Presentation on theme: "ILC Accelerator School Kyungpook National University"— Presentation transcript:
1 ILC Accelerator School Kyungpook National University Bunch compressorsILC Accelerator SchoolMayEun-San KimKyungpook National UniversityKorea
2 Locations of bunch compressors in ILC BCs locates between e- (e+) damping rings and main linacs, andmake bunch length reduce from 6 mm rms to 0.15 mm rms.1st stage ILC : 500 GeVSz=6 mm rms2nd stage ILC : 1 TeV- extension of main linac- moving of SR and BC
3 Why we need bunch compressors Beams in damping rings has bunch length of 6 mm rms.- Such beams with long bunch length tend to reduce effects ofbeam instabilities in damping rings.- Thus, beams are compressed after the damping rings.Main linac and IP in ILC require very short beams:- to prevent large energy spread in the linac due to the curvature of the rf.- to reduce the disruption parameter ( ~ sz) :(ratio of bunch length to strength of mutual focusing between colliding beams)Thus, bunches between DRs and main linacs are shortened.- Required bunch length in ILC is 0.15 mm rms.
4 Main issues in bunch compressors How can we produce such a beam with short bunch length?How can we keep low emittance (ex/ey= 8mm / 20nm) and high charge (~3.2 nC) of the e- and e+ beams in bunch compression?How large is the effects of incoherent and coherent synchrotron radiation in bunch compression?
5 How to do bunch compression Beam compression can be achieved:(1) by introducing an energy-position correlation along the bunch withan RF section at zero-crossing of voltage(2) and passing beam through a region where path length is energy dependent: this is generated by bending magnets to create dispersive regions.DE/E-zHeadTail(advance)lower energy trajectoryHead (delay)center energy trajectoryhigher energy trajectoryTo compress a bunch longitudinally, trajectory in dispersive region must beshorter for tail of the bunch than it is for the head.
6 Consideration factors in bunch compressor design The compressor must reduce bunch from damping ring to appropriate size with acceptable emittance growth.The system may perform a 90 degree longitudinal phase space rotation so that damping ring extracted phase errors do not translate into linac phase errors which can produce large final beam energy deviations.The system should include tuning elements for corrections.The compressor should be as short and error tolerant as possible.
7 Beam parameters in bunch compressors for ILC beam energy : 5 GeVrms initial horizontal emittance : 8 mmrms initial vertical emittance : 20 nmrms initial bunch length : 6 mmrms final bunch length : mmcompression ratio : 40rms initial energy spread : %charge / bunch : 3.2 nC (N=2x1010)
8 Different types of bunch compressor ChicaneDouble chicaneChicanes as a WigglerChicane Double chicane Chicane as a Wiggler Arc as a FODO-compressorArc as a FODO-compressor
9 Different types of bunch compressor Chicane : Simplest type with a 4-bending magnets for bunchcompression.Double chicane : Second chicane is weaker to compress higher charge density in order to minimize emittance growth due to synchrotron radiation.Wiggler type : This type can be used when a large R56 is required, as in linear collider. It is also possible to locate quadrupole magnets between dipoles where dispersion passes through zero, allowing continuous focusing across the long systems.Arc type : R56 can be adjusted by varying betatron phase advance per cell. The systems introduce large beamline geometry and need many well aligned components.
10 Path length in chicane h : longitudinal dispersion A path length difference for particles with a relative energy deviation d is given by:Dz = hd = R56d + T566 d2 + U5666 d3 ……h : longitudinal dispersiond : relative energy deviation (= DE/E)R56 : linear longitudinal dispersion(leading term for bunch compression)T566 : second - order longitudinal dispersionU5666 : third - order longitudinal dispersion
11 Longitudinal particle motion in bunch compressor Longitudinal coordinatesz : longitudinal position of a particle with respect to bunch centerPositive z means that particle is ahead of reference particle (z=0).d : relative energy deviationWhen a beam passes through a RF cavity on the zero crossingof the voltage (i.e. without acceleration, frf = p/2 )Let us consider effect of passing a bunch through a RF cavity on the zero crossing of the voltage (i.e. without acceleration)krf = 2p frf/c
12 Longitudinal particle motion in bunch compressor When reference particle crosses at some frf,reference energy of the beam is changed from Eo to E1.Initial (Ei) and final (Ef) energies of a given particle areThen,
13 Longitudinal particle motion in bunch compressor To first order in eVrf/Eo << 1,In a linear approximation for RF,
14 Longitudinal particle motion in bunch compressor In a wiggler (or chicane),In a linear approximation R56 >> T566 d1,Total transformationFor frf = p/2, R66=1, the transformation matrix is sympletic,which means that longitudinal emittance is a conserved quantitiy.
15 A simple case of 4-bending magnet chicane Zeuthen Chicane : a benchmark layout used for CSR calculation comparisons at 2002 ICFA beam dynamics workshopB2B3qoB1B4LBDLDLcDLLBBend magnet length : LB = 0.5mDrift length B1-B2 and B3-B4(projected) : DL = 5 mDrift length B2-B : DLc = 1 mBend radius : r = 10.3 mEffective total chicane length : (LT-DLc) = 12 mBending angle : qo = 2.77 deg Bunch charge : q = 1nCMomentum compaction : R56 = -25 mm Electron energy : E = 5 GeV2nd order momentum compaction : T566 = 38 mm Initial bunch length : 0.2 mmTotal projected length of chicane : LT = 13 m Final bunch length : 0.02 mm
16 Relations among R56, T566 and U5666 in Chicane qbaaIf a particle at reference energy is bent by qo, a particle with relative energy error d is bent by q = qo / (1+d).Path length from first to final bending magnets is
17 Relations among R56, T566 and U5666 in Chicane Difference in path length due to relative energy error isBy performing a Taylor expansion about d = 0For large d, d2 and d3 terms may cause non-linear deformations of thephase space during compression.
