High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA High Brightness Electron Beam Diagnostics and their ... - CASA
R10S(x)dx=R11S(x)dx=1=2R10S(x)dx. ingure2.7.Itisworthwhiletomentionthatthepointx=1isthemid-totalintegralpoint: 105cE4=(22),wherethenumericalfactoristheSand'sdenitionoftheradiationconstantE wherePtotistheinstantaneoustotalSRpoweremitted:inpracticalunits(GeV/s),Ptot=8:8575 andaretheelectronenergyinGeVandtheradiusoftrajectorycurvatureinmeters.S(x) inEqn.(2.16)istheso-calledUniversalfunction,S(x)=9p3 8xR1xK5=3(x)dx,whichisplotted chrotronradiationisproportionaltotheUniversalfunction. 2.5RudimentsonFEL-oscillatorTheory Figure2.7:PlotoftheUniversalfunctionS(!=!c).Thefrequencydistributionofthetotalsyn- Despitethefactthepresentreportdoesnotspecicallydealwiththephotonbeamgenerated free,indeeditmeanstheyareunbounded(contrarytoconventionallaser)butthereareconnedin amagnetostaticregionsincethefreeelectronswillnotradiateunlesstheyareexperiencingsome kindofacceleration. Asinaconventionallaser,FELconsistsinthreemainprocesses:(i)aspontaneousemissionis providedbysynchrotronradiationemittedaselectronswiggleinamagnet;(ii)theso-generated bytheIRFEL,webrieyexplainthebasesofFELtheorysincetheywillenablethereaderto all,weshouldnotethatthewordfreeinfree-electronlaserdoesnotmeanthattheelectronsare understandbettertherequirementsonthedriver-acceleratorelectronbeamparameters.Firstof radiationisrecirculatedinaresonator;(iii)andisampliedasitcopropagateswiththeelectron amagnetthatgeneratesaspatiallyperiodicmagnetostaticeld.InthecaseoftheIRFELof InaFEL,thespontaneousemissionisgeneratedastheelectronsareinjectedintoawiggler, beam(stimulatedemission). JeersonLab,theundulatorisaplanarone:itconsistsintworowsofNupermanentmagnets ofoppositepolaritiesstackedtogetherwithaperiodu;therowareseparatedbyaxgapas 2.5.1UndulatorRadiation S( ω/ω c ) 1 0.1 0.01 0.001 0.0001 0.001 0.01 0.1 1 10 ω/ω c
000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 000000000000000000000000000000000000000 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 111111111111111111111111111111111111111 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 111111 111111 111111 111111 111111 111111 111111 111111 111111 111111 000 000 000 000 111 111 111 111 00 00 00 11 11 11 01 00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000 11111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 1111111111111 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0000000000000000000000000000000000 1111111111111111111111111111111111 0000 0000 0000 0000 0000 0000 1111 1111 1111 1111 1111 1111 0000 0000 0000 0000 0000 0000 0000 0000 0000 1111 1111 1111 1111 1111 1111 1111 1111 1111 0000 0000 1111 1111 00000 00000 00000 00000 00000 00000 00000 00000 11111 11111 11111 11111 11111 11111 11111 11111 000000 000000 000000 000000 000000 000000 000000 111111 111111 111111 111111 111111 111111 111111 Electron Beam Resonant Cavity Length = 8.02 m Photon Beam λ u Figure2.8:FEL-oscillatorprinciple(CourtesyJ.Martz,JeersonLab). schematicallydescribedingure2.8.Insuchcongurationthegeneratedmagnetostaticeldis transversewithrespecttotheelectronvelocity.Aselectronstravelinthewiggler,theyareslightly deectedalternativelyupanddown(seeFigure2.8)andtherebyspontaneouslyemitsynchrotron radiationthatislinearlypolarized(inthecaseofaplanarwiggler). InthecaseofIRFEL,theundulatorproducesaweakmagnetostaticeldoftypically0.4Tesla. Theelectrontrajectorywhenitislocatedwithintheundulatorpolesisdescribedby: y=acos(2z=u) (2.17) dy dz=2a ucos(2z=u) Theforceontheelectronatthemaximumcurvaturecorrespondstothepeakvalueofthe magneticeld!B:=mec=(eB).Itiscommontocharacterizetheundulatormagnetbytheso