Field accuracy requirements for the undulator systems of the X-ray FELs at TESLA

In SASE FELs, the radiation power has to saturate in a single pass through the undulator. In the VUV and X-rayregime, with undulators ranging in length from several tens to hunderds of meters, even a few percent increase ingain length could mean a lengthening of the undulator by several meters. Therefore, determining what increasesthe gain length is of great importance.The influence of the electron beam quality has been studied in detail in many papers. For the TESLA X-rayFEL, with undulator lengths of up to 300 m, the gain degradation due to undulator imperfections has to be studied.Previous studies, for example for the TTF-FEL, have focused on the influence of dipole and quadrupole errors. Inthis report, similar results of simulations for the TESLA X-ray FEL undulators will be presented. In addition, othersources of errors, mainly related to the multi-segmented character of the undulators, will be discussed and upperlimits will be given