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

1. Analysis of beam-beam diffusion effects in RHIC and the LHC V. Ranjbar and T. Sen, FNAL

2. 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.

3. 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]

4. 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.

5. Preliminary lifetime Calculation using Diffusion versus direct Lifetime tracking in RHIC

6. 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.

7. 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

8. May 3rd Experiment Moving Yellow beam Q= .69,.70 4 Sig 2 Sig

9. BTF done at 4 Sig separation Qx=.0.6917, max= 8.313, Qy = .6964, max=209

10. 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

11. Simulated Results show change in tune of 10^-3 down And increase in vertical signal and decrease in horizontal signal

12. Loss Rate vs Beam seperation

13. 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.

14. 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

15. Tune footprints for Optics options

19. 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