  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.
