## 3 Simulation Verification
### The Effect of Multiple Factors on the Multipactor Threshold
Figure 11: Contour map of the PTFE-loaded SCLPFs multipactor threshold, with aspect ratio and groove number as coordinate axes. Theoretically speaking, the same aspect ratio should have a consistent multipactor suppression effect, but the simulation results shown in Table 1 do not support this prediction. Therefore, it is needed to reconsider the significance of groove depth when analyzing the multipactor threshold. The details of the grooved dielectric sheets filled in the SCLPFs are shown in Figure 13. As detailed in the drawing in Figure 13, the gap of REGION #2 remains at 1 mm, while the gap between the grooves in REGION #1, which is determined by the groove depth, increases greatly. The increase in the average gap cannot be ignored. According to the Hatch-Williams constant \(k\) model [42], it can be known that an increase in the gap means there will be more orders, which refers to the number of half cycles that the electron moves from one plane to another. At the same time, the threshold voltage will be higher, and the process of doubling is more difficult to establish, namely, the multipactor threshold is increased. It also ought to be mentioned here that, in addition to suppressing discharge by blocking electron path through the grooves, the passive increase in the gap between 47.5% of the areas is an important reason for mitigating multipactor. Taking the aspect ratio of 0.5 as an example, the multipactor threshold decreases from 710 W to 480 W when the groove number increases from 7 to 26. Correspondingly, the groove depth decreases from 0.23 mm to 0.0625 mm, namely, the gap distance at the groove decreases from 1.46 mm to 1.125 mm. However, for situations with fewer grooves, this rule may not apply. For example, the multipactor threshold of 3 grooves with an aspect ratio of 0.2 is 441.39 W, which is lower than that of 7 grooves, even though the former has a deeper depth. This indicates that the effect of depth on multipactor is also regulated by the number of grooves under the same aspect ratio. Referring to the contour map shown in Figure 11, it is known that the selection of the groove number and the aspect ratio is partly free to achieve the same effect on increasing the multipactor threshold. This allows the designers to choose different parameters for realizing the mitigation of multipactor free. Simply, more influence factors should be considered for suppressing multipactor between metal surfaces, which is different from that for dielectric surfaces. Specifically, for the multipactor induced by the electron avalanche between two metallic boundaries, the skin effect at high-frequency microw  
Figure 12: Microstructures with the same aspect ratio and groove ratio but different numbers of grooves. (**a**) four grooves. (**b**) two grooves. Figure 13: The symmetrical groove structure leads to an increase in the average spacing of the gap. REGION #2 achieves a larger multipactor threshold compared to REGION #1.  
on the metal surface, in this case, constructing deeper grooves to suppress the discharge induced by the secondary electron avalanche will affect the transmission performance of the devices. Under the circumstances, increasing the groove number and reducing the groove depth is a better solution. There are similar selection problems for the multipactor induced by the electron avalanche between two dielectric boundaries. On the other hand, for microwave devices loaded with dielectrics, constructing grooves on the dielectric is a subtractive processing method. The volume of the dielectric is reduced after subtractive processing, and the dielectric loss is correspondingly reduced, resulting in a slight reduction in the insertion loss of the device. Under the circumstances, intentionally increasing the subtractive volume within a suitable range can bring benefits to the improvement of transmission performance, which is a preferable choice. Therefore, suppressing multipactor through microstructures is a system engineering.