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In this paper we introduce an analytical solution (up to the third order) fora multistage bunch compression and acceleration system without collectiveeffects. The solution for the system with collective effects is found by aniterative procedure based on this analytical result. The developed formalism isapplied to the FLASH facility at DESY. Analytical estimations of RF tolerancesare given.

A Semi-Analytical Modelling of Multistage Bunch Compression with Collective Effects