High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA High Brightness Electron Beam Diagnostics and their ... - CASA
halfoftheelectronisdeceleratedwhiletheotherhalfisacceleratedresultinginanullamplication. Thisistrueintherstperiodofthewigglerbutinveryshorttime,themoreenergeticelectrons catchuptotheless-energetic,introducinganenergymodulationwithintheelectronbunchwhich, inturn,leadstoalongitudinaldensitymodulationormicro-bunching:theelectronbeamthat hasaninitialdistributiondependingonthepreviousdynamics,soonconsistsinasub-bunchesof electronsspacedatthespontaneouswavelength.Itturnsoutthatiftheelectronenergyisslightly higherthantheresonantenergyitresultsinanetgaini.e.anamplicationofthelightpulses. Thissimplemodelassumesthatelectronswithinabunchdonotinteracteachwithother,thatis single-particle-dynamicsmodelisvalid.Whensuchamodelisvalid,likeinthecaseoftheIRFEL, theFELissaidtooperateintheComptonregime. 2.5.3FELGain Theamplicationofthespontaneousemissionisquantiedbythegainthatcorrespondstothe ratiooftheenergytransmittedbytheelectronbeamtothecopropagatingelectromagneticwave totheinitialenergyofthecopropagatingelectromagneticwave.Thegain6isdenedas: beendiscussedbyS.Benson[12].Thegaincanbeparametrizedas: electronbeamparametersontheFEL-gainbyconsideringtheapproximate1Dmodelthathas whereisthereducedenergytransmittedbytheelectronbeamtotheelectriceldoftheoptical modeandW0istheenergyoftheopticalmodeconsidered(i.e.theonewhichissupposedtobe amplied).ThederivationofanalyticformulafortheFELgainhasbeenperformedinreference[11] andisbeyondthescopeofthisthesis.Howeveritseemsworthwhiletostudytheeectsofthe Gdef =mc2W0 (2.24) inEqn.(2.23).The'scoecientsinEqn.(2.25)representdegradationfactorsofthegain. oftheincomingelectronbeam:sinceelectronsinabunchdonotallhaveanenergyexactly whereandIaretheelectronbeamenergyandpeakcurrent.Qisafactorthathasbeendened correspondingtotheresonantenergy;thisfactorisdenedas: isthegaindegradationduetoenergyspreadandisaresultofthenon-mono-energeticcharacter g=0:0004IQNuN2~"f (2.25) onthecoecient: theharmonicnumber. whereisthereducedrms-energyspreadoftheincomingelectronbunches,andh,asbefore,is ~"isthedegradationduetobeamnon-zerotransverseemittance.Thisdegradationalsodepends = 1+4p2hNu=2 1 (2.26) ofimportancewhenconsideringthestartupofFELinteraction,ourprimaryconcerninthepresentsection. 6Inthisdissertation,gaindesignatestheso-called\smallsignalgain"intheFELliteraturesinceitisthequantity ~"= q1+(42~"N=)2 1 (2.27)
Bu(rms)0.28T ParameterValueUnit Nu u 40 where~"isthebeamtransverserms-emittanceandNisthenumberofbetatronoscillationsalong Table2.1:ParametersofthechosenwigglerfortheIR-DemoFEL. K2 Gap 0.5 12mm 2.7cm thewiggler.fisthegainreductionduetothellingfactorfortheopticalmode;itsimplyresults fromthenonintegraloverlapoftheelectronbunchandtheradiationpulseandisapproximatedby: isthegainreductionduetoslippage:=1 f=1 1+4~"= 1+hNu 3z (2.28) beamparametersrequiredtodrivetheIRFEL. wherezistherms-longitudinalbunchlength. tobemoreecient,requirehigh-charge,ultrashort-bunchelectronbeam.Wenowpresentthe FromEqn.