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

transversebeamsizeeectleadstoanunderestimateofthebunchlengthbyaapproximatelya factorof2.However,theeectofthebeamspotsizeisverysmallontheCSRandCTRspectrum. Inthecaseofellipsoidalbunch,i.e.theworstcasethatcanhappenintheIRFEL,theerrorisat the10%level. Hence,wewillassumethemeasurementofCTRorCSRintheIRFELisdirectlyrelatedtothe
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Figure5.5:Eectoftransversebeamsizeonthe3D-BFF.Forthreedierenttypeofbunch(ellipsoidal,pancakeandlinechargebunch),theBFF(A),theCTR(B)andCSR(C)powerspectrum (B) (C)
sizeeectorfromtheangularbunchformfactor. 5.3.1TheuseoftheBFFtocomputeandmonitorthebunchlength 0:3radandaregivenfora20%frequencybandwidth. longitudinalbunchdistribution,withoutany\contamination"comingfromthetransversebeam arenumericallycomputed.Thepowerspectrumarecomputedassuminganangularacceptanceof
Underthe\linecharge"assumptionmentionedearlier,theBFFonlydependsonthebunchlength. Inthissection,wederiveasimplerelation,withoutmakinganyassumptionsonthebunchdensity function,thatallowsonetocomputethermsbunchlengthfromthebunchformfactor.Let'sstart withtheBFFdenition,byintroducingthewavelengthnumber=1=forconvenience,andby replacingtheexponentialfunctionintheFouriertransformbyitsTaylorexpansion:
Power W/ A/20%BW
(A)
Power W/ A/20%BW
z=100 m, r=1000 m
(ellipsoidal bunch)
z=0 m, r=1000 m
(pancake bunch)
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(line charge bunch)