We study the tapering optimization scheme for a short period, less than two cm, superconducting undulator, and show that it can generate 4 keV X-ray pulses with peak power in excess of 1 terawatt, using LCLS electron beam parameters. We study the eff
ect of undulator module length relative to the FEL gain length for continous and step-wise taper profiles. For the optimal section length of 1.5m we study the evolution of the FEL process for two different superconducting technologies NbTi and Nb3Sn. We discuss the major factors limiting the maximum output power, particle detrapping around the saturation location and time dependent detrapping due to generation and amplification of sideband modes.
