Bunch compressors

ILC Accelerator School

May 20 2006

Eun-San Kim

Kyungpook National University

Locations of bunch compressors in ILC

2nd stage : 1 TeV

1st stage : 500 GeV

BC : bunch compressor

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 t

hen shortened. - Required bunch length in ILC is 150 m.

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= 8m/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?

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.

-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)

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.

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=2e10)

Different types of bunch compressors

Different types of bunch compressors

Chicane : Simplest type with a 4-bending magnets for bunch compression

Double chicane : Its R56 is simply sum of the R56 values for each chicane.

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 dipole magnets where dispersion passes through zero, allowing continuous focusing across these long systems.

Arc type : R56 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.

Path length in chicane

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

zR565662U5666 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

Longitudinal particle motion in bunch compressor

)cos(

)cos()1(

)1(

1

11

0

rfrfo

orfrfrfif

oi

eVEE

zkeVEEE

EE

00

01

01

2cos zk

E

eV

zz

RFRF krf = 2frf/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 Eo to E1.

Then,

1)cos(

)cos()1(

0

01

rfrf

orfrfRFo

eVE

zkeVE

)cos()cos)cos(

100

01

01

rforfrfRFrfRF zkE

eV

E

eV

zz

(

RFRFRF kE

eVR sin

065

To first order in eVrf/Eo << 1,

In a linear approximation for RF,

0

0

66651

1 01

z

RR

z

RFRF

E

eVR cos1

066

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 T566<< R56,

Total transformation

Forrf= /2 (i.e. no acceleration), R66=1, the transformation matrix is sympletic,

which means that longitudinal emittance is a conserved quantitiy.

zzs zzzz2222222 ,

Longitudinal particle motion in bunch compressor

• 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 = 5m

• Drift length B2-B3 : Lc = 1m

• Bend radius : = 10.3m

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

• 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

baababa

s

12

1cos2

cos(

21

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

a

d

dsR 2

056

Relations among R56, T566 and U5666 in Chicane

a ab

......22

3565656 RRRs

56566 2

3RT

565666 2RU

By performing a Taylor expansion about =0

Path length in a chicane 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.

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

f

i

if

z

z

ifz 56R

RF phase angle

The simplest compressor design is one composed of a single rf section followed by a dispersive region - this performs an approximate 90o 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, R66=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.

)cos(

)sin(65

rf

rfrfrf

VrfEo

kVR

dz

d

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

Coherent radiation for r > z

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

QW

o

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) hc (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.

3/43/222.0

zR

NLer

rmsE

E

Incoherent Synchrotron Radiation

56

32 IrC eq sI d35

H

• The increase in energy spread is given by:

35

342 IrC eq sI d

133

• The energy loss from incoherent synchrotron radiation is:

2400 2IE

CU

sI d

122

Transverse emittance growth is

Energy loss from incoherent synchrotron radiation is

Increase of energy spread is

Cq=3.84x10-13m

Hx'x'x

Incoherent energy spread is generated through a random process

and therefore cannot be corrected.

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 offersreduced emittance growth at z 150 μ m.

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.

Design types of bunch compressor for ILC

A wiggler type that has a wiggler section made up of Np 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)

A Baseline design for ILC

A baseline design for ILC

BC1 RF BC1

Wiggler

BC2 RF

BC1 Wiggler

A baseline design for ILC

Initial Energy Spread [%] 0.15

Initial Bunch Length [mm] 6.0

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] 0.15

End BC2 Energy [GeV] 11.7

End BC2 Energy Spread [%] 2.73

Chicane 1 Chicane 2Superconducting RF cavityMatching Quadrupoles

Main linac

A Alternative design for ILC

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 0.02

Beam energy (GeV) 5 13

- Performance 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

Alternative Baseline

Required bunch length achieved 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