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Influence of a linear energy chirp in the electron beam on a self-amplified spontaneous emission (SASE) Free Electron Laser (FEL) operation is studied analytically and numerically using a 1D model. Analytical results are based on the theoretical background developed by Krinsky and Huang [Phys. Rev. ST Accel. Beams 6, 050702 (2003)PRABFM1098-4402]. Explicit expressions for Green’s functions and for output power of a SASE FEL are obtained for the high-gain linear regime in the limits of small and large energy chirp parameters. Saturation length and power versus energy chirp parameter are calculated numerically. It is shown that the effect of linear energy chirp on FEL gain is equivalent to the linear undulator tapering (or linear energy variation along the undulator). A consequence of this fact is a possibility to perfectly compensate FEL gain degradation, caused by the energy chirp, by means of the undulator tapering independently of the value of the energy chirp parameter. An application of this effect for generation of attosecond pulses from a hard x-ray FEL is proposed. Strong energy modulation within a short slice of an electron bunch is produced by a few-cycle optical laser pulse in a short undulator, placed in front of the main undulator. Gain degradation within this slice is compensated by an appropriate undulator taper while the rest of the bunch suffers from this taper and does not lase. Three-dimensional simulations predict that short (200 attoseconds) high-power (up to 100 GW) pulses can be produced in Angstrom wavelength range with a high degree of contrast. A possibility to reduce pulse duration to sub-100 attosecond scale is discussed

Self-amplified spontaneous emission FEL with energy-chirped electron beam and its application for generation of attosecond x-ray pulses