Design considerations for a SASE X-ray FEL

The well developed theory of short wavelength SASE-FELs is now being used to design two X-ray lasers, LCLS and Tesla-FEL. However, the physics and technology of these projects present some unique challenges, related to the very high peak current of the electron beam, the very long undulator needed to reach saturation, and the importance of preserving the beam phase-space density even in the presence of large wake-field effects. In the first part of this paper, we review the basic elements of the theory, the scaling laws for an X-ray SASE-FEL, and the status of the experimental verification of the theory. We then discuss some of the most important issues for the design of these systems, including wake-field effects in the undulator, and the choice of undulator type and beam parameters