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

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

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multislits mask (copper)<br />

Aluminum Foil<br />

Incoming<br />

Emittance-Dominated<br />

<strong>Beam</strong><br />

<strong>Beam</strong>lets<br />

D<br />

w<br />

Foranelectronbeam,Dwrites tentialintroducedbythistestparticleisscreenedduetoreorganizationoftheneighborcharges. interceptstheincomingspace-charge-dominatedbeam.Thebeamletsissuedfromtheslitsare Figure4.18:Overviewofthephasespacesamplingtechnique.AnincomingAmultislitmask emittance-dominated.<br />

Tele-photo lens<br />

whereistheLorenzfactor,kBtheBoltzmanconstant,Tbthebeamtemperature,measuredinthe qualitatively,thislengthcharacterizetheregioncenteredaroundatestparticleinwhichthepo- D=s0kBTb<br />

5 mm L=620 mm<br />

CCD detector<br />

onthemagnitudeofDversustheinter-distanceparticleswithinthebeamlinter<strong>and</strong>thebeam beamreferenceframe,ntheparticledensity<strong>and</strong>0isthedielectricconstantofvacuum.Depending size,therearetwomainregimes: InthecaseDtheDebyescreeningwillbeineective<strong>and</strong>singleparticledynamicswilldominate<br />

Thereforetransversespace-chargecontributionisinsignicantifD>>eq,eqbeingtheequivalentbeamradius(eq=[xy]1=2).ForthesimplecaseofaK-Vdistributionthetransverse temperatureisgivenby[41]: toitsnearestneighborsthantothecollectiveeldofthebeamdistributionasawhole. forthecharge<strong>and</strong>theself-eldmaybeused;IfD'linterthenaparticleismoresensible ontheDebyelengthcomparedtotheinter-particlesdistance:IfD>linter,smoothfunction<br />

IntroducingtheAlfvencurrentIA=40mc3 Where~"ndenotesthenormalizedemittance. kBTb=8mc2~"2n e,thepeakcurrentIp=Nec z(withzbeingthebunch<br />

e2n (4.50)<br />

2eq (4.51)

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