Beam-beam studies for eRHIC

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Beam-beam studies for eRHIC

• Y. Hao, V.N.Litvinenko, C.Montag, E.Pozdeyev,
  V.Ptitsyn

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Features of beam-beam interaction of linac-ring
scheme

• Compared with usual beam-beam interactions in
  collider rings, the linac-ring collision scheme
  brings on very specific effects
• Electron beam disruption.
• Fluctuation of electron beam parameters.
• Kink instability of the proton beam.
• Effect of electron beam pinch on the incoherent
  proton beam emittance growth.

All those effect are studied in details using a
dedicated simulation code written by Y.Hao.
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Electron beam disruption

• Two effects
• Linear mismatch caused by the beam-beam
  interaction increases the effective emittance in
  design lattice (without beam-beam). Lower b -gt
  less mismatch. Also, the design lattice can
  include into the account the beam-beam lens.
  Techniques for fast (bunch-by-bunch) mismatch
  compensation are under consideration (fast
  quadrupoles, electron beam lens).
• The geometric emittance increases due to
  non-linear beam-beam force. 2 times. Not the
  big problem.

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Kink instabiity
Proton emittance growth caused by
transverse instability. The head of the proton
bunch affects the tail through the interactions
with the electron beam. Includes synchrotron
oscillations. Without tune spread (zero
chromaticity) the instability threshold is at
1.6e10 proton per bunch.
The tune spread stabilizes the
instability. Required chromaticity gt3
units. Nonlinearity character of the
beam-beam Interactions also helps.
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Effect of the Electron Pinch on Protons

• Source
• The electron beam is focused by strong beam-beam
  force.
• Electron beam distribution has a dense core.
• Enhanced beam-beam parameter value.
• Main Factors under Consideration
• Working Points (avoid nonlinear resonance )
• Electron optics and initial emittance
• (reduce synchrotron-betatron oscillation)

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Pinch Effect versus Electron b
Design ß 1m at IP Initial emittance 1nm
Design ß 0.25m at IP Initial emittance 4nm
The maximum beam-beam parameter of protons is
0.054 The average beam-beam parameter of proton
is 0.031
The maximum beam-beam parameter of protons is as
large as 0.19 The average beam-beam parameter of
protons is 0.067.
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Change the waist position to minimize pinch
The maximum beam-beam parameter for proton is as
large as 0.022 The average beam-beam parameter
for proton is 0.014, while design is 0.015
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Not only electron rms beam size counts
The nonlinear force will form a dense core in
electron beam distribution. The field is
different from Gaussian beam field which only
depends on rms beam size of opposite beam.
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L1.72 1033cm-2-s-1
L 2.46 1033cm-2-s-1
This shows the dense core of electron beam plays
a very important role in proton beam emittance
growth. Large emittance and small design beta
is preferred for electron beam.
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Summary

• Several features of the beam-beam interactions
  are under consideration.
• The kink instability is stabilized for design
  beam intensities by proper choice of the
  chromaticity.
• Techniques for compensation of the mismatch
  caused by the beam-beam are under consideration.
• Both electron beam disruption and proton
  beam-beam parameter benefit from lower b of
  electrons.
• More investigations are underway for incoherent
  proton beam emittance growth in the presence of
  electron pinch, including the optimal choice of
  the working point.