Relativistic Vacuum Electron Devices (RVEDs) generate High-Power Microwaves (HPMs) with peak powers typically exceeding 100 MW [1]-[3]. This makes them promising for applications in military [4]-[10] and civilian fields [11]-[14], such as high-power radar [15] [16], plasma confinement [17], space energy transmission [18]-[21], and medical research. Current research focuses are shifting towards developing more practical multi-frequency output HPM sources. Compact multi-frequency HPM sources not only meet the stringent volume and weight constraints of specific platforms but also significantly compensate for the limitations of conventional single-frequency HPM sources in addressing the need to target multiple different frequencies. To achieve compact multi-frequency HPM output, researchers primarily concentrate on the design and implementation of compact multi-frequency slow-wave structures (SWS), with less attention paid to the compact design of multi-frequency HPM transmission and radiation systems. In existing research on dual-frequency transmission and radiation antennas, there are mainly two technical approaches: one is based on a single-feed horn structure [22] [23], which suffers from high transmission loss and processing difficulties; the other is based on a frequency-selective surface feed array structure [24] [25], which is typically used in satellite applications. Considering the high power capacity requirements and special application scenarios of HPMs, both of these structures are difficult to directly apply to the needs of this paper. Therefore, it is necessary to carry out simulation research on compact transmission and radiation horns suitable for dual-band HPMs.

In our previous research, a dual-band high-power coaxial transit-time oscillator (TTO) based on a nested structure was proposed, in which the Ka-band TTO was coaxially nested inside the X-band TTO. An in-depth analysis of its working mechanism and performance was conducted [26]. The typical particle simulation results are as follows: under the conditions of a voltage of 460 kV and a guiding magnetic field of 0.6 T, it can simultaneously output 2.0 GW of X-band (8.4 GHz) and 0.9 GW of Ka-band (30.6 GHz) dual-band HPM, with an average device efficiency of about 40%.To achieve simultaneous effective radiation of dual-band HPM, meet the measurement requirements of microwave experiments, and ensure the overall compactness of the dual-band HPM source, this paper combines theoretical and simulation research to carry out the compact design of the dual-band HPM transmission support rod and radiation horn.

Due to the nested SWS design, the generation and transmission of X-band and Ka-band HPM are completed in separate spaces. Therefore, the support rods can be designed to achieve high transmission characteristics separately. The design of the support rods for coaxial TTO follows the following two principles [27]-[30]: 1) high transmission efficiency for the coaxial TEM mode (S₂₁ close to 1); 2) high transmission coefficient for common low-order TE modes (such as TE₁₁) in experiments, to avoid TE mode microwaves entering the SWS and interfering with the beam-wave interaction. Existing research has shown that the selection of the number of support rods for coaxial waveguides is based on the following criteria: near the operating frequency, when the first cutoff mode of the coaxial waveguide is the TE_n1 mode, while ensuring low reflection for the TE₁₁ mode, the number of support rods should be selected as n + 1, and they need to be uniformly distributed along the angular direction. In addition, using a double-row support rod structure with a spacing of (2m + 1)λ/4 (m is a natural number) can not only provide stronger mechanical support but also effectively broaden the transmission bandwidth of the coaxial TEM mode [27]-[29].

Using electromagnetic simulation software, the mode distribution of coaxial waveguides in the X-band and Ka-band was calculated respectively. As shown in Figure 1, for the X-band coaxial transmission structure, near the operating frequency of 8.42 GHz, the lowest-order cutoff mode is TE_14,1. To ensure that the TE₁₁ mode also has good transmission characteristics, the number of support rods is selected to be 15. Figure 2 shows the optimized design of the support rod model, and the structural parameters are shown in Table 1. The spacing between the two rows of support rods is 5λ_X/4. The transmission characteristics of the support rods

are shown in Figure 3. The results indicate that the S₂₁ parameter of the TEM mode is close to 1 near the operating frequency, and the S₁₁ parameter of the TE₁₁ mode is small, meeting the design requirements.