We study the generation of short (sub 10 fs) pulses in the X-ray spectral region using an energy chirped electron beam in a Self Amplified Spontaneous Emission Free Electron Laser (SASE FEL) and a self-seeding monochromator [1-4]. The monochromator filters a small bandwidth, short duration pulse from the frequency chirped SASE spectrum. This pulse is used to seed a small fraction of the long chirped beam, hence a short pulse with narrow bandwidth is amplified in the following undulators. We present start-to-end simulation results for LCLS operating in the soft X-ray self-seeded mode with an energy chirp of 1% over 30 fs and a bunch charge of 150 pC. We show the possibility to generate
5 fs pulses with a bandwidth 0.3 eV. We also assess the possibility of further shortening the pulse by utilizing one more chicane after the self-seeding stage and shifting the radiation pulse to a “fresh” part of the electron beam. Experimental study on this short pulse seeding mode has been planned at the LCLS.