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ILC Bunch compressor Damping ring

ILC Summer School

August 24 2007

Eun-San Kim

KNU

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Contents

Bunch compressor

Damping ring - Transverse motion - Longitudinal motion

We present the basic concepts than detailed present issues in ILC. ( Accelerator Physics Lecture in 3rd year class )

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Locations of bunch compressors

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

make bunch length reduce from 9 mm rms to 0.3 mm rms.

Beam diagnostics

Bunch compressor

Bunch compressor

make bunch length short.

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Why we need bunch compressors

Beams in damping rings has bunch length of 9 mm rms.

- Beams with long bunch length tend to reduce effects of beam instabilities in damping rings. - Thus, beams should be compressed after the damping rings.

Main linac and IP 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.

- ~ 0.3 mm rms.

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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?

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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.

-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)

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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.

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Initial beam parameters in bunch compressors

Initial beam energy : 5 GeV rms initial horizontal emittance : 8 m rms initial vertical emittance : 20 nm

rms initial bunch length : 9 mm rms final bunch length : 0.3 mm compression ratio : 30

rms initial energy spread : 0.15 % charge / bunch : 3.2 nC (N=2x1010)

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Different types of bunch compressor

Chicane

Double chicane

Chicanes as a Wiggler

Arc as a FODO-compressor

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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. 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.

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Path length in chicane

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

zR56 ……

: longitudinal dispersion : relative energy deviation (= E/E) R56 : linear longitudinal dispersion (leading term for bunch compression)

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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).

First-order path length dependence is

dsRd

dz

56

From the conservation of longitudinal emittance,

final bunch length is

iiff zz

ifz

56R

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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 greatly increase beam emittance in bunch compressors with shorter bunch length than the damping rings.

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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

Lo

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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 : baseline design

A chicane type that produces necessary momentum compaction with a chicane made of 4 bending magnets : alternative design

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Baseline design

BC1 RF BC1

Wiggler

BC2 RF

BC1 Wiggler

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Alternative design

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Initial Energy Spread [%] 0.15

Initial Bunch Length [mm]

Initial Emittance [m]

9.0

8 / 0.02

BC1 Voltage [MV] 348

BC1 Phase [°] -93

BC1 R56 [mm] -474.2

End BC1 Bunch Length [mm] 1.45

End BC1 Energy [GeV] 4.98

End BC1 Energy Spread [%] 1.63

BC2 Voltage [MV] 14,080

BC2 Phase [°] -36

BC2 R56 [mm] -50.8

End BC2 Bunch Length [mm]

End BC2 Emittance [m]

0.30

9.14 / 0.02

End BC2 Energy [GeV] 16.1

End BC2 Energy Spread [%] 2.4

Alternative design

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With optics and orbit corrections, emittance growth due to 6 machine errors shows 4% in vertical only.

Machine errors

300 m vertical misalign of Q

300 m horizontal misalign of Q

300 rad rotation error of Q

300 m vertical misalign of B

300 m horizontal misalign of B

300 rad rotation error of B

Tolerance of bunch compressor

Alternative design

0 200 400 600 800 1000

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10

RMS quadrupole horizontal alignment error (m)

x/ xo

xom without correction with correction

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Damping ring

Betatron motion

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Betatron motion • Mid-plane symmetry: magnetic field in the horizontal plane is perpendicular to the plane(s) = local radius of curvature

• Particles are kept on a nearly circular trajectory by bending and focusing magnetic fields.

• The reference trajectory is the equilibrium closed orbit for a particle of momentum p0. Quadrupoles act as focusing systems which produce small betatron oscillations around the reference trajectory

y

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Motion of equation

The linearized betatron motion is governed by Hill’s equation.

x” + Kx(s) x = 0 where Kx= 1/2 - (∂By/∂x) /B

y” + Ky(s) y = 0 and Ky= (∂By/∂x) /B

The focusing functions are periodic: Kx,y (s+L) = Kx,y (s)

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Transfer matrices

• Let y(s)= (y(s),y’(s)) be the “position vector” y(s) = M(s|s0) y(s0)

where M(s|s0) is the betatron transfer matrix.

• The passage through a magnetic element can be described by a 2x2 matrix, which transforms the "position vector" of a particle.

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Solution with constant K

• z” + K (s) z = 0 ( z = x or y ) z(s) = a cos(√Ks +b) K > 0 focusing quad z(s) = as + b K = 0 drift space z(s) = a cosh(√-Ks +b) K < 0 defocusing quad

• Mx = cosφsinφ/√|K| K > 0 focusing quad -√|K| sinφcosφφ= s √|K|• My = coshφsinhφ/√|K| K < 0 defocusing quad - √|K| sinhφcoshφ

• 1 L K = 0 0 1 L drift space of length

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Quadrupole

• Strenght Kx= (∂By/∂x) /B Ky= -(∂By/∂x) /B• Field Bx = (∂By/∂x)⋅y By = (∂By/∂x)⋅x

• A quadrupole is always focusing in one plane and defocusing in the other one

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One turn matrix

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One turn matrix

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Twiss parameters

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Twiss parameters

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Dispersion function

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Momentum compaction

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Chromaticity

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Chromaticity

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Damping ring

Synchrotron motion

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Radiated power

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Energy loss per turn

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Synchrotron oscillation

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Synchrotron oscillation

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Summary EDR Activity in Korea

- Damping rings (low emittance) : Ecloud and Ion beam instabilities - Bunch compressor (short bunch) : Beam dynamics - RF cavity (beam acceleration) : cavity design / processing - Beam instrumentation (beam diagnostics) : BPM design / processing

Welcome to ILC accelerator R&Ds !

Damping rings (e-,e+)RF cavity

Beam diagnostics

Bunch compressor

Bunch compressorBeam diagnostic