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Beam Control and Manipulation Beam Techniques { Beam Control and Manipulation Michiko G. Minty Stanford Linear Accelerator Center, Stanford, CA 94309, USA Frank Zimmermann CERN, SL Division, 1211 Geneva 23, Switzerland We describe commonly used strategies for the control of charged particle beams and the manipulation of their properties. Emphasis is placed on rela- tivistic beams in linear accelerators and storage rings. After a brief review of linear optics, we discuss basic and advanced beam control techniques, such as transverse and longitudinal lattice diagnostics, matching, orbit correction and steering, beam-based alignment, and linac emittance preservation. A variety of methods for the manipulation of particle beam properties are also presented, for instance, bunch length and energy compression, bunch rotation, changes to the damping partition number, and beam collimation. The different pro- cedures are illustrated by examples from various accelerators. Special topics include injection and extraction methods, beam cooling, spin transport and polarization. Lectures given at the US Particle Accelerator School, University of Chicago and Argonne National Laboratory, June 14{25, 1999 Contents for Ph513/IU-USPAS P671B 6/99 M. Minty (SLAC), F. Zimmermann (CERN) 1 Introduction 1 1.1ReviewofTransverseLinearOptics.................. 2 1.2ReviewofLongitudinalDynamics................... 4 1.3BeamMatrix.............................. 5 2 Transverse Optics Measurement and Correction - Part I 1 2.1BetatronTune.............................. 1 2.1.1 Introduction . ......................... 1 2.1.2 FastFourierTransform(FFT)................. 2 2.1.3 Swept-FrequencyExcitation.................. 6 2.1.4 PhaseLockedLoop....................... 7 2.1.5 SchottkyMonitor........................ 8 2.1.6 Application:NonlinearDynamicsStudies........... 9 2.2BetatronPhase............................. 11 2.2.1 Harmonic Analysis of Orbit Oscillations ............ 11 2.3BetaFunction.............................. 13 2.3.1 Tune Shift induced by Quadrupole Excitation . ........ 13 2.3.2 BetatronPhaseAdvance.................... 17 2.3.3 OrbitChangeinducedbyaSteeringCorrector......... 18 2.3.4 atInteractionorSymmetryPoint.............. 19 2.3.5 R MatrixfromTrajectoryFit.................. 19 2.4GradientErrorDetectionandCures.................. 22 2.4.1 FirstTurnTrajectories..................... 24 2.4.2 Closed-OrbitDistortion.................... 24 2.4.3 PhaseAdvance......................... 25 2.4.4 BumpMethod........................ 26 2.5References................................ 27 3 Transverse Optics Measurement and Correction - Part II 1 3.1OrbitMeasurementandControl.................... 1 3.1.1 BPMOffsets.......................... 1 3.1.2 Lattice Diagnostics and R Matrix Reconstruction ....... 3 3.1.3 Singular Value Decomposition . ................ 8 3.1.4 Beam-BasedAlignment.................... 9 3.1.5 OrbitFeedback......................... 19 3.2 Beam Emittance and Emittance Preservation . ............ 21 1 3.2.1 Single Wire Measurement of Beam Emittance . ........ 21 3.2.2 Multiple Wire Measurement of Beam Emittance ....... 24 3.2.3 Graphics............................ 24 3.2.4 Emittance Mismatch . ..................... 32 3.3BetaMatchinginaTransportLineorLinac.............. 38 3.4References................................ 42 4 Transverse Phase Space Manipulation 1 4.1BetatronCoupling............................ 1 4.1.1 FirstTurnAnalysis....................... 2 4.1.2 Beam Response after Kick . ................ 3 4.1.3 ClosestTuneApproach..................... 5 4.1.4 CompensatingtheSumResonance............... 5 4.1.5 Emittance near CouplingResonance.............. 5 4.1.6 CouplingTransferFunction.................. 7 4.2 Equilibrium Emittance ......................... 9 4.2.1 CircumferenceChange..................... 11 4.2.2 Wigglers............................ 12 4.3 Linac Emittance Control . ..................... 16 4.3.1 Introduction . ......................... 16 4.3.2 BNSDamping......................... 16 4.3.3 Trajectory Oscillations ..................... 17 4.3.4 Dispersion-FreeSteering.................... 18 4.4SpaceChargeCompensationinPhotoinjectors............. 20 4.5 Collimation and Beam Halo . ..................... 23 4.5.1 Linear Collider ......................... 23 4.5.2 StorageRings.......................... 25 4.6References................................ 30 5 Longitudinal Optics Measurement and Correction 1 5.1 Synchronous Phase and Synchrotron Frequency ............ 1 5.2DispersionandDispersionMatching.................. 6 5.2.1 RFFrequencyShift....................... 6 5.2.2 RF Modulation ......................... 8 5.2.3 RFAmplitudeorPhaseJump................. 9 5.2.4 Higher-Order Dispersion in a Transport Line or Linac . 