## 3 Beam-Wave Interaction Simulation  
To evaluate the output performance of the W-band TWT with the proposed dual-beam SV-SL SWS, we used the 3-D particle-in-cell (PIC) CST Particle Studio simulator [21]. In the simulation, we considered two identical 0.15 A electron beams (with a total current of 0.3 A) focused by a uniform magnetic field. And the beam voltage was 17.2 kV. The axis of the electron beam was positioned at 0.075 mm above the SWS. Considering the electron beam tunnel size, the transversal dimension of the beams was 0.8 mm \(\times\) 0.1 mm (current density of 187.5 A/cm\({}^{2}\)), corresponding to a broadside filling factor of 40%. The total length of the SWS with 50 periods plus the input/output coupling section was 66 mm. Considering the stable beam transportation without current interception by the beam tunnel walls, the uniform magnetic field should be 0.6 T or higher. Figure 8a depicts the output power and gain versus input power plot. The simulation maximum output power can reach 200 W with an input power of 0.12 W, and the corresponding gain is 32.2 dB at 90 GHz. By contrast, in Figure 8b, the driving power is set to 0.1 W. The simulation forecasts a maximal gain of 32.9 dB at 90 GHz, and the corresponding output power of 197 W. And the 3 dB bandwidth is 4 GHz. As shown in Figure 9a, we simulated the fluctuation of the SWS output signal with time at a 17.2 kV beam voltage, 90 GHz frequency, and 0.1 W input power. The signal is input from port 1, and after wave injection interaction, it is output from port 2, indicating that there is no noticeable oscillation and that it can be amplified stably. The output signal is stable across the whole frequency range, and we observed a clean single-frequency spectrum with no spurious mode excitation, as illustrated in Figure 9b. Figure 10 shows the corresponding beam phase-space diagram. It indicates the effective beam bunching along the axial direction. Most particles lose energy, and a few electrons gain energy, showing a sufficient beam wave energy transfer. According to studies [20; 22; 23; 24; 25; 26], as shown in Table 3, the saturated output power of microstrip-like structures is generally limited by the small size of the structure, which leads to low operating voltages and currents. Moreover, microstrip-like structures are usually held in place by dielectric substrates, which are susceptible to charge accumulation effects, and the meander line SWS using a dielectric substrate needs to take into account the high loss of the intermediate seed layer connecting the dielectric layer to the metal layer in actual processing, so \(S_{21}\) in experiments is usually below \(-30\) dB. The SV-SL SWS has a  
Figure 8: (**a**) Output power versus the input power at 90 GHz. (**b**) Output power versus frequency with 0.1 W input power. higher operating voltage, and its saturated output power can be more than twice that of the microstrip-like structure at approximately the same 3 dB bandwidth. Since the SV-SL SWS removes the seed and dielectric layers and adopts an all-metal structure, it is easier to process and assemble, and the transmission loss is smaller. Subsequent work should ensure that the operating voltage is reduced as much as possible and the efficiency of the electron interaction is improved with little change in bandwidth. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Operating** & **Simulation Output Power,** \\  & **Parameters** & **Efficiency and BW** \\ \hline Metalized ML TWT [20] & 9 kV, 0.028 A & 10 W, 4\%, 3 GHz \\ ML SWS with the CVD diamond & 15.6 kV, 0.043 A & 40 W, 5.96\%, 5 GHz \\ substrate [22] & 6.5 kV, 0.04 A & 36 W, 1.38\%, 5 GHz \\ PML SWS (cylindrical beam) [23] & 7.1 kV, 0.1 A & 20.77 W, 2.9\%, 7 GHz \\ ML SWS with a conformal substrate [25] & 6.55 kV, 0.1 A & 31.4 W,4.8\%, 6 GHz \\ Miniature ML SWS [26] & 14 kV, 0.2 A & 121 W, 4.32\%, 3.5 GHz \\ SV-SL SWS & 17.2 kV, 0.3 A & 200 W, 3.63\%, 4 GHz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of different planar SWSs in the W-band.