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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2<br />
1<br />
Figure3.8:Comparisonbetweenanenergychangeinducedbeamdisplacementalongthelattice<br />
0<br />
thelinac,theenergyosetiforanelectroncanbewrittenasafunctionofitsenergyoset0<strong>and</strong> longitudinalpositionz0atthewigglerexitas: reduced.Undertheassumptionofsingledynamicsrstorderopticsthisissimplybecauseafter <strong>and</strong>theresponsetoanangularperturbation. thatduringthedecelerationphase,forenergyrecoverypurpose,therelativemomentumspreadis<br />
−1<br />
R12 pattern<br />
Cavity Gradient Pattern<br />
−2<br />
properenergyforlasing.Thereforetheonlyparameterthatcanaecttheenergyspreadatthelinac TheR65transfermatrixelementofthelinacisgenerallyxed:sincethelinacissetuptoprovidethe i=Rlinac 65z0+Rlinac 65Rwiggler!linacentrance 56 0 (3.8)<br />
0 20 40 60 80 100<br />
Distance from Cryomodule exit (m)<br />
exitafterenergyrecoveryistheR56oftherecirculationfromthewigglerexittothelinacentrance. Anexampleoftheimportanceinsettingstheenergyrecoverytransportisshowningure3.10 wherewepresentsimulationoftheenergyrecoveryscheme:theparmelacodeisusedasaskeleton<br />
Forsakeofsimplicity<strong>and</strong>inordertoexpeditenumericalsimulations,wehaveturnedospace transportissimplysimulatedbytrackingparticlesusingthelongitudinaltransformation7. slippageduetothenon-relativisticnatureofthebeamaretakenintoaccount);therecirculation tosimulatetheacceleration<strong>and</strong>decelerationofthebeam(i.e.RF-inducedcurvature<strong>and</strong>phase<br />
chargeroutineinparmela.Theproperphasetoachievetheshortestbunchatthewigglerin- cavityviabeamloadingisdirectlyusedtosupplementtheavailablepowerfortheaccelerating sertionisapproximately8degocrest.Thebeamisrecirculated<strong>and</strong>re-injected8+180deg ocrestinthecryomodulesothatitisdecelerated<strong>and</strong>theelectromagneticenergystoredinthe zi=zi+R56i+T5662i+O(3i) i=i (3.9)<br />
linecomponent,norspacechargecollectiveforcearetakenintoaccount<br />
mode.Wepresenttheobtainedresultsin3.10,thelongitudinalphasespaceatthelinacexit(after 7Inthisnumericalanalysis,neitherlongitudinalwakeeldinducedintheacceleratingstructure<strong>and</strong>variousbeam-<br />
∆x (mm)
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