Beam-Beam Compensation Schemes

Several techniques have been proposed for compensating the effects of the head-on or long-range beam-beam interaction. These include alternating crossing at several interaction points, electromagnetic wires, electron lenses, and superbunches. I discuss some prominent compensation schemes and their R&D status, with special emphasis on the LHC and its upgrade. 1 HISTORY AND PERSPECTIVE The beam-beam interaction has limited the performance of almost all past and present storage-ring colliders. Therefore, not surprisingly, the history of accelerators has witnessed a number of ingeneous attempts to overcome this limitation by various compensation techniques. Famous are the 4-beam collisions with charge neutralization conceived around 1970 at the Orsay DCI [1]. Without net charges, all forces were cancelled in order to produce a vanishing beam-beam tune shift. Unfortunately, small offsets in the centroid positions of the oppositely charged beams were amplified exponentially, and the DCI performance was limited by the resulting collective beam-beam instabilities [2]. In 1975, head-on collisions with a high beam-beam tune shift were simulated in the CERN ISR by two vertically separated copper bars carrying 1000-A of electric current [3]. The ISR experiment showed that resonances of order 10 or higher contributed to the proton beam-beam limit. Although this was not strictly speaking an attempt at compensation, it pointed the way to future compensation experiments, like those employing current-carrying wires (see below). In 1982, the use of octupoles for reducing the beambeam tune spread was studied for LEP by means of simulations [4]. Later, octupoles were indeed shown to be beneficial, especially for background control, at BEPP-4, VEPP-2M [5, 6] and DAFNE [7]. Plasma-based compensation schemes were theoretically explored both for linear electron-positron [8] and for muon colliders [9], but have not yet been tested in practice. Compensation of beam-beam effects in hadron colliders by a low-energy electron beam was proposed for the SSC [10] and the LHC [11]. Since 2001, the first practical realization of such a scheme, the Tevatron Electron Lens (TEL), [12] is operational at FNAL. The TEL collides the antiprotons with an electron beam of appropriate shape and strength to compensate for the effect of the antiproton-proton collisions at other locations of the ring. The TEL can be pulsed with a different electron current for each bunch. In the near future, a pair of TELs will be capable of reducing both the intraand inter-bunch tune spread in the Tevatron antiproton beam [12, 13]. The present and future generations of hadron colliders (Tevatron Run-II, LHC, RHIC upgrade) accommodate not only head-on collisions at the design ‘interaction points’ (IPs) inside the particle-physics detectors, but also a significant number of ‘long-range collisions’ (sometimes called ‘parasitic collisions’), where the beams are separated by a few times the transverse rms beam size, but still notice each other’s fields. As a concrete example, Fig. 1 shows the overall LHC layout, with four primary interaction points (IPs), at the experimental detectors of ATLAS, ALICE, CMS, and LHCB, respectively. On the way to and from each primary IP, the LHC proton bunches suffer a maximum of 30 longrange collisions (15 on each side of the IP), as is illustrated in Fig. 2. Summed over the entire ring, the total number of long-range collisions experienced by a regular proton bunch is 120. The LHC beam consists of 39 trains of 72 bunches each, spaced by 25 ns. The trains are separated by gaps of 574, 599 or 2595 ns, in order to accommodate the rise and fall times of various injections and extraction kickers in the LHC and its injectors. Due to these gaps, where bunches in the opposing beam are missing, proton bunches at the end or start of a bunch train do not experience the full number of long-range collisions, and, as a result, may have different orbits and tunes. These bunches could exhibit a reduced lifetime. They are therefore called ‘PACMAN’ bunches. Only about half of the LHC bunches are regular bunches, all others belong to one of many different equivalence classes of PACMAN type [15]. The long-range collisions are a concern for all bunches, because they perturb the motion of protons at large betatron amplitudes, where they come close to the opposing beam. Thereby, they generate a ‘diffusive aperture’ [16], beyond which a particle is rapidly lost, i.e., the diffusive aperture can be considered equal to the short-term dynamic aperture. The diffusive aperture induced by the long-range collisions may result in high background at the experiments and in a poor beam lifetime. The effect of long-range collisions is a problem of increasing importance, from the SPS over the Tevatron Run-II to the LHC, i.e., for operation with a larger nunber of bunches, as is illustrated by Table 1. The experience from Tevatron Run-II confirms the potential danger of long-range encounters. Quoting T. Sen [17], “Long-range beam-beam interactions in Run II at the Tevatron are the dominant sources of beam loss and lifetime limitations of anti-protons, especially at injection enOctant 1 Oc tan t 8 O ct an t 3 Otant 2 Oc tan t 4 Octant 5 Otant 6