Operation of particle accelerators and correction of unavoidable magnet or alignment errors critically depend on the assessment of both global and local observables such as tune or resonance driving terms. With most of the observables being a sum of different error sources, careful disentangling is necessary in order to establish an optimal correction and allow for smooth operation. In the LHC, linear coupling has been proven to have a major impact on the beam dynamics and is taken to be one of the main sources of uncertainty when establishing corrections. In this paper an approach to evaluate the change of the Hamiltonian terms with linear coupling is presented. The validity of derived equations is demonstrated on a number of observables and benchmarked against simulations.

中文翻译：

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局部线性耦合对圆形加速器中线性和非线性可观测量的影响

粒子加速器的操作以及不可避免的磁体或对准误差的校正在很大程度上取决于对整体和局部可观测值（如调谐或共振驱动项）的评估。由于大多数可观测值是不同误差源的总和，因此有必要进行仔细的纠缠以便建立最佳校正并允许平稳运行。在大型强子对撞机中，线性耦合已被证明会对光束动力学产生重大影响，并且在进行校正时被视为不确定性的主要来源之一。本文提出了一种利用线性耦合评估哈密顿项变化的方法。导出的方程的有效性在许多观测值上得到了证明，并以模拟为基准。