Abstract
A simple analysis is given for the optimum length of undulator in a self-seeding free electron laser (FEL). The obtained relations show the correlation between the undulator length and the system parameters. The power required for the seeding in the second part of the undulator and the overall efficiency of monochromatizating the seeding determine the length of the first part of the undulator; the magnitude of seeding power dominates the length of the second part of the undulator; the whole length of the undulator in a self-seeding FEL is determined by the overall efficiency for getting coherent seed, and is about half as long again as that of SASE, not including the dispersion section. The requirement of the dispersion section strength is also analyzed.