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. nchro-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. ation 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.