Lattice Design for SuperB

1
Lattice Design for SuperB
http//www-kekb.kek.jp/MAC/2007/

• LNF, SLAC, ILC DR group, KEK?
• Y. Ohnishi/KEK
• March/20/2007
• The 12th KEKB Review

2
Topics

• Strategy of SuperB
• Machine parameters
• Lattice issues and Final Focus
• Dynamic aperture
• Summary

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Low Emittance and Low Beta Scheme
SuperB Workshop at LNF

• Luminosity
• Small emittance and large crossing angle (2fxltlt1)
  to make large Piwinski angle
• Beam-Beam parameters in the case of jgtgt1
• If N increases proportionally to szfx, xy is
  constant and luminosity increases with szfx. xx
  decreases with1/szfx. (if bx, by/ey are
  constant)

fx Half crossing angle
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Crabbed Waist Scheme
SuperB Workshop at LNF

• Waist position is adjusted by kick from
  sextupoles to suppress hourglass
  effect. Dsx/2fx
• Small sx and large fx
• Overlap area(longitudinal) of colliding bunches
  is sx/2fx.

by can be small, while sz is free.
Shift of waist Ds x/2fx
Dyxplp Dyyp/2np
e
e-
Dyxpkp Dyyp/2mp
sextupole for crabbed waist
crabbed waist
kleven, mnodd or klodd, mneven
x
2fx
Ds
original waist
Ds x/tan(2fx) x/2fx
Particles collide another beam at their waist
point.
sextupole for crabbed waist
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Comparison of Machine Parameters
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Machine Parameters of SuperB
SuperB CDR
Small beam currents are attractive!
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Characteristics of Ring

• Extremely small emittance
• Extremely small beta function at IP
• Large crossing angle at IP
• Long bunch length
• Crabbed waist optics

ex 0.8 nm
bx/by20mm/200mm
2fx34 mrad
sz6 mm
Strong sextupole pair at high beta region Need
proper phase advance to IP
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Layout of Ring
Circumference 2.3 km
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SuperB Lattice with Crabbed Waist
I -transformation
HER
Dfx20p Dfy11.5p
Dfx20p Dfy10.5p
bx60 m by240 m K2-11.2 m-2
bx60 m by240 m K211.2 m-2
IP
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Lattice Design of Final Focus
bx/by20/0.2 mm
P. Raimondi
Local Chromaticity Correction
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Lattice Design of Final Focus (cont'd)
Dp/p02
Dp/p0 0
Dp/p0-2
SD
SF
SD
SF
P. Raimondi
IP phase sextupoles
Small beta at on-momentum becomes large at
off-momentum.
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Chromatic Effect in Final Focus
Half of IR are considered to be a transport line.
Octupole OFF
Phase advance between end of IR and IP
Octupole ON
Deviation of alpha at IP
Deviation of beta function at IP
The second order chromaticity can be corrected by
octupoles.
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Arc Cells and Opposite Section of IP
SF
SD
SD
TME cell
HER
M. Biagini
Beta becomes large at sextupoles.
Betatron tunes are adjusted with 7 quadrupole
families.
12 cells x 6 arcs 72 cells in a ring
Dnx 0.5 Dny 0.5
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Wiggler/RF Straight Section
lp0.4 m / B00.83 T
Lattice design is similar to the ILC damping ring.
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Sextupoles for Crabbed Waist
Required K2 (only for 2 sextupoles)
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Chromaticity Correction with Crabbed Waist
whole ring
HER
36 sextupole families x 6 arcs
Sextupoles in an arc are decomposed.
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Dynamic Aperture
HER
ny0.05nx (fixed)
SCW1/SCW2 (sextupoles for crabbed waist) K20
nxx/sx
tTouschek16 min
Dnx 49.56 Dny 24.60
Np 2.94x1010 ey/ex 0.25
Dynamic aperture decreases when sextupoles for
crabbed waist turned on.
K2/4
K2/2
Synchrotron radiation ON Quantum excitation
OFF 1 damping time
K211.2
Dp/p0 ()
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Phase Space Crabbed Waist OFF
Synchrotron Radiation OFF
Synchrotron Radiation ON
SCW1/SCW2 K20 (1/m2)
px/p0
px/p0
5sx (Jx12.5ex)
x (m)
x (m)
py/p0
py/p0
y (m)
y (m)
0.2sx (Jy2ex)
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Phase Space Crabbed Waist ON
Synchrotron Radiation OFF
Synchrotron Radiation ON
SCW1/SCW2 K2-11.2/11.2
px/p0
px/p0
5sx (Jx12.5ex)
x (m)
x (m)
py/p0
py/p0
y (m)
y (m)
0.2sx (Jy2ex)
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Amplitude vs Tune dependence
nx
Crabbed waist ON
Dnx4x1021 Jx3
Crabbed waist OFF
Dnx1.2x105 Jx
Jx (m)
When fringe effects is turned off for all
magnets, amplitude dependence is disappeared. But
separatrix is similar and dynamic aperture is not
improved at all.
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Effects of Sextupoles to IP

• Transformation (Sextupole to IP)
• Coefficient of XPY2 (crabbed waist)
• Coefficient of X3

IP
Arc
FF
SCW1
Sextupoles in FF are connected with -I'.
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Summary

• Lattice of SuperB is designed for
• very small emittance
• Final Focus with very small beta functions at IP
• use of the PEP-II available magnets as much as
  possible.
• Crabbed waist is one of the most important
  issues.
• Dynamic aperture without crabbed waist sextupoles
  is fairly good as far as squeezing beta at IP
  very small.
• Dynamic aperture with crabbed waist is reduced by
  1/5(depends on strength of crabbed waist
  sextupoles). On-momentum aperture becomes small.
• In the crabbed waist scheme, good solution to
  keep large dynamic aperture has not been found so
  far.
• Nonlinearity limits the dynamic aperture.
• How to control the nonlinearity ? Combination of
  sextupoles can cancel it ? This issue is under
  study.