High Brightness Electron Beam Diagnostics and their ... - CASA

Withr1=r+c(==cwhereisthemirrorsrelativeposition),r2=r,Eqn.(5.42)takesthe Itisimportanttonotethatthequantity,intheaboveequation,isoftheorderofthebunch form: imageandthexedmirror,oftheorderof1m;hencereplacingr+cinEqn.(5.43)withrisa 5104eect.Therefore,withoutintroducingsignicanterrortheintensityonthedetectorcan planewithrespectofthepointofemissionwillresultinavalueofr,thedistancebetweenTR length(i.e.atmaximum500mforthepresentcase).A10%errorinthelocationofthefocal I()/1 r+c(0)()+cr((0)()) (5.43)
abovecanbeusedtoextractinformationfromatransitionradiationinterferogram. 5.5.3RelatinganInterferogramMeasurementtoaBunchLengthMeasurement Bymeasuringthefull-widthhalf-maximum(FWHM)oftheautocorrelation,onecanveryeasily bewrittenasforaTEMwave,thatisI()/((0)());andthestandardanalysispresented
getanestimateofthebunchlength.Let'sanalyzehowtheFWHMisrelatedtotheRMSvalues oftwotypicalparticledistributions:anormaldistributionthatischaracterizedbyitsrmsvalue
Table5.1:Relationshipsbetween\equivalent","RMS"and"FWHM"lengthsforagaussianand relatesFWHM,RMSandequivalentlengthforthesedistributions. (variance)zandasquaredistributionwhosecharacteristiclengthisitsfullwidthw.Table5.1
squarelongitudinalbunchdensity. DistributionEqu.LengthRMSFWHM Gaussian Square p2z w w=p12 z2zpln(2) w
CaseofaGaussiandistribution:
CaseofaSquaredistribution: HencetheRMSvalueoftheconvolutionisp2timestheRMSvalueofthedistribution.Using Table5.1,wededucethat S(z)=1=p22zexp(z2=(2z)).Forsuchdistribution,theautocorrelationis()=1=(2pz)exp(2=(42z)).
Wewritethisdistributionas:S(z)=((1=w)ifw=2