## 3 Simulation Verification
### The Effect of Multiple Factors on the Multipactor Threshold  
Via the analysis in Section 3.1-Section 3.3, it is clear that the groove aspect ratio, the groove number, and the groove depth do not affect the multipactor threshold independently. Therefore, it is needed to focus on the combined effect of these factors on the multipactor threshold. Here, we arrange the simulations for the SCLPFs with the grooved PTFE sheets loaded. The simulation results are shown in Table 1, with different groove numbers and aspect ratios. Figure 11 shows the contour map that describes the relationship among multipactor threshold, groove number, and aspect ratio. The groove depth is 0.5 mm, the number of grooves is set as 3, 7, 13, 20, and 26, as well as the aspect ratios vary from 0.1 to 3.9. It ought to be mentioned here that a smaller groove number cannot achieve a large aspect ratio since the small groove number implies a larger groove width, and it is limited by the groove depth of 0.5 mm. High aspect ratio grooves can only be achieved when the groove is narrow. Figure 10: Schematic model of the motion of secondary electrons excited by electrons incident on the center in a 2D groove. From Table 1 and Figure 11, three conclusions can be summarized. First, as the aspect ratio increases (keep the groove number constant), the multipactor threshold will increase and exceed 1100 W except for the condition that the groove number equals 3. Second, as the groove number increases (keep the aspect ratio constant), the multipactor threshold decreases. Third, different aspect ratios and groove numbers may achieve similar effects in multipactor mitigation. For example, the SCLPF possessing 7 grooves and 0.5 aspect ratio, has a similar multipactor threshold to the SCLPF possessing 20 grooves with 1 aspect ratio. Figure 11 reflects the combined effect of aspect ratio and groove number on the multipactor threshold and its saturation status. According to Table 1, the SCLPF with 26 grooves, which can achieve a larger aspect ratio at the depth of 0.5 mm, benefits more from a narrower groove compared with the SCLPF with 7 grooves. However, a larger aspect ratio did not significantly improve the saturation value. To be specific, keeping the depth as 0.5 mm, then the saturation multipactor threshold of the SCLPF with 7 grooves and 1 aspect ratio is 1133 W, and that of the SCLPF with 26 grooves and 3.9 aspect ratio is 1137 W. The former device achieves the same multipactor suppression effect as the latter one with fewer grooves and a smaller aspect ratio. Furthermore, from Figure 11, it can be observed that the threshold saturation appears when the groove aspect ratio exceeds 1.5. Thereafter, the rise of the aspect ratio will not result in a further increase for multipactor threshold. Then, we discuss the influence of groove number on the multipactor threshold of the SCLPFs. During the analysis, if we keep the aspect ratio constant, the groove depth becomes shallower as the groove number increases. Figure 12 shows the two groove structures with the same aspect ratio but different groove numbers. In this case, the electron number colliding with the sidewall above the critical angle \(\theta\) (the triangular area below the dashed line) is the same regardless of the number of grooves. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Groove Number**} & \multicolumn{8}{c}{**Aspect Ratio**} \\ \cline{2-10}  & **0.1** & **0.2** & **0.4** & **0.5** & **0.8** & **1** & **1.6** & **3** & **3.5** & **3.9** \\ \hline
3 & 417.95 & 441.39 & 568.33 & & & & & & & \\
7 & / & 472.64 & / & 710.89 & 960.91 & 1132.79 & & & & \\
13 & / & 425.76 & / & 558.58 & 738.25 & 851.53 & 1095.24 & & & \\
20 & / & 415.61 & / & 509.37 & 628.88 & 718.72 & 984.30 & 1164.04 & & \\
26 & 378.89 & 400.77 & / & 484.36 & / & / & 955.06 & / & 1160.10 & 1136.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulated multipactor threshold (W) of the PTFE-loaded SCLPFs with various aspect ratios and groove numbers.