1. Emittance Growth from Elliptical Beams and Offset Collision at LHC and LRBB at RHIC Ji Qiang US LARP Workshop, Berkeley, April 26-28, 2006

2. Outline Strong-strong simulation of elliptical colliding beams at LHC Offset beam-beam interactions at LHC Long-range beam-beam effects at RHIC

3. Elliptical colliding beams at LHC Using Dipole first with doublet focusing Focuing is symmetric about the IP Less magnets and lower nonlinear fields at IP Increase of luminosity

4. Computational Model Two collision points (no parasitic collisions) With 0.212 mrad half crossing angle Linear transfer map between IPs Tunes (0.31, 0.32) Beta* (0.25, 0.25) vs. (0.462,0.135) One million macroparticles for each beam 128 x 128 x 1 for strong-strong beam-beam force calculation

5. RMS Emittance Growth with Round and Elliptical Colliding Beams at LHC X elliptical Y elliptical Y round X round

6. Offset Beam-Beam Collisions at LHC

7. Beam energy (TeV) 7 LHC Physical Parameters for the Beam-Beam Simulations Protons per bunch 10.5e10  * (m) 0.5 Rms spot size (mm) 0.016 Betatron tunes (0.31,0.32) Rms bunch length (m) 0.077 Synchrotron tune 0.0021 Momentum spread 0.111e-3 Beam-Beam Parameter 0.0034

8. IP1 IP5 AB CDE F 1 2 34 5 6 A Schematic Plot of LHC Collision Scheme

9. One Turn Transfer Map M = Ma M1 Mb M2 Mc M3 Md M4 Me M5 Mf M6 M = M6 -1 Mf M6 Ma M1 Mb M1 -1 M1 M2 M3 M3 -1 Mc M3 Md M4 Me M4 -1 M4 M5 M6 Here, Ma and Md are the transfer maps from head-on beam-beam collisions; Mb,c,e,f are maps from long-range beam-beam collisions; M1-6 are maps between collision points. Linear half ring transfer matrix with phase advanced: 90 degree phase advance between long-range collision points and IPs 15 parasitic collisions lumped at each long-range collision point with 9.5  separation

10. RMS Emittance Growth vs. Horizontal Separation at LHC (No Parasitic Collisions) 0    

11. 0     RMS Emittance Growth vs. Horizontal Separation at LHC (With 60 lumped Parasitic Collisions)

12. Long-Range Beam-Beam Effects at RHIC Study the effects of long-range beam-beam (LRBB) at RHIC for the coming wire compensation experiment and find the maximum signal-to-noise ratio setting subject to some limits The effects of LRBB subject to Separation Tunes Chromaticity Sextupole nonlinearity etc

13. Beam energy (GeV) 100 RHIC Physical Parameters Protons per bunch 2e11  * (m) 1 Transverse Emittance [ mm-mrad] 15 Rms bunch length (m) 0.7 Tunes case 1 (28.68,29.69) and (28.73,29.72) Momentum spread 0.3e-3 Tunes case 2 (28.68,29.69) and (28.68,29.69) Tunes case 3 (28.73,29.72) and (28.73,29.72)

14. Computational Model 4 x 4 linear transfer map (146 linear map between sextupole) Sextupole nonlinearity (144 thin lens kicks) Self-consistent strong-strong beam-beam 1 Million macroparticle for each beam 128 x 128 x 1 mesh grid

15. Averaged Emittance Growth Rate vs. Vertical Separation Case 3 Case 2 Case 1

16. Vertical Emittance Growth without/with Chromaticity With 6x6 linear map With 6x6 linear map + chromaticity kick

17. Vertical Emittance Growth without/with Sextupoles With 6x6 linear map With 4x4 linear map + sextupoles

18. Summary Initial simulations indicate larger emittance growth from the elliptical colliding beams than the round colliding beams at LHC The effects of static offset beam-beam collisions on emittance growth is weak without parasitic collisions at LHC. It can be large with the including of parasitic collisions. LRBB at RHIC —Significant emittance growth for beam-beam separation below 4 sigmas —Emittance growth show some dependent on the machine tunes. For some tunes, the emittance growth shows a linear dependent on separations; Other shows nonlinear dependence. However, beyond 6 sigmas, the emittance growth is no longer sensitive to the machine tunes. —The effects of chromaticity depends on the machine tunes and becomes weaker for larger separation. —Stronger sextupole strength might help to improve the signal-to- noise ratio at large separation.

19. Future Studies Study of emittance growth including parasitic collisions and nonlinear longitudinal map Study of emittance using an updated LHC lattice parameters with distributed parasitic collision model LRBB at RHIC —Including both chromaticity + sextupole + LRBB in the simulation —Systematic comparison with experiment data —Wire compensation