The development of high-brightness X-ray free electron lasers (XFELs), such as hard X-ray self-seeding free electron lasers and XFEL oscillators (XFELOs), brings a severe challenge to the crystal monochromator due to a strong non-uniform thermal load. The distortion caused by spatial temperature gradients can severely affect the optical performance of crystals. Therefore, this paper presents a model to estimate the performance of non-uniform thermally distorted crystals. The model not only takes into account thermal strain, slope error and incident angle deviation, but also considers temperature-dependent factors such as the Debye–Waller factor and electric susceptibility. Our investigation indicates that the Debye–Waller factor reduces the height and bandwidth of rocking curves, and the impact of the electric susceptibility is tiny. The proposed model can describe the distortion of the reflectivity and transmissivity curves of non-uniform thermally loaded crystals and can be applied in the design of crystal monochromators, crystal splitters, crystal compressors and XFELOs.

提出基于束流相空间拍频产生锁模多色自由电子激光的方案，利用带有能量啁啾的电子束流和上海软X射线自由电子激光装置（SXFEL）上的两个调制段-色散段结构，在束流中通过拍频形成多个流强脉冲串，并在此基础上进行高次谐波辐射，产生锁模多色自由电子激光辐射脉冲。模拟结果表明，利用264 nm的种子激光，可在束流中形成18次谐波的群聚分量，并能最终产生中心波长约14.58 nm 的锁模多色FEL辐射。

Free-electron light sources feature extraordinary luminosity, directionality, and coherence, which has enabled significant scientific progress in fields including physics, chemistry, and biology. The next generation of light sources has aimed at compact radiation sources driven by free electrons, with the advantages of reduction in both space and cost. With the rapid development of ultra-intense and ultrashort lasers, great effort has been devoted to the quest for compact free-electron lasers (FELs). This review focuses on the current efforts and advancements in the development of compact FELs, with a particular emphasis on two notable paths: the development of compact accelerators and the construction of micro undulators based on innovative materials/structures or optical modulation of electrons. In addition, the physical essence of inverse Compton scattering is discussed, which offers remarkable capability to develop an optical undulator with a spatial period that matches the optical wavelength. Recent scientific developments and future directions for miniaturized and integrated free-electron coherent light sources are also reviewed. In the future, the prospect of generating ultrashort electron pulses will provide fascinating means of producing superradiant radiation, promising high brilliance and coherence even on a micro scale using optical micro undulators.

Attosecond soft X-ray pulses are of great importance for the study of ultrafast electronic phenomena. In this paper, a feasible method is proposed to generate isolated fully coherent attosecond soft X-ray free electron laser via optical frequency beating. Two optical lasers with the opposite frequency chirps are used to induce a gradient frequency energy modulation, which helps to generate a gradually varied spacing electron pulse train. Subsequently, the undulator sections with electron beam delay lines are used to amplify the target ultra-short radiation. Numerical start-to-end simulations have been performed and the results demonstrate that an isolated soft X-ray pulse with the peak power of 330 GW and pulse duration of 620 as can be achieved by the proposed technique.