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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100<br />
10 −3<br />
10 −2<br />
10 −1<br />
10<br />
thatthetransversemomentumimpartsasignicantcontributiontothetransverseprole.Hence Figure4.16:Relativeemittanceerrorversusdimensionlessspuriousdispersioncontributiontobeam size.<br />
1<br />
0<br />
1<br />
toperformveryfastmeasurementwithasimple<strong>and</strong>robustdatareductionalgorithm. thebeaminthedirectionwewishtoperformthemeasurement.Thischoicewasessentiallydone themeasureofthebeamletprolesontheuncorrelatedtransversemomentumspread. Thedierencesamongthevariousapparatusbasedonthisinterceptivetechniqueistheshape downstreamtoanalyzethebeamlets(wire-scanner,uorescentviewer,opticaltransitionradiation screen). Inthepresentcase,theselectingaperturewechoseiscomposedofparallelslits[38]thatsamples oftheselectingaperture(hole,slitsormatrixofaperture),<strong>and</strong>thekindofprolemonitorused<br />
ξ (no unit)<br />
Mathematically,theeectoftheslitscanbeseenasasampling:Ifbeforetheslitsthedensityin<br />
IftheprojectionisobservedafteradriftoflengthL,themulti-beamletproleis: wherenisthenumberofslits. spacedensity,thentheprojectioninthex-x0-planeaftertheslitsis: thespatialplane(x;y)isRR4(x;x0;y;y0)dx0dy0,where4(x;x0;y;y0)isthefourdimensionaltrace i=n Xi=1Zxi+w=2 xiw=2dx2(x;x0)'i=n ()=i=n Xi=1w2(xi;=L) Xi=1w2(xi;x0) (4.45)<br />
thesimplecaseofanormaldistributioninthetrace-space: whereisthehorizontalcoordinateinthebeamletobservationplane.Itisinstructivetoconsider 2(x;x0)=1 p2Nexp"Tx2+2Txx0+Tx02 2~"2 # (4.47)<br />
(4.46)<br />
(ε(ξ)−ε(0))/ε(0) (%)
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