachrun,socaremustbetakeninmanagingoutputdata.Inaddition,optionalcanbeproducedtostoreparticledistributionsatvariouspointsonthebeamline.Samplecodefragment:;ReA3_46Ar15_L016_to_JANUS_3MeV.inGEBEAM518.05e+07100000000000.41000.4100.000109700INPUT931.49446150.5520DRIFT14.2968QUAELEC15.1.13165.150FigureA.1:AsampleemittanceplotproducedusingdynacA.1.4DataVisualizationWhenthemaininputfordynaciscreated,theusermayspecifylocationsforvarioustypesofplots,suchasemittanceplots,beamgraphs,phaseandenergywidthasafunctionofbeamlineposition,etc.Allofthedatafortherequestedplotsisstoredinonelargeemit.plot.Thedynacpackageisdistributedwithdynplot,asetofroutinesforplottinggraphdatastoredintheemit.plotdynplotconvertsthestoredplotdatatognuplotformatanddisplaysthedatausingthatprogram,whichmustalsobeinstalledlocally.Whiledynplotallowsplotstobedisplayedorsaved,itisnotparticularlyinthattheplotsmayonlybeviewedsequentially,andmayonlybesavedingnuplotformat.dynacguiaddressesanumberoftheseissuesbyusingamenu-basedapproachtothegeneratedplots,andmatlab'sownbuiltinplottingfunctions.FigureA.1showsanexampleofanemittanceplotgenerated151withdynplot.A.1.5LimitationsThemaindrawbacksofdynacforthisprojectwereitslackofanysortofcapabilityanditsinabilitytotransportparticledistributionslongerthanoneperiodthroughanRFQmodel.Bothoftheseissueswereaddressedwithdynacgui.dynacguiwasalsousedtoimproveonthelimitationsofthebuiltinvisualizationroutines.dynacisalsonottheidealchoiceforuserswhoneedtousedetailedthreedimensionalmodelsforelementsratherthananalyticalapproximations.dynacdoesnotincludeanybuiltinfunctionalityforanalyzingperiodicsystemsorrings.A.2COSYINFINITY/cosy.fox‹Authors:BerzandMakino‹Institution:MichiganStateUniversity‹Type:MatrixCode(seebelow)‹Website:http://www.bt.pa.msu.edu/indexcosy.htm‹OpenSource:BeamLibrariesOnlyA.2.1Overviewcosyisnotexclusivelyabeamphysicscode.Itisaprogrammingenvironmentdesignedforsciencomputing.Itincludesalibraryofroutines(cosy.fox)spllydesignedforbeamphysicsapplications.Whilecosyitselfisnotopensource,thebeamphysicslibrariesare.152WhatisuniqueaboutcosyisthatitusesTaylorseriesandtialalgebradatatypestostoremuchofitsdata.Thishastheadvantageofallowingaccurate,highordercompu-tationsoftransfermatricestobecalculatedinreasonableamountsoftime.However,thisapproachalsohasdrawbacks.Forexample,modelingaperiodicsignalconsistingofmultiplefrequencycomponentsusingTaylorseriescanrequireunreasonablyhighordercomputation.Thislimitationmakesitimpracticalforsimulationofmultiharmonicbunchers.Thecosyenvironmentistlypowerfulthatthislimitationcouldpresumablybeovercome,butthiswasdeemednottobethemostentapproachfortheproject.cosyisstillunderactivedevelopmentatthetimeofwriting,andfeaturesextensivedocumentationoftheunderlyinglanguageandofthebeamphysicsroutines.A.2.2SimulationMethodandCapabilitiesSincecosyisaprogrammingenvironment,beamlinemodelsincosytaketheformoffullprogramswrittenusingthecosy.foxlibraryofbeamlineelements.Thisallowsforexten-siveprogrammingandanalysiscapabilitieswithinthebeamlinemodelitself,asopposedtorequiringpostprocessingofresultsaswithdynacandmostothercodes.Thestandardbeamlineelementsincludeawiderangeofmagnetic,electrostatic,andopticalelements,whichcanbesimulatedtoarbitrarilyhighorder.Further,cosyallowsdetailedtreatmentandspoffringemodels.Finally,cosy.foxincludesanumberofroutinesfortheanalysisofperiodicstructures,spectrographs,andaberrations.Bydefault,cosydoesnottrackensemblesofparticlesthroughabeamline.Rathertheoveralltransfermatrixofthelineiscalculatedtoarbitrarilyhighorder,andthenraysaretracedthroughthematrix.Thisapproachisusefulwhenageometricalopticalapproachtothebeamdynamicsiswarranted,butislesshelpfulwhenonewishestospecifyaninput153particledistributionasaseriesofparticlesorbyitsCourantSnyderparameters.Oneareainwhichcosyexcelsisusingitsbuiltinroutines.Usingcosy,itisveryeasytospecifyobjectivestobeachievedandparameterstobevaried,andthenuseavarietyofalgorithmstomatchthedesiredobjectives.Theroutinesincosyareamongthemostpowerfulandeasytouseofanybeamdynamicscode.Theotheradvantageofthefactthatcosyisaprogrammingenvironment,ratherthansimplyadynamicscode,isthatdesiredcapabilitiesthatarenotprovidedbydefaultcanbecodedbytheenduser.TheinitialmodelingofReAwasdonebyMaurcioPortillousingcosy[18].Sincecosydoesnotimplementtrackingofparticleensemblesbydefault,Portillo'smodelincludesalargenumberofroutinestogenerate,track,andanalyzeparticledistributionsthroughthetransfermapsproducedbythebeamlinemodel.Theseroutinesallowforeithertheimportofarbitraryparticledistributions,ortorandomlygeneratesuchdistributionsusinginitialCSparameters.Inturn,thesedistributionscanbesavedandthenanalyzed,andperformedbasedonthepropertiesofthesedistributions.Thistypeofdistributionbasedisnotaseasilyaccomplishedwith\stock"cosy.A.2.3InputandOuptutFilesAscosyisaprogrammingenvironment,ratherthanabeamphysicscodeperse,theonlyrequirementisforthebeamlinecodeitself.Aswithaprogramwritteninanyotherlanguage,theusermayspecifyinputandoutputwithanydesirednamesorformats.Theonlyinputrequirementisthatthecompiledbinaryofthecosy.foxbeamlibrarybeavailabletothebeamlinecode.Samplecodefragment:154INCLUDE'COSY';PROCEDURERUN;VARIABLEQ11;VARIABLEQ21;VARIABLEOBJ1;Q1:=.1;Q2:=-.1;OV520;RP1042;SB.05.050.05.05000000;FITQ1Q2;UM;CR;ER13131111;BP;DL2;MQ.4Q1.15;DL.2;MQ.4Q2.15;A.2.4DataVisualizationAsindicatedabove,nativelycosyisnotsetuptotracklargeensemblesofparticles,butratherindividualraysorsmallensemblesofrays.Itdoes,however,havequitesimpletousetoolsfordisplayingthebehaviorofthoserays.Inordertoaccessthosetools,onemustsuccessfulysetuponeofthesupportedgraphicsinterfaces(pgplot,grwin,aquaterm)noneofwhichareparticularlyintuitiveorcontemporary.Withthataccomplished,cosyproducesverygoodplotsofraysbeingtracedthroughthesystem,withthelocationsandrelativesizesofbeamlineelementsclearlyindicated.Furthermore,duetotheprogrammaticnatureofcosyitcanupdatetheseplotsasittriesvarioussolutionsforaroutine,sotheoverallsuitabilityofthestrategycanbevisuallyevaulated.cosydoeshavetheabilitytodisplaytheenvelopeofthebeam,consistingofthemax-imumtransverseextentofanyinitialraysatagivenpoint.Itcanalsodisplaycurvedreferencetrajectories,acapabilitynotsharedbymostotherbeamlinecodes.FigureA.2showsanenvelopeplotgeneratedusingcosy.155FigureA.2:AnexampleofalongitudinalplotproducedwithcosyA.2.5LimitationsIngeneral,thecosy.foxlibraryislessleinthelongitudinaldimensionthaninthetransversedirection.Partially,thisisduetothesystematiclimitationsnotedabove,andpartiallyduetothefactthattherearesimplyveryfewacceleratingelementsavailableinthelibrary.Furtherprogrammingcouldcertainlybedonebyaninterestedendusertoovercomethissecondlimitation.OncepossiblewaytoovercomethesystematicissuesmightbetofurtherexpandtheparticletrackingroutinesconstructedbyPortillo.OneotherfactorwhichpreventeduseofcosyformodelingtheentireReAbeamlineisthatwhileRFQshavebeensuccessfullymodeledinthisenvironment,thoseroutineswerenotpubliclyavailableatthetimeofwriting.A.3TRACK‹Authors:Ostroumov,Aseev,andMustapha‹Institution:ArgonneNationalLaboratory‹Type:NumericalTrackingCode156‹Website:http://www.phy.anl.gov/atlas/TRACK/‹OpenSource:NoA.3.1Overviewtrackisdesignedprimarilyasanumericalsimulationcodefortrackingdistributionsofparticlesthrough3Dnumericalsimulationsofelectricandmagneticeldsgeneratedbybeamlineelements.Anarbitrarynumberofcanbespecandthesecanbereusedthroughoutthebeamline.trackcanalsogenerateeldmodelsforidealizedversionsofmanycommonelementssuchasquadrupolesandsolenoids.trackwasstillinactiveuseatArgonneNationalLaboratoryatthetimeofthiswriting,butthedocumentationhadnotbeenupdatedtotthemostrecentversionsofthecode.A.3.2SimulationMethodandCapabilitiestrackisanumericalparticletrackingcodeintendedforionbeamsinlinearaccelerators.ItwilleithergenerateastartingparticledistributiongivenasetofparametersorimportonefromadistributionWhengeneratingthedistributionswithintrack,theonlyinitialdistributionssupportedare4DwaterbagwithaDClongitudinalbeamor6Dwaterbag.Althoughitwilltrackparticlesthroughidealizedmodelsofsomeelements,suchasthetextbookthinlensquadrupole,theprimaryfocusofthecodeisontrackingparticlesthrough3Dsimulatedmodels.Ofspinteresttothepresentprojectistheabilityoftracktosimulatebunchersusinga3Dmodel.Givenastatic3Delectromagneticdistributionforabuncher,trackcanscaletheamplitudeofthatwithagivenfrequencyandphaseforeach157modeofthebuncher.Thisallowsfortestingoftheofspelectrodegeometries,somethingwhichisnotpossibleineitherdynacorcosy.trackalsoincludestheabilitytosimulateanidealizedbuncherwithoutaforcomparisonpurposes.trackdoessupportsimulationofRFQsviaaspmodelformatwhichgivestheexpansioncotsoftheEMofeachcellofthedevice,inasimilarfashiontodynacandparmteq.However,theeformatisnotdirectlycompatiblewitheither,anditcanprovetomakeadirectconversionortoverifyonecodeagainsttheother.A.3.3InputandOutputFilesInputtotrackisgivenbytwotextThetrack.dat,sptheoptionsforrunningtheprogram,includingtheinitialconditionsofthebeam.Theother,sclinac.datspthebeamlineitself,includingthelayoutandsettingsforeachelement.A3Ddistributionmustalsobespforeachelementforwhichamodelisused.Thesamemodelmaybeusedmorethanonceinthesamebeamlineforidenticalelements.Becausetheinputnamesarealwaysthesame,caremustbetakentoseparateandidentifyeachsimulatedcase.When3Dareusedforelements,itisexpectedthesewillbegeneratedusingtheemstudiocomponentofthecststudio[55]suiteofmodelingcodes.(Thisispotentiallyanissueforsomeusers,foralthoughtrackitselfisfree,thesameisdecidedlynotthecaseforcststudio.)TheinputaresimpleASCIItablesofvaluesona3Dlattice,soitshouldinprinciplebepossibletogeneratethemusingother3Dcodessuchasopera.trackhashardcodedlimitsonthemaximumresolutionoftheinputlattice,althoughcertainversionsoftheprogrammaysupporttresolutions.(Theseexceptionsarenotwelldocumented.)Theconversionfromcststudiotoaformatusable158bytrackisviaasetofprovidedutilityprograms.Samplecodefragment:1drift4.453.03.00equad647215.015.05.0601drift3.03.03.00equad-841415.015.05.0601drift4.453.03.01drift10.53.03.01drift7.13.03.01drift4.33.03.0!1drift4.13.03.0!1drift7.63.03.0!1drift1.83.03.04mhb411.41143.151148502-7480334304-1500A.3.4DataVisualizationOneoftrack'sgreateststrengthsisitsabilitytodisplaygraphicalemittanceplotsforeachstepasthebeamistrackedalongthebeamline.Bycomparison,dynaconlyproducesemittanceplotsthatcanbeviewedaftertheentirelineiscalculated,andcosydoesnotnativelyproduceemittanceplotsatall.Interactionwithtrackduringthesimulationisviaagraphicalinterfacewhichdisplaysx,y,andzemittanceplots,aswellasalongitudinalplotduringtherun.Theinterfacealsodisplaysimportantbeamcharacteristicssuchasmassandcharge,aswellasprovidingoptionstoadvancebyaselectednumberofstepsatonce.Whiletheinterfaceisextremelyusefulforvisualizingthebeam,thereisunfortunatelynosimplewaytoentirelydisableitforautomatedrunsoftheprogram.Althoughthereisanoptionwhichwilldisablethedisplayoftheemittanceplots,oncethesimulationiscompleted,theuserisstillrequiredtomanually159FigureA.3:Anexampleoftrack'soutputscreen.