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Frequency up-conversion and amplification of laser radiation with use of laser and electron beams: Kapitsa-Dirac free-electron laser.

It is shown that a resonant interaction between a laser beam, a standing light wave, and a relativistic electron beam can be built up in a Lorentz frame different from that of the laboratory. The conditions for which external electromagnetic radiation with wavelength shorter than that of the laser pump field can be amplified via an electron-scattering process of the Kapitsa-Dirac type are then determined. The linear gain of this device is estimated and the possibility of building an «optical-wiggler» free-electron laser working from the IR to the VUV range is investigated