High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA High Brightness Electron Beam Diagnostics and their ... - CASA
and validundertheassumptionofauniformlypopulatedbeam.Usingthismethodwehavecomputed Eqn.4.16relatesthetemperatureatthebeamcenterandthetemperatureatthebeamedge.Itis Aluminum MaterialMeltingPointThermalConductivitydE=dx (K) 933I=PnEtcos W=m:K 237 eV=m 410 (4.17) themaximumbeamcurrentdierentfoilscanstandversustheequivalentbeamsizedenedas Table4.1:PhysicalpropertiesoftheconsideredmaterialforOTRscreens. Gold Carbon 1337 3700 317 333 6380 TheconsideredmaterialwiththeirpropertiesaregatheredinTable4.1.Theresultsarepresented prxrywhererxandryarethefullbeamsizerespectivelyinthehorizontalandverticaldirection. 130 typicalbeamsizeexpectedinthefree-electronlaser,aluminumfoilcaneasilywithstandaverage currentupto500Aevenwithabeamof300mradius.Eveninthelow-emittanceCEBAF radiusassumingtheTR-radiatorhasa0:8mthickness5.Forinstance,wecanseethatwiththe acceleratorthemaximumdesignof200Acanbereachedwithoutmeltingthefoilfortypical intheg.4.3whichdepictsthemaximumaveragecurrentthatcanbereachedforagivenbeam envelopeof200m. notstandhigherbeamaveragecurrentduetoitshigherdE=dxcoecient.Ingure4.4wepresent thesteadystatetemperatureversustheincomingbeamaveragecurrentfordierentaluminumfoil thicknessandabeamof2mm. observebackwardTR. Finallywenotethatdespiteitshigherthermalmeltingpointcomparedtoaluminum,golddoes onlyareconsidered.Unfortunatelythemaindrawbackofcarbon,aswewillseelater,isitslow coecientofreectionincomparisontoaluminumorgoldwhichdoesnotfacilitateitsuseto Obviously,wecannoticeingure4.3thatcarbonisthebestchoiceasfarasthermalaspects aluminumfoils.TheexperimentwasperformedintheCEBAFinjectorregion(foradescriptionof theinjectorseeReference[28]).Wecomparedthedatawithasemi-empiricalmodelandnumerical simulations. WenowturntothestudyofbeamdegradationduetoscatteringintheTRradiator.Inthissection, wepresentanexperimentdevotedtostudyscatteringofa45MeVelectronbeamonverythin 4.2.3StudyofMultipleScatteringinAluminumfoil degradation)stillhavingagoodsurfacereectioncoecient.Alsothicknessislimitedbytheframeonwhichthefoil ismounted:toothinfoilcouldnotbemountedonourholdingsupportbecausetheywouldanymoreself-support. 5thisthicknessisanoptimumvalue:itcorrespondstothethinnestfoilwecanhave(inordertominimizebeam
Maximum Average Beam Current ( A) 10 4 5 2 C foil Al foil Au foil 10 -1 2 5 10 0 2 5 10 1 2 Equivalent Beam Size (rx ry) 1/2 10 5 2 (mm) 2 10 5 2 3 Figure4.3:MaximumaveragecurrentthatcanwithstandaTRradiatorasafunctionofthe equivalentbeamradius.ThreetypesofTRradiatorhavebeenconsidered:Aluminum,Goldand Carbon.Thethreeradiatorare0:8mthick. Experiment WehaveperformedanexperimentintheCEBAFinjectorat45MeVtostudyscatteringeect asthebeampassthroughaluminumfoilofdierentthickness.Theexperimentalsetupisas scannerhasthreewires(seeg.4.1b)thatrespectively(fromrighttoleftinthegure)givesthe beamprolealongthehorizontal,verticaland45degaxes.Thefactthatthebeamsizeinthe prolemeasurementstation:awire-scanner.Allthequadrupoleandcorrectormagnetsbetween thefoilsandthewirescannerareturnedo.Ingure4.5wecomparetwotypicalwirescanner tracesobtainedwithandwithouta0:8maluminumfoilinsertedinthebeampath.Thewire