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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AppendixB<br />
B.1Linear<strong>and</strong>SecondOrderTransport:Convention <strong>Beam</strong>Dynamics:Notes&Tools<br />
B.1.1TransferMatrix Inthepresentreportweworkinthecoordinatesystem(x;x0;y;y0;;)where: x,y,arethecoordinateinthest<strong>and</strong>ard3Dpositionspace(notethat=2z=RFrepresentsthelongitudinalpositionoftheparticleinunitoftheRFwavelengthoftheacceleratorTopropagateavector!rinalongasectionofbeamline,weuse,providedthesecond-orderapprox- x0<strong>and</strong>y0arethedivergenceinthetransverseplane (withinafactor2))<br />
imationoftheequationofmotionisapplicable: reportcoincidentwiththeenergyaverageofthebunch). istherelativeenergyosetoftheparticlewithareferenceparticle(whichisinthepresent<br />
Rijistherstordermatrix<strong>and</strong>Tijkarethesecondorderterms. B.1.2<strong>Beam</strong>Matrix rout;i=XjRijrin;j+XkXj>kTijkrin;jrin;k+O(r3) (B.1)<br />
Thebeamormatrix,e.g.forthex-x0phasespaceisdenedasfollows: Thesamematrixcanbedenedforthey-y0phasespaces(3j4)or-longitudinalphasespaces (5j6).wehavethefollowingdenitions/properties: xdef =1j2def = 1112 1222!= 174hxx0ihx02i!<br />
hx2ihxx0i (B.2)
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