Investigations of scaling laws of dynamic aperture with time for numerical simulations including weak-strong beam-beam effects

A scaling law describing the time-dependence of the dynamic aperture, i.e., the region of phase space where stable motion occurs, was proposed in previous papers, about ten years ago. It was showed that dynamic aperture has a logarithmic dependence on time, which would be suggested by some fundamental theorems of the theory of dynamical systems. So far, such a law was applied to single-particle effects, only, i.e., the only source of non-linear effects was the magnetic imperfections. In this paper an attempt of extending the scaling law to the case of weak-strong beam-beam effects is made. The results of numerical simulations performed including both non-linear magnetic imperfections and weak-strong beam-beam effects are presented and discussed in detail