## 3 Results
### Optical Image of Discharge Channels  
The subsequent process during repetitive breakdowns is inevitably influenced by the preceding one, as evidenced by changes in the morphology and distribution of the discharge channel. Therefore, the optical image of repetitive breakdowns in the corona-stabilized switch is analyzed under different working conditions in this section. The channels of 50 consecutive breakdown processes are superimposed on each photograph.  
Figure 12 displays the optical images of the breakdown channels in a corona-stabilized switch with high-voltage electrodes of varying geometric structures at PRFs of 10, 100, and 1000 Hz. The most obvious pattern in optical imaging is that as the repetition frequency decreases, the breakdown channels become more concentrated near the electrode axis. In other words, breakdowns are more likely to develop along the axis of the electrode gap at low frequencies, while at higher operating frequencies, they may develop from multiple directions and paths.  
Figure 11: The influence of gap spacing on the repetitive breakdown voltage and its dispersion of the switch (electrode R1, SF\({}_{6}\), 0.1 MPa): **(a)** breakdown voltage; **(b)** voltage dispersion.  
Figure 12: Optical images of breakdown channels for repetitive breakdowns with different electrodes. The first through seventh columns display the channel images of various high-voltage electrodes, while the first through third rows depict images at frequencies of 1000, 100, and 10 Hz respectively.  
The channel images of the corona-stabilized switch using different gas media at various repetition frequencies are shown in Figure 13. Regardless of whether the medium was pure gas (nitrogen, helium, and SF\({}_{6}\)) or a mixture (SF\({}_{6}\)-N\({}_{2}\), SF\({}_{6}\)-He), the distribution of breakdown channels followed a similar pattern: at low-repetition frequencies, repetitive breakdown channels tended to concentrate in the axis direction of the electrode gap and its vicinity. As the operating frequency increased, the channels became more widely spread out. The trend is consistent with that of switches employing varying high-voltage electrodes. In addition, in mixtures of SF\({}_{6}\)-N\({}_{2}\) and SF\({}_{6}\)-He, the channel became more dispersed as the content of SF\({}_{6}\) gas increased under the same repetition frequency. This may be because the concentration of residual SF\({}_{6}\) negative ions in the gap increases with a higher SF\({}_{6}\) content, resulting in subsequent breakdowns occurring from multiple directions and a more dispersed distribution of the breakdown channels.  
Figure 14 illustrates the impact of operating pressure and gap spacing on the distribution of the breakdown channels. The distribution of channels was more scattered at high-repetition frequency than at low-repetition frequency, which is consistent with the trend observed in switches with different electrode structures and gas media.  
Figure 14: Images of discharge channels from repetitive breakdowns with different operating pressures and gap spacings: (**a**) operating pressure; (**b**) gap spacing.  
Figure 13: Optical images of the breakdown channels for repetitive breakdowns with different gas types: (**a**) SF\({}_{6}\)-N\({}_{2}\); (**b**) SF\({}_{6}\)-He.