High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA High Brightness Electron Beam Diagnostics and their ... - CASA
Slope(Mev/m)36.170633.741231.206727.9008 C1 X+RMS(mm)1.84343.28604.72586.1368 #zero.cav1 C0 XRMS(mm)0.87892.42823.93525.4319 z(mm) 1.16561.08731.00560.8991 3.70287.405711.108514.8114 0.39000.39010.39150.3913 2 3 4 casesandwehaveestimatedthisvariationforthenormalizedslopeddzto0.54%/m. Table5.3:rmsbeamhorizontalsizesimulatedwiththeparmelaparticlepushingcodeonthe 5.6.2NumericalSimulationoftheMethod energyrecoverytransferlineprolemeasurementstation. Wehavenumericallyperformedabunchlengthmeasurementforthenominalsettingsusingthe onando.Itisnoticedthatthevariationoftheslopeduetospacechargeisthesameforallthe distance).ThebeamsizemeasuredattheOTRlocationareshowningure5.25,forthetwozerophasingvalues90deg,versusthenumberofzero-phasingcavities.Inthegurewealsosimulate bunchlengthof370mthecomputedbunchlengthisalwaysoverestimatedbyabout20m. statementthatwecouldunambiguouslydeconvolvetransversespacechargeeectcontributionto OntheotherhandthecoecientC1isdependentonthenumberofcavities(infactonthedrift themeasurementwiththeparmelaspace-chargeroutineturnedotoverifyagainourprevious checktheconstancyofthemethod.Table1summarizestheresultsweobtained.Forthenominal relationsderivedabove.Wehavedonesuchmeasurementusing1,2,3,and4zerophasingcavitiesto thebeamsize.Ingure5.26,wepresentthebeamdistributioninthetransverseplanealongwith thehorizontalbeamprojection,inthecasewherefourcavitiesareusedaszerophasingcavities. 5.6.3ExperimentalResults Duringtheearlystageofthecommissioningofthelinac,weattemptedabunchlengthmeasurement usingthezerophasingmethod.Wetriedtozerophasedierentnumbersofcavitiesandsincethe bunchlengthwaslargerthanexpectedweneededonlytousetwocavities. phasespaceslopedE UsingEqn.(5.52)wegetanrmsbunchlengthestimateofz'488112mandthelongitudinal thesevaluesyieldXRMS'1:9mmandX+RMS'4:7mm. Thermssizeofthehorizontalprojectionofthebeamspots,presenteding.5.27,recordedduring thezerophasingexperimentarerespectively:0x'3:5mm,90 Duringourexperiment,thegradientofthetwozerophasingcavitieswassetto7:33MV=m,the C0denedinEqn.(5.49)isapproximatelyC0'7:19. totalenergyoftheincomingbeamwasestimatedtobe23.75MeV;withsuchvaluetheconstant optimized.Alsonotethattheerrorbaronthebunchlengthmeasurementisobtainedusingthe wasperformed:theinjectorbeamdynamicswasnotyetfullyunderstoodandthesettingsnot predictedwithparmela.Thesediscrepancieswerenotrelevantatthetimethemeasurement dz'82MeV=m.Bothofthesevaluesareindisagreementwiththeparameters x'5:8mmand+90 x'4:0mm;
errorpropagation8theoryappliedonEqn.(5.49),assuminganuncertaintyof10%on,VRF,and 5.7.1Method thebeamsizesmeasurement,andarelativeerrorof2%onthebeamenergyinferredfromthedipole magnetstrength. Theestimationofthebeamenergyspreadisperformedbymeasuringtransversebeamproleina planewherethereissignicantdispersion.InthecaseoftheIRFEL,severallocationscanbeused 5.7IntrinsicEnergySpreadMeasurement horizontalplaneinourcase,thermsbeamsizeiswritten: andvariouslocationintherecirculationarc.Intheplanewheredispersionoccurs,i.e.inthe tomeasuretheenergyspread.Typicalhigh-dispersionpointare,symmetrypointsofthechicane suredorestimatedviamagneticopticscode,thelatterrequiresanemittancemeasurement(ina dispersionfreeregion)andthepropagationoftheTwissparameterstothedispersiveregionwhere FromEqn.(5.57)weseethattodeducetheenergyspreadwemustknowthedispersionfunction, Thiscommonlyusedrelationisvalidaslongasnonlinearitiesinthetransportisnegligible.Typically,forthenominalenergy(withoutlasing)spreadintheIRFEL(0.2%RMS)itcanbeused.,butalsothebetatroncontribution~"tothebeamsize.Thoughtheformercanbeeasilymea- x=h()2+~"i1=2 (5.57) energyspreadistobemeasured.Indeedwecanavoidtheemittancemeasurement9byvaryingthe strengthofanupstreamquadrupolewhileobservingthebeamsizeonthedispersivelocation,until thebeamsizeisminimum.Atthatpointthebetatrontermcontributiontothebeamsizeisthe smallestpossible.Ingure5.28,wepresentthebeamsizevariationfortwoscenariiofenergyspread (i.e.thecasewerethelaserisoi.e.'0:2%andoni.e.'2%).Forthelowestenergyspread entranceofamagneticsystem,withazero-energyspread,andletx0;,x0;bethesamecoordinates onederivedfromEqn.