1. Bunch compressors ILC Accelerator School May 20 2006 Eun-San Kim Kyungpook National University

2. Locations of bunch compressors in ILC 2 nd stage : 1 TeV 1st stage : 500 GeV BC : bunch compressor

3. Purposes of bunch compressors  Damping ring produce beams with bunch length of 6 mm rms. - Such beams with long bunches tend to reduce effects of beam instabilities - Thus, beams are compressed after the damping rings  On the other hand, main linac and interaction point 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.  Bunches between damping ring and main linac are then shortened. - Required bunch length in ILC is 150  m.

4. Main issues in bunch compressors  How can we produce such a beam with short bunch length?  How can we keep the low emittance (H/V= 8  m/20nm) and high charge (~3.2 nC) of the beam in bunch compression?  How large are the effects of incoherent and coherent synchrotron radiation in bunch compression?

5. How to do bunch compression  Beam compression is achieved (1) by introducing an energy-position correlation along the bunch with an RF section at zero-crossing phase (2) and then passing beam through a region where path length is energy dependent – this is generated using bending magnets to create dispersive regions. -z  E/E lower energy trajectory higher energy trajectory center 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)

6. Consideration factors in bunch compressor design  The compressor must reduce bunch length extracted from damping ring to appropriate size in the linac.  The system must 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 must not significantly dilute transverse emittances and should include tuning elements for corrections.  The compressor should be short and as error tolerant as possible.

7. Parameters of bunch compressor for ILC  beam energy : 5 GeV  rms horizontal emittance : 8  m  rms vertical emittance : 20 nm  rms initial bunch length : 6 mm  rms final bunch length : 0.15 mm  compression ration : 40  rms energy spread : 0.15 %  charge/bunch : 3.2 nC (N=2e 10 )

8. Different types of bunch compressors

9.  Chicane : Simplest type with a 4-bending magnets for bunch compression  Double chicane : Its R 56 is simply sum of the R 56 values for each chicane.  Wiggler type : This type can be used when a large R 56 is required, as in linear collider. It is also possible to locate quadrupole magnets between dipole magnets where dispersion passes through zero, allowing continuous focusing across these long systems.  Arc type : R 56 can be conveniently adjusted by varying betatron phase advance per cell in the bend plane. The systems chromatic aberrations, introduce large beamline geometry excursions and produce many well aligned components.

10. Path length in chicane A path length difference for particles with a relative momentum deviation  is given by   z  R 56  566  2  U 5666  3 ……  : longitudinal dispersion,  : relative energy deviation (=  E/E)  R 56 : linear longitudinal dispersion,  leading term for bunch compression  T 566 : second-order longitudinal dispersion  U 5666 : third-order longitudinal dispersion

11. Longitudinal particle motion in bunch compressor k rf = 2  f rf /c When beam passes a bunch through a RF cavity on the zero crossing of the voltage (i.e. without acceleration) In general, when reference particle crosses at some  rf that is not be zero crossing. Then reference energy of the beam is changed from E o to E 1. Then,

12. To first order in eV rf /E o << 1, In a linear approximation for RF, Longitudinal particle motion in bunch compressor

13. In a wiggler (or chicane), In a linear approximation T 566   << R 56, Total transformation For  rf  =  /2 (i.e. no acceleration), R 66 =1, the transformation matrix is sympletic, which means that longitudinal emittance is a conserved quantitiy. Longitudinal particle motion in bunch compressor

14. Zeuthen Chicane : a benchmark layout used for CSR calculation comparisons at 2002 ICFA beam dynamics workshop A simple case of 4-bending magnet chicane B3B2 B4 B1 LBLB LBLB LcLc  L LL   Bend magnet length : L B = 0.5m Drift length B1-B2 and B3-B4(projected) :  L = 5m Drift length B2-B3 :  L c = 1m Bend radius :  = 10.3m Effective total chicane length (L T -  L c ) = 12m Bending angle :  o = 2.77 deg Bunch charge : q = 1nC Momentum compaction : R 56 = -25 mm Electron energy : E = 5 GeV 2 nd order momentum compaction : T 566 = 38 mm Initial bunch length : 0.2 mm Total projected length of chicane : L T = 13 m Final bunch length : 0.02 mm

15. If a particle at reference energy is bent by  o, a particle with relative energy error  is bent by    Path length from first to final dipoles is  Relations among R 56, T 566 and U 5666 in Chicane a ab

16. By performing a Taylor expansion about  =0 Path length in a chicane is Relations among R 56, T 566 and U 5666 in Chicane For large ,   and   terms may cause non-linear deformations of the phase space during compression.

