Ultrahigh harmonics generation in a FEL with a seed laser

One of the most challenging problems in modern FEL technology is to operate in the X-ray region, especially in the open-quotes water windowclose quotes. Because of the absence of optical resonators in this range of wavelengths, only a single-pass device may be suitable for this task. The Self-Amplified Spontaneous Emission (SASE) mechanism is now under active discussion as a realistic way to provide high-power coherent emission in the X-ray range. Both the undulator parameters and the electron beam parameters required for the lasing are achieveable at today's technological level. On the other hand, the SASE approach implies a very long and expensive periodic magnetic structure, typically several tens of meters long. This is mainly because of the rather long build-up time necessary to establish a coherent mode from incoherent noise. A mechanism of shortening this time would be therefore highly desirable. In the present paper we consider a scheme using two undulators and a seed-laser to produce coherent X-ray emission. The first undulator and the seed-laser provide a pre-modulation of the beam while the second undulator serves as a source of coherent spontaneous radiation at a very high harmonic of the seed-laser frequency; the whole scheme may then be considered to be an FEL-based frequency upconvertor. The total length of the periodic magnetic structure is shown to be of the order of several meters, nearly an order of magnitude shorter than in the SASE case. For the same beam quality as in the SASE scheme and with realistic seed-laser parameters, the efficiency of the beam pre-modulation at the 50-th (exclamation point) harmonic is shown to be as high as 15%. The output radiation is tunable between discrete harmonics of the seed-frequency