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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15<br />
Effect of RMS energy Spread<br />
10<br />
Figure6.17:Emittancegrowthduetochromaticaberrationversusthemomentumspread<strong>and</strong><br />
5<br />
bendssystem)cancoupletothetransverseplane<strong>and</strong>yieldemittancedegradation.Thelinearized energyosetofthebeam.<br />
Effect of Energy Centroid Offset<br />
equationofmotionofanelectroninabend,assumingnoexternalfocusing<strong>and</strong>nocouplingbetween thetwotransversephasespaces,forthebendingplane(thex-x'planeinthecaseoftheIRFEL) is[59]: haveshowthatitisverysmallforourbeamparameters.Infactallthebeamlinecomponentshave beenspeciedinsuchawaythatthetotallongitudinallossfactoriswithinsomeimpedancebudget sothatthepotentialbeamdegradationisverysmall[65]. Inthissectionwewouldliketoshowhowenergyspreadgeneratedinadispersiveregion(i.e.a<br />
0<br />
0 0.5 1 1.5<br />
δ (%)<br />
radiusofcurvatureofthetrajectory<strong>and</strong>istherelativeenergyosetw.r.t.thereferenceorbit. wheresisthelongitudinalpositionreferredw.r.t.theentranceofthebendingsystem,xisthe Let'sassume,forsimplicity,thatthemechanismgeneratesanenergyspreadthatisonlydependent onthecurvilinearcoordinates10,i.e.=(0)+(s).Undersuchanassumption,thelatter equationtakestheform: d2x<br />
10generallyspeakingthemechanismisalsodependentontime,foracompletetreatmentsee[69]<br />
d2x ds2+x2x=(0)+(s)<br />
∆ε/ε (%)<br />
ds2+x2x=x (6.22)<br />
x (6.23)
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