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CAS-CERN Accelerator School - Intermediate Particle Accelerator Physics PDF

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CERN–2006–002 26January2006 ORGANISATION EUROP(cid:131)ENNE POUR LA RECHERCHE NUCL(cid:131)AIRE CERN EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN Accelerator School Intermediate accelerator physics DESY, Zeuthen, Germany 15–26 September 2003 Proceedings Editor: D. Brandt GENEVA 2006 CERN–360copiesprinted–January2006 Abstract The fifth CERN Accelerator School (CAS) Intermediate course on Accelerator Physics was held at the DESY-Zeuthen Laboratory, Zeuthen, Germany from 15 to 26 September 2003. Its syllabus was based on the decision to definitively associate the Intermediate level course with the concept of afternoon courses. Con- sequently, the programme was composed of lectures in the mornings (dedicated to core topics) and of three ‘specialization’ courses in the afternoons, whereby each participant selected one of the proposed subjects and followed this course every afternoon for a detailed tuition on this specific topic. This year, the three proposed afternoon courses were ‘Optics Design, Measurement and Correction’, ‘Instrumentation, Beam Diagnostics and Feedback Systems’, and ‘Linac Structures’. Keeping in mind that the afternoon courses are not meant to be lectures but rather a mixture of theory and experimental applications, it follows that it is not possible to incorporate these courses in the proceedings. Consequently, the proceedings present the lectures given during themorningsessions. The lectures can be classified in three distinct categories: first, the core topics already introduced at the Introductory level but treated at a more advanced level, such as transverse and longitudinal dynamics, linear imperfections, vacuum, magnet design, particle sources, and beam instabilities. Secondly, the topics requir- ing some preliminary knowledge, and thus only introduced at the Intermediate level, such as non-linear ef- fects, sources of emittance growth, Landau damping, dynamics with damping, insertion devices, luminosity and beam–beam effects. The third category is composed of plenary lectures directly related to the proposed afternoon courses, i.e., lattice cells, insertions, beam instrumentation and feedback, beam diagnostics, linac structures,andsuperconductingRFcavities. These32lectureswerecompletedbythreeseminars,sixtutorials withsixhoursofguidedstudy,a10-hourafternooncourse,andaPostersession. iii iv Foreword The CERN Accelerator School was established in 1983 with the mission to preserve and disseminate the knowledge accumulated at CERN and elsewhere on particle accelerators and storage rings of all kinds. Until 1993, this was carried out principally by means of a biennial programme of introductory and advanced two- weekcoursesongeneralacceleratorphysicsaimingtobridgethegapbetweenthelevelofknowledgeattained withauniversitydegreeandthatrequiredforstartingacceleratorresearchwork. In1995, itwasrecognizedthattheleveloftheadvancedcoursewaspossiblytoohighandnotnecessarily adapted anymore to the needs of the young scientists entering the field of accelerator physics. Consequently, the advanced level course was replaced by an intermediate level course. The first Intermediate course was organizedin1995inEger,Hungary. Although the present proceedings are for the fifth Intermediate course on general accelerator physics held inZeuthen, GermanyinSeptember2003,theyarethefirstproceedingstobepublishedasaCERNReportfor acourseattheintermediatelevel. The intermediate level, which is clearly meant to be a logical follow-up of the introductory course, is composed of three distinct parts: first, some core topics (introduced at the introductory level) are reviewed at a more advanced level. Secondly, essential topics, which require some preliminary basic knowledge, are introduced(e.g.,non-lineareffects,Landaudamping,beam–beameffects). Finally,thespecificityoftheInter- mediatecourse, namelythe‘afternooncourses’, whereeachparticipantselectsoneofthreeproposedsubjects andfollowsthiscourseeveryafternoonforadetailedtuitiononthisspecifictopic. Thebasicobjectiveoftheintermediatelevelisthereforenotonlythattheparticipantsfollowregularlectures inthemornings,butthattheyalsohaveanopportunitytoacquirea‘solid’introductiontoatopicwhich,ideally, shouldbenewtothem. Thisspecializationshouldnotbecomposedoflectures,butratherofamixtureoftheory andexperimentalapplications. Thiscoursewasmadepossiblebytheactivesupportofseverallaboratoriesandmanyindividuals. Inpartic- ular, the help and collaboration of the DESY-Zeuthen Laboratory management and staff, especially Professor U. Gensch, K. Varschen, M. Mende, A. Hagedorn, and Dr. P. Wegner were most invaluable. Their endless enthusiasm and the provision of a first-class infrastructure for the lecture