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

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CaseInterferogramx (b) (d) (a) (c) (e) FWHM(m)(mm)(mm)(mm) 200 240 320 280 0.42150.34150.3794 0.53160.39870.4604 0.78430.57630.6723 1.25541.11641.1839 1.46671.62401.5433 ypxy Table5.2:MeasuredbunchlengthandtransversebeamdimensionforthecasesreportedinFig.5.16. Computationofthelongitudinalbunchdistribution Usingthemethodologypreviouslyexposed,wehavedevelopedano-lineanalysiscodethatallows thecomputationofthebunchlongitudinaldistribution. henceforthisthe\average"method. theinterferogram,ortherightpart;wecanalsosymmetrizetheinterferogrambycomputingthe Fouriertransform.Wehaveimplementedthreemethods:wecaneitheruseonlytheleftpartof averageoftheleftandrightpartoftheinterferogram.Theautocorrelationsso-obtainedandtheir correspondingFouriertransformsarepresentedrespectivelyinFig.5.17-AandFig.5.17-B.Wecan noticethatthereisnotmuchdierencebetweenthecomputedspectra.Themethodwewilluse form,i.e.theenergyspectrum,willnotbereal.HencetherststepconsistsofsymmetrizingtheBecausetheexperimentallyobtainedinterferogramisnotperfectlysymmetric,itsFouriertransmirrordisplacement.Howevertheinformationcontainedatlargedisplacementmightnotberelevanttocomputetheenergyspectrum.Toverifysuchassumption,wehaveuseddierentlengthof thecentralpartofautocorrelationpresentedingure5.14:weused64,128,256,and512points; pointsinthesequencemustbeapowerof2.Fromourpreviousdiscussionwenoticedthatthe stepsizeintheFourierplane(i.e.theenergyspectrum)increasesinverselytothenumberofpoints inthestandardplane(i.e.,theinterferogram).Thereforeanaiveargumentwouldbe,foragiven notethatbecauseweusedanFFTalgorithmthatemploysaradix-2algorithm,thenumberof Moreover,theinterferogram(andthereforetheautocorrelation)canbemeasuredforarbitrary smoothed.Ontheopposite,ifthenumberofpointsistoolarge,becausepointscorrespondingto notprovideanyinformationforthepowerspectrum(i.e.theautocorrelationistheoreticallyzero). Fromgure5.18weseethatindeedthereisacompromiseonthenumberofpoints;ifthisnumber istoosmall,thenestructureofthespectrumislostandthereconstructedbunchdistributionis twoargumentsagainstthisfact:(1)themeasurementcantakeuptoonehours(dependingon themirrordisplacementstepsize)and(2)forlargevaluesofthedisplacementthetwoTRpulses associatedwiththeelectronbunchdonotoverlapanymoreandthereforetheinterferogramdoes mirrordisplacementstep,tomeasuretheinterferogramoveralargerange.Practicallythereare Thislowfrequencypartofthespectrummustsomehowbereconstructed,otherwisetheexperi- frequencycutoinducedbytheniteaperturesizeoftheGolaycelldetectorentrancewindow. pointitseemstovanish.Inourcasetypicalvaluesare1:5mm. mentallycomputedenergyspectrumcannotbeusedtorecoverthebunchlongitudinaldistribution. Forsuchapurposeweextrapolatethislowfrequencyregionofthespectrumusingthefactthat largedisplacementsconsistsonlyofnoise,thisnoisepropagatesonthespectrumandagreatdetail offakestructureappears.Aproperchoiceisto\manually"cutadvisotheautocorrelationatthe Experimentallywecanclearlydistinguish,forawavenumberofapproximately10cm1,thelow
expansionoftheBFFderivedinthischapter,thespectrumcanbeextrapolatedusingtheequation: I()=a0+a22+O(3).Thepointofattachmentofthisparabolaischosentobeintheneighbor- thefrequency;theCTRspectrumhasthesamedependence.Hence,usingthegeneralpolynomial hoodofthelowfrequencycuto.Thecoecienta2anda0arecomputedbyusingthecontinuity conditionsatthecutopoint:weassumeboththespectrumanditslocalderivativewithrespect towavelengtharecontinuous.Ingure5.19weperformdierentlowfrequencyextrapolationsof forlargefrequency(i.e.lowwavelength),thebunchformfactorhasaquadraticdependenceon ontherecoveredlongitudinalbunchdistributionisshowningure5.20.Itisinterestingtonote thatonewaytorejectunphysicaldistributionistorejectalltheparabolicextrapolationsthatgive asignicantnumberofnegativevaluesinthebunchlongitudinaldistributions. atthecut-opointtocomputethecoecienta0.Theinuenceofthesedierentextrapolations theenergyspectrumbyvaryingtheparametera2andusingonlythecontinuityofthespectrum 5.6ZerophasingTechniqueforBunchLengthMeasurement awaythatthebunchcentroidcoincideswithazeroacceleratingelectriceld.Hencethecavities investigatedthepossibilityofitsapplicationtomeasurethebunchlengthintheIRFELaccelerator. ThezerophasingmethodusesRFacceleratingcavitiesphased90degreesocresti.e.insuch Ithasbeendemonstratedtoresolvebunchlengthinthesubpicosecondregime[52].Thereforewe Theso-calledzerophasing(orbackphasing)techniquehasproventobeaverypowerfulmethod. 