An elegant and convenient rigorous approach for solving canonical circular open-ended dielectric-loaded waveguide diffraction problems is presented. It uses the solution of corresponding Wiener–Hopf–Fock equation and leads to an infinite linear system for reflection coefficients (S-parameters) of the waveguide, and the latter can be efficiently solved numerically using the reducing technique. As a specific example directly applicable to beam-driven radiation sources based on dielectric-lined capillaries, diffraction of a slow TM symmetrical mode at the open end of a circular waveguide with uniform dielectric filling is considered. A series of such modes forms the wakefield (Cherenkov radiation field) generated by a charged particle bunch during its passage along the waveguide axis. Calculated S-parameters were compared with those obtained from COMSOL simulation and an excellent agreement was shown. This method is expected to be very convenient for analytical investigation of various electromagnetic interactions of terahertz (THz) waves (both free and guided) and charged particle bunches with slow-wave structures perspective in context of modern beam-driven THz emitters, THz accelerators, and THz-based bunch manipulation and bunch diagnostic systems.

中文翻译：

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开放式介质加载圆波导的衍射：严格的方法

提出了一种优雅而便捷的严格方法来解决经典的圆形开放式介质加载的波导衍射问题。它使用了相应的Wiener-Hopf-Fock方程的解，并得到了波导的反射系数（S参数）的无限线性系统，并且可以使用归约技术有效地求解后者。作为直接适用于基于衬有电介质的毛细管的束驱动辐射源的具体示例，考虑了在具有均匀电介质填充的圆形波导的开口端处的慢TM对称模式的衍射。一系列这样的模式形成由带电粒子束沿波导轴通过时产生的尾波场（切伦科夫辐射场）。将计算出的S参数与从COMSOL仿真获得的S参数进行比较，并显示出极好的一致性。在现代束驱动的THz发射器，THz加速器，以及基于太赫兹的束处理和束诊断系统。