A study of the Coherent Beam-Beam Effect in the Framework of the Vlasov Perturbation Theory

A number of factors which can influence coherent beam-beam oscillations are studied on the basis of the Vlasov equation:difference in the intensities and single-particle tunes in the beams;difference in the phase advances between interaction points;long-range interactions; synchro-betatron coupling due to betatron phase advance variation in the vicinity of IP chromatic tune modulation and crossing angle. The synchro-betatron coupling appears to have a principal stabilizing effect:at synchrotron tune values in the neighborhood of half the beam-beam parameter it provides Landau damping of the discrete spectral lines by overlapping sidebands; the damping rate being higher with negative chromaticity. At smaller synchrotron tune values a specific mode of the head-tail damping sets in which is not sensitive to chromaticity. Application to LHC shows that with the design values of parameters the coherent beam-beam oscillations should be Landau damped, probably with the help of negative chromaticity of a moderate absolute value

On the Landau Damping and Decoherence of Transverse Dipole Oscillations in Colliding Beams

Coherent transverse dipole oscillations in colliding head-on non-rigid bunches are studied using the Vlasov equation. The corresponding eigenvalue problem is solved numerically in the case of round Gaussian bunches of equal size but with not necessarily equal intensities. Transition from the weak-strong to the strong-strong cases is found at the intensity ratio of about 60% when a discrete p-mode frequency emerges from continuum of eigenfrequencies related to the beam-beam tunespread in the weaker bunch. In the strong-strong case the large coherent beam-beam tuneshift dominates over interchange processes between coherent and incoherent motion; it can switch off Landau damping of dipole transverse oscillations, slows down incoherent emittance growth due to external kicks on the beams. The consequences for the transverse feedback operation in collision are discussed

Simulation of Beam-Beam Effects and Tevatron Experience

Effects of electromagnetic interactions of colliding bunches in the Tevatron had a variety of manifestations in beam dynamics presenting vast opportunities for development of simulation models and tools. In this paper the computer code for simulation of weak-strong beam-beam effects in hadron colliders is described. We report the collider operational experience relevant to beam-beam interactions, explain major effects limiting the collider performance and compare results of observations and measurements with simulations.Comment: 23 pages, 17 figure

Coherent Beam-Beam Effects in the LHC

In the Large Hadron Collider (LHC) two proton beams of similar intensities collide in several interaction points. It is well known that the head-on collision of two beams of equal strength can excite coherent modes whose frequencies are separated from the incoherent spectrum of oscillations of individual particles. This can lead to the loss of Landau damping and possibly to unstable motion. The beam-beam effect in the LHC is further complicated by a large number of bunches (2808 per beam), a finite crossing angle and gaps in the bunch train. The coherent beam-beam effects under various conditions and operational scenarios are studied analytically and with multiparticle simulations. We give an overview of the main results and present proposals to overcome these difficulties together with possible side effects

Measurement and correction of the 3rd order resonance in the Tevatron

At Fermilab Tevatron BPM system has been recently upgraded resulting in much better accuracy of beam position measurements and improvements of data acquisition for turn-by-turn measurements. That allows one to record the beam position at each turn for 8000 turns for all BPMs (118 in each plane) with accuracy of about 10-20 ìm. In the last decade a harmonic analysis tool has been developed at CERN that allows relating each FFT line derived from the BPM data with a particular non-linear resonance in the machine. In fact, one can even detect the longitudinal position of the sources of these resonances. Experiments have been performed at the Tevatron in which beams have been kicked to various amplitudes to analyze the 3rd order resonance. It was possible to address this rather large resonance to some regular machine sextupoles. An alternative sextupole scheme allowed the suppression of this resonance by a good factor of 2. Lastly, the experimental data are compared with model calculations

Muon Collider

Both e+e- and {\mu}+{\mu}- colliders have been proposed as possible candidates for a lepton collider to complement and extend the reach of the Large Hadron Collider (LHC) at CERN. The physics program that could be pursued by a new lepton collider (e+e- or {\mu}+{\mu}-) with sufficient luminosity would include understanding the mechanism behind mass generation and electroweak symmetry breaking; searching for, and possibly discovering, supersymmetric particles; and hunting for signs of extra spacetime dimensions and quantum gravity. However, the appropriate energy reach for such a collider is currently unknown, and will only be determined following initial physics results at the LHC. It is entirely possible that such results will indicate that a lepton collider with a collision energy well in excess of 1 TeV will be required to illuminate the physics uncovered at LHC. Such a requirement would require consideration of muons as the lepton of choice for such a collider.Comment: v.2., 6 pp. To appear in the 2nd edition of the book Elementary Particles, Landolt-Boernstein Series published by Springer. arXiv admin note: text overlap with arXiv:physics/9901022 by other autho

Low emittance lattice for LEP

In order to obtain the largest luminosity with LEP2, it is attractive to make the beam emittance as small as possible because the beam-beam effect is not a limitation at the energy of E~90 GeV for the obtained bunch currents. This can be achieved with a high tune lattice. Two possible candidates are lattices with a horizontal phase advance of 108o or 135o per cell. Both have a vertical phase advance of 60o. These lattice were developed during 1994 and the results are presented. tests to reach high intensity for the 108o lattice were performed and the bunch current achieved is compared with expectations. For this lattice the detuning v.s. intensity and several optics parameters were measured as well