High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA High Brightness Electron Beam Diagnostics and their ... - CASA
AppendixB B.1LinearandSecondOrderTransport:Convention BeamDynamics:Notes&Tools B.1.1TransferMatrix Inthepresentreportweworkinthecoordinatesystem(x;x0;y;y0;;)where: x,y,arethecoordinateinthestandard3Dpositionspace(notethat=2z=RFrepresentsthelongitudinalpositionoftheparticleinunitoftheRFwavelengthoftheacceleratorTopropagateavector!rinalongasectionofbeamline,weuse,providedthesecond-orderapprox- x0andy0arethedivergenceinthetransverseplane (withinafactor2)) imationoftheequationofmotionisapplicable: reportcoincidentwiththeenergyaverageofthebunch). istherelativeenergyosetoftheparticlewithareferenceparticle(whichisinthepresent RijistherstordermatrixandTijkarethesecondorderterms. B.1.2BeamMatrix rout;i=XjRijrin;j+XkXj>kTijkrin;jrin;k+O(r3) (B.1) Thebeamormatrix,e.g.forthex-x0phasespaceisdenedasfollows: Thesamematrixcanbedenedforthey-y0phasespaces(3j4)or-longitudinalphasespaces (5j6).wehavethefollowingdenitions/properties: xdef =1j2def = 1112 1222!= 174hxx0ihx02i! hx2ihxx0i (B.2)
B.2Anoteonspacecharge Wedenetheslopeofthephasespaceas:dx=dx0=hxx0i=hx02i thetransversermsemittanceisthedeterminantdet(z) originatesfromCoulombrepulsionbetweenelectronswithinabunch.Spacechargetendstoinduce emittancegrowth.Inthissection,wewouldliketoshowthattheseforcesareonlyaconcernfor lowenergybeam,inourcase(Q'60pCthespacechargecollectiveeectisonlyimportantin Wehavealreadymentionedthatchargedparticlebeamaresubjecttospacechargeforcethat theinjectorbeamline.Forsuchapurposeweconsideraverysimplemodelofauniformlycharged Thelongitudinaleldcanalsobecomputedconsideringthebeaminsideapuremetalliccylindrical magneticeldsinsidethebeam,andinthebeamreferenceframe,caneasilybecomputedfromthe Maxwellequationandare(forr
- Page 145 and 146: inducedbyspacechargeisnotaconcernin
- Page 147 and 148: Golay Cell Signal (V) Golay Cell Si
- Page 149 and 150: Golay Cell Ouput (V) Golay Cell Oup
- Page 151 and 152: 150 100 5 4 Figure5.19:Energyspectr
- Page 153 and 154: Figure5.23:picturaleectoflongitudin
- Page 155 and 156: . .. .. . .. . . .. . .. . . .. . .
- Page 157 and 158: σ x (m) x 10−3 5 4 3 2 1 0 0 5 1
- Page 159 and 160: BeamDynamicsStudies Chapter6 undula
- Page 161 and 162: x,y (mm) 6.0 4.8 3.6 2.4 1.2 x y 0.
- Page 163 and 164: Space Charge over Emittance Ratio (
- Page 165 and 166: numericalsolution[56].Thisapproxima
- Page 167 and 168: 0.03 . .... . .. ... . .. ..... . .
- Page 169 and 170: ε x (mm−mrad) Nominal 6 4 2 cryo
- Page 171 and 172: 2.2 2 1.8 Figure6.10:Comparisonofth
- Page 173 and 174: 6 4 2 Figure6.12:\R55"transfermapfo
- Page 175 and 176: 10 1 5 10 0 500 1000 1500 2000 2500
- Page 177 and 178: EnergySpread(%) BunchLength(mm) Par
- Page 179 and 180: 15 Effect of RMS energy Spread 10 F
- Page 181 and 182: 6.4.4BunchSelfInteractionviaCoheren
- Page 183 and 184: 100 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0
- Page 185 and 186: Inthesecondseriesofrun,wewereableto
- Page 187 and 188: Conclusion Chapter7 Therecirculator
- Page 189 and 190: [2]Y.Shibata,T.Takahashi,T.Kanai,K.
- Page 191 and 192: [29]J.-C.Denard,C.Bochetta,G.Traomb
- Page 193 and 194: [65]B.C.Yunn,\ImpedancesintheIRFEL"
- Page 195: TEM:transverseelectricmagnetic. TOF
- Page 199 and 200: B.3.3PARMELA FeaturesofJeersonLabVe
- Page 201 and 202: Initialization MAIN Stop INPUT DECK
- Page 203 and 204: C.0.6TheDispersionRelationsfor^S(!)
- Page 205 and 206: have: Howeveritshouldbenotedthatweh
- Page 207: FigureD.1:OverviewoftheRF-controlsy
B.2Anoteonspacecharge Wedenetheslopeofthephasespaceas:dx=dx0=hxx0i=hx02i thetransversermsemittanceisthedeterminantdet(z)<br />
originatesfromCoulombrepulsionbetweenelectronswithinabunch.Spacechargetendstoinduce emittancegrowth.Inthissection,wewouldliketoshowthattheseforcesareonlyaconcernfor lowenergybeam,inourcase(Q'60pCthespacechargecollectiveeectisonlyimportantin Wehavealreadymentionedthatchargedparticlebeamaresubjecttospacechargeforcethat theinjectorbeamline.Forsuchapurposeweconsideraverysimplemodelofauniformlycharged<br />
Thelongitudinaleldcanalsobecomputedconsideringthebeaminsideapuremetalliccylindrical magneticeldsinsidethebeam,<strong>and</strong>inthebeamreferenceframe,caneasilybecomputedfromthe Maxwellequation<strong>and</strong>are(forr
Change language