Smith-Purcell radiation from periodic beams

Smith-Purcell effect is well known as a source of monochromatic electromagnetic radiation. In this paper we present the generalized theory of Smith-Purcell radiation from periodic beams. The form-factors describing both coherent and incoherent regimes of radiation are calculated. The radiation characteristics are investigated in two practically important frequency ranges, THz and X-ray, for two modulation profiles, most frequently used in practice - a train of microbunches and a Gaussian-shaped one, characterized by sinusoidal modulation with an arbitrary modulation depth. On the base of the theory developed we show that a modulated electron beam consisting of a set of bunches makes it possible to improve significantly the spectral line monochromaticity of the light emitted, reaching values better than 1% for short gratings. We demonstrate as well that Smith-Purcell radiation can be used for non-destructive diagnostics of the depth of modulation for partially modulated beams. These findings not only open up a new way to manipulate the light emission using Smith-Purcell effect but also promise a profound impact for other radiation sources based on charged particle beams, such as undulator radiation in FELs, next-generation X-ray radiation source based on inverse Compton scattering, in a wide range from THz to X-rays.