18 Momentum compactionThe momentum compaction R56 of a chicane made up of rectangular bend magnets is negative (for bunch head at z<0).The required R56 is determined from the desired compression, energy spread and rf phase.First-order path length dependence isFrom the conservation of longitudinal emittance,final bunch length is
19 RF phase angle Energy-position correlation from an rf section is In general case that beam passes through RF away zero-crossing of voltage, that is R66 = 1, there is some damping(or antidamping) of the longitudinal phase space,associated with acceleration (or deceleration).
20 Synchrotron Radiation Incoherent synchrotron radiation (ISR) is the result of individual electrons that randomly emit photons.Radiation power P ~ N(N : number of electrons in a bunch)Coherent synchrotron radiation (CSR) is produced when a group of electrons collectively emit photons in phase. This can occur when bunch length is shorter than radiation wavelength.Radiation power P ~ N2ISR and CSR may increase beam emittance in bunch compressors with shorter bunch length than the damping rings.
21 Coherent synchrotron radiation Opposite to the well known collective effects where the wake-fields produced by head particles act on the particles behind, radiation fields generated at tail overtake the head of the bunch when bunch moves along a curved trajectory.CSR longitudinal wake function islrszLoRCoherent radiation for lr > szqR=Lo/qOvertaking length : Lo (24 sz R2)1/3
22 Coherent synchrotron radiation CSR-induced relative energy spread per dipole for a Gaussian bunch isThis is valid for a dipole magnet where radiation shielding of a conducting vacuum chamber is not significant, that is, for a full vacuum chamber height h which satisfiesh (psz√R)2/3 hc.Typically the value of h required to shield CSR effects (to cutoff low frequency components of the radiated field) is too small to allow an adequate beam aperture(for R 2.5 m, h « 10 mm will shield a 190 mm bunch.)With very small apertures, resistive wakefields can also generate emittance dilution.
23 Incoherent Synchrotron Radiation When an electron emits a photon of energy u, the change in the betatron actionis given byH=bxh'2+2axhh'+gxh2Transverse emittance growth isIncrease of energy spread isCq=3.84x10-13mThe increase in energy spread is given by:Beam energy loss isCq=3.84x10-13m
24 Bunch compressors for ILC Two-stages of bunch compression were adopted to achieve σz = 0.15 mm.Compared to single-stage BC, two-stage system provides reduced emittance growth.The two-stage BC is used : (1) to limit the maximum energy spread in the beam (2) to get large transverse tolerances (3) to reduce coherent synchrotron radiationthat is produced
25 Designed types of bunch compressors for ILC A wiggler type that has a wiggler section made up of 12 periods each with 8 bending magnets and 2 quadrupoles at each zero crossing of the dispersion function : baseline design (SLAC)A chicane type that produces necessary momentum compaction with a chicane made of 4 bending magnets : alternative design (E.-S. Kim)
26 Baseline design for ILC BC A wiggler based on a chicane between each pair of quadrupolesEach chicane contains 8 bend magnets (12 chicanes total).
27 Baseline design for ILC BC BC2 RFBC1 RFBC1 WigglerBC1 Wiggler
28 Baseline design for ILC BC First stage BC- contains 24 9-cell RF cavities arranged in 3 cryomodules.- Because the bunch is long, relatively strong focusing is used to limit emittance growth from transverse wakefields.Second stage BC- contains cell RF cavities arranged in 57 cryomodules.- A wiggler has optics identical to the wiggler in the first BC, but with weaker wiggler.
29 Parameters of baseline design Initial Energy Spread [%]0.15Initial Bunch Length [mm]Initial Emittance [mm]6.08 / 0.02BC1 Voltage [MV]253BC1 Phase [°]-100BC1 R56 [mm]-750End BC1 Bunch Length [mm]1.14End BC1 Energy [GeV]4.96End BC1 Energy Spread [%]0.82BC2 Voltage [MV]12,750BC2 Phase [°]-58BC2 R56 [mm]-41End BC2 Bunch Length [mm]End BC2 Emittance [mm]8.2 / 0.02End BC2 Energy [GeV]11.7End BC2 Energy Spread [%]2.73
30 Alternative design for ILC BC Main linacMatchingChicane 1QuadrupolesChicane 2RF section
31 Parameters of alternative design Initial Energy Spread [%]0.15Initial Bunch Length [mm]Initial Emittance [mm]6.08 / 0.02BC1 Voltage [MV]348BC1 Phase [°]-114BC1 R56 [mm]-474.2End BC1 Bunch Length [mm]1.1End BC1 Energy [GeV]4.86End BC1 Energy Spread [%]BC2 Voltage [MV]11,800BC2 Phase [°]-45BC2 R56 [mm]-50.8End BC2 Bunch Length [mm]End BC2 Emittance [mm]8.3 / 0.02End BC2 Energy [GeV]13.26End BC2 Energy Spread [%]2.2
32 Bunch compressors for ILC AlternativeBaselineChicane length68.4 m480 mMatching4 m310 mNumber of RF cavity452488Total length680 m1400 mAlternativeBaselineRequired bunch lengthachievedSystem lengthshorterlongerTolerence of emittanceacceptablecomparableGDERequirementcorrection of vertical dispersionshortensystem length
33 SummaryCompared to single-stage BC, two-stage BC system provides reduced emittance growth at σz = 0.15 mm.Two stage system can be tuned to ease transverse tolerances.Two stage system is longer than one-stage system.A shorter 2-stage may be also possible.
34 ProblemsShow that emittance growth and increase of energy spread due to incoherent synchrotron radiation are given by1)2)
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