High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
1.1<br />
1 mrad<br />
0.9<br />
5 mrad<br />
mainlyduetothelongitudinaldistribution: zeff=zcos;<strong>and</strong>deriveacriteriononthermsbeamsizetoensurethewavelengthdependenceis latterequation,wec<strong>and</strong>enetheeectivecoordinatesxeff=xsinsin,yeff=ysincos<strong>and</strong> Figure5.2:AngularBFFforthreedierentvalueoftheRMSbeamdivergence.<br />
0.7<br />
10 mrad<br />
0.5<br />
0 0.02 0.04 0.06<br />
whichcanbeexpressedintermofRMSquantitieswithoutlossofgenerality: or ztanhx2sin2+y2cos2i1=2 zeffhx2eff+y2effi1=2 (5.6) (5.5)<br />
θ (rad)<br />
Ifthislattercriterionisfullledwecanusethelinechargeapproximation,i.e.,treatabunchasaline witha1Dchargedistribution.Insuchcase,analysisofthecoherentemissionofthebunchreveals informationonthebunchlongitudinaldistribution<strong>and</strong>isnotcontaminatedbythetransverseeect aforementioned,<strong>and</strong>wecanwritetheBFFasitisgenerallywrittenintheliterature: ~S()=jZ+1 ztanh2xsin2+2ycos2i1=2 (5.7)<br />
ThecomputationoftheBFFforanormaldistributionorasquaredistributionissimple;theresults arepresentedinFig.5.3wherewehaveassumedthebunchisacontinuum<strong>and</strong>itsRMSextentis withthebunch.Wehaveintroducedthewavenumber=1==!=(2c)forconvenience. 300m.Forbothtypesofdistribution,theBFFssuddenlytakeoatwavelengthoftheorderof<br />
whereasbeforeSz(z)isthelongitudinalbunchdensityalongthelongitudinalaxiszmovingalong 1Sz(z)exp(2iz)dzj2 (5.8)<br />
Angular Bunch Form Factor (a.u.)
Change language