Simulations of beam-beam effect in the presence of general chromaticity

Optics parameters such as betatron tunes, beta functions, and dispersions depend on momentum deviation. Such dependence is characterized by general chromaticity. General chromaticity can induce emittance growth and luminosity degradation in colliders. To investigate the influence of general chromaticity on beam dynamics, a symplectic map for chromaticity was implemented in the beam-beam codes and used in simulations at KEKB. A systematic investigation revealed that chromatic X-Y couplings can deteriorate the machine luminosity in the order of 10% with head-on colliding beams. The results of this study triggered the installation of skew sextupoles to KEKB rings for the purpose of correcting the chromatic X-Y couplings. Beam commissioning with skew-sextupole tuning knobs at KEKB has proved to be very successful; a new world’s record luminosity of 2.1×10^{34} cm^{-2} s^{-1} was achieved with Belle taking data in June, 2009. In this paper, we discuss the approach of general chromaticity and present the results of simulations at KEKB