XFEL中二次谐波的精确解
Exact Solution for the Second Harmonic Generation in XFELs
摘要：
在高增益自由电子激光（FEL）中，通过非线性机制在基频聚束驱动下产生谐波辐射是一个重要的选择。在大规模设施中使用谐波产生可以导致对于相同的电子束能量实现较短的辐射波长。本文介绍了平面波荡器中的二次谐波产生理论，特别是X射线自由电子激光（XFEL）。我们的研究是基于一个精确的解析解的麦克斯韦方程组，来自与格林函数方法的帮助。相反，最新的理论理解的二次谐波产生仅限于一些估计的总辐射功率的基础上的源部分的波动方程。此外，我们发现，这部分的波动方程是提出了几个不正确的操作，其中是遗漏的一个重要贡献。我们的工作产生正确的参数依赖性和具体的预测，如偏振，角分布的辐射强度和总功率的附加属性。最令人惊讶的预测是二次谐波辐射的垂直偏振部分的存在，而最新的理解假设场是水平偏振的。总之，本文提出了高增益自由电子激光二次谐波产生的第一修正理论。
英文摘要：
The generation of harmonic radiation through a non-linear mechanism driven by bunching at fundamental frequency is an important option in the operation of high gain Free-Electron Lasers (FELs). The use of harmonic generation at a large scale facility may result in achieving shorter radiation wavelengths for the same electron beam energy. This paper describes a theory of second harmonic generation in planar undulators with particular attention to X-Ray FELs (XFELs). Our study is based on an exact analytical solution of Maxwell equations, derived with the help of the Green's function method. On the contrary, up-to-date theoretical understanding of the second harmonic generation is only limited to some estimation of the total radiation power based on the source part of the wave equation. Moreover, we find that such part of the wave equation is presented with several incorrect manipulations among which is the omission of an important contribution. Our work yields correct parametric dependencies and specific predictions of additional properties such as polarization, angular distribution of the radiation intensity and total power. The most surprising prediction is the presence of a vertically polarized part of the second harmonic radiation, whereas up-to-date understanding assumes that the field is horizontally polarized. Altogether, this paper presents the first correct theory of second harmonic generation for high gain FELs.
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