High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA High Brightness Electron Beam Diagnostics and their ... - CASA
30 25 20 Figure4.21:Fractionofincidentelectronthatscattersontheslitsedgeversusthebeamincident 15 anglewithrespecttothenormalaxisofthemultislitmask.Thedepthoftheslitsis5mm.A of10%oftheincidentelectronwiththematerial. 10 oftheelectronbeam. 5 Theacquireddata,inourcaseaprojectionthatcontainsthebeamletproles,isdigitizedby misalignmentofthemaskof1:2mradcomparetothebeamaxisyieldsapproximatelytheinteraction 0 theframegrabberandthentransferredtoanIOConwhichVxWorksroutineshavebeenimple- 0.0 0.5 1.0 1.5 2.0 2.5 3.0 mented[39].Afteridentifyingeachbeamletproleandtheslititcomesfrom,thecodecomputes Beam Incident Angle (mrad) theEPICSchannel-accessprotocol.WedevelopedX-windowbasedscreensthatdisplayemittance, Twiss-parametersandpossiblyphase-spaceisocontours.Theachievedspeedsare,respectively, theemittanceandTwissparameters.TheresultscanthenbeaccessedfromanyX-stationvia phasespaceparametersinrealtimewhiletuningtheinjector.Storingrawdataandprojectionsis alsopossibleateachstageoftheprocessformoredetailedo-lineanalysis,e.g.using(timeand about1and2secforupdatingparametersandplotrefresh,aspeedthatallowsobservingthe CPUconsuming)powerfulimageprocessingtools. N Edge/N IN (%) = Parmela =0.5 Parmela =3 Parmela
Table4.7:TypicalsystematicerroronemittanceandTwiss-parametersforthenominalemittance valueandtwoextremecases. 1.15972.5 0.39569.9 0.204019.9 ~" ~"=~"(%)=(%)=(%) 2.6 9.9 19.9 2.6 10.4 20.9 priorifollowanykindofanalyticalfunction.Forthesereasonsweperformthiserrorpropagation alotofapproximationandassumptions,especiallysincethetrace-spacedistributiondoesnota 4.5.4ErrorAnalysis ErrorPropagation Theerrorpropagationisquitetedioustoperformanalyticallysincedirectcalculationsrequire errorontherms-emittanceasafunctionofthesecond-ordermoments: Theerroronthehxx0iisgivenby: numerically.Followingpreviousderivation[45],itisstraightforwardtocomputethesystematic (~")2=1~"20@hxx0i2hxx0i2+ (hxx0i)2=PihPjw2i;jx2i(hx0i)2+Pjw2i;jhx0i2i(x)2i hx02i2 PiPjwi;j 4!2hx0i2 hx2i2 4!2(hxi)21A (4.61) Similarly,theerroronhx02iwrites:hx02i=PjhPi2wi;jx0ji2 Wheretheuncertaintyontheaveragethedivergenceissimplyhx0i'x0.Theerroronhx2iis: hx2i=Pih2Pjwi;j(x0j)i2 PiPjwi;j (4.63) (4.62) Wheretheerroronthedivergenceisestimatedtox0=1Lq2+D2(L)2 oftheOTRmonitor('60m),hasbeenaddedinquadrature.Theuncertaintyonthedriftlength tocomputeerrorsondierentsetsofdata.Typicaluncertaintiesassociatedwiththeemittanceand TwissparametersarepresentedonTable4.7forthenominalexpectedemittanceandtwoextreme L,isapproximately5mm.Allthepreviousformulaehavebeengatheredinaprogramthatallows PiPjwi;j L2where,theresolution (4.64) chargeeld.thiseectisduetothefactthatwhenanelectronbunchgetveryclosetotheslits OtherSourceofErrors cases;asexpected,thiserrorincreasesastheemittancevaluedecreases. Asmentionedinreference[44],theslits(directedalongyaxis)willreducethex-transversespace
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Table4.7:Typicalsystematicerroronemittance<strong>and</strong>Twiss-parametersforthenominalemittance value<strong>and</strong>twoextremecases. 1.15972.5 0.39569.9 0.204019.9 ~" ~"=~"(%)=(%)=(%) 2.6 9.9 19.9 2.6 10.4 20.9<br />
priorifollowanykindofanalyticalfunction.Forthesereasonsweperformthiserrorpropagation alotofapproximation<strong>and</strong>assumptions,especiallysincethetrace-spacedistributiondoesnota 4.5.4ErrorAnalysis ErrorPropagation Theerrorpropagationisquitetedioustoperformanalyticallysincedirectcalculationsrequire errorontherms-emittanceasafunctionofthesecond-ordermoments: Theerroronthehxx0iisgivenby: numerically.Followingpreviousderivation[45],itisstraightforwardtocomputethesystematic (~")2=1~"20@hxx0i2hxx0i2+ (hxx0i)2=PihPjw2i;jx2i(hx0i)2+Pjw2i;jhx0i2i(x)2i hx02i2 PiPjwi;j 4!2hx0i2 hx2i2 4!2(hxi)21A (4.61)<br />
Similarly,theerroronhx02iwrites:hx02i=PjhPi2wi;jx0ji2 Wheretheuncertaintyontheaveragethedivergenceissimplyhx0i'x0.Theerroronhx2iis: hx2i=Pih2Pjwi;j(x0j)i2 PiPjwi;j (4.63) (4.62)<br />
Wheretheerroronthedivergenceisestimatedtox0=1Lq2+D2(L)2 oftheOTRmonitor('60m),hasbeenaddedinquadrature.Theuncertaintyonthedriftlength tocomputeerrorsondierentsetsofdata.Typicaluncertaintiesassociatedwiththeemittance<strong>and</strong> TwissparametersarepresentedonTable4.7forthenominalexpectedemittance<strong>and</strong>twoextreme L,isapproximately5mm.Allthepreviousformulaehavebeengatheredinaprogramthatallows PiPjwi;j L2where,theresolution (4.64)<br />
chargeeld.thiseectisduetothefactthatwhenanelectronbunchgetveryclosetotheslits<br />
OtherSourceofErrors cases;asexpected,thiserrorincreasesastheemittancevaluedecreases. Asmentionedinreference[44],theslits(directedalongyaxis)willreducethex-transversespace
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