9 5.3MomentumCompactionFactor..................... 10 5.3.1 SynchrotronTune........................ 13 5.3.2 BunchLength.......................... 13 5.3.3 Lifetime............................. 14 2 5.3.4 PathLengthvs.Energy..................... 15 5.3.5 BeamEnergyviaResonantDepolarization.......... 15 5.3.6 Change in Field Strength for Unbunched Proton Beam . 18 5.4Chromaticity.............................. 18 5.4.1 RFFrequencyShift....................... 18 5.4.2 Head-TailPhaseShift..................... 19 5.4.3 NaturalChromaticity...................... 19 5.4.4 Local Chromaticity: d =d .................. 21 5.4.5 Chromaticity Control in Superconducting Proton Rings . 22 5.4.6 Application:MeasuringtheCentralFrequency........ 24 5.5References................................ 28 6 Longitudinal Phase Space Manipulation 1 6.1BunchLengthCompression...................... 1 6.2BunchLengthPrecompression..................... 4 6.3BunchCoalescing............................ 7 6.4 Bunch Splitting ............................. 8 6.5 Harmonic Cavities . ......................... 12 6.6EnergySpread.............................. 15 6.7EnergyCompression.......................... 21 6.8BeamLoading.............................. 21 6.9 Multibunch Energy Compensation . ................ 24 6.10 Damping Partition Number Change via RF Frequency Shift . 25 6.11References................................ 33 7 Polarization Issues 1 7.1Thomas-BMTEquation......................... 1 7.2SpinoralgebrausingSU(2)....................... 3 7.3SpinEquationofMotion........................ 5 7.4PeriodicSolutiontotheSpinEquationofMotion........... 6 7.5DepolarizingResonances........................ 7 7.6PolarizationPreservationinStorageRings............... 9 7.6.1 Harmoniccorrection...................... 10 7.6.2 Adiabaticspinflip....................... 11 7.6.3 Tunejump........................... 12 7.7SiberianSnakes............................. 12 7.8PartialSiberianSnakes......................... 18 7.9Spinresonancetheory.......................... 19 7.10References................................ 24 3 8 Injection and Extraction 1 8.1TransverseSingle-TurnInjection.................... 2 8.2 Multi-Turn Injection . ......................... 7 8.2.1 Transverse Multi-Turn Injection ................ 7 8.2.2 Longitudinal and Transverse Multi-Turn Injection ....... 7 8.2.3 Longitudinal Multiturn Injection ................ 8 8.2.4 Phase-SpacePainting...................... 8 8.3 H ChargeExchangeInjection.................... 10 8.4ResonantInjection........................... 11 8.5 Continuous Injection . ......................... 11 8.6InjectionEnvelopeMatching...................... 12 8.7FastExtraction............................. 19 8.8KickerandSepta............................ 20 8.9SlowExtraction............................. 26 8.10CrystalExtraction............................ 28 8.11References................................ 30 9 Cooling 1 9.1 Introduction . .............................. 1 9.2ElectronCooling............................ 5 9.3LaserCooling.............................. 14 9.3.1 IonBeams........................... 14 9.3.2 ElectronBeams......................... 16 9.4 Thermal Noise and Crystalline Beams . ................ 20 9.5BeamEchoes.............................. 22 9.5.1 Illustration........................... 23 9.5.2 CalculationofTransverseEcho................ 23 9.5.3 MeasurementsofLongitudinalEchoes............. 27 9.6IonizationCooling........................... 29 9.7ComparisonofCoolingTechniques.................. 33 9.8References................................ 33 10 Acknowledgements 1 4 Chapter 1 Introduction This report describes commonly used strategies for the control of charged particle beams and the manipulation of their properties. Emphasis is placed on relativistic beams in linear accelerators and storage rings. After briefly reviewing the fundamen- tals of accelerator optics, we discuss basic and advanced beam control techniques, such as transverse and longitudinal lattice diagnostics and matching procedures, or- bit correction and steering, beam-based alignment, and linac emittance preservation. Techniques for the manipulation of particle beam properties are presented next, in- cluding bunch length and energy compression, bunch rotation, changes to the damp- ing partition number, and beam collimation issues. Finally, we discuss a few special topics, such as injection and extraction methods, beam cooling, spin transport and polarization. The different techniques are illustrated by examples from various existing or past accelerators: the large electron-positron collider LEP 1 at CERN, the SLAC PEP-II 3 B factory 2 , the linac of the KEK B factory , the Stanford Linear Collider (SLC) ;5 6 7 4 , TRISTAN at KEK , the synchrotron light source SPEAR at
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