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Mathieu unit cell as a template for low emittance lattices
Physical Review Accelerators and Beams ( IF 1.7 ) Pub Date : 2021-03-24 , DOI: 10.1103/physrevaccelbeams.24.031601
B. Riemann

The multibend 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 undulatorlike 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.

中文翻译:

Mathieu晶胞作为低发射晶格的模板

多弯消色差透镜(MBA)通常用作现代低发射率存储环的组成部分,由重复的具有优化光学功能以降低消色差中心中的发射率的晶胞以及用于分散和消散的端池组成。与插入设备匹配的光学元件。在这项工作中,我们描述了基于纵向傅立叶展开的最简单稳定的晶胞类别,将Hill方程转换为Mathieu方程。所得的单元类别沿光路表现出连续变化的偶极和四极矩。尽管此基本模型仅由三个参数定义,但它捕获了在MBA设计中应用的大量概念。这尤其令人感兴趣,因为Mathieu细胞可以看作是Christofilos交替梯度聚焦原始模型的基本扩展,而它们的正弦弯曲和聚焦功能则使其可以在起伏似的结构中进一步应用。Mathieu电池可用于估计合理的电池调谐范围,并着重于纵向梯度弯曲和反向弯曲的组合以及对水平方向的强聚焦以达到低于经典理论最小发射率电池的发射率。此外,此模型中的最低发射率伴随着较小的绝对动量压缩系数。Mathieu电池可用于估计合理的电池调谐范围,并着重于纵向梯度弯曲和反向弯曲的组合以及对水平方向的强聚焦以达到低于经典理论最小发射率电池的发射率。此外,此模型中的最低发射率伴随着较小的绝对动量压缩系数。Mathieu电池可用于估计合理的电池调谐范围,并着重于纵向梯度弯曲和反向弯曲的组合以及对水平方向的强聚焦以达到低于经典理论最小发射率电池的发射率。此外,此模型中的最低发射率伴随着较小的绝对动量压缩系数。
更新日期:2021-03-25
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