Generation of ultrahigh harmonics with a two-stage free electron laser and a seed laser

We consider the possibility to premodulate an ultrarelativistic electron beam on the nanometer length scale, so that it can produce coherent spontaneous radiation in the x-ray range. The scheme that uses the same basic elements as the high gain harmonic generation (HGHG) scheme, two wigglers and a conventional seed laser, is shown to suit this task if the process of premodulation occurs at zero net gain of the feed-laser wave. Operation with zero gain provides the opportunity to reach much higher harmonics than in the original HGHG technique. The output radiation is tunable between discrete harmonics of the seed frequency. The total length of the periodic magnetic structure is shown to be of the order of several meters. an order of magnitude shorter than that required for self-amplified spontaneous emission (SASE). For a beam quality similar to that in the SASE scheme and with realistic seed-laser parameters, the efficiency of the beam premodulation at the 50th harmonic (5 nm for a seed wavelength of 250 nm) is shown to be as high as 15%.