(5.57).Thisdisagreementcomesfromthenon-negligiblenonlineardispersion atthelocationofthebeamsizemeasurementwhichrendersEqn.(5.57)diculttouse(becauseit onlycontainslineardispersion):Letx0;0,x0;0bethepositionanddivergenceofanelectronatthe theminimumbeamrmssizesimulatedwithdimadiscomparabletothequantity.Howeverfor associatedtoanelectronwithanenergyspread.Insidethebendingsystemthatgeneratesenergy largerenergyspread,weobservediscrepanciesbetweenthevaluecomputedfromdimadandthe spread,wewillhave: 8Thesystematicerror,z,onthebunchlengthcomputationis: E202RF(X+RMS)2+(XRMS)2 (z)2=2RF(X+RMS)2+(XRMS)2 xf;0=R11x0;0+R12x0;0 xf;=R11x0;+R12x0;+R16+T1662 822V2RF (E0)2+E202RF(X+RMS)2+(XRMS)2 842V2RF ()2+ (5.58) 9SuggestionfromD.R.Douglas 822V4RF (VRF)2+E202RF16(0x)2(0x)2+4(x)2(x)2+4(+x)2(+x)2 3222V2RF(X+RMS)2+(XRMS)2
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errorpropagation8theoryappliedonEqn.(5.49),assuminganuncertaintyof10%on,VRF,<strong>and</strong><br />
5.7.1Method thebeamsizesmeasurement,<strong>and</strong>arelativeerrorof2%onthebeamenergyinferredfromthedipole magnetstrength.<br />
Theestimationofthebeamenergyspreadisperformedbymeasuringtransversebeamproleina planewherethereissignicantdispersion.InthecaseoftheIRFEL,severallocationscanbeused 5.7IntrinsicEnergySpreadMeasurement<br />
horizontalplaneinourcase,thermsbeamsizeiswritten: <strong>and</strong>variouslocationintherecirculationarc.Intheplanewheredispersionoccurs,i.e.inthe tomeasuretheenergyspread.Typicalhigh-dispersionpointare,symmetrypointsofthechicane<br />
suredorestimatedviamagneticopticscode,thelatterrequiresanemittancemeasurement(ina dispersionfreeregion)<strong>and</strong>thepropagationoftheTwissparameterstothedispersiveregionwhere FromEqn.(5.57)weseethattodeducetheenergyspreadwemustknowthedispersionfunction, Thiscommonlyusedrelationisvalidaslongasnonlinearitiesinthetransportisnegligible.Typically,forthenominalenergy(withoutlasing)spreadintheIRFEL(0.2%RMS)itcanbeused.,butalsothebetatroncontribution~"tothebeamsize.Thoughtheformercanbeeasilymea- x=h()2+~"i1=2 (5.57)<br />
energyspreadistobemeasured.Indeedwecanavoidtheemittancemeasurement9byvaryingthe strengthofanupstreamquadrupolewhileobservingthebeamsizeonthedispersivelocation,until thebeamsizeisminimum.Atthatpointthebetatrontermcontributiontothebeamsizeisthe smallestpossible.Ingure5.28,wepresentthebeamsizevariationfortwoscenariiofenergyspread (i.e.thecasewerethelaserisoi.e.'0:2%<strong>and</strong>oni.e.'2%).Forthelowestenergyspread entranceofamagneticsystem,withazero-energyspread,<strong>and</strong>letx0;,x0;bethesamecoordinates onederivedfromEqn.(5.57).Thisdisagreementcomesfromthenon-negligiblenonlineardispersion atthelocationofthebeamsizemeasurementwhichrendersEqn.(5.57)diculttouse(becauseit onlycontainslineardispersion):Letx0;0,x0;0betheposition<strong>and</strong>divergenceofanelectronatthe theminimumbeamrmssizesimulatedwithdimadiscomparabletothequantity.Howeverfor associatedtoanelectronwithanenergyspread.Insidethebendingsystemthatgeneratesenergy largerenergyspread,weobservediscrepanciesbetweenthevaluecomputedfromdimad<strong>and</strong>the spread,wewillhave: 8Thesystematicerror,z,onthebunchlengthcomputationis: E202RF(X+RMS)2+(XRMS)2 (z)2=2RF(X+RMS)2+(XRMS)2 xf;0=R11x0;0+R12x0;0 xf;=R11x0;+R12x0;+R16+T1662 822V2RF (E0)2+E202RF(X+RMS)2+(XRMS)2 842V2RF ()2+ (5.58)<br />
9SuggestionfromD.R.Douglas<br />
822V4RF (VRF)2+E202RF16(0x)2(0x)2+4(x)2(x)2+4(+x)2(+x)2 3222V2RF(X+RMS)2+(XRMS)2
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