We develop design considerations on the possibility of generating free elec
tron laser radiation in the x-ray region of the spectrum (50-60 Angstrom),
by exploiting a frequency multiplier scheme. We propose a free electron dev
ice consisting of a relatively low energy linac (750 MeV) and three section
s: an oscillator at 150 nm, an amplifier tuned at the fifth harmonic of the
first and a second amplifier operating at a subharmonic of the second ampl
ifier. The seedless amplification is ensured by the e-beam bunching, induce
d in the oscillator and in the second section, which plays the role of ampl
ifier and modulator. We also explore the possibility of overcoming the prob
lems associated with the bunching efficiency dilution, due to intracavity s
aturation of the first section, by discussing the regeneration of the bunch
ing by the use of a cavity dumping, realized with a suitable e-beam energy
or cavity detuning modulation. (C) 1999 American Institute of Physics. [S00
21-8979(99)01622-9].