High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA High Brightness Electron Beam Diagnostics and their ... - CASA
2 1 −5 −3 −1 1 3 5 k (m q −2 ) or k (m s −3 0 Figure3.11:Momentumcompactionandnonlinearmomentumcompactionforonearcversusthe secondfamilyoftrimquadrupolesexcitationstrength(kq).nonlinearmomentumcompactionversus −1 thesecondfamilysextupolesstrengthks(forthiscalculation,thetrimquadrupolesareunexcited). M from trim quadrupoles 56 −2 phase-energycorrelation).Inthesemeasurements,thebunchisconsideredasamacroparticleand thetime-of-ight(TOF)ofitscentroidismeasuredbetweenthelocationswherethevariationis T /10 from trim quadrupoles 556 −3 −4 Thephase-phasecorrelation,hinjoutirequiresthemeasurementoftime-of-ight(TOF)ofthe impressedandapointwherethetimeofarrivalcanbeestimated. CompressionEciency ) FELdriver-accelerator,thisquantityisonlymeasuredstartingfromthephotocathodesinceitis bunchcentroidversusavariationofits\injectionphase"inthesectionwewishtostudy.Inthe theonlylocationthe\injectionphase"incanbevariedorthogonallywithrespecttotheinjection withrespecttothemasteroscillator(andalltheRF-elementsettingsarekeptconstant).Thephase variationanarbitrarylocationdownstreamthephotocathodeoutasafunctionoftheinjection phaseperturbationinwrites:out=@out energybyvaryingthephaseofthephoto-cathodedrivelaserthatilluminatesthephotocathode Thereforebyvaryinginaknownfashiontheinjectionphaseandmeasuringtheassociatedresponse downstream,weobtainthephase-phaseresponseofthesectioncomprisedbetweentheperturbation andthemeasurementstation.Fromthisphase,usingthestandardnotationofthetransport @inindef =hinjoutiin (3.11) M 56 or T 556 /10 (meters) T 566 /10 from sextupoles
latticecode9,wehave: MomentumCompaction thisphase-phasetransfermapyieldsthearbitraryordertransfermatrixelementhinjouti. whererkisk-thco-ordinateofthevectorr=(xin;x0in;yin;y0in;in;in)Therefore,nonlineartof hinjoutiin=(R55+Xk
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latticecode9,wehave:<br />
MomentumCompaction thisphase-phasetransfermapyieldsthearbitraryordertransfermatrixelementhinjouti. whererkisk-thco-ordinateofthevectorr=(xin;x0in;yin;y0in;in;in)Therefore,nonlineartof hinjoutiin=(R55+Xk
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