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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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1
Bunch compressors
ILC Accelerator School
May 20 2006
Eun-San Kim
Kyungpook National University
Korea
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.
3
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.
4
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?
5
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)
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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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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)
8
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, 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.
10
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
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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 )
12
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
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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
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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 ,
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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
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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
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.
18
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
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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
20
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.
21
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
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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
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
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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
25
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)
26
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).
27
Baseline design for ILC BC
BC1 RF BC1
Wiggler
BC2 RF
BC1 Wiggler
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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
29
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
30
Chicane 1 Chicane 2RF section
Matching Quadrupoles
Main linac
Alternative design for ILC BC
31
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
32
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
33
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.
34
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