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.

中文翻译：

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周期性光束的史密斯-珀塞尔辐射

史密斯-珀塞尔效应是众所周知的单色电磁辐射源。在本文中，我们介绍了来自周期性光束的Smith-Purcell辐射的广义理论。计算描述辐射的相干和不相干状态的形状因子。在两个实际上最常用的调制曲线中，在两个非常重要的频率范围（THz和X射线）中研究了辐射特性-一连串的微束和高斯形的调制束，其特征在于具有任意调制深度的正弦调制。根据发展的理论，我们表明，由一组束组成的调制电子束可以显着改善发射光的光谱线单色性，对于短光栅，其值优于1％。我们还证明了史密斯-珀塞尔辐射可以用于部分调制光束的调制深度的非破坏性诊断。这些发现不仅开辟了一种利用史密斯-珀塞尔效应控制光发射的新方法，而且还有望对基于带电粒子束的其他辐射源产生深远影响，例如FEL中的波动辐射，下一代X射线辐射源基于康普顿逆散射，范围从太赫兹到X射线。