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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Resolutionofbeamsizemeasurement Itisveryimportanttohaveapreciseknowledgeofthesystematicerroronabeamsizemeasurement sincewewillhavetoincludetheseerrors<strong>and</strong>propagatethemtondtheerrorbarduetosystematic<br />
function,istoimageviathissystemasharpedge[43].Forsuchapurposeatargetimagethat errorsonthetransverseemittancecomputation. Thereareprincipallytwotypesofeectsthatenterintheresolutionofthistypeofimagingdevices systemweuse:opticalresolution<strong>and</strong>electronicresponse.Theformereectcanbeevaluatedin consistsofansharpedgebetweenanopticallyblack<strong>and</strong>opticallywhiteregionispositionedat waytocharacterizetheresolutionofthewholesystemi.e.includingoptical<strong>and</strong>electronictransfer ourcasesinceoursystemisoptimizedtominimizespherical<strong>and</strong>chromaticaberration,theoptical degradationofresolutionisessentiallyduetothedepthofeldeectthatresultsbecausethe planeweareimaging,thefoil,makesa45deganglewithrespecttotheCCDarray.Thebest TRradiatorlocation.Thederivativeofthecorrespondingdigitizedimagewillprovideinformation ontheimpulseresponseofthesystem<strong>and</strong>itswidthcanbeusedtoquantifytheresolutionof thesystem.Typicalresolutionmeasuredwereatmaximum1:5timesthepixelsizeintheobject plane.Fortypicalmagnicationweuse,thepixelsizeintheobjectplaneisabout40mwhich givesatypicalrmsresolutionof60mwellbelowthetypicalbeamsizemeasured(oftheorderof approximately1mmrms).<br />
ThemethodtomeasureemittanceinthehighenergyregionoftheFEListheusualenvelope 4.4.1GeneralConsiderations 4.4MeasurementofEmittanceinthe38+MeVRegion<br />
betweenthehorizontal<strong>and</strong>verticalplanes,<strong>and</strong>thatthedispersionisnegligibleatthelocationof themeasurement.Ifthelatterassumptionsarefullledthenonecanusetransportformalismto transfermatrixbetweenthemR ttingtechnique.Itassumesthatthebeamcanberstordertransport,thatthereisnocoupling<br />
Exp<strong>and</strong>ingtheabovematrixrelation(recallisthebeammatrix)wecanrelatetheRMSbeam ndtherelationbetweenbeamparametersattwodierentlocationsinthebeamlineknowingthe<br />
systemofNequations(correspondingtoNdierenttransfermatrices)withonly3unknowns.Such sizeatthelocationiwiththeRMSdivergence,beamsize<strong>and</strong>beamcorrelationofthebeamatthe location0.Hencevaryingthetransfermatrixforagivensetofinitialvaluesin0,providesdierent beamsizeatthestationlocationi.Thereforeonecaneasilygeta(generallyoverdetermined) (i)=R(0)RT<br />
systemistraditionallyinvertedbythemeansoftheleastsquaremethod:GiventheNsquared- (4.24)<br />
the2: beamsizemeasurements,oneneedstondthesetofparameter((0) 2=NXi=1h(i)(R211(i)(0) 11+R212(0) (i)2 22+R11R12(0) 11,(0) 12)i212,(0)<br />
22)thatminimizes (4.25)
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