Analysis of beam-beam diffusion effects in RHIC and the LHC

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Analysis of beam-beam diffusion effects in RHIC
and the LHC

• V. Ranjbar and T. Sen, FNAL

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Motivations

• To better understand the impact of beam-beam and
  to settle on optics and compensation methods to
  minimize its negative effect in the LHC
• RHIC is a good test bed for the LHC as a result
  there are plans to install a wire compensation
  scheme in RHIC and to benchmark simulation codes
  against beam-beam experiments in RHIC.
• There is now an effort underway to bring
  beam-beam modeling results closer to
  experimental. However modeling beam-beam effects
  in a realistic way including higher order fields
  can very computationally intensive using standard
  lifetime tracking methods.
• Another approach is to consider Diffusion
  Coefficients as various initial particle
  distributions.
• This approach coupled with the Fokker-Planck
  diffusion equation can provide lifetime estimates
  much faster however there are limits to the
  validity of this approach.

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Validity of Diffusion Description

• We assume a radomized phase or nearly random.
• No global Chaos
• We require that the evolution of the distribution
  be described in terms of a Markov process in the
  Action.
• Also if the system is Hamiltonian we can equate
  the frictional and diffusion coefficients in the
  Fokker-Planck equation.1

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Estimating beam lifetime from Diffusion
Coefficients

• The approach is to first calculate the Diffusion
  Coefficient as a function of Action D(J). This
  can be done by tracking a small number of
  particles at various actions and using
• To estimate the Diffusion at each Action.
• Using the fit to the Diffusion an escape time can
  be calculated using
• Where Ja is the action at the aperture (we use
  10sigma) this provides a estimate of the
  lifetime. This is what we present today. Of
  course ideally the FP equation should be
  numerically integrated.

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Preliminary lifetime Calculation using Diffusion
versus direct Lifetime tracking in RHIC
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RHIC Experiments and Simulations

• Several experiments were conducted at collision
  energy in RHIC
• April 5th 1 bunch per beam, interaction at
  nominal location
• April 12th 1 bunch per beam, interaction at IP6
• May 3rd - 10 bunches per beam, interaction at
  nominal location
• May 24th - 10 bunches per beam, interaction at
  nominal location, tune scan. Octupoles used to
  increase nonlinearities.
• May 30th - 10 bunches per beam, interaction at
  nominal location, operate near 0.75. Octupoles
  on.
• We consider the May 3rd since setup most closely
  resembles simulations.

Qx,Qy (0.69,0.68) (0.72,0.73)
Qx,Qy 2,2
B.B. Par 9.77E-3
rms bunch length 2 nsec
ex , ey 15p mm-mrad
Intensity 2 1.5E11
rms momentum deviation 3.11E-4
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RHIC resonance lines

• Tune footprints with sextupoles and single
  parasitic interaction at (1) 3s separation, (2)
  10s separation. Blue beam base tunes (0.68,
  0.69). The closest resonances are the 3rd, 6th
  and 10th order resonances but the footprint is
  clear of these resonances at both separations.

10th Order
3rd and 6th Order
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May 3rd Experiment Moving Yellow beam Q .69,.70
4 Sig
2 Sig
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BTF done at 4 Sig separation Qx.0.6917, max
8.313, Qy .6964, max209
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BTF done at 2 sigma Qx .6905, max 8.34,
Qy.6959, max 330.84 - Qx went down by 1.2E-3
and Qy by 0.5E-3. - Power went up by 8 units in
vertical and .5 in horizontal
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Simulated Results show change in tune of 10-3
down And increase in vertical signal and decrease
in horizontal signal
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Loss Rate vs Beam seperation
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Conclusions from RHIC Experiments

• Tunes
• BBSIM simulations show that both the vertical and
  horizontal tunes in the blue beam move down by
  about 0.001 when the separation is decreased from
  4 to 2 sigma by moving the yellow beam.
  Observations Measuring from 4. sigma to 2.
  sigma the horizontal tunes went down by 0.0005
  and the vertical tunes went down by 0.0012. In
  the horizontal plane the measured tune variation
  was probably within error of the tune measurement
  since measurements made at intermediate sigma
  separations yielded lower tune measurements. The
  magnitude and direction of the tune change agreed
  with BBSIM predictions in the vertical plane.
• Power in the Tune signal
• BBSIM finds the power halves in the horizontal
  plane while the power doubles in the vertical
  plane again when the vertical separation is
  reduced from 4 to 2 sigma. Observations The
  peak power in the horizontal plane went up from
  7.66 to 8.23 and the peak power in the vertical
  plane went up from 245 to 253. The power in the
  horizontal plane went in the opposite direction
  predicted by BBSIM. The power in the vertical
  plane matches the direction of BBSIM prediction
  but not the size (assuming the BTF units are
  linear). However here again the power fluctuated
  at each measurement while moving the yellow beam
  from 4 to 2. sigma, reaching a maximum of 330 at
  2.8 sigma.
• Experimental Lifetime Estimates
• Problematic since there was not enough time to
  sit and fit a lifetime cure at each separation.
  However we do have max loss rates which should
  correlate with lifetimes.

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LHC Simulations and Estimations of Diffusion

• Consider Several Optics options
• Baseline ? 64 LR BB
• Quad 1st ? 64 LR BB
• Dipole 1st Interaction ? 32 LR BB

LHC Injection LHC Flattop
Energy (GeV) 450 7000
Revolution Frequency (kHz) 11.245 11.245
Synchrotron Frequency (Hz) 61.8 21.4
rms bunch length (nsec) .37 .25
Emittance 22.5 pi 22.5 pi
Bunch Intensity 1e11 1e11
BB. Par 3.4E-3 3.4E-3
Tune .31, .32 .31, .32
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Tune footprints for Optics options
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Conclusion

• Results from experiments in RHIC show some
  agreement with BBSIM simulations
• Diffusion approach is a good first estimate of
  the impact of beam-beam effects
• There maybe be some promise in extracting
  lifetimes using this approach, however more work
  needs to be done in this vein
• Results from LHC simulations show clearly the
  negative impact due to beam-beam effects with the
  Quad 1st option.
• However a Dipole 1st option in some instance
  maybe better than the Baseline.

1 . A. J. Lichtenberg and M. A. Lieberman,
Regular and Stochastic Motion, Springer-Verlag
1983