High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA High Brightness Electron Beam Diagnostics and their ... - CASA
InthecaseofarigidlinechargewithaGaussiandistribution(s)=N=p22zexps2=(22z), presentedingure6.20alongwithsimulationresultsusingamodiedversionofparmelathat oneobtainsfortheenergychange[68]: withthefunction12FdenedasF()=R1d0 wakeeldwherethetrailingelectronsinthebunchgenerallyloseenergy,CSReectsyieldanenergy d(ct)= dE(2)1=231=32=34=3 2Ne2 gainforelectronslocatedintheheadofthebunch. includesasimplemodelforCSRbunchselfinteraction(seeAppendixB).Contrarytostandard (0)1=3d zF(s=z) d0e02=2Aplotofthisenergychangeis (6.28) Bunch at Present time Bunch Trajectory R Limitationsofthepreviousmodel Figure6.19:SchematicsofCSRselfinteractionofabunch. S’ Bunch at Retarded time ∆Θ thestraightsectiontothebendsection.(2)thebunchpropagatesinmetallic(e.g.stainlesssteel) intwoways:(1)itassumesthebunchhasbeenorbitingonacircularpathforever(steadystate assumption)and(2)itassumethebunchisinfreespace.Bothofthisassumptionsarenottruein practice:(1)anaccelerator(evencircular)consistsofstraightsectionsjoinedbybendingelements thereforeamorerealisticpictureofCSRshouldincludethetransientCSR,i.e.thepassagefrom ThemodelofCSRbunchselfinteractionbrieyoutlinedintheprevioussectionisoversimplied O cut-ofrequencyassociatedwiththegeometricparametersofthevacuumchamber). vacuumchambersandthereforeCSRcanbeshielded(i.e.notallowtopropagatebecauseofthe 12sometimetermedas\overtake"function S
100 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .. . ... . . . . . . . . . . ... . . . . . . . . .. . . . . 100 . 50 . 0 -50 -100 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 (deg.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 50 . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .. . . . . . . . .. . . .. . . . 0 . . . . . . . . . . . . . .. . . . . . -50 predictionusingasimplenumericalmodelinamodiedversionofthescparmelacodefor200m Figure6.20:AnalyticalcomputationforCSR-inducedenergylossalongagaussianbunchand -100 (A)and100m(B).Thesystemconsideredisasimpleachromaticchicane(macroparticlewith >0areinthebunchtail). (B) TheprimarypurposeoftheexperimentthatwasattemptedintheIRFEListomeasurewhether locatedinthebacklegtransport. 6.5PreliminaryExperimentalResultsonEmittanceandEnergySpreadMea- AnothermotivationwastotrytosetuptheIRFELopticssothatwecouldgenerateemittance thetransversehorizontalemittanceissignicantlydegradedaftertherecirculationarc1.ThereasonistoconrmtheviabilityoftheenvisionedUpgradeIRFELinwhichseveralwigglerswillbesurements Theexperimentwasattemptedintwoseriesofruns.Duringtherstrun,wevariedthelinac degradationandperformsomeparametricstudies. TheexperimentalsetuptomeasureemittancefollowsourdiscussionofChapter3. ofrun,becausetheemittancewasfoundtobelarge(technicalproblemwiththeinjector),we acceleratingphaseandmeasuredtheemittancebeforeandafterthearc1.Inthesecondseries concentratedonmeasuringtheenergyspreadmeasurementonly. E (keV) (A)
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InthecaseofarigidlinechargewithaGaussi<strong>and</strong>istribution(s)=N=p22zexps2=(22z),<br />
presentedingure6.20alongwithsimulationresultsusingamodiedversionofparmelathat oneobtainsfortheenergychange[68]: withthefunction12FdenedasF()=R1d0 wakeeldwherethetrailingelectronsinthebunchgenerallyloseenergy,CSReectsyieldanenergy d(ct)= dE(2)1=231=32=34=3<br />
2Ne2<br />
gainforelectronslocatedintheheadofthebunch. includesasimplemodelforCSRbunchselfinteraction(seeAppendixB).Contrarytost<strong>and</strong>ard (0)1=3d zF(s=z) d0e02=2Aplotofthisenergychangeis (6.28)<br />
Bunch at Present time<br />
Bunch<br />
Trajectory<br />
R<br />
Limitationsofthepreviousmodel Figure6.19:SchematicsofCSRselfinteractionofabunch.<br />
S’<br />
Bunch at Retarded time<br />
∆Θ<br />
thestraightsectiontothebendsection.(2)thebunchpropagatesinmetallic(e.g.stainlesssteel) intwoways:(1)itassumesthebunchhasbeenorbitingonacircularpathforever(steadystate assumption)<strong>and</strong>(2)itassumethebunchisinfreespace.Bothofthisassumptionsarenottruein practice:(1)anaccelerator(evencircular)consistsofstraightsectionsjoinedbybendingelements thereforeamorerealisticpictureofCSRshouldincludethetransientCSR,i.e.thepassagefrom ThemodelofCSRbunchselfinteractionbrieyoutlinedintheprevioussectionisoversimplied<br />
O<br />
cut-ofrequencyassociatedwiththegeometricparametersofthevacuumchamber). vacuumchambers<strong>and</strong>thereforeCSRcanbeshielded(i.e.notallowtopropagatebecauseofthe 12sometimetermedas\overtake"function<br />
S
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