17. Momentum compaction  The momentum compaction (R 56 ) of a chicane made up of rectangular bend magnets is negative (for bunch head at z<0).  The required R 56 is determined from the desired compression, energy spread and rf phase. First-order path length dependence is  From the conservation of longitudinal emittance, final bunch length is

18. RF phase angle  The simplest compressor design is one composed of a single rf section followed by a dispersive region - this performs an approximate 90 o rotation of the longitudinal phase space.  Energy-position correlation from an rf section is  In general case that beam passes through RF away zero-crossing, R 66 =1, there is some damping (or antidamping) of the longitudinal phase space, associated with acceleration (or deceleration).  RF phase may be chosen to be other than zero crossing to compensate the effect of the nonlinear phase slip.

19. Coherent synchrotron radiation  Opposite to the well known collective effects in accelerators where the wake-fields produced by head particles act on the particles behind, radiation fields generated at the tail overtake the head of the bunch when bunch moves along a curved trajectory.  CSR longitudinal wake function is r R R=L/   xx Coherent radiation for r >  z

20. Coherent synchrotron radiation  CSR-induced rms relative energy spread per dipole for a Gaussian bunch under steady-state conditions is  This is valid for a dipole magnet where radiation shielding of a conducting vacuum chamber is not significant; i.e., for a full vertical vacuum chamber height h which satisfies h  (  z √R)  h c (unshielded).  Typically the value of h required to adequately 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 « 10mm will shield a 190  m bunch.)  With very small apertures, resistive wakefields can also generate emittance dilution.

21. Incoherent Synchrotron Radiation The increase in energy spread is given by: The energy loss from incoherent synchrotron radiation is: Transverse emittance growth is Energy loss from incoherent synchrotron radiation is Increase of energy spread is C q =3.84x10 -13 m H  x  '   x  '  x    Incoherent energy spread is generated through a random process and therefore cannot be corrected.

22. Bunch compressors for ILC  Two-stages of bunch compression are used to attain σ z =150  m.  Compared to single-stage BC, two-stage system offers reduced emittance growth at  z  150 μm.  The first stage is a 90 degree rotation performed immediately after damping ring and second stage is a 360 degree rotation performed at 13 GeV after in energy spread has been reduced again after acceleration.  The two-stage procedure is used to: (1) limit the maximum energy spread in the beam (2) to get large transverse tolerances (3) reduce coherent synchrotron radiation that is produced (4) perform a net 90 degree rotation between damping ring and IP so that phase errors in the damping ring beam do not become energy errors at IP.

23. Design types of bunch compressor for ILC  A wiggler type that has a wiggler section made up of N p periods each with 8 bending magnets and 2 quadrupoles at each zero crossing of the dispersion function (present baseline design in ILC)  A chicane design type that produces necessary momentum compaction with a chicane made of 4 bending magnets. (present alternative design for ILC)

24. A Baseline design for ILC

25. A baseline design for ILC BC1 RF BC1 Wiggler BC2 RF BC1 Wiggler

26. A baseline design for ILC Initial Energy Spread [%]0.15 Initial Bunch Length [mm]6.0 BC1 Voltage [MV]253 BC1 Phase [°]-100 BC1 R 56 [mm]-750 End BC1 Bunch Length [mm]1.14 End BC1 Energy [GeV]4.96 End BC1 Energy Spread [%]0.82 BC2 Voltage [MV]12,750 BC2 Phase [°]-58 BC2 R 56 [mm]-41 End BC2 Bunch Length [mm]0.15 End BC2 Energy [GeV]11.7 End BC2 Energy Spread [%]2.73

27. Chicane 1Chicane 2 Superconducting RF cavity MatchingQuadrupoles  Main linac A Alternative design for ILC

28. Incoming to BC1 After BC2 Bunch length (mm) 6 0.15 Energy spread (%) 0.15 2.6 Horizontal emittance (  m) 8 8.3 Vertical emittance (  m) 0.02 Beam energy (GeV) 5 13 - P erformance of bunch compressor chicane 1 chicane 2 Number 4 4 Bending angle (deg.) 10.43 3.43 Length of a bend (m) 6.8 6.4 - Bending magnet A Alternative design for ILC

29. Alternative Baseline Required bunch length achieved System length shorter longer Tolerence of emittance acceptable comparable acceptable comparable BCD alternative baseline GDE Requirement correction of vertical dispersion shorten system length Alternative Baseline Chicane 68.4 m 480 m Matching 4 m 310 m Number of RF cavity 452 488 Total length 680 m 1400 m Comparison of ILC Bunch compressors