Semianalytical modeling of multistage bunch compression with collective effects

In this paper we introduce, for the first time, an analytical solution (up to the third order) for a multistage bunch compression and acceleration system without collective effects. The solution for the system with collective effects is found by an iterative procedure based on this analytical result. The developed formalism is applied to the two-stage Free Electron Laser in Hamburg (FLASH) and to the three-stage European XFEL. Analytical estimations of rf tolerances are given and a simple formula for the optimal compression factor in the first bunch compressor is derived.