rooms definitely contributed to the successoftheschool. As always, the backing of the CERN management, the guidance of the CAS Advisory and Programme Committees, and the attention to detail of the Local Organizing Committee (DESY-Zeuthen) ensured that the schoolwasheldunderoptimumconditions. Very special thanks must go to the lecturers for the enormous task of preparing, presenting, and writing up their topics. Similarly, the enthusiasm and positive feedback of the participants was convincing proof that an Intermediate level course with afternoon courses was the appropriate complement to the Introductory level course. Finally,wethanktheCERNScientificTextProcessingServicefortheirdedicationandcommitmenttothe productionofthisdocument. DanielBrandt CERNAcceleratorSchool v Friday26/9/03Students’Feedback ClosingSession Thursday25/9/03InsertionDevices J. BahrdtT6Instabilities FELs P.SchmüserParticleSources R. Scrivens C1 C2 C3 Coffee/TeaSeminarNeutrino-Astro-PhysicsC.Spiering M E A L Wednesday24/9/03TransverseInstabilities K. SchindlGS6Instabilities Coffee & TeaFeatures of HighPerformanceStorage RingsLight SourcesA. WrülichAcceleratorMagnets Design S. RussenschuckN C H F R E E U eptember 2003) MondayTuesday22/9/0323/9/03InstabilitiesLongitudinalin LinacsInstabilities M. FerrarioK. SchindlT4T5SpaceDynamicsChargewith Damping DynamicsConcept ofwithLuminosityDamping I L. RivkinW. HerrDynamicsBeam-BeamwithEffectsDamping II L. RivkinW. HerrL Course 1 Course 2 Course 3 Coffee & TeaGS5SeminarDynamicsPhysics madewithin BerlinDampingS. Brandt DINNERBERLINM E A L S n ( y3 Zeuthe Sunda21/9/0 E X C U R S I O N n ate CAS School i Saturday20/9/03Introductionto BeamInstabilities K. SchindlT3Imperfections Space ChargeEffects M. FerrarioGS4Space Charge F R E E di Programme for the Interme WednesdayThursdayFriday17/9/0318/9/0319/9/03LinearNonlinearSources ofImperfectionsImperfectionsEmittanceGrowth O. BruningO. BruningD. MöhlT1GS2T2LongitudinalTransverseTransverseDynamicsDynamicsDynamics Coffee & TeaSC - RFNon-LandauCavitiesLinearities forDamping ILS’s P. SchmüserA. StreunA. HofmannVacuum inLattices forLandauAcceleratorsLSsDamping II O. GröbnerA. StreunA. HofmannL U N C H Course 1V Course 2I SCourse 3 ICoffee & TeaSeminarGS3The MotherImperfectionsTof allAcceleratorsA. De Rujula E V E N I N G M E A L and Correction” ostics and Feedback Systems” nt gn RSION 10.09.2003 meMondayTuesday15/9/0316/9/0330Opening TalkTransverseDynamics 30U. GenschE. Wilson30Recap.LongitudinalTransverseDynamicsDynamics 30E. WilsonJ. LeDuff 50Recap.InsertionsLongitudinalDynamics 50J. LeDuffB. Holzer50Intro. BeamIntroduction toInstrumentationBeam& FeedbackDiagnostics 50R. JonesR. Jones 30Lattice CellsC1 30B. HolzerC230LinacStructures C3 30N. PichoffCoffee & Tea00SchoolGS1OrganisationLongitudinalDynamics 00D. Brandt 30COCKTAIL30 urse 1 = “Optics Design, Measuremeurse 2 = “Linac Structures”urse 3 = “Instrumentation, Beam Dia VE Ti 08: 09:09: 10: 10: 11:11: 12: 14: 15:15: 16: 17: 18: 18:19: CoCoCo vi Contents Foreword D.Brandt ...................................................................................... v Transversebeamdynamics E.J.N.Wilson ................................................................................... 1 Latticedesigninhigh-energyparticleaccelerators B.J.Holzer .................................................................................... 31 Introductiontobeaminstrumentationanddiagnostics R.JonesandH.Schmickler ..................................................................... 75 IntroductiontoRFlinearaccelerators N.Pichoff .................................................................................... 105 Linearimperfections O.Bru¨ning ................................................................................... 129 BasicprinciplesofRFsuperconductivityandsuperconductingcavities P.Schmu¨ser .................................................................................. 183 Non-linearitiesinlightsources A.Streun ..................................................................................... 203 Latticesforlightsources A.Streun ..................................................................................... 217 Sourcesofemittancegrowth D.Mo¨hl ..................................................................................... 245 Landaudamping A.Hofmann .................................................................................. 271 Spacecharge K.Schindl .................................................................................... 305 Instabilities K.Schindl .................................................................................... 321 Wakefieldsandinstabilitiesinlinearaccelerators M.Ferrario,M.MiglioratiandL.Palumbo ...................................................... 343 Conceptofluminosity W.HerrandB.Muratori ...................................................................... 