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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30<br />
25<br />
20<br />
Figure4.21:Fractionofincidentelectronthatscattersontheslitsedgeversusthebeamincident<br />
15<br />
anglewithrespecttothenormalaxisofthemultislitmask.Thedepthoftheslitsis5mm.A of10%oftheincidentelectronwiththematerial.<br />
10<br />
oftheelectronbeam.<br />
5<br />
Theacquireddata,inourcaseaprojectionthatcontainsthebeamletproles,isdigitizedby misalignmentofthemaskof1:2mradcomparetothebeamaxisyieldsapproximatelytheinteraction<br />
0<br />
theframegrabber<strong>and</strong>thentransferredtoanIOConwhichVxWorksroutineshavebeenimple-<br />
0.0 0.5 1.0 1.5 2.0 2.5 3.0<br />
mented[39].Afteridentifyingeachbeamletprole<strong>and</strong>theslititcomesfrom,thecodecomputes<br />
<strong>Beam</strong> Incident Angle (mrad)<br />
theEPICSchannel-accessprotocol.WedevelopedX-windowbasedscreensthatdisplayemittance, Twiss-parameters<strong>and</strong>possiblyphase-spaceisocontours.Theachievedspeedsare,respectively, theemittance<strong>and</strong>Twissparameters.TheresultscanthenbeaccessedfromanyX-stationvia phasespaceparametersinrealtimewhiletuningtheinjector.Storingrawdata<strong>and</strong>projectionsis alsopossibleateachstageoftheprocessformoredetailedo-lineanalysis,e.g.using(time<strong>and</strong> about1<strong>and</strong>2secforupdatingparameters<strong>and</strong>plotrefresh,aspeedthatallowsobservingthe CPUconsuming)powerfulimageprocessingtools.<br />
N Edge/N IN (%)<br />
= Parmela<br />
=0.5 Parmela<br />
=3 Parmela
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