LONG%20RANGE%20BEAM-BEAM%20INTERACTIONS%20IN%20PEP-II%20To%20have%20or%20not%20to%20have%20a%20crossing%20angle?%20(W.%20Shakespeare)

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LONG RANGE BEAM-BEAM INTERACTIONS IN PEP-IITo
have or not to have a crossing angle? (W.
Shakespeare)
M. Biagini, LNF-INFN
2
Crossing angle issues

• Large crossing angles can induce synchro-betatron
  resonances in the beams. Piwinski angle
• Q f sz/sx
• Unwanted beam-beam interactions at Parasitic
  Crossings
• Luminosity and tune shifts are affected L , x
  (geometrical reduction) reduction for high x
  at small angles (bb simulations)

CESR PEP-II (sz 5 mm, bx 28 cm) DAFNE KEK-B
f (mrad) 2.3 3.5 12 14.5 11
Q (mrad) 0.1 0.16 0.22 0.29 0.57
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Parasitic Crossings Effect

• The unwanted beam interaction at the PCs has 2
  effects
• x and y tune shifts are induced, similarly to the
  main IP, depending on the beam separation at
  the PC
• beam lifetime is affected, if the separation is
  lower than 10 sx

x, y beam separation at PCs Gaussian beam
distribution
J. Jowett, Handbook of Accelerator Physics and
Engineering Beam-beam tune shifts for gaussian
beams
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Parasitic Crossings Effect (contd)

• Two differtent phenomena arise when dealing with
  a crossing angle
• The long range beam-beam interactions become as
  important as the main one
• The luminosity as well as the main IP tune shifts
  are degraded
• The choice to collide with or without a c.a. is a
  trade-off between these two effects
• It is important to determine the minimum beam
  separation required in order to have acceptable
  bb tune shifts at the PC this sets the choice on
  the f value

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PEP-II June record day

• Tune shifts due to PCs were computed with the
  present PEP-II parameters, as from the June
  record day
• - bx50 cm
• - by12.5 mm
• - xxLER.109
• - xyLER.082
• - xxHER.04
• - xyHER.04
• - Nb 1034
• - Npart/bunch6.9x1010/5.22x1010 (/-)
• The PCs tune shifts were scaled with the number
  of particles/bunch so to keep constant the total
  beam current.
• Note that each xPC counts twice (two sides of IP)
  !!

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PEP-II PCs Tune shifts (June 2003)
Y on log scale
by_1
by_2
by_3
by_4
The PC tune shifts are normalised to the main IP
tune shifts
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Working in a by_2 pattern

• The Luminosity upgrade is designed with 1700
  bunches, that is a by_2 bunch pattern. Then we
  can concentrate only on th 2nd PC (watch out
  there will also be a factor 20 contribution
  from the 4th PC)
• The PC tune shifts are computed as a function of
  the by for different IR geometry, from head-on
  collision to 5 mrad crossing angle
• For the different by values the main IP tune
  shifts were scaled so to keep the goal Luminosity
  constant (3.3x1034), by decreasing the bunch
  length accordingly, always keeping sl/by 1,
  except for by 6 mm where sl 6.5/7.5 (Johns
  Table), and considering a hourglass reduction
  factor from 0.8 to 0.66 (could rise I instead!)

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Beam parameters

• Tune shifts due to PCs were computed with Johns
  projection of PEP-II parameters for July 2007
• - bx28 cm
• - by6 mm
• - xxLER.0981
• - xyLER.0909
• - xxHER.0761
• - xyHER.0743
• - Nb 1700
• - Npart/bunch12.2x1010/5.95x1010 (/-)
• and corrected by the by as described above.
  The tune shifts keep reasonable values (see Table
  in following slide)

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Tune shifts scaling with by
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HER PC tune shifts in by_2 patternvs. by and f
Comparison of PC tune shifts for different by
and crossing angles. The head-on solution is the
red curve
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LER PC tune shifts in by_2 patternvs. by and f
Comparison of PC tune shifts for different by
and crossing angles. The head-on solution is the
red curve
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Results

• HER LER xx shows a gt1 effect by the 2nd PC for
  head-on geometry, always below 1 for crossing
  angle
• HER LER xy is gt10 for head-on case and 1 to 3
  mrad crossing angle, between 6 and 10 for
  larger c.a.
• The by reduces the effect by 50 increasing
  from 6 mm to 9 mm the vertical tune shifts are
  reduced by a factor 2
• Note that beam separation at 2nd PC is 11 sx for
  head-on collision

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And...

• Unfortunately there is not only the PC tune
  shifts issue to limit the colliders performances
• With a crossing angle we can get rid of the
  previous problem, with some costs as apertures in
  the IR, but another issue arises Luminosity,
  tune shifts and beam sizes they all degrade when
  introducing the crossing angle
• Formulae show a lt 5 geometric reduction factor
  up to 8 mrad crossing angle, but bb simulations
  (Cai, Ohmi) show much more dramatic results

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Tune shifts with crossing angle

• Tune shifts geometric reduction due to crossing
  angle vs. c. a.
• Y scale tune shift with c.a. normalized to the
  head-on one.
• Horizontal x drops faster. Beam footprint is
  smaller

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Luminosity with crossing angle
Luminosity geometric reduction due to the
crossing angle vs c.a. Y scale Luminosity with
c.a. normalized to the head-on one. Lhead on
3.3x1034
16
Cais beam-beam simulation
Lb
sx
sy
Looks like small crossing angles are worst than
large crossing angle for high values of x!!
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Questions conclusions on the c.a.

• Could it be possible to work with a smaller
  number of bunches with higher current/bunch to
  get the same peak Luminosity, with the same tune
  shifts?
• Or is it wiser to accept a degraded Luminosity
  from c.a. but operate with a larger number of
  bunches, larger total beam current, with the same
  tune shifts?
• Can we really obtain very short bunches (6.5 mm)
  with the present PEP-II layout?
• Simulations are the only way we have now to
  answer to these questions. It is mandatory to
  include the PC effect in a 3D beam-beam
  simulation!
• More work for Yunhai !!!!