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Transcript of Bunch compressors
Bunch compressorsILC Accelerator SchoolMay 20 2006
Eun-San KimKyungpook National University Korea
Locations of bunch compressors in ILC 2nd stage ILC : 1 TeV - extension of main linac - moving of SR and BC 1st stage ILC : 500 GeV BCs locates between e- (e+) damping rings and main linacs, and make bunch length reduce from 6 mm rms to 0.15 mm rms.
Why we need bunch compressorsBeams in damping rings has bunch length of 6 mm rms.
- Such beams with long bunch length tend to reduce effects of beam 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.
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?
How to do bunch compressionBeam compression can be achieved: (1) by introducing an energy-position correlation along the bunch with an 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.-zDE/E lower energy trajectoryhigher energy trajectorycenter energy trajectory To compress a bunch longitudinally, trajectory in dispersive region must be shorter for tail of the bunch than it is for the head. Tail (advance)Head (delay)
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.
Beam parameters in bunch compressors for ILC beam energy : 5 GeV rms initial horizontal emittance : 8 mm rms initial vertical emittance : 20 nm
rms initial bunch length : 6 mm rms final bunch length : 0.15 mm compression ratio : 40
rms initial energy spread : 0.15 % charge / bunch : 3.2 nC (N=2x1010)
Different types of bunch compressor ChicaneDouble chicaneChicanes as a WigglerArc as a FODO-compressor
Different types of bunch compressor Chicane : Simplest type with a 4-bending magnets for bunch compression.
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.
Path length in chicaneA path length difference for particles with a relative energy deviation d is given by: Dz = hd = R56d + T566 d2 + U5666 d3
h : longitudinal dispersion d : relative energy deviation (= DE/E) R56 : linear longitudinal dispersion (leading term for bunch compression) T566 : second - order longitudinal dispersion U5666 : third - order longitudinal dispersion
Longitudinal particle motion in bunch compressorkrf = 2p frf/c Longitudinal coordinates z : longitudinal position of a particle with respect to bunch center Positive z means that particle is ahead of reference particle (z=0). d : relative energy deviation
When a beam passes through a RF cavity on the zero crossing of the voltage (i.e. without acceleration, frf = p/2 )
Longitudinal particle motion in bunch compressor Then, 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 are
- Longitudinal particle motion in bunch compressor To first order in eVrf/Eo
Longitudinal particle motion in bunch compressorIn 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.
Zeuthen Chicane : a benchmark layout used for CSR calculation comparisons at 2002 ICFA beam dynamics workshopA simple case of4-bending magnet chicane
B1LBLBDLc DLDL qoBend magnet length : LB = 0.5mDrift length B1-B2 and B3-B4(projected) : DL = 5 mDrift length B2-B3 : DLc = 1 mBend radius : r = 10.3 m Effective 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
If 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 isqRelations among R56, T566 and U5666 in Chicaneaab
By performing a Taylor expansion about d = 0Difference in path length due to relative energy error is Relations among R56, T566 and U5666 in ChicaneFor large d, d2 and d3 terms may cause non-linear deformations of the phase space during compression.
- Momentum compactionThe momentum compaction R56 of a chicane made up of rectangular bend magnets is negative (for bunch head at z
RF phase angleEnergy-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).
Synchrotron RadiationIncoherent 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 ~ N2
ISR and CSR may increase beam emittance in bunch compressors with shorter bunch length than the damping rings.
Coherent synchrotron radiationOpposite 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 islrRR=Lo/qqszCoherent radiation for lr > sz Overtaking length : Lo (24 sz R2)1/3 Lo
Coherent synchrotron radiationCSR-induced relative energy spread per dipole for a Gaussian bunch is
This 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 satisfies h (pszR)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.
Incoherent Synchrotron RadiationThe increase in energy spread is given by:Transverse emittance growth is Beam energy loss is Increase of energy spread is Cq=3.84x10-13mH=bxh'2+2axhh'+gxh2When an electron emits a photon of energy u, the change in the betatron action is given by
Bunch compressors for ILCTwo-stages of bunch compression were adopted to achieve z = 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 radiation that is produced
Designed types of bunch compressors for ILC