Symplectic maps and chromatic optics in particle accelerators
Symplectic maps and chromatic optics in particle accelerators
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DOI：
10.1016/j.nima.2015.06.059
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发表时间：
2015-10-11
影响因子：
1.4
通讯作者：
Cai, Yunhai
中科院分区：
文献类型：
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作者：
Cai, Yunhai
我们应用非线性映射方法来全面表征粒子加速器中的色光学。我们的方法建立在磁性元素辛传递图的基础上。色晶格参数可以通过贴图从一个元素传输到另一元素。我们引入了雅可比算子，它提供了映射和具有参数依赖性的矩阵之间的内在联系。该链接允许我们直接应用线性光学公式来计算色晶格参数。作为说明，我们分析了具有非线性六极子、八极子和十极子的交替梯度单元，并通过分析推导了它们的局部色度补偿设置。结果，细胞在动量偏差的三阶范围内变得近乎完美。 (C) 2015 Elsevier B.V. 保留所有权利。
We have applied the nonlinear map method to comprehensively characterize the chromatic optics in particle accelerators. Our approach is built on the foundation of symplectic transfer maps of magnetic elements. The chromatic lattice parameters can be transported from one element to another by the maps. We introduce a Jacobian operator that provides an intrinsic linkage between the maps and the matrix with parameter dependence. The link allows us to directly apply the formulation of the linear optics to compute the chromatic lattice parameters. As an illustration, we analyze an alternating-gradient cell with nonlinear sextupoles, octupoles, and decapoles and derive analytically their settings for the local chromatic compensation. As a result, the cell becomes nearly perfect up to the third-order of the momentum deviation. (C) 2015 Elsevier B.V. All rights reserved.