Simulation of the beam-beam effects in e(+)e(-) storage rings with a method of reduced region of mesh

A highly accurate self-consistent particle code to simulate the beam-beam c ollision in e(+)e(-) storage rings has been developed. It adopts a method o f solving the Poisson equation with an open boundary. The method consists o f two steps: assigning the potential on a finite boundary using Green's fun ction and then solving the potential inside the boundary with a fast Poisso n solver. Since the solution of Poisson's equation is unique, our solution is exactly the same as the one obtained by simply using Green's function. T he method allows us to select a much smaller region of mesh and therefore i ncrease the resolution of the solver. The better resolution makes more accu rate the calculation of the dynamics in the core of the beams. The luminosi ty simulated with this method agrees quantitatively with the measurement fo r the PEP-II B Factory ring in the linear and nonlinear beam current regime s, demonstrating its predictive capability in detail.