1. Beam-Beam simulation and experiments in RHIC By Vahid Ranjbar and Tanaji Sen FNAL

2. Motivations ► We are interested in compensating beam-beam effects in LHC. During 2007 we plan to test long range beam-beam compensation using wire compensation for the first time in RHIC. ► To correctly use the wire in RHIC we will need first to understand the nature of the long range beam- beam effects in RHIC. ► For this reason a set of experiments were recently conducted in RHIC. These results can be compared with our simulations and we can then correctly implement wire compensation.

3. Baseline Conditions ► The experiments was conducted at collision energy in RHIC at two tunes points, 0.68, 0.69 and 0.72, 0.73. 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  x,  y 15  mm-mrad Intensity 2 – 1.5E+11 rms momentum deviation 3.11E-4

4. RHIC tune foot print ► Tune footprints with sextupoles and single parasitic interaction at (1) 3  separation, (2) 10  separation. At 10  separation, the impact of the parasitic interaction is very small and the footprint is almost entirely due to sextupoles.

5. RHIC resonance lines ► Tune footprints with sextupoles and single parasitic interaction at (1) 3  separation, (2) 10  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. 10 th Order 3 rd and 6 th Order

6. RHIC tune footprints and resonance lines at (0.72, 0.73) ► Tune footprints with sextupoles and single parasitic interaction at (1) 3  separation, (2) 10  separation. Blue beam base tunes = (0.72, 0.73). The closest resonances are the 7th and 11th order resonances. At 3  separation, the footprint spans these resonances but at 10  separation, only the 11th order resonances are spanned.

7. Dynamic Aperture ► Dynamic aperture without beam- beam interactions is ~ 10σ ► DA at tunes (0.68, 0.69) is about 1 σ larger than the beam separation ► DA at tunes (0.72,0.73) is nearly equal to the beam separation – the smaller DA at this set of tunes is expected from the tune footprint

8. BBSIM Model ► Sextupoles included ► Synchrotron oscillations included ► Dipole noise to mimic gas scattering ► Chromaticities set to (+2,+2) ► Intensity = 2E11, Emittance = 15π

9. Simulation results ► Diffusion Coefficients, and lifetimes as a function of beam separation and initial action (J).  Diffusion Coefficients: ► With and without sextupoles ► At Q=0.68,0.69 and 0.73,0.72 ► Error is estimated by comparison with results using an order of magnitude more particles ~ 20% ► We are in the process of direct lifetime tracking the inclusion of sextupoles makes this process very long if one wants good statistics.

10. Diffusion vs Action ► These plots show the diffusion vs action at beam separations varying from 7 – 10 σ ► These curves suggest an exponential dependence on the action: D(J) ~ exp(J) ► Similar dependence at the other tune Hor. Diffusion (left), Vert. Diffusion (right) vs action. Tunes (0.68, 0.69)

11. Diffusion vs Beam Separation Diffusion vs beam separation (at constant action) show that the diffusion increases only gradually as the separation is decreased. There is not a sharp jump in the diffusion. This contrasts with the results without sextupoles that showed a jump in the diffusion as the separation decreased below 5σ. Similar results seen at the other tune. Tunes: (0.68, 0.69)

12. Estimating beam lifetime from Diffusion Coefficients ► The best fit to the Diffusion data is an exponential. From the Diffusion equation: ► Given D(J) ~ A*Exp(B*J) an escape time can be calculated using: Where Ja is the action at the aperture (we use 9) Where Ja is the action at the aperture (we use 9  )

13. Lifetime vs beam separation ► Escape time from hor. Diffusion (left), vert. diffusion (right) ► These suggest lifetime τ ~ D, linearly with the beam separation

14. Lifetime vs beam separation ► Escape time from hor. Diffusion (left), vert. diffusion (right) ► These suggest lifetime τ ~ D, linearly with the beam separation, similar behavior as with other tune

15. Other simulation work ► Three other groups:  Jack Shi  Andreas Kabel  Ji Qiang : will report on Fridays meeting

16. Comparing results of these three cases suggests that the long-range beam-beam interaction could have a very similar effect on the emittance when separation = 4 sigma in the collision lattice of tune=(0.73, 0.72), or when separation = 5 sigma in the collision lattice of tune=(0.69, 0.68), or when separation = 4 sigma in the injection lattice. Therefore, there will probably not have a significant long-range beam-beam effect unless the beam separation is smaller than 6 sigma. To see a clear benefit of the wire compensation, you may have to move the tune closer to the 4th-order resonance. : J. Shi results: Gas scattering was not included. Sextupoles not yet included Synchrotron oscillations not yet included

17. Preliminary low-resolution studies showed that sextupoles are an essential part of the dynamics. Lifetimes with beam-beam elements as the only source of diffusion are orders of magnitudes higher than those including sextupoles. The results of the higher-resolution studies including sextupoles indicate that : The presence of a single parasitic crossing will dramatically decrease beam lifetime The lifetime in the presence of a parasitic crossing is not too sensitively dependent on the beam separation in the range of 3.5..6sigma. An optimal (in the sense of the experiment) settings seems to be a separation of 4sigma The weak dependence on separation is surprising and needs to be clarified by studies with longer runtime. Andreas Kabel’s results: uses weak-strong model With and without sextupoles No gas scattering Includes synchrotron motion

18. Preliminary Results from RHIC Beam-Beam experiment: Bunch fill pattern used six bunches in each ring with only one blue and yellow pair Experiencing long-range beam-beam kick at IP6 (marked by x )

19. April 5 th results moving only blue beam at Q=0.69,0.695 Comparison with non-interacting beam demonstrate a clear beam-beam effect beginning at only 4 sigma separation. However beam intensity is ~ 1.5E+11 about 33% less than original simulations.

20. When blue beam was only moved Blue tunes went from qx=0.69 to 0.697 And qy=0.695 to 0.682 avoiding a large overlap of the resonance lines.

21. April 5 th results moving only yellow beam at Q= 0.69,0.695 Here comparison with the yellow non-interacting bunch demonstrate the addition of A non beam-beam effect due to the yellow tunes overlapping resonance lines.

22. When yellow beam moved yellow tunes moved from qx = 0.690 to 0.684 and qy= 0.695 to 0.698 overlapping the resonances lines.

23. Conclusion ► Preliminary experimental results show a clear effect from beam-beam interaction below 3 sigma ► The experimental data still needs to be analyzed to determine the nature of the power law relation between separation and lifetime.  However it is clearly less strongly correlated at Collision than previous experiments at injection energy.  Further at least two simulation results suggest a weaker correlation between separation and lifetimes than was observed at injection.

24. Future Plans ► In the next several months this data will be more thoroughly analyzed and our different simulation groups should re-run simulations to match the experimental conditions more exactly.  Continue with Diffusion analysis approach ► We plan to look for an exact solution to the diffusion equation. (if not possible then numerically)  Do direct lifetime tracking  As we compare our simulated results with the experimental data we might need to improve our model by consider including the nonlinear effect of the triplets ► Once we are satisfied with the ability of our model to replicate reality in RHIC we will then consider the impact of wire compensation in our model and predict optimal current and distance to beams.