Phase space is a mathematical construct that encompasses particle positions and their corresponding momenta. In general, discrete phase space structures are experimentally measured due to the limited spatial and angular resolutions of individual devices. From the perspective of beam focusing characteristics, beams are discussed in terms of core components and halo components. While the beam core is typically the primary component with low divergence, it may occasionally consist of multiple components with different velocity distributions. Mathematical modeling of the beam core in phase space is essential for accurately quantifying beam divergence and emittance. This paper presents a model that can be applied to beam cores with inner structures and reconstructs the phase space structure using kernel density interpolation. The reconstructed phase space structure is then utilized to determine beam divergence and emittance with greater precision. Additionally, these insights contribute to an enhanced understanding of beam physics.

中文翻译：

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使用核密度估计对相空间中的梁核进行建模

相空间是一种数学结构，包含粒子位置及其相应的动量。一般来说，由于单个器件的空间和角度分辨率有限，离散相空间结构是通过实验测量的。从光束聚焦特性的角度，从核心部件和光晕部件两个方面对光束进行了讨论。虽然梁芯通常是低发散的主要组件，但它有时可能由具有不同速度分布的多个组件组成。相空间中束芯的数学建模对于精确量化光束发散度和发射度至关重要。本文提出了一种可应用于具有内部结构的梁芯的模型，并使用核密度插值来重建相空间结构。然后利用重建的相空间结构来更精确地确定光束发散度和发射度。此外，这些见解有助于增强对光束物理的理解。