High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
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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:<br />
beendiscussedbyS.Benson[12].Thegaincanbeparametrizedas: electronbeamparametersontheFEL-gainbyconsideringtheapproximate1Dmodelthathas whereisthereducedenergytransmittedbytheelectronbeamtotheelectriceldoftheoptical mode<strong>and</strong>W0istheenergyoftheopticalmodeconsidered(i.e.theonewhichissupposedtobe amplied).ThederivationofanalyticformulafortheFELgainhasbeenperformedinreference[11] <strong>and</strong>isbeyondthescopeofthisthesis.Howeveritseemsworthwhiletostudytheeectsofthe Gdef =mc2W0 (2.24)<br />
inEqn.(2.23).The'scoecientsinEqn.(2.25)representdegradationfactorsofthegain. oftheincomingelectronbeam:sinceelectronsinabunchdonotallhaveanenergyexactly where<strong>and</strong>Iaretheelectronbeamenergy<strong>and</strong>peakcurrent.Qisafactorthathasbeendened correspondingtotheresonantenergy;thisfactorisdenedas: isthegaindegradationduetoenergyspread<strong>and</strong>isaresultofthenon-mono-energeticcharacter g=0:0004IQNuN2~"f (2.25)<br />
onthecoecient: theharmonicnumber. whereisthereducedrms-energyspreadoftheincomingelectronbunches,<strong>and</strong>h,asbefore,is ~"isthedegradationduetobeamnon-zerotransverseemittance.Thisdegradationalsodepends = 1+4p2hNu=2 1 (2.26)<br />
ofimportancewhenconsideringthestartupofFELinteraction,ourprimaryconcerninthepresentsection.<br />
6Inthisdissertation,gaindesignatestheso-called\smallsignalgain"intheFELliteraturesinceitisthequantity ~"= q1+(42~"N=)2 1 (2.27)
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