calleddeectionparameterKdenedasK=dy=dzjmax=2ua.Togetherwiththerelation (2=)2a=eB=(mec),Ktakestheform:K=eBu 2mec (2.18) thisdeectionparameteristhemaximumangularexcursionofthebeaminunitsof1=.Itis interestingtocomputethemaximumamplitudeinthecaseoftheIRFEL:a=Ku=(2)'60m whichissmallerthattheelectronbeamsizesatthislocation(x'y'200m). Thewavelengthoftheradiationemittedbytheundulatorisdeterminedbythetimecontraction factordt=dt0=1cos,tbeingthetimereferenceinthemovingframewhereast0isthelaboratory (i.e.undulator)time.Intheelectronrestframe,theelectron\sees"theNuperiodsofthewiggler
- Page 1 and 2: HighBrightnessElectronBeamDiagnosti
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- Page 11 and 12: ListofTables 3.2Comparisonofcoecien
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- Page 27 and 28: !Vjitsthevelocity,and!Xjisthepositi
- Page 29 and 30: equation boundarybetweenvacuumandam
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- Page 33: 1.0 0.8 0.6 0.4 0.2 E=10 MeV E=42 M
- Page 37 and 38: harmonicwithproperchoiceoftheKvalue
- Page 39 and 40: Bu(rms)0.28T ParameterValueUnit Nu
- Page 41: 2.7TheJeersonLabIRproject usedasexp
- Page 44 and 45: Study TheFELdriveraccelerator:Latti
- Page 46 and 47: ParameterValue x -0.178 x(m) 8.331
- Page 48 and 49: Thepurposeofmeasuringthetransverser
- Page 50 and 51: computedusingthelatticeset-upuseddu
- Page 52 and 53: etatronexcitationaspicturedingure3.
- Page 54 and 55: ∆ x (mm), Corrector 0F00H ∆ x (
- Page 56 and 57: 1 0.5 0 spreadoftheparticlewassetto
- Page 58 and 59: 2 1 −5 −3 −1 1 3 5 k (m q −
- Page 60 and 61: Experimentallythecalibrationcoecien
- Page 62 and 63: tioned.FromthetransferfunctioninFig
- Page 64 and 65: Pickup Experiment #2 #3 #4 Simulati
- Page 66 and 67: Fromthesebothmeasurementitispossibl
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- Page 80 and 81: 1000 900 800 700 Figure4.4:Steadyst
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<strong>Electron</strong><br />
<strong>Beam</strong><br />
Resonant Cavity Length = 8.02 m<br />
Photon <strong>Beam</strong><br />
λ u<br />
Figure2.8:FEL-oscillatorprinciple(CourtesyJ.Martz,JeersonLab).<br />
schematicallydescribedingure2.8.Insuchcongurationthegeneratedmagnetostaticeldis<br />
transversewithrespecttotheelectronvelocity.Aselectronstravelinthewiggler,theyareslightly<br />
deectedalternativelyup<strong>and</strong>down(seeFigure2.8)<strong>and</strong>therebyspontaneouslyemitsynchrotron<br />
radiationthatislinearlypolarized(inthecaseofaplanarwiggler).<br />
InthecaseofIRFEL,theundulatorproducesaweakmagnetostaticeldoftypically0.4Tesla.<br />
Theelectrontrajectorywhenitislocatedwithintheundulatorpolesisdescribedby:<br />
y=acos(2z=u) (2.17)<br />
dy<br />
dz=2a<br />
ucos(2z=u)<br />
Theforceontheelectronatthemaximumcurvaturecorrespondstothepeakvalueofthe<br />
magneticeld!B:=mec=(eB).Itiscommontocharacterizetheundulatormagnetbytheso<br />
calleddeectionparameterKdenedasK=dy=dzjmax=2ua.Togetherwiththerelation<br />
(2=)2a=eB=(mec),Ktakestheform:K=eBu<br />
2mec (2.18)<br />
thisdeectionparameteristhemaximumangularexcursionofthebeaminunitsof1=.Itis<br />
interestingtocomputethemaximumamplitudeinthecaseoftheIRFEL:a=Ku=(2)'60m<br />
whichissmallerthattheelectronbeamsizesatthislocation(x'y'200m).<br />
Thewavelengthoftheradiationemittedbytheundulatorisdeterminedbythetimecontraction<br />
factordt=dt0=1cos,tbeingthetimereferenceinthemovingframewhereast0isthelaboratory<br />
(i.e.undulator)time.Intheelectronrestframe,theelectron\sees"theNuperiodsofthewiggler
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