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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electronwithnoenergyoset=0,as: Thereforewec<strong>and</strong>eneanorbitosetwithrespecttothe\referenceorbit",i.e.theorbitofthe xdef =xf;xf;0=R12x0;+R16+T1662 =xf;0+R16+T1662<br />
in<strong>and</strong>takingthephysicalsolution: Hencetheenergyspreadcanbeexpressedasafunctionofxbysolvingtheseconddegreeequation =R16 2T166"11+4T166 R216(x)21=2# (5.59)<br />
InthecaseofpracticalvalueinthebendingsystemsoftheIRFEL,athird-orderTaylorexpansion islargelysucient,thereforetheenergyosetofanelectronatpositionxwithrespecttothe referenceorbitis: =x R16+T166(x)2 R3162T166(x)3 R516<br />
(5.60)<br />
monitorlocatedinthecenterofoneoftheby-passchicanes:Usingthesecondordermagneticoptics codedimad,wecomputedtransferthematrixelementstobeR16'42cm<strong>and</strong>T166'45cm. Asanexampleweshallconsideranenergy-spreadmeasurementperformedusingabeamprole (5.61)<br />
Animportantparametertopermitthelasertoturnon,aswewilldiscussindetailinChapter6, 5.8EstimateofLongitudinalEmittanceintheUndulatorVicinity isthelongitudinalemittance.Wedeneitas:<br />
(seeg.5.29).Howeveranenergyspreadmeasurementcanbeperformedonlyinahighdispersion whereisthelongitudinalcoordinateexpressedinunitsofRF-degree<strong>and</strong>isthemomentum spread. energyspread.AttheundulatorlocationwecanmeasurethebunchlengthusingCTRmethods coecienthivanishes<strong>and</strong>thereforetheemittanceissimplytheproductofrmsbunchlength<strong>and</strong> Attheundulatorlocation,thelongitudinalphasespaceisatalongitudinalwaisti.e.thecorrelation ~"=qh2ih2ihi2 (5.62)<br />
thereforeimportanttocheckhowthemeasuredenergyspreadrelatestotheenergyspreadatthe pointi.e.inthemiddleofoneofchicanethankstoanOTRprolemonitor(seeg.5.29).Itis bunchlengthmeasurementstation.Underthevalidityoflineartransfermatrixformalism,itis force<strong>and</strong>wakeeldeects.Theformerhasbeenstudiedbyperformingnumericalsimulationsusing thecodeparmela.Aspicturedingure5.30,wherewecomparethelongitudinalphasespaceat clearthatenergyspreadshouldbethesameoverthewholeregionprovidedtheFEListurnedo. However,wemustbecautiousabouttheapplicabilityoflinearoptics:thereareafeweectsthat chicanemidpoint,theenergydistributionchangeisinsignicant.Thedegradationofenergyspread<br />
thewigglerinsertion<strong>and</strong>theoneatonepotentialpointofmeasurement,namelythedownstream cansignicantlyspoiltheenergyspread.Theprincipaleectsarethelongitudinalspacecharge
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