Compact short-wavelength free-electron laser

A new nonclassical model is proposed for the radiation from electrons skimming over and colliding at grazing incidence with a conducting diffraction grating. Radiation originating from induced surface currents and bremsstrahlung is amplified as it passes through spatially modulated wave functions above the grating. The predicted magnitude and dependence on electron beam thickness agree with experiments at visible wavelengths and suggest the possibility of a compact x-ray laser.