## 4 Discussion
### Distribution of Discharge Channels  
Residual space charges have a significant impact on the initiation and development of subsequent breakdowns [45; 46]. Therefore, the distribution characteristics of discharge channels for repetitive breakdowns in corona-stabilized switches can be explained by the diffusion mechanism of residual space charges. After the breakdown is completed, many residual space charges remain in the channel. The HTHP (high-temperature and high-pressure) discharge plasma expands outward as a cylindrical shock wave, causing the diffusion of residual charges toward both sides of the channel, as illustrated in Figure 18a. Due to the strong electronegativity of SF\({}_{6}\) gas molecules, the residual charges mainly consist of SF\({}_{6}\) negative ions in corona-stabilized switches. During repetitive breakdowns with a high-repetition frequency, numerous SF\({}_{6}\) negative ions migrate to both sides of the channel and disperse in the electrode gap, as shown in Figure 18b. The subsequent voltage causes electron desorption from SF\({}_{6}\) negative ions, providing a significant number of initial free electrons for subsequent breakdown events. Due to the dispersed distribution of negative ions, the initial electrons are also scattered throughout, resulting in an electron avalanche that can initiate and propagate from various directions (see Figure 18c). As a result, the channel distribution of repetitive corona-stabilized switch exhibits dispersion. In cases where the repetition frequency is low, most residual SF\({}_{6}\) negative ions dissipate before the next voltage arrives due to a longer recovery time of the switch after the previous discharge has ended. This weakens their influence on subsequent breakdown and makes it easier for a breakdown channel to develop along the shortest distance (axis) of the electrode gap. As a result, there is a more concentrated distribution of discharge channels during breakdown processes with low-repetition frequency, while they are significantly more dispersed during high repetition frequency breakdowns. As the radius of high-voltage electrodes increases in corona-stabilized switches, the distribution of repetitive breakdown channels becomes more dispersed. The larger surface area of the thicker rod electrode may limit the expansion of the HTHP plasma channel, resulting in the almost radial development of shock waves along the discharge channel and migration of residual space charges to both sides of the electrode axis. A smaller electrode radius leads to a more dispersed diffusion direction of shock waves, a faster dissipation of residual charges, and a faster recovery rate for neutral gas density. Therefore, axial development tends to occur in the breakdown channel. Figure 17: Schematic diagram of the corona discharge in a rod-plate electrode. From Figure 13, it can be observed that whether pure gases (N\({}_{2}\), He, and SF\({}_{6}\)) or mixed gases (SF\({}_{6}\)-N\({}_{2}\), SF\({}_{6}\)-He) were utilized, the distribution of repetitive breakdown channels followed a consistent pattern: at low repetition rates, multiple channels tend to concentrate along the axis direction of the electrode gap. As the frequency increases, the distribution of breakdown channels becomes more dispersed. This pattern is consistent with the channels for switches with different electrode shapes. Additionally, in the SF\({}_{6}\)-N\({}_{2}\) and SF\({}_{6}\)-He mixtures, at the same repetition frequency, the higher the SF\({}_{6}\) content in the mixture, the more dispersed its breakdown channels become. This phenomenon is related to the concentration of residual SF\({}_{6}\) negative ions in the discharge gap. The higher the SF\({}_{6}\) content, the greater concentration of residual SF\({}_{6}\) negative ions after breakdown occurs, leading to the possibility of subsequent breakdown developing in multiple directions and resulting in a more dispersed distribution of channels.