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

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AppendixC C.0.4Introduction BeamDistributions DispersionRelationsforBunched emissionfromabunchedelectronbeamhavebeenusedbymanyauthors.Howeverwebelieve givethephase,butonlyonetermcontributingtothephase(dependingonthebunchlongitudinal distributionproperties). Dispersionrelationstocomputethephaseassociatedtotheelectriceldgeneratedviacoherent C.0.5Background themathematicalproofisnotalwaysproperlyderived:thesedispersionrelationsareappliedto aderivationofsuchrelationsanddiscussthefactthatthesedispersionrelationdonotafortiori functionswhichcannotbeexpressedasCauchyintegrals.Inthepresentaddendumwepresent showninthecaseofbunchedelectronbeamthatiftheemittedradiationisobservedatwavelength comparableorlargerthatthebunchlength,theelectronsinthebunchemitcoherently.Insucha Therearemanywayselectronscanemitradiationastheirenvironmentismodied.Ithasbeen where^S(!)istheFouriertransformofthelongitudinaldistributionS(t).Theproblemthathas case,thespectrumoftheradiationwritesas: transformoftheelectriceld,tocomputethebunchformfactorphase. Inthemanypapers,thefunctionlog(^S(!))isdenedandthecomplexpartofthisfunction(which beenstudiedistousethepowerspectrum,whichisproportionaltothemodulusoftheFourier isthephaseof^S(!))iscalculatedusingthestandarddispersionrelations.Howeverweshallsee Etotal(!)=qN(N1)qj^S(!)jE1e(!) (C.1) belowthatlog^S(!)doesnothavethe\right"propertiesandcannotbegenerallywrittenasa log^S(!)function. Cauchyintegralandmorecareshouldbeusedwhentryingtorecovertheimaginarypartofthe 180
C.0.6TheDispersionRelationsfor^S(!) WhenS(t),thebunchdistributionhasthe\right"properties,itsFouriertransformhassome interestingproperties:itsimaginaryandrealpartareHilbertconjugate,i.e.theyarerelatedvia Hilberttransformation.The\right"propertiesS(t)mustsatisfyareasfollows: ThelastiteminsureS(t)isacausalfunctionandthetwootherareequivalenttoS(t)2L2,the limt!1S(t)=0andS(t)!0fasterthan1=t, S(t)=08t
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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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shortterm,touseasbeamdensitymonitor
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Alongwiththeseimplementedoperations
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whereiistheerrorontheithbeamsizemea
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Let'sassumethethinlensapproximation
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obtainedviathestatisticalanalysis.T
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20 18 16 . 14 . 12 . Figure4.14:Rel
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100 10 −3 10 −2 10 −1 10 that
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multislits mask (copper) Aluminum F
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TheReductionoftheSpaceChargeconditi
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. . . . . . . . . . . . . . . . . .
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Table4.7:Typicalsystematicerroronem
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180 8 160 6 Figure4.22:Anexampleof2
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4.0 3.5 3.0 2.5 Figure4.24:Emittanc
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Characterization LongitudinalPhaseS
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concentrateonthebeamparametersinthe
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1.1 1 mrad 0.9 5 mrad mainlyduetoth
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Population Population 100000 90000
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Theequation5.8yields: f()=jZ+1 11Xn
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presentanoutlineofthisproofbelow,an
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contrastintheCEBAFmachine,varyingas
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1.5 1 correspondtothevarianceofveco
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Ε’ 2 B Mirror M 2 Ε2 Polarizer
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FinallyitisinterestingtonotethatFou
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Itsautocorrelationis:S(z)=8>:(1=w2)
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drivelaserwhereasin(A),suchoperatio
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expansionoftheBFFderivedinthischapt
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Asarstapproximation,wecanestimatetr
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errorpropagation8theoryappliedonEqn
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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
Page 151 and 152: 150 100 5 4 Figure5.19:Energyspectr
Page 153 and 154: Figure5.23:picturaleectoflongitudin
Page 155 and 156: . .. .. . .. . . .. . .. . . .. . .
Page 157 and 158: σ x (m) x 10−3 5 4 3 2 1 0 0 5 1
Page 159 and 160: BeamDynamicsStudies Chapter6 undula
Page 161 and 162: x,y (mm) 6.0 4.8 3.6 2.4 1.2 x y 0.
Page 163 and 164: Space Charge over Emittance Ratio (
Page 165 and 166: numericalsolution[56].Thisapproxima
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Page 169 and 170: ε x (mm−mrad) Nominal 6 4 2 cryo
Page 171 and 172: 2.2 2 1.8 Figure6.10:Comparisonofth
Page 173 and 174: 6 4 2 Figure6.12:\R55"transfermapfo
Page 175 and 176: 10 1 5 10 0 500 1000 1500 2000 2500
Page 177 and 178: EnergySpread(%) BunchLength(mm) Par
Page 179 and 180: 15 Effect of RMS energy Spread 10 F
Page 181 and 182: 6.4.4BunchSelfInteractionviaCoheren
Page 183 and 184: 100 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0
Page 185 and 186: Inthesecondseriesofrun,wewereableto
Page 187 and 188: Conclusion Chapter7 Therecirculator
Page 189 and 190: [2]Y.Shibata,T.Takahashi,T.Kanai,K.
Page 191 and 192: [29]J.-C.Denard,C.Bochetta,G.Traomb
Page 193 and 194: [65]B.C.Yunn,\ImpedancesintheIRFEL"
Page 195 and 196: TEM:transverseelectricmagnetic. TOF
Page 197 and 198: B.2Anoteonspacecharge Wedenetheslop
Page 199 and 200: B.3.3PARMELA FeaturesofJeersonLabVe
Page 201: Initialization MAIN Stop INPUT DECK
Page 205 and 206: have: Howeveritshouldbenotedthatweh
Page 207: FigureD.1:OverviewoftheRF-controlsy
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