基于方阵的六维收敛图法用于非线性束流动力学分析
Square matrix-based six-dimensional convergence map for nonlinear beam dynamics analysis
AI总结：
本文提出一种基于方阵的六维收敛图法，用于非线性束流动力学分析，有效解析高阶共振结构并应用于电子离子对撞机的动态开口研究。
摘要：
基于方阵的收敛图（CM）方法已在几个4维动力系统中证明了其在刻画非线性动力学方面的有效性。然而，当存在时间依赖的扰动，如对撞机中的蟹式 kicks 时，进行全面的6维分析变得至关重要，以准确捕捉横向和纵向运动之间的耦合。在本工作中，我们通过采用基于特征分解的方阵公式结合迭代过程，将CM方法扩展到完整的6维相空间。所提出的6维CM方法首先使用简化的蟹式图进行验证。我们证明了6维CM通过仅使用一-turn图保持了计算效率，同时成功解析了传统频率图分析（FMA）无法解析的高阶共振结构。该方法随后应用于未来电子离子对撞机（EIC）的动态开口（DA）研究。CM分析所得结果与FMA得出的结果表现出高度一致，证明其作为非线性束流动力学分析和DA评估的强大工具的潜力，以及在其他非线性动力学系统中的广泛应用前景。
英文摘要：
The square matrix-based convergence map (CM) method has proven effective in characterizing nonlinear dynamics in several 4-D dynamical systems. However, when time-dependent perturbations, such as crabbing kicks in colliders, are present, a comprehensive 6-D analysis becomes essential to accurately capture the coupling between transverse and longitudinal motions. In this work, we extend the CM method to the full 6-D phase space by employing an eigen-decomposition-based formulation of the square matrix combined with iterative procedures. The proposed 6-D CM approach is first validated using a simplified crabbing map. We demonstrate that the 6-D CM preserves computational efficiency by using only one-turn map, while successfully resolving high-order resonance structures that remain unresolved by conventional frequency map analysis (FMA). This method is subsequently applied to the dynamic aperture (DA) study of the future Electron-Ion Collider (EIC). The results obtained from the CM analysis exhibit close agreement with those derived from FMA, demonstrating its potential as a powerful tool for nonlinear beam dynamics analysis and DA evaluation, as well as for broader applications in other nonlinear dynamical systems.
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