Radiation of charged particles moving in the presence of dielectric targets is of essential importance for various applications in accelerator and beam physics. As a rule, the sizes of these targets are much larger than the wavelengths under consideration. This fact gives an obvious small parameter of the problem and allows developing approximate methods for analysis. Here we apply one such method (called the “aperture method” in our preceding papers) to analysis of Cherenkov radiation from a charge flying through a vacuum channel in a dielectric sphere. We present analytical results and describe the main physical effects. Typical angular and radial distributions of the radiation field are also presented. In particular, it is shown that the field has an expressed maximum at a certain distance from the sphere. Special attention is paid to the far-field area where the radiation is formed, and corresponding angular distribution does not depend on the distance from the sphere.

中文翻译：

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带通道的电介质球产生的契伦科夫辐射

在电介质靶的存在下运动的带电粒子的辐射对于加速器和射束物理学中的各种应用至关重要。通常，这些目标的尺寸远大于所考虑的波长。这个事实为问题提供了一个明显的小参数，并允许开发近似的分析方法。在这里，我们将一种这样的方法（在我们之前的论文中称为“孔径方法”）应用于分析通过电介质球体中的真空通道飞行的电荷产生的Cherenkov辐射。我们提出分析结果并描述主要的物理影响。还显示了辐射场的典型角度和径向分布。特别地，示出了场在距球体一定距离处具有表示的最大值。