High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA High Brightness Electron Beam Diagnostics and their ... - CASA
10 5 Sext. ON Figure3.20:EectofthesextupolesintheArc3Fontheenergy-phasecorrelation.(Simulations Sext. OFF andexperimentaldataareosetforclarity). 0 Sext. ON Sext. OFF −5 −10 −0.01 −0.005 0 0.005 0.01 δE/E (no unit) φ OUT (RF−Deg)
Characterization TransversePhaseSpace Chapter4 4.1Introduction ThepresentChapterisintendedtodiscusstheemittancemeasurementthatwehavedeveloped intheIRFEL.Techniquestomeasurebothemittance-dominated1andspace-charge-dominated2 beamaredescribed.BecausebeamprolemeasurementisanintegralpartofanemittancemeasurementwedescribetheOTR-basedbeamdensitymonitorthathavebeeninstalledintheIRFEL. Beforediscussingingreatdetailthetechniquesweusetomeasurethetransverseemittanceand phasespaceparameters,andbecauseofthedierentdenitionsthatvaryfromsourcetosourcein thecontemporarybeamdynamicsliterature,wenditimperativetosettlethedenitionofbeam Bydenition,abeamisacollectionofparticlesthatarecontainedwithinaniteregionofthephase 4.1.1Beam,HamiltonianDynamicsandLiouville'sTheorem emittancethatwewillusethroughoutthisdissertation. space.Inthemostgeneralcase,thephasespaceisa6-dimensionalspace[26]andtheparticles representationconcernsthesimplestcase:inothercases,additionalcoordinatesuchasspin,for (assumedtobepoint-like)arerepresentedbytheirpositionvector(x;y;z)andkineticmomentum vector(px;py;pz),andoccupiesasix-dimensionalhyper-volumegenerallyreferredas6.This repulsion) polarizedbeams,orchargeandmass,formultiple-speciesbeams,mightberequired.Thenotion whichthekineticmomentumismuchgreaterthanthemomentuminthetwootherdirections.The choiceof(x;y;z)and(px;py;pz)ascoordinateissimplycomingfromtheHamiltoniandescription oftheparticlesystemwhichrequirescanonicallyconjugatevariables.Inthesix-dimensionalphase ofabeamalsoentailstheexistenceofaprivilegeddirection,thedirectionofpropagation,along 1emittancedominatedbeammeansthatthebeamevolutionisdrivenbyexternalforces(e.g.externalfocussing) 2emittancedominatedbeammeansthatspace-chargeforcesdominatesthebeamevolution(i.e.Coulombian 49
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Characterization TransversePhaseSpace Chapter4<br />
4.1Introduction ThepresentChapterisintendedtodiscusstheemittancemeasurementthatwehavedeveloped intheIRFEL.Techniquestomeasurebothemittance-dominated1<strong>and</strong>space-charge-dominated2 beamaredescribed.BecausebeamprolemeasurementisanintegralpartofanemittancemeasurementwedescribetheOTR-basedbeamdensitymonitorthathavebeeninstalledintheIRFEL. Beforediscussingingreatdetailthetechniquesweusetomeasurethetransverseemittance<strong>and</strong> phasespaceparameters,<strong>and</strong>becauseofthedierentdenitionsthatvaryfromsourcetosourcein thecontemporarybeamdynamicsliterature,wenditimperativetosettlethedenitionofbeam<br />
Bydenition,abeamisacollectionofparticlesthatarecontainedwithinaniteregionofthephase 4.1.1<strong>Beam</strong>,HamiltonianDynamics<strong>and</strong>Liouville'sTheorem emittancethatwewillusethroughoutthisdissertation.<br />
space.Inthemostgeneralcase,thephasespaceisa6-dimensionalspace[26]<strong>and</strong>theparticles representationconcernsthesimplestcase:inothercases,additionalcoordinatesuchasspin,for (assumedtobepoint-like)arerepresentedby<strong>their</strong>positionvector(x;y;z)<strong>and</strong>kineticmomentum vector(px;py;pz),<strong>and</strong>occupiesasix-dimensionalhyper-volumegenerallyreferredas6.This<br />
repulsion) polarizedbeams,orcharge<strong>and</strong>mass,formultiple-speciesbeams,mightberequired.Thenotion whichthekineticmomentumismuchgreaterthanthemomentuminthetwootherdirections.The choiceof(x;y;z)<strong>and</strong>(px;py;pz)ascoordinateissimplycomingfromtheHamiltoni<strong>and</strong>escription oftheparticlesystemwhichrequirescanonicallyconjugatevariables.Inthesix-dimensionalphase ofabeamalsoentailstheexistenceofaprivilegeddirection,thedirectionofpropagation,along 1emittancedominatedbeammeansthatthebeamevolutionisdrivenbyexternalforces(e.g.externalfocussing) 2emittancedominatedbeammeansthatspace-chargeforcesdominatesthebeamevolution(i.e.Coulombian 49
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