(Phasevs.zplotnotshown)thattheywishtoexit.FigureA.3showsanexampleofthegraphicalinterfacefortrack.A.3.5Limitationstrackdoesincludesomefunctionality,butthisfunctionalityhighlightsoneofthebiggestproblemswithtrack:theincompletenessofthedocumentation.Althoughthereisanextensive(68page)documentationavailableforthecode,atthetimeofthiswritingitwastwoversionsoutofdateandnotbeingmaintained.Thefunctionalityisnotevenmentionedinthedocumentation,andwhileafewsampleareavailable,itisanon-trivialundertakingtoextrapolatehowtodousingthecode.Thisissueextendstoanumberofotherundocumentedchangestoexistingfeaturesorundocumentednewfeatures.Andastrackisnotopensource,itisnotpossibletosimplyexaminethesourcecodetoreverseengineerthebehaviorofthecode.Also,astrackisintendedforlinearheavyionaccelerators,itdoesnothaveanyfunc-tionalityforsimulatingsynchrotronradiationorforanalyzingperiodicstructures.160A.3.6ErrataandCommentsProvidedhereareafewcorrectionsandcommentsonversion37ofthetrackmanual.‹Theenergyspreadoftheinputbeamisgivenas,notEEasinmostothercodes.=1(+1)EE[24].‹Undocumented:Afourharmonicidealbuncherisgivenby:nmhb4delemrapMHBph01Ef1ph12Ef2ph23Ef3ph34Ef4ph4wherethemeaningsoftheseparametersarethesameasforthetwoharmonicbuncher.‹Thevalueusedforvoltageforelectrostaticquadrupolesisthevoltageencethetwoplates.Thisisdoublethevalueusedbycosyanddynacwhichusethevalueofthevoltageonasingleplaterelativetoground.‹igraph=0isthecommandintrack.dattorunthecodewithouttheGUI.‹Theout.datisreferencedinthev37documentation.Thishasbeenreplacedwiththebeam.out.‹TheDW/W[rel.u.]columninthebeam.outisthe1RMSvalue,notthe100%valueasindicatedinsection8ofthemanual.‹Undocumented:ireaddis=2andiwritedis=2canbeusedtoreadandwriteparticledistributionsinASCII,ratherthanbinaryformat.A.4MAD‹Authors:Grote,Schmidt,Deniau,andRoy‹Institution:CERN‹Type:MatrixCode‹Website:madx.web.cern.ch161‹OpenSource:YesA.4.1Overviewmadanditsvariantshavealonghistoryinthedesignoflargescaleacceleratorsandstoragerings.DevelopedatCERN,Stanford,andFermilab,madwastheprimarycodeusedinthedesignoftheLEPandLHC,amongothermachines.madisprimarilygearedtowardhighenergy,periodicsystems,buthasanumberofmodulesthatexpanditscapabilitiesinotherways.Likecosy,madexecutesscriptsratherthanmerelyinterpretingadescriptionofabeam-line,soprogrammaticcontroloforotherroutinesfromwithinmadispossible.ThecodeisstillinactiveuseatCERNandatotherlaboratoriesaroundtheworld,andisstillunderactivedevelopment.Inadditiontoextensivedocumentation,therearealsoawiderangeofsampleandintroductoryguidesavailable.Thereareanumberofmaddescendentsandvariants,includingdimadandbmadwhichalsoextendorfromtheparentprograminvariousways.A.4.2SimulationMethodandCapabilitiesmadisprimarilyconcernedwiththeanalysisofthemachinelattice.Tothatend,theuserde\sequences"usingasimplescriptinglanguage.Thelanguageisdeliberatelyconstructedwithacceleratorsimulationinmind,somanycommandsaresptailoredforthispurpose.Forexample,elementpositionscanberelativetootherelementswithasinglecommand.Oncethelatticeismadcomputesthematrixrepresentationofthemachineand162thenperformsanydesiredoperationsonthatmatrix.BuiltinmodulesallowforplottingofCSanddispersionfunctions,matchingfordesiredconditionssubjecttoconstraints,con-versionofcoordinatestoCartesiancoordinatesformachinealignment,andawidearrayofotheracceleratortasks.Whilethedefaultbehaviorisnottotrackensemblesofparticles,thistaskcanbeaccomplishedeitherwithinthescriptinglanguage,orbytheuseofexternalmodulesormacros.A.4.3InputandOutputFilesLikecosy,sincemadisessentiallyascriptinglanguage,thebasicunitofinputistheprogramusuallydesignatedbyextension*.madx.Sinceallelementsarerepresentedbytheirmatrixnoauxiliaryinputforionsarerequired.Somemadmodulesdouseinputoroutputtostoredata.Forexample,theorbitcorrectionmoduleuses\before"and\after"forthevaluesofthecorrectorsandbeampositionmonitorsusedintheprocess.Itisalsopossibletobreakbeamlinesegments,called\sequences,"outintoexternalandthenimportthemfromtheprimarymadxTheinputformatusedbymadisusedbyarangeofothercodesinadditiontomaditself.Samplecodefragment:while(n<=ncell-5){qfsps:qfsps,at=(n-1)*lcell;mbsps:mbsps,at=(n-1)*lcell+16.0;qdsps:qdsps,at=(n-1)*lcell+32.00;mbsps:mbsps,at=(n-1)*lcell+48.00;n=n+1;}m1:m1,at=(ncell-5)*lcell;qf1:qf1,at=(ncell-5)*lcell;163FigureA.4:Anexampleofageneratedwithmadmbsps:mbsps,at=(ncell-5)*lcell+16.0;qd1:qd1,at=(ncell-5)*lcell+32.00;mbsps:mbsps,at=(ncell-5)*lcell+48.00;A.4.4DataVisualizationmadhasbuiltinsupportforwritinggraphicaloutputusingPostscript.Forplotsrelativetotheaxisofthemachine,thereisalsotheabilitytoaddacartoonschematicoftheelementsalongthedisplayedportionofthebeamline.Plottingisviabasiccommandswithinmad,sonoeditingofplotsispossibleoncetheyaregenerated.FigureA.4showsaplotoftheCSbetafunctiongeneratedusingmad.A.4.5Limitationsmadwasdesignedwiththeintentionofsimulatinghighenergybeams.Assuch,itisimpor-tanttomakesurethatifitisusedtosimulatebeamsfarfrom=1thatnoassumptionsarebeingmadewhichwouldcompromisetheresults.Asaresultofthishighenergyfocus,maddoesnotincludenativelyanyelectrostaticfocusingelements,whichprecludeditscon-164siderationforthepresentdissertation.However,shouldtheneedarise,maddoesallowforuserelements.madalsohasnosupportforRFQsatthetimeofthiswriting.A.5Trace-3D‹Authors:Crandall,K.R.andRusthoi,D.P.