Long-range and head-on beam-beam compensation studies in RHIC with lessons for the LHC ∗ W. Fischer † , Y. Luo, N. Abreu, R. Calaga, C. Montag, G. Robert-Demolaize, BNL, U. Dorda, J.-P. Koutchouk, G. Sterbini, F. Zimmermann, CERN H.-J. Kim, T. Sen, V. Shiltsev, A. Valishev, FNAL, J. Qiang, LBNL, A. Kabel, SLAC Abstract Long-range as well as head-on beam-beam effects are expected to limit the LHC performance with design pa- rameters. They are are also important consideration for the LHC upgrades. To mitigate long-range effects, current car- rying wires parallel to the beam were proposed. Two such wires are installed in RHIC where they allow studying the effect of strong long-range beam-beam effects, as well as the compensation of a single long-range interaction. The tests provide benchmark data for simulations and analyt- ical treatments. Electron lenses were proposed for both RHIC and the LHC to reduce the head-on beam-beam ef- fect. We present the experimental long-range beam-beam program at RHIC and report on head-on compensations studies based on simulations. INTRODUCTION Beam-beam effects have limited the performance of previous and existing hadron colliders [1, 2] such as the Sp¯ S [3–6], Tevatron [7–9] and RHIC [10,11], and are also p expected to limit the performance of the LHC [12–27]. Beam-beam effects can be categorized as either inco- herent (dynamic aperture and beam lifetime), PACMAN (bunch-to-bunch variations), or coherent (beam oscillations and instabilities) [21]. These effects can be caused by both head-on and long-range interactions. Head-on ef- fects, leading to tune shifts and spreads, are important in all hadron colliders. Total beam-beam induced tune shifts as large as 0.028 were achieved in the Sp¯ S [6] and Teva- p tron [9]. Long-range effects, however, differ in previous and ex- isting colliders. In the Sp¯ S, with both beams in the same p pipe and only 3 bunches per beam, there were only a few long-range interactions distributed over the ring circumfer- ence, and due to the difference in the bunch intensities, the effect on the antiproton was stronger. In the Tevatron, also with both beams in the same pipe but 36 bunches per beam, there are more long-range interactions, and with the increased intensity of the antiproton bunches, protons can also be affected. In RHIC, where both beams share a pipe only in the interaction regions, there are nominally no long- range beam-beam interactions under store conditions, but ∗ Work supported by US DOE under contract DE-AC02-98CH10886 and the US LHC Accelerator Research Program. † Wolfram.Fischer@bnl.gov This work was also supported by the U.S. Department of Energy under Figure 1: Beam-beam interactions in RHIC and locations of wires and electron lenses. The shown β ∗ values are for the polarized proton design configuration at 250 GeV, which has not been implemented yet. long-range interactions have affected the ramp transmis- sion in the past [10]. In the LHC there are 30 long-range beam-beam interactions localized in each of 4 interaction regions [21]. Figure 2: Lattic, β-functions, and phase advances in an LHC interaction region. At location s = 13.433 km, with approximately equal horizontal and vertical β-functions, a long-range wire compensator or electron lens could be placed. Contract No. DE-AC02-05CH11231.