High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA High Brightness Electron Beam Diagnostics and their ... - CASA
1000 900 800 700 Figure4.4:SteadystatetemperatureversusaveragebeamcurrentforthreedierentTRradiator thicknessandabeamequivalentradiusof2mm. 600 distribution): 500 00000 11111 00000 11111 00000 11111 00000 11111 400 2 m 00000 11111 0.5 micron 00000 11111 00000 11111 2 1micron m 00000 11111 00000 11111 RewritingtheaboveequationintheFourierspaceyieldsthescatteringdistributionfunctionofthe whereistheconvolutionproduct. S()=(TB)() (4.18) 00000 11111 1 0.5 micron m 00000 11111 00000 11111 300 0 100 200 300 400 500 600 700 Average Beam Current ( A) Fromthisgurewecanseethatthelargerthethicknessis,thelargerthermsscatteringangle(i.e. varianceofthescatteringdistribution)is. ComparisonwiththeTheory TheF1istheinverseFouriertransformation.Wehavenumericallyperformedthisdeconvolution, andthecalculatedscatteringfunctionsforthreedierentfoilthicknessareshowningure4.6. Itisusefultocomparethepreviousresultswiththetheory,inordertoseehowaccuratelyweare abletopredicttheeectsofanOTRradiatoronthebeam.Thereareseveraltheoreticalmodel Temperature ( o K) Melting point foil: T=F1SB (4.19)
Wire Scanner Readback (mV) 1200 1000 Foil out 800 600 400 whichdependsonthemeanaverageofcollisionanelectronexperiencesasitpassthroughthe foil:simplescattering(1), beamismeasuredusingawirescannerlocateddownstreamthefoil. describingscatteringinsideverythintargetseachofthemhavetheirowndomainofapplicability Figure4.5:Anexampleoftheeectofa0:8mthickaluminumfoilonthebeamprole.The 0.8 m Foil in 200 0 0 10 20 30 40 50 60 pluralscattering(1 20), Position (mm) thatdescribesmultiplescattering.ThedetailedstudyofKeilmodelisoutofthescopeofthis thesis.Inbrief,KeilusedtheFouriertransformofthescatteringdistributionderivedbyMoliere Inthecaseofaluminumfoilwiththicknessthinnerthan5m,themeannumberofcollisionbeing lessthen20weareinthepluralscatteringregime.Thistypeofscatteringiswelldescribedby thesemi-empiricalmodelelaboratedbyKeil[30]whichisanextrapolationoftheMolieremodel multiplescattering(20). andonlyconsideredthetworsttermsofthisseries,avalidapproximationifthemeannumber ofcollisionisbelow20.Hethenempiricallycalculatedthenumericalcoecientoftheseriesusing theexperimentalmeasurementsperformedbyLeisegang[31]ashewasexperimentallystudying scatteringthroughverythingoldfoils.Therelationthatgivestheangularscatteringdistribution
- Page 29 and 30: equation boundarybetweenvacuumandam
- Page 31 and 32: 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.
- Page 33 and 34: 1.0 0.8 0.6 0.4 0.2 E=10 MeV E=42 M
- Page 35 and 36: 00000000000000000000000000000000000
- 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
- Page 68 and 69: . . . . . . . . . . . . . . . . . .
- Page 70 and 71: 10 5 Sext. ON Figure3.20:Eectofthes
- Page 72 and 73: spaceabeamthatconsistsofNparticles,
- Page 74 and 75: Asforthegeometricemittanceonecanden
- Page 76 and 77: (a) ceramic radiator beam x-wire be
- Page 78 and 79: and validundertheassumptionofaunifo
- Page 82 and 83: Fraction of Beam enclosed within (%
- Page 84 and 85: 5 2 2 3 4 5 6 7 8 9 10 0 10 5 2 Foi
- Page 86 and 87: Actuator Inserts Foil and Mirror CI
- Page 88 and 89: shortterm,touseasbeamdensitymonitor
- Page 90 and 91: Alongwiththeseimplementedoperations
- Page 92 and 93: whereiistheerrorontheithbeamsizemea
- Page 94 and 95: Let'sassumethethinlensapproximation
- Page 96 and 97: obtainedviathestatisticalanalysis.T
- Page 98 and 99: 20 18 16 . 14 . 12 . Figure4.14:Rel
- Page 100 and 101: 100 10 −3 10 −2 10 −1 10 that
- Page 102 and 103: multislits mask (copper) Aluminum F
- Page 104: TheReductionoftheSpaceChargeconditi
- Page 107 and 108: . . . . . . . . . . . . . . . . . .
- Page 109 and 110: Table4.7:Typicalsystematicerroronem
- Page 111 and 112: 180 8 160 6 Figure4.22:Anexampleof2
- Page 113 and 114: 4.0 3.5 3.0 2.5 Figure4.24:Emittanc
- Page 115 and 116: Characterization LongitudinalPhaseS
- Page 117 and 118: concentrateonthebeamparametersinthe
- Page 119 and 120: 1.1 1 mrad 0.9 5 mrad mainlyduetoth
- Page 121 and 122: Population Population 100000 90000
- Page 123 and 124: Theequation5.8yields: f()=jZ+1 11Xn
- Page 125 and 126: presentanoutlineofthisproofbelow,an
- Page 127 and 128: contrastintheCEBAFmachine,varyingas
- Page 129 and 130: 1.5 1 correspondtothevarianceofveco
1000<br />
900<br />
800<br />
700<br />
Figure4.4:SteadystatetemperatureversusaveragebeamcurrentforthreedierentTRradiator thickness<strong>and</strong>abeamequivalentradiusof2mm.<br />
600<br />
distribution):<br />
500<br />
00000<br />
11111<br />
00000<br />
11111<br />
00000<br />
11111<br />
00000<br />
11111<br />
400<br />
2 m 00000<br />
11111 0.5 micron<br />
00000<br />
11111<br />
00000<br />
11111 2 1micron m 00000<br />
11111<br />
00000<br />
11111<br />
RewritingtheaboveequationintheFourierspaceyieldsthescatteringdistributionfunctionofthe whereistheconvolutionproduct. S()=(TB)() (4.18)<br />
00000<br />
11111 1 0.5 micron m 00000<br />
11111<br />
00000<br />
11111<br />
300<br />
0 100 200 300 400 500 600 700<br />
Average <strong>Beam</strong> Current ( A)<br />
Fromthisgurewecanseethatthelargerthethicknessis,thelargerthermsscatteringangle(i.e. varianceofthescatteringdistribution)is. ComparisonwiththeTheory TheF1istheinverseFouriertransformation.Wehavenumericallyperformedthisdeconvolution, <strong>and</strong>thecalculatedscatteringfunctionsforthreedierentfoilthicknessareshowningure4.6.<br />
Itisusefultocomparethepreviousresultswiththetheory,inordertoseehowaccuratelyweare abletopredicttheeectsofanOTRradiatoronthebeam.Thereareseveraltheoreticalmodel<br />
Temperature ( o K)<br />
Melting point<br />
foil: T=F1SB (4.19)
Change language