‹Institution:LosAlamosNationalLaboratory‹Type:MatrixCode‹Website:http://laacg.lanl.gov‹OpenSource:NoA.5.1Overviewtrace3Disapurematrixsimulationcode.Thetransfermatrixforeachbeamlineelementiscalculatedanalyticallyfromtheparametersoftheelement.Itisprimarilyintendedfordesignandtuningofasimulatedbeamlinetomatchthebeamtosomedesiredparameters.Thebeamitselfisrepresentedpurelybya6x6˙-matrixandcannotconsistofanarbitraryparticledistribution.Trace3Disanextremelymaturecode.Theoriginaltracedatedfrom1973,andwasdevelopedforanumberofentsystemsuntilthemostrecentversion,releasedin1997.Itshowsitsageinthesimplecharacterbasedinterface,butisnonethelessaveryttoolforcertaintypesofbeamdynamicsproblems.Italsofeaturesanextensivemanualwhichisanexcellentreferencefortransfermatricesfortheelementssupportedbytheprogram.165A.5.2SimulationMethodandCapabilitiesAsapurematrixcode,trace3Dcanonlytransportparticledistributionsthatcanbedescribedintermsofa6x6˙-matrix.Thisrulesout,forexample,unbunchedbeams,orbeamswithnon-ellipsoidalphasespaceprojections.Oncetheinitialbeamisexpressedintermsofthismatrix,transportingthatbeamthroughthebeamlineisasimplematterofmatrixmultiplication.Theonlynonlinearthatissimulatedinthiscodeisamodelofspacecharge,whichistreatedasaninstantaneouselectrostatic\kick"totheshapeoftheellipsoid.trace3Dhasalimitedlibraryofavailablebeamlineelementswhichitcansimulate.Althoughthedocumentationreferstotheabilitytoaddelementstothecode,sincethesourcecodeisnotactuallyavailable,theuserisinpracticelimitedtotheprovidedelements.Oneotherbuiltincapabilityofinterestistheabilitytocalculatetheemittanceofabeamgivenmeasurementsofthebeamsizeatthreepointsalongthebeamline.Thisisawellknowntechnique,butthepresenceofabuiltinutilitycouldpotentiallyproveuseful.A.5.3InputandOutputFilesEachtrace3dmodelconsistsofasingleinputwhichcontainsalloftheinformationonbeamdescription,beamlineelements,andsimulationparametersinasingleInaddition,ifanymatchingistobeperformed,theparametersofthisarealsoincludedintheAllofthisinformationiscontainedwithintheinasetofname-valuepairs.Whenthisisloadedintotrace3D,theuserhasaseriesofone-lettercommandsforexecutingthesimulation,editingtheparametersfromwithintrace3D,andvisualizingtheresultsin166variousways.Thereareonlytwomeanstoproduceanoutpute.Ifthe\HardCopy"switchisenabled,trace3dwillimmediatelystorealloutputtoawhichisdumpedtothedefaultprinterwhentheswitchisturned(Fortunately,thereistheoptiontoselectanoutputastheprinter.)Thereisalsoacommandoptionthatwillproduceasummarytableofthebeamenvelopesizeforagivenrun,althoughitwillnotincludeCSparametersormatchinginformation.Samplecodefragment:&DATAER=1875.60000Q=1.W=2.00000XI=100.000EMITI=60.00000060.0000001000.000000BEAMI=3.114000.75360-2.620200.578900.121000.56870BEAMF=0.000000.415400.000001.328900.000000.35700BEAMCI=0.000000.000000.000000.000000.000000.00000FREQ=80.000PQEXT=2.50ICHROM=0IBS=0XC=0.0000XM=14.0000XPM=60.0000YM=20.00DPM=30.00DWM=100.00DPP=30.00XMI=14.0000XPMI=60.0000XMF=14.0000XPMF=60.0000DPMI=30.0000DPMF=30.0000DWMI=100.0000DWMF=100.0000N1=1N2=20SMAX=5.0PQSMAX=2.0NEL1=1NEL2=20NP1=1NP2=20NPRIN=6IJPRIN=1,0011,0021,0061,0101,0141,018MT=8NC=4IPLANE=000MP=1,0041,0081,0121,0160,0000,000MVC=0,000,00,000,00,000,00,000,00,000,00,000,0VAL=0.00000000.00000000.00000000.00000000.00000000.0000000CMT(001)='RFQ'NT(001)=11A(1,001)=-.71000000110.486.44-28.70.0CMT(002)='RFQ'NT(002)=11A(1,002)=0.71000000110.486.44-180.00.0CMT(003)=''NT(003)=1A(1,003)=173.00000CMT(004)='Quad#1'NT(004)=3A(1,004)=-26.20000096.00.00.00.0CMT(005)=''NT(005)=1A(1,005)=39.750000CMT(006)='RFGap'NT(006)=10A(1,006)=0.18155000-40.00.01.00.0CMT(007)=''NT(007)=1A(1,007)=39.750000CMT(008)='Quad#2'NT(008)=3A(1,008)=26.20000096.00.00.00.0A.5.4DataVisualizationThemainscreenoftrace3D(showninFigureA.5)includesseveralavailableplotsforvisualizingtheresultofthebeamcalculation.Theprimaryoneoftheseconsistsofapairof\before"and\after"emittanceplotsinthetransverse(xandyoverlaid)andlongitudinalplanes.Inaddition,thisviewshowsaschematiclayoutofthebeamlinewiththesizeofthe167FigureA.5:Themainscreenoftrace3Dshowingagraphandbeforeandafteremittanceplots.x,yandzenvelopesoverlaidontheplot.Ausefulfeatureisthatsubsequentsimulationscanbeoverlaidontheexistingplot,showingtheofchangingcertainbeamparameters.Theotheravailablevisualizationsisasetofrealspaceprojectionsofthebeam.A.5.5LimitationsBecausethiscodeproducesfewoutputadecentanalogywouldbea\graphingcalcu-lator"forbeamlinesimulation.Theprogramallowsforquickdisplayofbeamlineenvelopes,andwilloverlaytheresultsofmanualchangesforeasyvisualization.Itwillalsoperformbasicofbeamlineparameterstoachieveadesiredbeamshape.However,whilethesettingscanbemoandresaved,anyotherinformationmustbeeithercopiedthescreenorprinted,asnotevenrudimentarycut-and-pastefunctionalityissupported.168A.6TRANSPORT‹Authors:Brown,Carey,andRothacker‹Institutions:Fermilab,SLAC,CERN‹Type:MatrixCode‹Website:https://cdcvs.fnal.gov/redmine/projects/fermitools/wiki/Transport‹OpenSource:Yes‹GraphicalTransportFramework{Author:Rohrer{Institution:PSI{Website:http://aea.web.psi.ch/UrsRohrer/MyWeb/trans.htmA.6.1Overviewtransportisthepredecessorandspiritualancestorofvirtuallyallmodernacceleratorcodes.Firstwritteninalgolin1963,ithasbeenexpandedrepeatedlyovertheyears,andisroutinelycitedbyauthorsofothercodesasaprimaryThecodeisstillinusetodaybysomescientists,andhasbeenwitharelativelyrobustgraphicaluserinterface,ararityinthisprimarilytext-focusedcategory.Themanualforthecodeisextensiveandincludesagreatdealoftheory,butcareshouldbetakenthattheversionofthemanualusedmatchestheversionoftheprogrambeingrun.A.6.2SimulationMethodandCapabilitiesLiketheothermatrixcodesdescribedhere,transportcalculatesthetransfermatrixel-ementsforeachitemonthebeamlineandthenaggregatestheseelementstoproducean169analytictransportmodelfortheentireline.Themostrecentversionoftransportcancalculatematrixelementsuptothirdorderformostdevicetypes,whichisahigherorderthananyothercodedescribedherebesidescosy.Althoughtransportdoesnotnativelysupportparticletracking,arelatedcodecalledturtlecanbeusedforsituationswhichrequiretracking,suchasspacecharge.Beamlineelementssupportedbytransportcomprisearelativelylimitedlist,includingmultipolemagnets,solenoids,andsimpleacceleratinggaps,butnotelectrostaticelements,oranyelementswithatimedependentcomponentsuchasbunchers.transportdoesincludetheabilitytousetransportmatrices.Inadditiontosimulationofbeamlinestothirdorder,transportalsoincludesastrongsetofcommandsforbeamlineOneofthestrengthsoftheroutinesinthisprograminparticularistheabilitytoplaceexplicitconstraintsontheindependentvariablestobeadjusted.A.6.3InputandOutputFilesWhileearlierversionsoftransportusedanativespfortheformatoftheinputin1984theprogramwasalteredtoalsoaccepttheinputformatusedbymad(seeA.4).Thisdoesnotincludethemorecomplexscriptingcommandsusedbymaditself,butonlythespedescriptionsofbeamlinesegments.Uponexecution,transportgeneratesapotentiallylengthysingleoutputThisincludesacompletelistingoftheinputline,thetransportmatrixforeachelementoftheline,thebeammatrixateachpointintheline,andinformationonanyothercommandswhichmayhavebeenexecutedduringtherun.The\print"commandmaybeinsertedintheinputtorequesttheoutputofanumberoftypesofinformationaboutthebeamor170thetransportsystematthatpointinthebeamline.Therequesteddatawillbeaddedtothemasteroutput.Inaddition,foreach\plot"commandissuedintheinputscript,aseparateoutputwillbegeneratedwiththedataforthatplot.Availableplottypesincludeplotsofanyvariablevs.accumulatedlength,schematiclayoutsofthebeamlinegeometry,plotsofthebeamellipse,andplotsoftheofvaryingaspbeamlineelementonanothervariable.Thistypeofplotcanalsoincludestepsbetweeneachiteration.Samplecodefragment(originaltransportnotation):013.48.0/ANG/;15.1.0/MM/0.1;16.14.00.0/SLIT/;16.3.01836.69/MASS/;-17./SEC/;-1.2.53.52.54.20.00.01.2048/BOT/;1.2.58.52.58.50.00.01.198/BEAM/;-1.2.58.52.58.50.00.01.198/NARR/;-1.2.58.52.58.50.01.01.198/WIDE/;-1.2.58.52.58.50.00.01.198/BEA2/;3.0.03;3.0.19;6.1.013.443.013.44;3.0.25;6.1.028.713.028.71/KHE0/;3.1.51/MHB5/;3.0.02;6.1.040.03.040.0/KHE1/;A.6.4DataVisualizationWhiletransporthastheabilitytogeneratedataforplotsasoutlinedabove,itdoesnothaveanybuiltinmechanismforplottingthisdatadirectly,soitmustbeimported171FigureA.6:Asampleplotgeneratedbythegraphictransportframeworkinterfacetotransport.intoanotherprogramforgraphicalvisualization.However,aGUIfortransport,titledgraphicaltransportframeworkhasbeendevelopedbyUrsRohreratPSI.Inadditiontoallowingthedirectplottingofthetheplotsspabove,thisinterfacealsoallowsforvisualizationofmostofthedataintheoutputAfurthercapabilityaddedbythissoftwareissupportforapointandclickapproachtobuildingthebeamlineintheplace;elementscanbearranged,edited,anddeletedusingamenubasedsystemratherthanbyeditingtextFigureA.6showsasampleplotproducedbythisGUI.A.6.5Limitationstransportisnolongerinwideuse-theCERN/SLAC/Fermilabversionhasnotbeenupdatedsince1999.TheGUIversionavailablefromPSIismorerecent(2006),butitisunclearifeitherhasongoingsupport.Neitherversionappearstosupportfor172electrostaticelements,renderingitunsuitableforapplicationswhichrequiretheseelements.Asapurematrixcode,transportdoesnotsupportthesimulationofarbitraryparti-cledistributions,andsocannotsimulateparticledistributionswithcomplextimedomaindistributions.A.7IMPACT‹Authors:Qiang,Ryne,Habib,andDecyk‹Institution:LawrenceBerkeleyNationalLaboratory‹Type:ParticleTrackingCode‹Website:http://blast.lbl.gov/BLASTcodesImpact.html‹OpenSource:NoA.7.1Overviewimpactisaparticletrackingcodespdesignedtohandlehighcurrentsituationswherespacechargearet.Itistechnicallyapairofcodes:impact-z,whichuseslongitudinalpositionastheindependentvariable,andimpact-t,whichusestime.Thecodeisspdesignedwithparallelprocessinginmind,asthissortofhighlynumericalparticletrackingisextremelycomputationallyintensive.Whileimpactisstillinactiveuse,therearelimitedexamplesavailable.Adocumentationdoesexistforimpact-t,butisnotavailableontheprojectwebsite,andthereislessinformationavailableforimpact-z.173A.7.2SimulationMethodandCapabilitiesimpactusesdirectnumericalintegrationthrough3dimensionalgridsofforallcal-culations.Thismethodhasthepotentialtobeextremelyaccurate,becausetheofbeamlineelementsarecalculatedinamorepreciseway,andspacechargecanbecalculatedinfarmoredetail.Thismethodisalsoextremelycomputationallyintensive,andexecutionrequiresapowerfulcomputerorampletimetowaitforresults.Startingparticledistributionscanbeeitherimportedfromanexternalorgeneratedfromawiderangeofstartingrations.Inadditiontousingarbitrarydistributionssuppliedfromexternalcalculations,impactcanalsoautomaticallycalculateforasmalllibraryofstandardelementssuchasquadrupolesandsolenoids.A.7.3InputandOutputFilesThebasicinputforimpactconsistsofaseriesofstatementsgtheconditionsofthesimulationfollowedbyalistofelementscontainedintheacceleratorlattice.impactmayhavetheleasthumanreadableinputofanyacceleratorcode,sinceeverystatementinthisconsistsentirelyofstringsofnumbers.Forexample,alineaquadrupoleelementmightlooklike:0.304201-5.670.0.0140.0.0.0.0.impactwillgeneratearangeofoutputinparticulareithercompleteparticledistri-butionsorsummariesofparticledistributionpropertiesatselectedpointsonthebeamline.Theoutputnamesarebytheprogram,andareamixofdescriptivenames(forexample,Xprof.data)andfortrandefaultoutput(suchasfort.8)Thevaluesintheoutputareofteninnormalizedunitswhichneedtobecombinedwithvaluesinother174toproducemeaningfulresults.Samplecodefragment:21620000202656512940.1400000.1400000.102544616001200000.02.6838596289025144e-100.1400979E-020.1198306E-03-0.9950372E-011.0001.0000.0000.0000.1400979E-020.1198306E-03-0.9950372E-011.0001.0000.0000.0000.2073764E-010.1029707E-050.1337864E+001.0001.0000.0000.0000.00.6e6931.49432e60.25080.50e60.00.0040-210.4/0.7500000E+00752000.400000E-01/0.2239500E+00222000.400000E-01/0.2000000E+0012030.200000E+010.000000E+000.200000E-01/0.1230000E+00122000.400000E-01/0.2400000E+0048201030.200000E+000.805000E+080.142956E+030.1000E+010.150000E-01/0.1230000E+00122000.400000E-01/0.2000000E+0012030.245000E+010.000000E+000.200000E-01/0.2239500E+00222000.400000E-01/A.7.4DataVisualizationTheimpactpackagehasnobuiltindatavisualizationtools.A.7.5Limitationsimpactisanextremelyaccurateandpowerfulcodetoaddresstheclassesofproblemsitissuitedfor.However,itisextremelytouse.Fieldmodelsmustbepreparedforallbutthesimplestelements,andtheprocessforconvertingthosemodelsforusebythecodeisnottrivial.Generatinglatticerequiresadaptationtoapurelynumericscriptinglanguage,andthereisnosimplewaytovisualizetheoutputdataonceitisproduced.Verylimiteddocumentationandexamplesexistforeitherversionofthecode.175A.8OtherCodesThereareanenormousnumberofotheracceleratorsimulationcodesavailable.Whileonlydynac,cosy,andtrackweredirectlyusedforthisproject,anumberofothercodesweretestedandfoundtobeundesirableforonereasonoranother.OftentherewassimplytdocumentationorsupportforaparticularcodetobeusablewithoutagreatdealofOthercodesdidnotincludesupportforlowenergyelectrostaticcomponents.Somesimplydidprovideanyadditionalfunctionalitynotrepresentedbythethreecodesused.Nosinglecodeisa\kitchensink"capableofsolvingallproblemsputtoit,whichisprobablythereasontherearesomanytincompletecodesinexistence.Eachnewcodewaswrittentobeusefulinaspcinstance,andnosingleauthorhasanincentivetoextendtheircodetocoverthemissingusecasesofothers.Also,documentationmaintenance,letaloneuserinterfacedesign,istimeconsumingandoftennotregardedasthebestinvestmentoflimitedtimeorresources.Forreference,TableA.1isatableofunitsusedbyanumberofacceleratorcodes.176FigureA.7:ImageCredit:xkcd.com.UsedunderCreativeCommonsAttribution-Non-commercial2.5License[2].177178DYNACCOSYTRACKTRACE-3DIMPACTMADPARMTEQParticlesx/ycmmcmmmmmcmx'/y'radradradmradradpxp,pypmradz˚(rad)(tto)vo1+nsDf(deg)mpzdegz'MeVKKooDW(keV)radpzpMeVMass(output{mmoamu{eV/c2GeV/c2{Chargeqqqoqqqq{BeamParametersAlpha(x/y)nonenonenonenonenonenonenoneBeta(x/y)mm/mradm/radcm/radm/radm/radm/radcm/radEmittance(x/y)mm*mrad(4RMS)m*rad(1RMS)cm*radm*rad(1RMS)mm*mrad(RMS)m*rad(1RMS)cm*radAlpha(z)nonenonenonenonenonenone{Beta(z)deg/keVmdeg/(DW/W)(%)deg/keVdeg/%m/rad{Emittance(z)keV*deg(4RMS)mdeg*(DW/W)(%)deg*keVns*keV/u(RMS)m*rad(1RMS){OtherParametersParticleMassamuamuamuMeV/c2eV/c2GeV/c2amuLengthcmmcmmmmmcmEnergyMeVMeVMeV/uMeVeVGeVMeVVoltagekVkVVkVVMVVB-FieldkGTGGTTGB-FieldGradientdimensionlessT/m{T/mT/mT/mG/cmFrequencyHz/MHzHzHzMHzHzMHz{TableA.1:ComparisonofUnitsUsedinSeveralAcceleratorCodesAppendixBDynacGUIAsdiscussedinAppendixA,dynacisaparticletrackingcodedevelopedoriginallybyPierreLapostolle,SalbyValero,andEugeneTanke,andmaintainedbyValeroandTanke.Whileitisanextremelypowerfulandcode,ithasafewlimitationsbothintermsoftechnicalcapabilitiesandeaseofuse.Overthecourseofthisproject,dynacgui[56]wasdevelopedasagraphicalfrontendtothedynaccodetoaddresssomeoftheselimitations.dynacguiwaswritteninthematlabcomputingenvironment,andrequirestheusertohaveaninstalledandlicensedcopyofthatprogram.B.1BasicDynacOperationWhenabasicinstallationofdynacwithoutdynacguiisused,thesoftwareconsistsoftwoexecutabletheprimarydynacexecutablewhichperformsalloftheparticletrack-ingandsimulation,andanauxiliaryprogramwhichhandlesplotting.Inordertorunasimulation,aninputiscreatedwhichspthestartingconditionsofthebeamandthentheparametersofeachelementonthebeamlinesequentially.Thisinput(some-timesanachronisticallyreferredtoasa\deck")containsalloftheinformationdescribingthebeamlineitself.Certainbeamlineelements,inparticularacceleratingcavities,solenoids,andRFQs,mayrefertoexternaldistributionInaddition,iftheuserwishestospecifyastartingparticledistributiononaparticle-by-particlebasis,ratherthaninterms179ofCSparameters,acontainingthatdistributionmustbespaswell.Thelocationofeachofthesesupportinglesisspwithintheinputdeck.Oncetheinputdeckisprepared,thedynacexecutableisrunwiththeinputdeckasanargumentand,assumingnoerrorsoccur,theparticlesaretransportedthroughthesimulatedbeamline.dynacthengeneratesanumberofoutputofwhichthefollowingareofinteresthere:‹dynac.short-ashortelementbyelementsummaryofthebeamline,givingthebasicparametersofeachelementandthenumberofparticlesremainingattheendofthatelement.Ifthe\EMIT"or\EMITGR"commandsareencounteredintheinputdeck,ashortsummaryofbeamparametersatthatpointisalsoaddedtothis‹dynac.long-Amoredetailedelementbyelementlistingofbeamlineobjects.Thisalsoreportstransportmatricesforquadrupoles,dipoles,andsolenoids.‹dynac.print-Atabularsummaryofbeamparameterswithoneormoreline(s)perbeamlineelement.