Mathieu单胞作为低发射度晶格的模板
The Mathieu unit cell as a template for low emittance lattices
摘要：
多弯曲消色差透镜（MBA），这往往是作为现代低发射率储存环的构建块，是由重复的单位细胞具有优化的光学功能，在消色差中心的低发射率，以及端部细胞的色散和光学匹配插入设备。在这项工作中，我们描述了最简单的稳定类的单位细胞的基础上的纵向傅立叶展开，变换希尔方程Mathieu方程。由此产生的细胞类具有连续变化的偶极和四极矩沿光束路径。虽然这个基本模型是由只有三个参数定义的，它捕获了大量的概念，应用在MBA的设计。这是特别有趣的，因为Mathieu细胞可以被看作是Christofilos的交替梯度聚焦的原始模型的基本扩展，而它们的正弦弯曲和聚焦功能有助于未来在类似波动器的结构中的应用。Mathieu单元可用于估计合理单元调谐的范围，并强调纵向梯度弯曲和反向弯曲的组合，以及强水平聚焦以达到低于经典理论最小发射度单元的发射度。此外，在这个模型中，最低的发射率伴随着小的绝对动量压缩因子。
英文摘要：
The multi-bend achromat (MBA), which often serves as a building block for modern low-emittance storage rings, is composed of a repetition of unit cells with optimized optical functions for low emittance in the achromat center, as well as end cells for dispersion and optics matching to insertion devices. In this work, we describe the simplest stable class of unit cells that are based on a longitudinal Fourier expansion, transforming Hill equations to Mathieu equations. The resulting cell class exhibits continuously changing dipolar and quadrupolar moments along the beam path. Although this elementary model is defined by only three parameters, it captures a significant amount of notions that are applied in the design of MBAs. This is especially interesting as Mathieu cells can be viewed as an elementary extension of Christofilos' original model of alternating-gradient focusing, while their sinusoidal bending and focusing functions lend themselves to future applications in undulator-like structures. Mathieu cells can be used to estimate the range of reasonable cell tunes and put an emphasis on the combination of longitudinal gradient bending and reverse bending, as well as on strong horizontal focusing to reach emittances lower than the classic theoretical minimum emittance cell. Furthermore, the lowest emittances in this model are accompanied by small absolute momentum compaction factors.
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