Bunch compressors
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Bunch compressors. ILC Accelerator School May 20 2006 Eun-San Kim Kyungpook National University Korea. Locations of bunch compressors in ILC. BCs locates between e - (e + ) damping rings and main linacs, and make bunch length reduce from 6 mm rms to 0.15 mm rms.

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Bunch compressors

ILC Accelerator School

May 20 2006

Eun-San Kim

Kyungpook National University

Korea


Locations of bunch compressors in ILC

  • BCs locates between e- (e+) damping rings and main linacs, and

  • make bunch length reduce from 6 mm rms to 0.15 mm rms.

1st stage ILC : 500 GeV

2nd stage ILC : 1 TeV

- extension of main linac

- moving of SR and BC


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 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 compression

  • Beam 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 isenergy dependent

    : this is generated by bending magnets to create dispersive regions.

DE/E

-z

Tail

(advance)

lower energy trajectory

Head (delay)

center energy trajectory

higher 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.


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

Chicane

Double chicane

Chicanes as a Wiggler

Arc 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 chicane

  • A path length difference for particles with a relative energy deviationd is given by:

  • Dz = hd = R56d + T566 d2 + U5666d3……

  • 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 compressor

  • 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)

krf = 2p frf/c


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 are

Then,


Longitudinal particle motion in bunch compressor

To first order in eVrf/Eo << 1,

In a linear approximation for RF,


Longitudinal particle motion in bunch compressor

In a wiggler (or chicane),

In a linear approximation R56 >> T566d1,

Total transformation

For frf=  p/2, R66=1, the transformation matrix is sympletic,

which means that longitudinal emittance is a conserved quantitiy.


A simple case of4-bending magnet chicane

  • Zeuthen Chicane : a benchmark layout used for CSR calculation comparisons at 2002 ICFA beam dynamics workshop

B2

B3

qo

B1

B4

DL

LB

DL

DLc

LB

  • Bend magnet length : LB = 0.5m

  • Drift length B1-B2 and B3-B4(projected) : DL = 5 m

  • Drift length B2-B3 : DLc = 1 m

  • Bend radius : r = 10.3 m

  • Effective total chicane length : (LT-DLc) = 12 m

  • Bending angle : qo = 2.77 deg Bunch charge : q = 1nC

  • Momentum compaction : R56 = -25 mm Electron energy : E = 5 GeV

  • 2nd order momentum compaction : T566 = 38 mm Initial bunch length : 0.2 mm

  • Total projected length of chicane : LT = 13 m Final bunch length : 0.02 mm


Relations among R56, T566 and U5666 in Chicane

q

b

a

a

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 is


Relations among R56, T566 and U5666 in Chicane

Difference in path length due to relative energy error is

By performing a Taylor expansion about d = 0

For large d, d2 and d3 terms may cause non-linear deformations of the

phase space during compression.


Momentum compaction

  • The 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 is

  • From the conservation of longitudinal emittance,

    final bunch lengthis


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).


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 ~ N2

  • ISR and CSR may increase beam emittance in bunch compressors with shorter bunch length than the damping rings.


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 is

lr

sz

Lo

R

Coherent radiation forlr > sz

q

R=Lo/q

Overtaking length : Lo (24 sz R2)1/3


Coherent synchrotron radiation

  • CSR-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  (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.


Incoherent Synchrotron Radiation

When an electron emits a photon of energy u, the change in the betatron action

is given by

H=bxh'2+2axhh'+gxh2

  • Transverse emittance growth is

  • Increase of energy spread is

  • The increase in energy spread is given by:

  • Beamenergy loss is

Cq=3.84x10-13m


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 radiation

    that is produced


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)


Baseline design for ILC BC

A wiggler based on a chicane between each pair of quadrupoles

Each chicane contains 8 bend magnets (12 chicanes total).


Baseline design for ILC BC

BC2 RF

BC1 RF

BC1 Wiggler

BC1 Wiggler


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 456 9-cell RF cavities arranged in 57 cryomodules.

    - A wiggler has optics identical to the wiggler in the first BC, but with weaker wiggler.


Parameters of baseline design


Alternative design for ILC BC

 Main linac

Matching

Chicane 1

Quadrupoles

Chicane 2

RF section


Parameters of alternative design


Bunch compressors for ILC


Summary

  • Compared 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.


Problems

  • Show that emittance growth and increase of energy spread due to incoherent synchrotron radiation are given by

    1)

2)


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