‹emit.plot-Thiscontainsthedataforeveryplotgeneratedbythesimulation.Plotsaregeneratedeachtimeanappropriatecommandsuchas\EMITGR"or\ENVEL"isencounteredintheinputdeck.Allplotdataareappendedintothissingle‹OutputDistributionFiles-Whenevera\WRBEAM"commandisencounteredintheinputdeck,dynacwillwriteacontainingthecompleteparticledistributionatthatpoint.Oncetheisrun,anyplotsgeneratedcanbeviewedbyrunningtheauxiliaryplottingprogram.Thisprogramsequentiallydisplayseachplotintheemit.plotwiththeoption180ofsavingtheplottoaseparategraphicsAllotherdataaboutthesimulationiscontainedinthetextoftheoutputThisall-textapproachistypicalofmanyacceleratorcodes,andadesiretoexpendlimitedavailablecodingtimeonimprovingtheunderlyingmodelratherthanfocusingonuserinterfacedesign.However,inthelongrun,amorestreamlinedinterfacecanactuallysavemoretimethanrequiredforitscreation,andhascertainlydonesointhiscase.Thegoalsofdynacguiaretoprovideasimplewaytoquicklyaltertheparametersofabeam-line,enhancedtoolsforviewingresults,bothgraphicalandtextual,tofacilitatesavingandrestoringpriorsimulations,andtoprovideotherutilitiesthatenhancethebasicfunction-alityofdynac.dynacguiisNOTitselfanacceleratorsimulationcode,merelyatooltofacilitatetheuseofdynac.B.2FileStructureofDynacGUIRatherthanhavingonemastercontainingalloftheinformationforaparticularsimula-tion,dynacguidividestheinformationcontainedinthedynacinputintothreethedevicewhichcontainsthephysicalparametersofthedevicesusedtobuildthebeam-line,thelayoutwhichdescribesthearrangementofthosedeviceswithintheaccelerator,andthetunesettingswhichsummarizesthesettingsofthetunableparametersforeachdeviceforagivensimulation.Thesedivisionscorrespondroughlytothefrequencywithwhichthisinformationisex-pectedtochange.Thephysicaldimensionsofamagnetorcavityareunlikelytobealteredoncetheyarebuilt.Thelayoutofabeamlinemaychangeoccasionally,butforthemostpartisalsolikelytoremainstatic.Ontheotherhand,thesettingsfortheindividualdevicesare181likelytochangeforeachnewsimulationrun.Whendynacguiisused,itcombinesthesethreetosynthesizeavaliddynacinputdeckcontainingalloftheseparameters.Auxiliarydevicesuchasdistributions,muststillbespaspartofthedeviceinthedevicesExternalforstartingparticledistributionscanalsobeidenSincedynacguidoesnotchangetheactualoperationofdynacinanyway,oncetheinputdeckisconstructed,anddynacisrun,thesameoutputasdescribedaboveareproduced.B.3UsingDynacGUIOncetheinputhavebeenprepared,dynacguiisrunfromwithinmatlabanddisplaysacontrolpaneltotheuserwhichallowsthemtoselectwhichlayout,device,andtunetheywishtocombine(FigureB.1).TheoptionisalsopresenttoselectaninputparticledistributionalthoughtheCSparameterswillbeusedbydefault.Theusergeneratestheinputwhichcanbevieweddirectlyfromwithindynacguitocheckforerrors,andthenselects\RunDeck"tocallthedynacexecutabletoprocesstheinput.Oncetheprogramcompletesexecution,thedynac'sexecutionreturnmessageisdisplayedintheoutputpane,andallofthegraphsintheemit.plotaresummarizedinthe\GeneratedGraphs"pane.B.3.1DataVisualizationThegraphicaldisplayofgenerateddataistheareainwhichDynacGUIsubstantiallyimprovesontheusabilityofbaredynac.Regardlessofthespplotsselectedwithinthe182FigureB.1:dynacguiMainControlPanelFigureB.2:dynacguiMainZ-AxisPlot183inputthe\Envelope/EnergyPlot"buttonisalwaysavailabletoproduceaplotofthebeamparametersinthedynac.printrelativetothepositiononthezaxis(FigureB.2).Theseparametersinclude:‹xandyRMSbeamandenvelopes‹Longitudinalemittance‹Referenceparticleenergy‹Numberofparticlesremaining‹xandybetafunctions‹Timeandenergyspread‹xandydispersionfunctionsThelocationsofthegeneratedemittancegraphs(seebelow)canalsobeoverlaidontheplot,andtheplotnarrowedtoonlyshowspportionsofthebeamline.Foremittanceplots,dynacguireplacestheplottingroutinesuppliedwithdynacwitharoutinebuiltaroundmatlab'sinternalplottingfunctions.Ratherthanrequiringuserstocyclethrougheachgeneratedplot,alistofallplotsisgeneratedatthetimethesimulationisrun,andtheusermayselectanindividualplotfromthelist.Whenanemittanceplot(FigureB.3)isselected,dynacguigeneratesthestandardfour-panellayoutofgraphs-xvs.x0,yvs.y0,xvs.y,andtimevs.energy.Inaddition,histogramsandRMSwidthsareshownfortheaxesofthelasttwographs.Whileinthisview,a\Tools"menuisalsoavailabletoprovideotherfunctionalitiestotheuser.Toolsincludetheabilitytodisplaybeamdataatthispoint,savethisparticledistributiontoan184FigureB.3:dynacguiEmittancePlotexternalindynac,cosy1,ortrackformat,anddisplayagroupoflessfrequentlyusedplots,suchasxvs.zordp=pvs.x.Inparticular,theabilitytoquicklysaveaparticledistributionatagivenpointwhichcanthenbereimportedintodynacguiasastartingdistributionisquiteuseful.Afurtheradvantageofusingmatlab'splottingtoolsisthatinadditiontothetoolsexplicitlyindynacgui,matlab'sownploteditingtoolsarestillavailable.Thesecanbeusedfortaskssuchasmanualscalingofaxesandsavingimagesinvariousformats.B.3.2Editing,Loading,andSavingInformationInadditiontotheabilitytosaveandloadparticledistributionsdescribedsofar,dynacguihasseveralotherwaystomodifyandsavedata.First,usingthe\EditTuneSettings"button,theusercanalteranyofthetunableparameterslocatedinthetunesettings1cosyisnotnativelyaparticletrackingcode,sothereisnosetformatforaparticledistributionforthatcode.dynacguiexportstothecosyparticledistributionformatdevelopedbyMauricioPortilloatNSCL.185fromwithindynacgui.ThisallowstheusertoquicklyalteroneormoreparametersandrerunthesimulationwithoutmanuallyeditingtextTunessoalteredcanalsobesavedtonewtunesettingsforfutureusewithoutalteringtheexistingInaddition,dynacguicansavetheresultsofanentirerun,includingallplots,inputandoutputandbeaminformationtoaspdirectory,whereitcanbeviewedlaterwithoutre-runningtheentiresimulation.B.3.3FittingOnemajordrawbackofdynacisitslackofanybuiltincapabilityforautomatedofbeamlineparameters.Thiscapability,presentinanumberofotheracceleratorcodes,isextremelyusefulwhenthebeamlinemustbetunedforadesiredconditionatacertainpoint.dynacguicompensatesforthisabsencebyusingthecapabilitiesofmatlab'sOptimizationToolbox.Aftergeneratinganinputdeck,theuserselectsthe\FittingTool"fromthe\Tools"menuwithindynacgui(FigureB.4).Theyarepresentedwithalistofeveryparameterwithinthedeck,includingnon-tunableparameterssuchaselementdimensionsanddriftlengths.Theuserselectswhichparametersaretobeusedasindependentvariables,andoptionallymayselectapointonthebeamlineatwhichadesiredconditionistobemet.