361 Beam–beaminteractions W.Herr ...................................................................................... 379 Electromagneticdesignofacceleratormagnets R.Russenschuck .............................................................................. 411 Insertiondevices J.Bahrdt ..................................................................................... 441 Free-electronlasers P.Schmu¨ser .................................................................................. 477 Electronandionsourcesforparticleaccelerators R.Scrivens ................................................................................... 495 AMAD-Xprimer W.Herr ...................................................................................... 505 ListofParticipants .............................................................................. 529 vii TRANSVERSE BEAM DYNAMICS E. Wilson CERN, Geneva, Switzerland Abstract This contribution describes the transverse dynamics of particles in a synchrotron. It builds on other contributions to the General Accelerator School for definitions of transport matrices and lattice functions. After a discussion of the conservation laws which govern emittance, the effects of closed orbit distortion and other field errors are treated. A number of practical methods of measuring the transverse behaviour of particles are outlined. 1. INTRODUCTION During the design phase of an accelerator project a considerable amount of calculation and discussion centres around the choice of the transverse focusing system. The lattice, formed by the pattern of bending and focusing magnets, has a strong influence on the aperture of these magnets which are usually the most expensive single system in the accelerator. Figure 1 shows the lattice design for the SPS at CERN. The ring consists of a chain of 108 such cells. The principles of designing such a lattice have been treated elsewhere in this school by Rossbach and Schmüser [1] and the methods of modifying the regular pattern of cells to make matched insertions where space is needed for accelerating structures, extraction systems and for experiments where colliding beams interact, will be the subject of another talk [2]. Fig. 1 One cell of the CERN 400 GeV Super Proton Synchrotron representing 1/108 of the circumference. The pattern of dipole and quadrupole magnets (F and D) is shown above. Beam particles make betatron oscillations within the shaded envelopes. 1 E.J.N. WILSON In this series of lectures I shall concentrate on those aspects of transverse dynamics which frustrate the designer or plague the person whose job it is to make the machine perform as well as theory predicts. I shall start with Liouville's theorem because this is an inescapable limitation to the beam size. Next I shall explain the distortion of the central orbit of the machine due to errors in the bending field. I shall then move on to explain how errors in quadrupole gradients may lead to instability of the betatron motion at certain Q values known as stopbands. Finally I shall explain why it is necessary to correct the variation of Q with momentum with sextupoles in order to avoid these stopbands. The more advanced topics of the influence of fields which couple the two transverse phase planes together and fields whose non-linear nature can excite resonances which extract particles are given in two separate talks in this school [3,4]. In those talks we shall move away from the predictable linear behaviour to glimpse the fascinating jungle of effects which stretch our minds at the boundaries of accelerator theory and which will be fully developed in the Advanced Course of this school. Since the effects I shall mention are annoying and best eliminated I shall try to indicate how measurements may be made on a circulating beam and its transverse behaviour corrected. Many of the effects I shall describe need only to be estimated rather than accurately predicted but it is very important to understand their mechanism. I shall therefore prefer to introduce concepts with approximate but physically revealing theory. I make no apologies for building the theory from elementary definitions. These have to be restated to give those not fortunate enough to have eaten and slept in phase space a firm basic understanding. I hope that others who become impatient with the redefinition of basic quantities will be eventually gratified by the later stages in the exposition of the theory and the references I have given for further study. 2. LIOUVILLE'S THEOREM Fig. 2 Liouville's theorem applies to this ellipse Particle dynamics obey a conservation law of phase space called Liouville's theorem. A beam of particles may be represented in a phase space diagram as a cloud of points within a closed contour, usually an ellipse (Fig. 2). 2

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