In this paper, we report on recent advances in strong-strong beam-beam simulation. Numerical methods used in the calculation of the beam-beam forces are reviewed. A new computational method to solve the Poisson equation on nonuniform grid is presented. This method reduces the computationsl cost by a half compared with the standard FFT based method on uniform grid. It is also more accurate than the standard method for a colliding beam with low transverse aspect ratio. In applications, we present the study of coherent modes with multi-bunch, multi-collision beam-beam interactions at RHIC. We also present the strong-strong simulation of the luminosity evolution at KEKB with and without finite crossing angle.

Collective instabilities caused by the formation of anelectron cloud (EC) are a potential limitation to the performances of the damping rings for a future linear collider. In this paper, we present recent simulation results for the electron cloud build-up in damping rings of different circumferences and discuss the single-bunch instabilities driven by the electron cloud.