Introduction
Terahertz (THz) technologies have attracted many researchers [1], which have wide application potential in many fields: imaging technology, radar, communication, far-infrared spectroscopy, biomedical diagnostics, plasma science. In contrast to solid-state devices, in the THz regions, vacuum electronic devices (VEDs) are able to transport high currents and support higher output power. Due to its high power, high efficiency, compact configuration, extended interaction devices (EIDs) are seen as a new kind of THz radiation source. EIDs combing the merits of traditional klystrons and traveling wave tubes can be divided into two categories, including extended interaction oscillator (EIO) and extended interaction amplifier (EIA). Even though VEDs have many advantages, many challenges will be faced as operating frequency increases in the THz band, which directly affect the efficiency and stability of beam-wave interaction. For example, since the dimension of devices must be compatible to the operating wavelength, it may lead to the difficulty of micro-fabrication technology, especially in the millimeter or micrometer range. In addition, a small beam tunnel could cause the cooling effect and the reduction of thermal loading. Hence, it is necessary to design a larger beam tunnel that can improve the power-handling capacity. To release such problems, adopting high order mode as the operating mode is an effective method [2], [3]. Overmoded structure device can enlarge the size on the radial direction and improve energy storage at certain breakdown values.