(Theendofthebeamlineisusedbydefault.)Finally,adesireddependentvariable,suchasbeamsizeorenergy,isselectedforoptimization.Thetoolcanattempttomaximizeorminimizethedependentvariable,orittoadesiredvalue.Instructionsarealsoincludedforsettingupcustomizedcombinationsofdependentvariables,althoughthisrequirestheusertoeditthedynacguisourcecodethemselves.Oncetheconditionsaresetup,thematlaboptimizeriscalled.Foreachiterationofthe186FigureB.4:dynacgui'stoolscreen.optimizer,dyancguigeneratesanewdeckbasedonthetrialvaluesoftheindependentvariable(s),runsdynaconthedeckandreturnsthevalueofthedependentvariableattheselectedpoint.Fromthepointofviewoftheoptimizer,Dynfuncissimplyablackbox-inputvaluesarefedinandoutputvaluesarereturned.Thisallowsstandardoptimizationmethodstobeusedtotunethesimulationforadesiredcondition.Onedrawbackofthisapproachisthatsinceitisentirelybasedonreadingandwritingdynacinputandoutputitisinherentlyslowerthanacorrespondingstrategywhichdoesnotuserepeateddiskaccess.B.3.4OtherCapabilitiesAsdiscussedinSection5.7,onemajorchallengeinsimulatingReAfromendtoendisthatnoneofthecodesavailable,includingdynac,willsimulateadistributionofparticlesinan187RFQlongerthanoneRFperiod.dynacguiincorporatesasetofroutinestoovercomethislimitation.Whenthe\Gen/Runfort>RFQ"optionisselected,theparticledistributionisownfromthestartofthesimulationtotheentranceoftheRFQ.Atthatpoint,thedistributionissavedtoaanddynacguisplitsthatintoaseriesofsmallerparticledistributioneachcontainingonlyoneRFperiodoftheoriginaldistributionattheentrance.ThosedistributionsarewnoneatatimethroughthesimulatedRFQ,andtheresult-ingoutputdistributionsrejoinedintoasinglelargedistributionwhichisthentransportedthroughtheremainderofthesimulatedbeamline.Mostdataisretainedthroughthispro-cess,sotheemittanceandenvelopeplotsstillfunctionproperly,althoughrunningtotalswithintheRFQitselfmaynotplotproperly.Inadditiontothiscapability,dynacguicangenerateascaledversionofatuneforatmasstochargeratioorenergysetting.Thisfeatureisusefulwhenrescalingabeamlineforaspecieswithatmasstochargeratio.Itshouldstillbeusedwithcaution,however,asdynacguicannotdetermineaheadoftimewhattheactualenergyoftheparticlewillbeatanypointofthebeamline.Assuch,anyscalingthattakesplaceinthemiddleofanacceleratingsectionwillnecessarilybeanapproximation.Finally,dynacguihastheabilitytoexportarudimentaryversionofacosydeckforagivendynacsimulation.Thiscapabilityisextremelylimited,assomeelementsindynacaretorepresentequivalentlyincosy.Further,sincecosyisaray-tracingcodeanddynacisaparticletrackingcode,itistoensureaonetoonecomparisonbetweentheinitialconditionspresentinbothsimulations.188BIBLIOGRAPHY189BIBLIOGRAPHY[1]D.EdwardsandM.Syphers.AnIntroductiontothePhysicsofHighEnergyAccelerators.Wiley-VCHVerlagGmbH&Co.,Weinheim,Germany,1993.[2]RandallMunroe.xkcd.com,xkcd927-Standards.http://imgs.xkcd.com/comics/standards.png,July2011,cited2014-12-02.[3]H.Koivisto,D.Cole,A.Fredell,C.Lyneis,P.Miller,J.Moskalik,B.Nurnberger,J.Ottarson,A.Zeller,J.DeKamp,P.A.Vondrasek,P.A.Zavodszky,andZ.Q.Xie.Artemis-TheNewECRIonSourcefortheCoupledCyclotronFacilityatNSCL/MSU.InProceedingsoftheWorkshopontheProductionofIntenseBeamsofHighlyChargedIons,volume72,page135,Catania,Italy,24-27Sep.2000.ItalianPhysicalSocietyConferenceProceedings.[4]P.A.Zavodszky,B.Arend,D.Cole,J.DeKamp,G.Machicoane,F.Marti,P.Miller,J.Moskalik,J.Ottarson,J.Vincent,andA.Zeller.DesignofSuSI|SuperconductingSourceforIonsatNSCL/MSU|I.TheMagnetSystem.InAIPConferenceProcedings,volume749,pages131{134,Berkeley,CA,2005.AIP.[5]P.A.Zavodszky,B.Arend,D.Cole,J.DeKamp,G.Machicoane,F.Marti,P.Miller,J.Moskalik,J.Ottarson,J.Vincent,andA.Zeller.DesignofSuSI{SuperconductingSourceforIonsatNSCL/MSU{II.TheConventionalParts.NuclearInstrumentsandMethodsinPhysicsResearchSectionB:BeamInteractionswithMaterialsandAtoms,241(1{4):959{964,December2005.[6]H.G.Blosser.ApplicationofSuperconductivityinCyclotronConstruction.InProced-ingsofthe9thInternationalConferenceonCyclotronsandtheirApplications,pages147{157,Caen,France,September1981.[7]P.Miller,F.Marti,D.Poe,M.Steiner,J.Stetson,andX.Y.Wu.CommissioningoftheCoupledCyclotronFacilityatNSCL.InParticleAcceleratorConference,2001.PAC2001.Proceedingsofthe2001,volume4,pages2557{2559vol.4,Chicago,IL,USA,2001.[8]X.Wu,H.G.Blosser,D.Johnson,F.Marti,andR.C.York.TheK500-to-K1200CouplingLinefortheCoupledCyclotronFacilityattheNSCL.InProcedingsofthe1999ParticleAcceleratorConference,pages1318{1320,NewYork,NY,USA,1999.190[9]AvailableBeams|NationalSuperconductingCyclotronLaboratory|MichiganStateUniversity.http://nscl.msu.edu/users/beams.html,cited2014-12-16.[10]D.J.Morrissey.PlanningforaStandardin-FlightRNBExperiment.https://groups.nscl.msu.edu/a1900/experimentplanning/a1900_flowCa.pdf,July2003,cited2014-12-16.[11]X.Wu,D.J.Morrissey,B.M.Sherrill,R.C.York,andA.F.Zeller.TrackingstudiesandperformancesimulationsoftheNSCLA1900fragmentseparator.InProceedingsoftheParticleAcceleratorConference,1997,volume1,pages198{200,Vancouver,CA,1997.IEEE.[12]D.J.Morrissey,B.M.Sherrill,M.Steiner,A.Stolz,andI.Wiedenhoeve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