follow:dierentaluminumfoilaremountedonasupport,andcanbeinsertedintothebeampath remotely.Thescatteredbeamthendriftsthroughalengthof7:43muptoatransversebeam horizontaldirectionismuchsmallerthantheverticaldirectiononeissimplyduetotheopticstune upstream.Asonecanexpectthebeamproleislargerasthe0:8mfoilisinserted.Moregenerally itgetswiderasthefoilthicknessincreases.Forquantitativeanalysisofthescattering,weonly theconvolutionofthebeamproleBwiththefoil\scatteringtransferfunction"T(orscattering considerthetailofthebeamprolelocatedontherightsideofthehorizontalprole(rightpeak) becausetheotherpeaksoverlapandwouldyieldatediousdeconvolution.Wealsoassumethatwe havescanned100%ofthebeam.LetS()bethefunctionassociatedtothetail.S()isindeed
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<strong>and</strong> validundertheassumptionofauniformlypopulatedbeam.Usingthismethodwehavecomputed Eqn.4.16relatesthetemperatureatthebeamcenter<strong>and</strong>thetemperatureatthebeamedge.Itis Aluminum MaterialMeltingPointThermalConductivitydE=dx (K) 933I=PnEtcos W=m:K 237 eV=m 410 (4.17)<br />
themaximumbeamcurrentdierentfoilscanst<strong>and</strong>versustheequivalentbeamsizedenedas Table4.1:PhysicalpropertiesoftheconsideredmaterialforOTRscreens. Gold Carbon 1337 3700 317 333 6380<br />
Theconsideredmaterialwith<strong>their</strong>propertiesaregatheredinTable4.1.Theresultsarepresented prxrywhererx<strong>and</strong>ryarethefullbeamsizerespectivelyinthehorizontal<strong>and</strong>verticaldirection. 130<br />
typicalbeamsizeexpectedinthefree-electronlaser,aluminumfoilcaneasilywithst<strong>and</strong>average currentupto500Aevenwithabeamof300mradius.Eveninthelow-emittanceCEBAF radiusassumingtheTR-radiatorhasa0:8mthickness5.Forinstance,wecanseethatwiththe acceleratorthemaximumdesignof200Acanbereachedwithoutmeltingthefoilfortypical intheg.4.3whichdepictsthemaximumaveragecurrentthatcanbereachedforagivenbeam envelopeof200m. notst<strong>and</strong>higherbeamaveragecurrentduetoitshigherdE=dxcoecient.Ingure4.4wepresent thesteadystatetemperatureversustheincomingbeamaveragecurrentfordierentaluminumfoil thickness<strong>and</strong>abeamof2mm. observebackwardTR. Finallywenotethatdespiteitshigherthermalmeltingpointcomparedtoaluminum,golddoes onlyareconsidered.Unfortunatelythemaindrawbackofcarbon,aswewillseelater,isitslow coecientofreectionincomparisontoaluminumorgoldwhichdoesnotfacilitateitsuseto Obviously,wecannoticeingure4.3thatcarbonisthebestchoiceasfarasthermalaspects<br />
aluminumfoils.TheexperimentwasperformedintheCEBAFinjectorregion(foradescriptionof theinjectorseeReference[28]).Wecomparedthedatawithasemi-empiricalmodel<strong>and</strong>numerical simulations. WenowturntothestudyofbeamdegradationduetoscatteringintheTRradiator.Inthissection, wepresentanexperimentdevotedtostudyscatteringofa45MeVelectronbeamonverythin 4.2.3StudyofMultipleScatteringinAluminumfoil<br />
degradation)stillhavingagoodsurfacereectioncoecient.Alsothicknessislimitedbytheframeonwhichthefoil ismounted:toothinfoilcouldnotbemountedonourholdingsupportbecausetheywouldanymoreself-support.<br />
5thisthicknessisanoptimumvalue:itcorrespondstothethinnestfoilwecanhave(inordertominimizebeam
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