5.6.1BasisoftheMethod inducealongitudinallydependentenergyrampalongthebunch.Then,bymeansofaspectrometer, theenergydistributionismappedintothetransversedirection,andthebeamtransversedensity thedispersioninthechicaneatthebeamprolemeasurementstationisabout2timeslessthan anoptimumchoice:themaximumbeamenergythatcanbedeectedintothedumpisabout readilyavailabletoperformsuchmeasurements:wecanusetheenergyrecoverydumplineorthe thismethodweonlyneedacceleratingcavitiesandspectrometers.Therearetwospectrometers theoneattheOTRprolemonitorlocatedintheenergyrecoverydump. Despitethefactthattheenergyrecoverydumphasbeenchosenasaspectrometer,itisnot ismeasuredwithabeamprolestationlocatedinthedispersiveregion.Thereforetoimplement 24MeV5whichimpliesthatthefourlastcavitiesofthecryomodulemustbeturnedoand/or usedaszerophasingcavities.Thenon-zerophasedcavitiesareoperatedundertheirnominalsettings (acceleratinggradient7.33MV/m,phase-9.6deg)givingabeamenergyof23.74MeV.Atsuchan rst4-bendchicane.Preliminaryconsiderationshaveshownthatthelatterisnoteasilyworkable: intermediateenergy,thedynamicsof60pCbunchesisnotemittancedominated,requiringastudy ofspacechargeeectsonthemeasurement. IntheFEL,theenergyrecoverydumplineconsistsofaquadrupoleandanOTRprolemonitor. ThedispersionattheOTRlocationwhenthequadrupoleisturnedoisexpectedtobe=75cm; thislattervaluecanbereduced,ifneeded,usingtheupstreamquadrupole. Itshouldbestressedthatthemeasuredbunchlengthisthebunchlengthattheexitofthefourth cavityi.e.inthemiddleoftheSRF-linac(theparmelapredictedbunchlengthandphasespace slopeatthislocationare370mand-48.74MeV/mrespectively). FollowingnotationofReference[52],wewritethehorizontalpositionxonthebeamprole 5PrivatecommunicationfromR.Legg,January1998
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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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Study TheFELdriveraccelerator:Latti
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ParameterValue x -0.178 x(m) 8.331
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Thepurposeofmeasuringthetransverser
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computedusingthelatticeset-upuseddu
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etatronexcitationaspicturedingure3.
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∆ x (mm), Corrector 0F00H ∆ x (
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1 0.5 0 spreadoftheparticlewassetto
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2 1 −5 −3 −1 1 3 5 k (m q −
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Experimentallythecalibrationcoecien
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tioned.FromthetransferfunctioninFig
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Pickup Experiment #2 #3 #4 Simulati
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Fromthesebothmeasurementitispossibl
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. . . . . . . . . . . . . . . . . .
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10 5 Sext. ON Figure3.20:Eectofthes
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spaceabeamthatconsistsofNparticles,
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Asforthegeometricemittanceonecanden
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(a) ceramic radiator beam x-wire be
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and validundertheassumptionofaunifo
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1000 900 800 700 Figure4.4:Steadyst
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Fraction of Beam enclosed within (%
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5 2 2 3 4 5 6 7 8 9 10 0 10 5 2 Foi
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Actuator Inserts Foil and Mirror CI
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Page 123 and 124: Theequation5.8yields: f()=jZ+1 11Xn
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Page 159 and 160: BeamDynamicsStudies Chapter6 undula
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Page 187 and 188: 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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