Investigation and optimization of transverse non-linear beam dynamics in the high-energy storage ring HESR [Elektronische Ressource] / vorgelegt von Dominic Markus Welsch

Investigation and optimization of transverse non-linear beam dynamics in the high-energy storage ring HESR [Elektronische Ressource] / vorgelegt von Dominic Markus Welsch

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akult?tInelscvBonnestigationh-NaturwissenscandFOptimizationonofBonnThenransvRheiniscerseh-Wilhelms-UnivNon-LinearorgelegtBeamMarkusDynamicsausinMathematiscthehaftlicHigh-EnergyFStoragederRinghenHESRriedricDissertationersit?tzurvErlangungvdesDominicDoktorgradesW(Dr.hrer.Bonnnat.)2009derGutacAngefertigt10.03.2010mitBispliGenehmigungRudoderDr.MathematiTsungsjahr:cMaierh-Naturwissenscter:haftlicnhengFderakult?theiderDr.Rheinisclfhen2.FhriedricProf.h-Wilhelms-UnivJeerssint?thoBonnag1.Promotion:GutacErschnter:2010Prof.dTanoMaxBritta1:5 15GeV=c3moreisout.partbofgnetstheyupdicomingaFThacilitoleryelopforeenAnbtiprotonusingandonIonaResearcparticleheen(FhAIR)ofwhicushroisThplannedvastheirahamahniquejoralsoextensionatohoicethebpresenntlong-termfacilitvyedofoftheh.Helmholtzzenfortrumhasf?rtuneScemittancehresonances.wscerio-apnenforscerrorshquadrupungincluded(GSI)In-ineDarmstadt.settingsTheeenHEScalculationsRanalysis.wiecienlllong-termprokvidetheanatipsroastonfactorsofinapthebmomenincreasedtumumrangehasfromenc(HESR)theRinghrotronStorageFtotrumrgycescHigh-EnHESRforoletheeenintoternalandtargetminimizeex-wthpberimenctyPhasAthroughNDcalcu-A.

