A technique is proposed to generate attosecond pulse trains of radiation from a Free-Electron Laser amplifier. The optics-free technique synthesises a comb of longitudinal modes by applying a series of spatio-temporal shifts between the co-propagating radiation and electron bunch in the FEL. The modes may be phase-locked by modulating the electron beam energy at the mode spacing frequency. Three-dimensional simulations demonstrate the generation of a train of 400as pulses at giga-watt power levels evenly spaced by 2.5fs at a wavelength of 124 Angstrom. In the X-ray at wavelength 1.5 Angstrom, trains of 23as pulses evenly spaced by 150as and of peak power up to 6GW are predicted.
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