Radiation of charged particles moving in the presence of dielectric targets is of significant interest for various applications in the accelerator and beam physics. The size of these targets is typically much larger than the wavelengths under consideration. This fact gives us an obvious small parameter of the problem and allows developing approximate methods for analysis. We develop two methods, which are called the "ray optics method" and the "aperture method". In the present paper, we apply these methods to analysis of Cherenkov radiation from a charge moving through a vacuum channel in a solid dielectric sphere. We present the main analytical results and describe the physical effects. In particular, it is shown that the radiation field possesses an expressed maximum at a certain distance from the sphere at the Cherenkov angle. Additionally, we perform simulations in COMSOL Multiphysics and show a good agreement between numerical and analytical results.

中文翻译：

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穿过电介质球面目标的电荷辐射：射线光学和孔径方法

在存在介电目标的情况下移动的带电粒子的辐射对于加速器和束物理学中的各种应用具有重要意义。这些目标的尺寸通常比所考虑的波长大得多。这一事实为我们提供了一个明显的问题的小参数，并允许开发用于分析的近似方法。我们开发了两种方法，称为“射线光学法”和“孔径法”。在本文中，我们将这些方法应用于通过固体介电球中的真空通道移动的电荷的切伦科夫辐射分析。我们展示了主要的分析结果并描述了物理效应。特别是，结果表明，辐射场在距离球体一定距离的切伦科夫角处具有最大表达。此外，我们在 COMSOL Multiphysics 中进行了仿真，结果表明数值和解析结果之间具有良好的一致性。