High Brightness Electron Beam Diagnostics and their ... - CASA

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Let'sassumethethinlensapproximationtobevalid7.Thenthetransfermatrixbetweenthe entranceofthequadrupoleandtheprolemonitoris: Thex;yinthepreviousrelationaretheminimum-functiononewishestoachieveattheprole monitorstation.Thechoiceoftheminimum-functionhastwoimplications. betatronfunctionatthequadrupoleentrance(forinstanceinthehorizontalplane): HencethebetatronfunctionattheOTRlocationcanbeexpressedasafunctionoftheinitial R= x(k)=R212 R21R22! R11R12 f2x;0+R212 1=f1! 10 x;0 (4.38) wherewehaveusethefactthatx;0=x;0=Lwhenonehastakencareofsettingtheupstream opticstosatisfytherelationderivedpreviouslyinEqn.(4.37). Introducingthefocallength(1=f=k1l)andrecallingthatR12=x;0=x(k=0)yields: x(k)=x(0)+R412k21l2 x(0) (4.39) whosederivativewithrespecttothequadrupolestrengthk1is: dx(k) dk=2R212k21l2 x(0) (4.40) latterequationshowsthatthechoiceofx;0,whichwehavesuggestedearliertobeaslargeas possibletoreducetheerroronthebeamsizemeasurement,directlyaectstheslopeofthebeam sizevariationontheprolemonitor:atoolargex;0willgivea\atlooking"variation.Therefore thereisanoptimumbeamvalueforx;0;thisoptimumshouldbedeterminedviaaniterative withthesamekindofrelationintheverticalplane(replacingxindexbyyandR12byR34).The processusingnumericalsimulations. (4.41) 4.4.3Themulti-monitormethod theTwissparametersatthereferencepointbyEqns.(4.24).Indeed,weneedtomakesurethat Anotherwayofvaryingthetransfermatrixbetweenthereferencepointwhereonewishestocompute thesetwoequationsarenotredundant,namelythat: ofthismeasurementisthatnoelementhastobevaried.Howevertogetaprecisemeasurementa dedicatedopticallatticesettinggenerallyneedtobeelaborated. Letanalyzequantitativelythemethod.Thebeamsizeonaprolestationkandlarerelatedto requiresatleastthreemonitorsbutoneshouldusemoreofthemforredundancy.Anadvantage thebeamparametersandthebeamprolemeasurementstationistomeasurethebeamproleat dierentpositionalongthebeamlinewhichareseparatedbynon-dispersiveoptics.Thismethod 20)butitprovideseasieranalyticalresultsanddoesnotchangesignicantlythephysicsofthepresentdiscussion. Thetreatmentofthefullproblemincludingthethicklenstransfermatrixisdonevianumericalmodeling. 7Thisisafalsestatementifweconsiderthewholerangeofthemagneticstrengthforthequadrupoles(20
zero): Thesethreedeterminantsyieldthesameequation(assumingtheR11andR12tobedierentfrom Henceinorderthelatterequationtobeveried,onemusttakecaretosettheopticallatticeso advancebetweenkandl: whichimplies,usingthegeneralformulationofabeamtransfermatrixintermofbetatronphase R11;kR12;lR12;kR11;i6=0 sin()6=0 (4.44) (4.43) Anothercarethathastobetakenistomakesurethatattheprolemeasurementstationthebeam isnotatawaist;thiswillenlargetheerrorbarsonthemeasurement(oneshouldmakethebeam aslargeaspossiblecomparedtotheerroronthebeamsizemeasurement). 4.4.4SimulationofEmittanceMeasurementintheIRFEL (withn2N). thatthebetatronphasebetweentheviewersbeingusedinthemeasurementisdierentfromn Afterthedecompressorchicane,thebeamlineconsistsofaquadrupoletripletandisinstrumented theOTRlocation(suchoptimizationwillbediscussedinmoredetailinChapter5).Afterhaving makesurewecanhavea\right"beamsizevariationoverthequadrupoleexcitationrange.Typically theprolemonitor.Toperformsuchmeasurementoptimallyweneedtosettheupstreamopticsto weusethemagneticopticscodedimadtottheupstreamquadrupolestosatisfyEqn.(4.37)at scanmethod,weusetheOTRmonitorlocatedinthedumpbeamline3.43mdownstreamtheexitof thelastquadrupoleofthistripletquadrupole.Thereforeinthiscasewehaveinvestigatedwhether thisquadrupolecouldbeusetovarythetransfermatrixwhileobservingbeamsizevariationon withtwoOTRviewers.Forthesimulationoftheemittancemeasurementusingthequadrupole minimumbetatronvalueattheOTRlocationminimizestheerrorbarsonthededucedemittance (andontheotherdeducedTwissparameters).Itisseenthat6misareasonablenumberforwhich thesystematicerrorsachievedonemittancemeasurementcanbewellwithinthedesired10%level. plottedinFigure4.14.Fromthisgureonecanobviouslynoticethatthechoiceofthelargest sizevariationispresentedingure4.13.Thededuceduncertaintiesontheemittanceforthesetwo dierentvaluesoftheminimumbetatronfunctionversustheerrorsonbeamsizemeasurementis properlytunedtheseupstreamquadrupoles,wehavenumericallystudiedthevariationofbeam Tofullysimulatethewholemeasurementandbenchmarkourdataanalysisalgorithm,wepropagate sizefortwodierentminimum-functionsatthelocationoftheOTRviewer.Atypicalbeam wesimulatethemeasurement:wevarythequadrupolestrengthandforeachsettingpropagatethe parametersuptothelocationoftheOTRmonitorwherewecomputeandrecordthebeamsize. theentranceofthevaryingquadrupole(i.e.lastquadrupoleofthetripletaforementioned).Then usingthedimadcodetheexpectedparameteratthelinacexit(ascomputedwithparmela)upto Intable4.4wecomparetheresultsobtainedonthecomputedbeamparametersatthequadrupole entrancefacewiththedimadinitialparameters:theresultsareinexcellentagreement.Wealso comparetheerrorbarsobtainedwithourerroranalysiswiththeerrorbarsstatisticallycomputed onasetof200simulationsofthemeasurementinwhichthebeamsizeisrandomlygeneratedalong anormaldensitycenteredonthebeamsizecomputedwiththeopticscodewithavarianceequalto thermsresolution(60m).Theconclusionisthattheerrorpropagationagreeswiththevariances