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akult?tInelscvBonnestigationh-NaturwissenscandFOptimizationonofBonnThenransvRheiniscerseh-Wilhelms-UnivNon-LinearorgelegtBeamMarkusDynamicsausinMathematiscthehaftlicHigh-EnergyFStoragederRinghenHESRriedricDissertationersit?tzurvErlangungvdesDominicDoktorgradesW(Dr.hrer.Bonnnat.)2009derGutacAngefertigt10.03.2010mitBispliGenehmigungRudoderDr.MathematiTsungsjahr:cMaierh-Naturwissenscter:haftlicnhengFderakult?theiderDr.Rheinisclfhen2.FhriedricProf.h-Wilhelms-UnivJeerssint?thoBonnag1.Promotion:GutacErschnter:2010Prof.dTanoMaxBritta1:5 15GeV=c
3
moreisout.partbofgnetstheyupdicomingaFThacilitoleryelopforeenAnbtiprotonusingandonIonaResearcparticleheen(FhAIR)ofwhicushroisThplannedvastheirahamahniquejoralsoextensionatohoicethebpresenntlong-termfacilitvyedofoftheh.Helmholtzzenfortrumhasf?rtuneScemittancehresonances.wscerio-apnenforscerrorshquadrupungincluded(GSI)In-ineDarmstadt.settingsTheeenHEScalculationsRanalysis.wiecienlllong-termprokvidetheanatipsroastonfactorsofinapthebmomenincreasedtumumrangehasfromenc(HESR)theRinghrotronStorageFtotrumrgycescHigh-EnHESRforoletheeenintoternalandtargetminimizeex-wthpberimenctyPhasAthroughNDcalcu-A.estimatedThethedemandiolengmagnetsrequiremenbtstheofdynamicsPestigationsANDhaAeeniniontermtheseofvbapeamthequalitfrequencyyreanddiusionluwmtoiynositparticleyng.togetherreductionwioletherrorsatlimitedtunprotheductionertureratevofroughlyanwtipinnerrodtonsicallwhereforisaonlongwbinclueamAbstractlifeorbittimematrixandbabminimhmarkumatofCobSynceamCOSYloss.theTherefore,orscanungszeneJ?licectivAehromaticitclosedcorrectionohemerbtheitconsistingcorrectionsextupandmagnetsabsuciendevtlyedlargereducedy-spreadnamicthaptoerturetheofgrothecausedHESRyareetatroncrucial.TheWithhthismaticitthesiscorrectionIhemepresenbtoptimizedmdynamicyerturewlations.orkeoneldbofothHESRofptheseandtopics.oleThehaexpeectedeenmisalignmenintsnon-linearofeambstudies.eamvguidingconcerningmagnetsoptimizationhavvbecarriedbTheeenopticalesti-ofmatedHESRandvusedbtoimprosimedulatedynamictheertureclosedandorbittecinofthemapHESR.TheAlclosedtedorbitcocorrectiontscashemeusedhaspredictbstabiliteenbaseddevshort-termeloptracediforWithdierenreasonabletofionquadrupopticalmasettingseldofandthedierenHESRcanofden,umericaldynamicsimpulationswhaimprovedeybaeentpo.erformedetoareavthealidateytheamsccheme.ertureThethepropmotionosedstaclosedleorbitacorrectionscalemethoasThetobdesizethantheecieddeamwhicandhspusesmaximtheclosedorbitdeviations.response26Con.ten.ts.1.In.tro24duction.1y2.Theorywith3.2.1.Linear.b.eam.dynamics......co.........analysis.22.AIR.....hain.3.1.3............3Beam2.1.1.Charged.particlesIonin.e.l.ec.tro-magnetic2.2.5elds....2.2.6....3Storage2.1.2bCo-mo.ving.coHESRordinate.system..24.....exp................4.2.1.33.2.2Hamiltonian......................................theorem......4.2.1.4.Multiprequencyolar.expansion.of.magnetic.eldsThe.ing.An.at......6.2.1.524LinearFequation.of.motion.and.b.etatronInjectionfunctionsan..7.2.1.6.MatrixANDformalismt.........HESR.............3.2.1..............9.2.1.7.Disp.ersion.and.Chromaticit.y29...........3.2.4...........3210prop2.1.8.Momen.tum.com.p3.3ac.ti.o.n.and.transitionviienergy.......11.2.1.9.Orbit.resp20onseKAMm.atrix..................21.F.map..........12.2.1.10.Inuen.c3eHigh-EnergyofRelectronHESRco3.1olerstiprotontoroideamsmagnetsFon.closed.orbit..............3.1.1.at.AIR.....................3.1.2.c.for.tiprotons......14.2.2.Non-linear25bPeamAdynamicserimen...................3.2.design..............16.2.2.1.Symplectic.Maps....27.La.out.........................27.Magnets..16.2.2.2.Driving.terms................3.2.3.parameters...................31.Electron.oler18.2.2.3.T.rac.king.co.de........3.2.5.optical.erties.................34.Comparison.COSY........20.2.2.4.Dynamic.ap.erture..35.. = 6:2tr
= 13:3tr
.correction.system.for.HESR..of..................38une4.1.1.Alignmen.t.errorsand.......Closed.................75.........the..38correc-4.1.2.Sim.ulation.of55orbit.distortions..The.......une.....59........39.4.1.3.orbitOrbit.correction.elemen.ts................ole.....79......41hromaticit4.1.4.Closed.orbit.correction.for.HESR......Field.HESR.......56.correction.ts4.2.4.1.5.Orbit.correction.including5.4.1eld.errors..........Design......45.4.1.6.Closed5.4.3lo.cal.orbit.bumps.for.HESRThe.viii.......5.5.1........46.4.2.ClosedDesignorbit.correction.at.COS.Y..5.5.3...........5.6.rrection...........Discussion49.4.2.1.COSY.settings....6.ok.y.tion..............................495.34.2.2errorsMeasuringtheorbitmagnetsresp.o.n.se.matrix......5.4.38.orbit.4.lattice......49.4.2.3.Comparison.of.measured.and.calculated.orbit58re-Tspscansonse.matrix....................5.4.2.tunes....................50634.2.4OptimizationOrbit.correction...............4.1.Closed715.5.ten.Con...lattice.....................7551T4.3scansDiscussion.of.re.s.ults..............5.5.2.tunes.....................75.Optimization..51.5.Dynamic.ap.erture.and.frequency.map.analysis.54785.1MultipDynamiccoap.erture.calculations..................5.7.of.results........54.5.2.Arrangemen.t.of.sextup80oleSummarymagnetsoutlofor81c1:5 15GeV=c
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