High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
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structure<strong>and</strong>length.Alsowecannoticethatthesquaredistribution,<strong>and</strong>generallyalltypeof distributionwithsharpedge,inducesBFFwithlowwavelength(highfrequency)components.It thebunchlength.Hencemeasuringthecoherentradiationpoweratwavelengthcomparabletothe bunchlength,i.e.wherethecoherentenhancementoccurs,canprovideinformationonthebunch<br />
10 -4<br />
2 5 10 -3<br />
2 5 10 -2<br />
10<br />
(m)<br />
8<br />
10 9<br />
10 10<br />
10 11<br />
10 12<br />
10 13<br />
10 14<br />
10 15<br />
10 16<br />
10 17<br />
10 18<br />
N<br />
N<br />
2<br />
(solidline)bunches. isinterestingtonumericallycomputetheBFFusingaMonte-Carlosimulationtechnique,fora factorfor106macro-particles.Inthecaseofthebunchchargeweareinterestedini.e.60pC,the Figure5.3:Bunchformfactorcomputedfora300m(RMS)square(dashline)<strong>and</strong>gaussian<br />
distribution: macro-particlerepresents375electrons.Thechoicetosimulateonly106macro-particleinsteadof thewholenumberofelectroni.e.3:75108wasimposedbythedesiretoeconomizeCPUtime<strong>and</strong> expeditesimulations.TheMonte-CarlogenerateddistributioncanbewrittenasaKlimontovich nitenumberofmacro-particlesinthebunch.Ingure5.4wepresentcomputationofbunchform<br />
<strong>and</strong>theassociatedbunchformfactor,underthelinechargeassumption,reducestoasum: S(z)=i=N Xi=1(zzi) Weseeingure5.4thatbecauseofthenitenumberofparticles,thebunchdistribution<strong>and</strong> ~S()=i=N Xi=1jsin2zij2+jcos2zij2 (5.10) (5.9)<br />
theBFFcannotbetreatedascontinuum.Thesefeaturesshouldbekeptinmindevenifinthe followingwewillassumethebunchdistributiontobecontinuum. Ifoneusesst<strong>and</strong>ardbeamparametersexperimentallyachievedintheIRFELaccelerator,i.e.transversebeamsizeofapproximately1mm,minimumbunchlengthof140m,Eqn.(5.7)isnotafortiori P tot/P 1e - (no unit)
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