(2.25)weseethatthegainisproportionaltopeakcurrentwhichinturnisproportional tothechargeperbunchandinverselyproportionaltothelongitudinalbunchlength.HenceFELs, (2.29) 2.6CharacteristicsoftheIRFELdriver-accelerator TodiscussthecharacteristicsrequiredfortheelectronbeamgeneratedbytheIR-Demodriver accelerator,welistinTable2.1thespecicationsonthewigglermagnetwhichhavebeenderived fromtherequirementsonphotonbeamparametersdenebytheexperimentalists.IntheJLabFEL IR-demo[15](seegure2.11),thechargeperbunchwasinitiallychosentobe60pC,themaximum valuethatyieldsatolerableemittancegrowthduetospace-charge.Theaveragecurrentshouldbe ashighaspossibletomaximizetheaveragepowerofthelaser.Itisafunctionofthechargeper bunch,andthebunchrepetitionthatdependsonthephotocathodedriver-laserwhichinturnmust beasub-harmonicofthesuperconductinglinacoperatingfrequency(1497MHz).Themaximum arbitrarywavelengthbychoosingtheproperenergy.Experimentally,theoutputwavelengthislimitedtoacertain bunchrepetitionrateis74:85MHzanditislimitedbytheelectronsource.Therepetitionrate astheoneusedtolasewithanoutputwavelengthof6m rangethatdependsontheFEL-opticalcavitymirror.Forinstancethemirrorusedtolaseat3marenotthesame currentthatcanbereachisapproximately5mA. Sincetheenergydoesnotaectthegain,anditsonlyimplicationisonFELwavelength:theIR- oftheelectronbunchwasindeedinitiallysetto37:425MHzwhichmeanthemaximumaverage demoisforeseentoinitiallylaseintheregion3m-6mrange7(laterthisrangewillbeextended 7Theoreticallytheoutputwavelengthonlydependsonenergy.Hencewecould,intheIRFELoperateatany
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Bu(rms)0.28T ParameterValueUnit Nu u 40<br />
where~"isthebeamtransverserms-emittance<strong>and</strong>Nisthenumberofbetatronoscillationsalong Table2.1:ParametersofthechosenwigglerfortheIR-DemoFEL. K2 Gap 0.5 12mm 2.7cm<br />
thewiggler.fisthegainreductionduetothellingfactorfortheopticalmode;itsimplyresults fromthenonintegraloverlapoftheelectronbunch<strong>and</strong>theradiationpulse<strong>and</strong>isapproximatedby: isthegainreductionduetoslippage:=1 f=1 1+4~"= 1+hNu 3z (2.28)<br />
beamparametersrequiredtodrivetheIRFEL. wherezistherms-longitudinalbunchlength. tobemoreecient,requirehigh-charge,ultrashort-bunchelectronbeam.Wenowpresentthe FromEqn.(2.25)weseethatthegainisproportionaltopeakcurrentwhichinturnisproportional tothechargeperbunch<strong>and</strong>inverselyproportionaltothelongitudinalbunchlength.HenceFELs, (2.29)<br />
2.6CharacteristicsoftheIRFELdriver-accelerator TodiscussthecharacteristicsrequiredfortheelectronbeamgeneratedbytheIR-Demodriver accelerator,welistinTable2.1thespecicationsonthewigglermagnetwhichhavebeenderived fromtherequirementsonphotonbeamparametersdenebytheexperimentalists.IntheJLabFEL IR-demo[15](seegure2.11),thechargeperbunchwasinitiallychosentobe60pC,themaximum valuethatyieldsatolerableemittancegrowthduetospace-charge.Theaveragecurrentshouldbe ashighaspossibletomaximizetheaveragepowerofthelaser.Itisafunctionofthechargeper bunch,<strong>and</strong>thebunchrepetitionthatdependsonthephotocathodedriver-laserwhichinturnmust beasub-harmonicofthesuperconductinglinacoperatingfrequency(1497MHz).Themaximum<br />
arbitrarywavelengthbychoosingtheproperenergy.Experimentally,theoutputwavelengthislimitedtoacertain bunchrepetitionrateis74:85MHz<strong>and</strong>itislimitedbytheelectronsource.Therepetitionrate<br />
astheoneusedtolasewithanoutputwavelengthof6m<br />
rangethatdependsontheFEL-opticalcavitymirror.Forinstancethemirrorusedtolaseat3marenotthesame currentthatcanbereachisapproximately5mA. Sincetheenergydoesnotaectthegain,<strong>and</strong>itsonlyimplicationisonFELwavelength:theIR- oftheelectronbunchwasindeedinitiallysetto37:425MHzwhichmeanthemaximumaverage demoisforeseentoinitiallylaseintheregion3m-6mrange7(laterthisrangewillbeextended 7Theoreticallytheoutputwavelengthonlydependsonenergy.Hencewecould,intheIRFELoperateatany
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