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HighBrightnessElectronBeamDiagnosti
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eratedupto48MeVpriortothelasingsyst
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IthanktheCEBAFmachineoperators,with
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3.4MeasurementoftheLongitudinalResp
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5.6ZerophasingTechniqueforBunchLeng
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ListofTables 3.2Comparisonofcoecien
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ListofFigures 1.1Comparisonoftheexp
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3.11Momentumcompactionandnonlinearm
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4.18Overviewofthephasespacesampling
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5.16Interferogrammeasuredfordierent
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6.10Comparisonofthermstransversehor
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Chapter1 UVdomainandareplannedtogen
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space-chargeinthelowenergyregime,an
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!Vjitsthevelocity,and!Xjisthepositi
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equation boundarybetweenvacuumandam
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10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.
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1.0 0.8 0.6 0.4 0.2 E=10 MeV E=42 M
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00000000000000000000000000000000000
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harmonicwithproperchoiceoftheKvalue
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Bu(rms)0.28T ParameterValueUnit Nu
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2.7TheJeersonLabIRproject usedasexp
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inducedbyspacechargeisnotaconcernin
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Golay Cell Signal (V) Golay Cell Si
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Golay Cell Ouput (V) Golay Cell Oup
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150 100 5 4 Figure5.19:Energyspectr
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Figure5.23:picturaleectoflongitudin
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σ x (m) x 10−3 5 4 3 2 1 0 0 5 1
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BeamDynamicsStudies Chapter6 undula
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x,y (mm) 6.0 4.8 3.6 2.4 1.2 x y 0.
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Space Charge over Emittance Ratio (
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numericalsolution[56].Thisapproxima
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0.03 . .... . .. ... . .. ..... . .
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ε x (mm−mrad) Nominal 6 4 2 cryo
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2.2 2 1.8 Figure6.10:Comparisonofth
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6 4 2 Figure6.12:\R55"transfermapfo
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10 1 5 10 0 500 1000 1500 2000 2500
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EnergySpread(%) BunchLength(mm) Par
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15 Effect of RMS energy Spread 10 F
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6.4.4BunchSelfInteractionviaCoheren
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100 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0
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Inthesecondseriesofrun,wewereableto
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Conclusion Chapter7 Therecirculator
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[2]Y.Shibata,T.Takahashi,T.Kanai,K.
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[29]J.-C.Denard,C.Bochetta,G.Traomb
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[65]B.C.Yunn,\ImpedancesintheIRFEL"
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TEM:transverseelectricmagnetic. TOF
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B.2Anoteonspacecharge Wedenetheslop
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B.3.3PARMELA FeaturesofJeersonLabVe
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Initialization MAIN Stop INPUT DECK
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C.0.6TheDispersionRelationsfor^S(!)
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have: Howeveritshouldbenotedthatweh
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FigureD.1:OverviewoftheRF-controlsy
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High Brightness Electron Beam Diagnostics and their ... - CASA

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