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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!Vjitsthevelocity,<strong>and</strong>!Xjisthepositionvectorthatlocatesthej-thelectronwithrespecttothe bunchcenter. eachelectron[2,3]1:!ET(P)=X wherekjVj<strong>and</strong>Xjarerespectivelythewavevectoroftheelectriceldemittedbythej-electron, Underthefar-eldapproximation,wecan,withoutsignicantlychangingtheresults,replacethe j=1:::N!kj^(!kj^!Vj) j!kj^(!kj^!Vj)jj!E1e(k)jei!kj!Xj, (2.1)<br />
observationP.Introducingthenormalizedvelocity,j,theformerequationtakestheform: <strong>and</strong>bnistheunitvectorpointingfromthecenterofthechargedistributiontowardthepointof Figure2.1:Geometryoftheproblem.Inthecaseofsynchrotronemission(A),theopticalpulse referencecoordinatearetheoneoftheelectronbunchattheretardedtime.Forbackwardtransition radiation(B),thereferencecoordinatesarethespecularreectionoftheelectronbunchcoordinate asitstrokethealuminumradiator. wavevectorkjby2bn==!=cwhere(resp.!)isthewavelength(resp.frequency)ofobservation ThetotaldensitypowerradiatedatthelocationPisthenETET;itwrites: d2P(!) d!d=E1e(!)E1e(!)8
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