34
1 Bunch compressors ILC Accelerator School May 20 2006 Eun-San Kim Kyungpook National University Korea

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. - PowerPoint PPT Presentation

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Page 1: Bunch compressors

1

Bunch compressors

ILC Accelerator School

May 20 2006

Eun-San Kim

Kyungpook National University

Korea

Page 2: Bunch compressors

2

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.

Page 3: Bunch compressors

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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 ( ~ z) : (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.

Page 4: Bunch compressors

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Main issues in bunch compressors

How can we produce such a beam with short bunch length?

How can we keep low emittance (x/y= 8m / 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?

Page 5: Bunch compressors

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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 is energy dependent

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

-zE/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)

Page 6: Bunch compressors

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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.

Page 7: Bunch compressors

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Beam parameters in bunch compressors for ILC

beam energy : 5 GeV rms initial horizontal emittance : 8 m 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)

Page 8: Bunch compressors

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Different types of bunch compressor

Chicane

Double chicane

Chicanes as a Wiggler

Arc as a FODO-compressor

Page 9: Bunch compressors

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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.

Page 10: Bunch compressors

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Path length in chicane

A path length difference for particles with a relative energy deviation is given by

zR565662 U5666 3 ……

: longitudinal dispersion : relative energy deviation (= E/E) R56 : linear longitudinal dispersion (leading term for bunch compression) T566 : second - order longitudinal dispersion U5666 : third - order longitudinal dispersion

Page 11: Bunch compressors

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Longitudinal particle motion in bunch compressor

00

01

01

2cos zk

E

eV

zz

RFRF krf = 2frf/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).

relative energy deviation

When a beam passes through a RF cavity on the zero crossing of the voltage (i.e. without acceleration, rf = /2 )

Page 12: Bunch compressors

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1)cos(

)cos()1(

0

01

rfrf

orfrfrfo

eVE

zkeVE

Then,

)cos(

)cos()1(

)1(

1

11

0

rfrfo

orfrfrfif

oi

eVEE

zkeVEEE

EE

When reference particle crosses at some rf,

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

Page 13: Bunch compressors

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Longitudinal particle motion in bunch compressor

)cos()cos)cos(

100

01

01

rforfrfrfrfrf zkE

eV

E

eV

zz

(

0

0

66651

1 01

z

RR

z rfrfrf kE

eVR sin

065

To first order in eVrf/Eo << 1,

In a linear approximation for RF,

rfrf

E

eVR cos1

066

Page 14: Bunch compressors

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Longitudinal particle motion in bunch compressor

1

156

2

2

10

1

zRz

12

315666

2156615612

UTRzz

6665

66565665

0

0

2

2 1

RR

RRRRzzMM

In a wiggler (or chicane),

In a linear approximation R56 >> T566 ,

Total transformation

Forrf= /2, R66=1, the transformation matrix is sympletic,

which means that longitudinal emittance is a conserved quantitiy.

zz zzzz2222222 ,

Page 15: Bunch compressors

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

A simple case of4-bending magnet chicane

B3B2

B4B1

LB LBLcL L

• Bend magnet length : LB = 0.5m

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

• Drift length B2-B3 : Lc = 1 m

• Bend radius : = 10.3 m

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

• Bending angle : o = 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

Page 16: Bunch compressors

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baababa

s

21

12

1cos2

cos(

2

If a particle at reference energy is bent by o, a particle with relative energy error is bent by o

Path length from first to final bending magnets is

a

d

dsR 2

056

Relations among R56, T566 and U5666 in Chicane

a ab

Page 17: Bunch compressors

17

......22

3565656 RRRs

56566 2

3RT 565666 2RU

By performing a Taylor expansion about = 0

Difference in path length due to relative energy error is

256

2

)1(

11

2

1

1((

Raasss

Relations among R56, T566 and U5666 in Chicane

For large , and terms may cause non-linear deformations of the phase space during compression.

Page 18: Bunch compressors

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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, e

nergy spread and rf phase.

First-order path length dependence is

dsRd

dz

56

From the conservation of longitudinal emittance,

final bunch length is

iiff zz

ifz

56R

Page 19: Bunch compressors

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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).

)cos(

)sin(65

rfrfo

rfrfrf

VE

kVR

dz

d

Page 20: Bunch compressors

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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.

Page 21: Bunch compressors

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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

r

R

R=Lo/

z

Coherent radiation for r > z

3/1242/3 )3()2(// z

QW

o

Overtaking length : Lo (24 z R2)1/3

Lo

Page 22: Bunch compressors

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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 (z√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 m bunch.)

With very small apertures, resistive wakefields can also generate emittance dilution.

3/43/222.0

zR

NLer

rmsE

E

Page 23: Bunch compressors

23

Incoherent Synchrotron Radiation

56

32 IrC eq sI d35

H

• The increase in energy spread is given by:3

5342 IrC eq sI d

133

2400 2IE

CU

sI d

122

Transverse emittance growth is

Beam energy loss is

Increase of energy spread is

Cq=3.84x10-13m

Hx'x'x

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

is given by H

2

oE

uJ

Page 24: Bunch compressors

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Bunch compressors for ILC

Two-stages of bunch compression were adopted to achieve σ 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

Page 25: Bunch compressors

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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)

Page 26: Bunch compressors

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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).

Page 27: Bunch compressors

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Baseline design for ILC BC

BC1 RF BC1

Wiggler

BC2 RF

BC1 Wiggler

Page 28: Bunch compressors

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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.

Baseline design for ILC BC

Page 29: Bunch compressors

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Parameters of baseline design

Initial Energy Spread [%] 0.15

Initial Bunch Length [mm]

Initial Emittance [m]

6.0

8 / 0.02

BC1 Voltage [MV] 253

BC1 Phase [°] -100

BC1 R56 [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 R56 [mm] -41

End BC2 Bunch Length [mm]

End BC2 Emittance [m]

0.15

8.2 / 0.02

End BC2 Energy [GeV] 11.7

End BC2 Energy Spread [%] 2.73

Page 30: Bunch compressors

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Chicane 1 Chicane 2RF section

Matching Quadrupoles

Main linac

Alternative design for ILC BC

Page 31: Bunch compressors

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Initial Energy Spread [%] 0.15

Initial Bunch Length [mm]

Initial Emittance [m]

6.0

8 / 0.02

BC1 Voltage [MV] 348

BC1 Phase [°] -114

BC1 R56 [mm] -474.2

End BC1 Bunch Length [mm] 1.1

End BC1 Energy [GeV] 4.86

End BC1 Energy Spread [%] 1.1

BC2 Voltage [MV] 11,800

BC2 Phase [°] -45

BC2 R56 [mm] -50.8

End BC2 Bunch Length [mm]

End BC2 Emittance [m]

0.15

8.3 / 0.02

End BC2 Energy [GeV] 13.26

End BC2 Energy Spread [%] 2.2

Parameters of alternative design

Page 32: Bunch compressors

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Alternative Baseline

Required bunch length achieved achieved

System length shorter longer

Tolerence of emittance acceptable

comparable

acceptable

comparable

GDE

Requirement

correction of vertical dispersion

shorten

system length

Alternative Baseline

Chicane length 68.4 m 480 m

Matching 4 m 310 m

Number of RF cavity 452 488

Total length 680 m 1400 m

Bunch compressors for ILC

Page 33: Bunch compressors

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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.

Page 34: Bunch compressors

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Problems

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

1) 56

32 IrC eq

2)

sI d35 H

35

342 IrC eq sI d33

1