Abstract
Model-independent analysis of beam dynamics in circular accelerators reveals spatial-temporal modes due to beam oscillations. Although such modes have been shown to be informative, their usefulness is limited by the lack of quantitative understanding in general. Here we present a simple approach to studying the modes analytically, which results in a quantitative understanding of the modes and an algorithm to extract the physical modes by untangling the mixed singular value decomposition modes. Particularly, we focus on the coupled betatron modes that are of great interest for high-energy colliders. A simple relationship between the coupling modes and the lattice functions is established, which not only provides a quantitative understanding but also lays the foundation for using these modes to measure machine properties and beam motion in phase space.
Highlights
In recent years, model-independent analysis (MIA) has emerged as a new approach to studying beam dynamics by analyzing simultaneously recorded beam histories at a large number of beam position monitors (BPMs) [1,2]
Similar to Fourier analysis, singular value decomposition (SVD) mode analysis decomposes the spatial-temporal variation of the beam centroid into superpositions of various orthogonal modes by effectively accomplishing a major statistical data analysis, namely, the principal component analysis [3,4]
It turns out that there is a simple approach to overcome this obstacle and reveal the relationship between the SVD modes and the underlying physics. This is remarkable since it provides the muchneeded quantitative understanding and lays the foundation for using these modes to measure machine properties as well as beam motion in phase space. We present this new approach to untangle the mixed SVD
Summary
Model-independent analysis (MIA) has emerged as a new approach to studying beam dynamics by analyzing simultaneously recorded beam histories at a large number of beam position monitors (BPMs) [1,2]. A basic technique used in MIA is the spatial-temporal mode analysis via a singular value decomposition (SVD) of the data matrix containing beam histories. For a better understanding of the SVD modes, it is necessary to establish the relationship between the SVD modes and the underlying physics by analytically solving the SVD problem This has been done only for betatron motion in 1 degree of freedom, and the result allows accurate measurement of phase advances and beta function in storage rings with little coupling [14]. It turns out that there is a simple approach to overcome this obstacle and reveal the relationship between the SVD modes and the underlying physics This is remarkable since it provides the muchneeded quantitative understanding and lays the foundation for using these modes to measure machine properties as well as beam motion in phase space. Coupling modes are discussed here as an illustration and one important application
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