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

σ x (mm)
1.5
Figure4.17:Anexampleoftransverseemittancemeasurementinthehighenergyregionofthe
1
andvertical(bottom)rmsbeamsizeversustheexcitationofthequadrupole.Thedashedlines
2.5
deducedfromthet.Thechargeperbunchwasapproximatelysetto40pC. areobtainedwiththeleastsquarettechnique.Thereportednumberarethebeamparameters IRFELusingquadrupolescanmethod.Thetwoplotspresentvariationofthehorizontal(top)
2
1.5
ε =8.70 mm−mrad
y
α =1.02 y
1
β =1.44 m
y
0.5
−1000 0 1000 2000 3000
Henceeachbeamletwidthyieldsameasureofthewidthofthetransversedivergenceatthecor- whereNisthenumberofparticlesinthebeam.Forsuchadistribution,theprojectionwrites: ()=Nw 2i=n Xi=1exp2442 2L2~" 2xi+!235exp1~"L22 2 (4.48)
Quadrupole Excitation B’dl (Gauss)
respondingslit(i.e.uncorrelateddivergence),whereasthebeamletscentroidsgiveinformationon theslopeofthetransversephasespace(i.e.thecorrelateddivergencedistribution). Asweunderlinedpreviously,oneadvantageofsuchdeviceistobeabletomeasuretheemittanceof
Iftheincomingbeamonthemultislitmaskisemittance-dominated,SCwillbeinsignicantwith shouldincludetheangularspreadSCinducedbyspace-chargeforce: aspace-charge-dominatedbeam.Infact,intheEqn.(4.46)thereplacementofthedivergencex0by
respecttox0.However,inthecaseofaspace-charge-dominatedincomingbeam,theslitswidth =Lispermittedprovidedthebeamletscanberst-ordertransported.Otherwisethedivergence
shouldbeoptimizesothatthebeamletsbecomeemittance-dominated. AcriteriontodeterminatetheneededslitwidthcanbederivedbyintroducingtheDebyelength D,afundamentalparameterinPlasmaPhysicsthatcanalsobebyappliedtoBeamPhysics:
=Lx0+ZdsdSC ds(s) (4.49)
σ y (mm)
2.5
2
ε x =10.41 mm−mrad
α x =−0.704
β x =1.12 m