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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inducedbyspacechargeisnotaconcerninthepresentdiscussion.<br />
undulatorvacuumchamberwhichhasarectangularsectionof489mm2. bunchlengthmeasurement<strong>and</strong>theenergyspreadmeasurementstation,thelargestdiscontinuityis introducedbythebeampipesizevariationclosethewigglermagnet:thereisatransitionbetween thest<strong>and</strong>ardbeamvacuumchamber,thathasacircularsectionof50.8mmdiameter,<strong>and</strong>the Thesecondmechanismthatcanpotentiallydeterioratethebeamenergyspreadisduetowakeeld generationasthebeamencountersdiscontinuitiesinthevacuumchamber.Betweenthepointof<br />
functionwrites:!W(x;y;s)=1eZ1 Wakeeldforcesareduetothechangeinboundaryconditionssurroundingaparticle,whichobligate theCoulombeldtoreorganize.Anelectronintheheadofthebunchcancauseanelectriceld atthelocationwheretheboundaryconditionchanges.Anelectronbehindcaninteractwiththis Foranelectrontraversingastructurewithanoset(x;y),withitsvelocityparalleltoz,thewake Ifweassumealltheelectronsarecenteredinthestructure,i.e.x=y=0,theprincipaleect ofwakeeldistointroduceenergyvariationalongthebunchwhichinturncanspoiltherms electriceld<strong>and</strong>therebymodifyitsorbit.Typicallywakeeldsaredescribedbywakefunctions.<br />
energyspread.Thermsenergyspreadinducedbythiseectispurelycomingfromthelongitudinal wakeeld,Wk;itwrites:;wake=e2Z1 1dz!E(x;y;z;t)+cbz^!B(x;y;z;t) (5.63)<br />
where(s)isthebunchdistributionfunction,<strong>and</strong>kkdef energyspreadincreasetothewakeeldeectispresentedingure5.31:itisnoticedthatthe factor. Inthepresentcasethecomputationofthewakeeldisestimatedbyusinga2Dcodetbciwhichalso assumesthebunchisarigidlinechargedistributedalongagaussi<strong>and</strong>istribution.Theexpected 1ds(s)W2k(s)k2k1=2 =1=eR11Wk(s)(s)dsisthetotalloss (5.64)<br />
<strong>and</strong>thecircularvacuumchamberhasbeensmoothedbyintroducinga\trumpet"shapedcopper piece. expectedtohaveasignicantcontributionsincethetotalenergyspreadisthequadraticsumofthe intrinsic<strong>and</strong>wakeeldinducedenergyspread.Moreoverthesteptransitionbetweenthewiggler spread(oftypically50keVat38MeVasachievedinnumericalsimulations).Henceitisnot associatedenergyspreadis,intheworstcase25timeslessthanthebeamintrinsicrmsenergy<br />
Thisismuchlargerthantheexpectedvaluefromtheparmelacode(11:7deg-keV)butstillwithin <strong>and</strong>=0:250:05%whichyieldalongitudinalemittanceofapproximately18:85:5deg-keV. undulatorvicinity<strong>and</strong>istheenergyspreadmeasuredinoneofthehighdispersionlocationsin thechicanes).Typicalbunchlength<strong>and</strong>energyspreadmeasuredduringthecommissioningofthe IRFEL,intheperiodjustpriortorstlaserlightproduction,arerespectivelyz=11030m thelongitudinalemittancereducesto~"z'z(wherezisthebunchlengthmeasuredinthe Henceundertheassumptionthatthereisnomechanismtospoilsignicantlytheenergyspreadof<br />
thespecication33deg-keV.<br />
thebeam,whenthelongitudinalenvelopeisatawaistclosetotheundulatorlocation(.e.hzi'0),
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