Using the Beam-Echo Effect for Generation of Short-Wavelength Radiation

We propose to use the mechanism of an echo effect previously observed in hadron accelerators for up-frequency conversion of density modulation in an electron beam. We show that, for generation of high harmonics, this method is much more efficient in comparison with the currently used approach. A one-dimensional model of the effect is developed which allows us to optimize the amplitude of the modulation for a given harmonic number.