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Description
Quantifying differences between high-dimensional phase space distributions is essential for analyzing beam measurements and simulations. While f-divergences such as KL or JS divergence are increasingly used for this purpose, including in machine learning applications, their values lack physical interpretability. This work conducts the first systematic study of the difference quantification characteristics of several typical f-divergences for high-dimensional beam distributions commonly used in accelerators. The aims are to identify the most suitable f-divergence metric for the field of accelerator beam physics and to reveal the physical meanings represented by f-divergences values within this field. We first study the f-divergences properties among different types of beam distributions with the same covariance matrix. Subsequently, we demonstrate that various f-divergences between these distributions exhibit definite correspondences with the mismatch factors and the emittance differences. Finally, based on these correspondences, we establish assessment standards for f-divergences, which can interpret the specific meanings represented by their values in the context of beam phase space distributions. These findings provide guidance for selecting statistical divergences to quantify differences in high-dimensional phase space beam distributions.
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