## 2 SWS Design and Discussion
### S-Parameters  
Figure 4 depicts the whole assembly model of the proposed SWS with coupling devices. A thin central sheet of metal is laser-engraved with periodic staggered vane grooves, and the metal enclosure is divided into two halves that can be fabricated with a computer numerical control (CNC) milling or casting machine. The gap between the middle metal sheet and the upper and lower enclosures can serve as a dual electron injection channel. To eliminate extra reflections, a transition section, as seen in Figure 5, is employed to connect the SWS to the input/output structure. A stepped ridge waveguide is usually adopted as the transmission transition structure for a planar meander-line SWS, where impedance matching can be achieved by adjusting the height of the ridge waveguide (the dimension along the x-direction); during this process, the transition from the TE\({}_{10}\) mode of the standard rectangular waveguide to the quasi-TEM mode of the meander line can be realized. However, this matching method requires the meander-line and ridge waveguide to be processed separately and then assembled as a whole unit, which is troublesome to accurately assemble and prone to introduce more assembly erro  
Figure 3: (**a**) Normalized phase velocity curve and (**b**) coupling impedance curve of the SV-SL SWS with frequency. Figure 2: The dispersion diagram of the proposed SWS. the assembly of the whole SWS, in this SV-SL SWS, we controlled the height of the ridge waveguide in the x-direction to match the thickness of the centerpiece, i.e., the beam tunnel height, and achieved impedance matching by adjusting the dimensions of the ridge waveguide in the z- and y-directions. The dimensional parameters are listed in Table 2.  
Meanwhile, the electric field distribution of the transmission model of the proposed SWS is shown in Figure 6. After optimizing the dimensional parameters of the connection portion, this model can complete the wave transmission. To examine the transmission characteristics of the SWS, we simulated a 50-period circuit with input/output couplers on both sides using the CST Studio Suite simulator [17]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Dimension (mm)** & **Parameters** & **Dimension (mm)** \\ \hline \(s1\) & 0.5 & \(w3\) & 0.6 \\ \(s2\) & 0.4 & \(w4\) & 0.9 \\ \(s3\) & 0.8 & \(g1\) & 0.95 \\ \(w1\) & 0.24 & \(g2\) & 1 \\ \(w2\) & 0.39 & \(g3\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dimension parameters for transition. Figure 4: Assembly model of the proposed SWS with coupling structures. Figure 5: Schematic of the SV-SL SWS with transition coupler parts. In our previous research [18], the effects of laser cutting, acid cleaning, and copper plating on the surface roughness and S-parameter of the meander slot-line were investigated. The experimental results show that after plating a 3-5 \(\upmu\)m copper layer on the surface of the laser-cut molybdenum sheet, the surface roughness reaches 1.67 \(\upmu\)m, and its effective conductivity is 1.48 \(\times\) 10\({}^{7}\) S/m. Therefore, in the SV-SL SWS simulation, the upper and lower shells are assumed to be copper with a conductivity of 3 \(\times\) 10\({}^{7}\) S/m. And the central slot-line is considered to be a molybdenum sheet with an effective conductivity of 1.48 \(\times\) 10\({}^{7}\) S/m; the effective conductivity \(\sigma_{\textit{ef}}\) was calculated according to the well-known formula. \[\delta=\sqrt{\frac{2}{\omega\mu\sigma}} \tag{1}\]  
\[\sigma_{\textit{ef}}=\frac{\sigma}{(1+\frac{2}{n}\mathrm{arctan}(1.4\times( \frac{R}{\delta})^{2}))} \tag{2}\]  
where the \(\delta\) is the skin depth, \(\omega\) is the angular frequency, \(\mu\) = 4\(\pi\)\(\times\) 10\({}^{-7}\) H/m is the magnetic conductivity, \(\sigma\) = 5.8 \(\times\) 10\({}^{7}\) S/m is the bulk conductivity of copper, and \(R\) is the surface roughness. The obtained S-parameters are presented in Figure 7a.