Gadjev, I.I. Emma, C. Nause, A. Rosenzweig, J.B. TUP008 FEL space-charge undulator electron simulation 2015 2015-12 While FEL technology has reached the EUV and X-ray regime at existing machines such as LCLS and SACLA, the scale of these projects is often impractical for research and industrial applications. Sub-millimeter period undulators can reduce the size of a high-gain EUV FEL, but will impose stringent conditions on the electron beam. In particular, a high-gain EUV FEL based on undulators with a sub-millimeter period will require electron beam currents upwards of 1 kA at energies below 100 MeV. Coupled with the small gap of such undulators and their low undulator strengths, K < 0.1, these beam parameters bring longitudinal space-charge effects to the foreground of the FEL process. When the wavelength of plasma oscillations in the electron beam becomes comparable to the gain-length, the 1D theoretical FEL model transitions from the Compton to the Raman limit. In this work, we investigate the behavior of the FEL's gain-length and efficiency in these two limits. The starting point for the analysis was the one-dimensional FEL theory including space-charge forces. The derived results were compared to numerical results of Genesis 1.3 simulations. This theoretical model predicts that in the Raman limit, the gain-length scales as the beam current to the -1/4th power while the efficiency plateaus to a constant.