Nuclear Instruments and Methods in Physics Research A 429 (1999) 243}248

22603 Hamburg, Germany Numerical simulation codes are basic tools for designing Free Electron Lasers (FEL). They are used to study the impact of di!erent parameters, e.g. wiggler errors and external focusing, which allow FEL users to optimize the performance. For faster execution some simulation codes assume radial symmetry or decompose the radiation "eld into a few azimuthal modes, although then this treatment does not include the full description of the FEL. This contribution describes the new FEL code GENESIS 1.3 which uses a fully three-dimensional representation of the FEL equations in the paraxial approximation for time-dependent and steady-state simulations of single-pass FEL. In particular this approach is suitable for cases where the radial symmetry is broken by the electron beam distribution as well as by wiggler errors, betatron motion and o! axis injection of the electron beam. The results, presented here, are based on th