## 4 Discussion
### Behavior of Residual Space Charges
#### 4.1.1 Electric Field Inhomogeneity  
Under pulsed voltage, gas switches equipped with a uniform-field electrode exhibited the poorest repetitive breakdown stability, as depicted in Figure 7. The reason for this is that in the switch using SF\({}_{6}\) as the insulation medium, many negative SF\({}_{6}\) ions were generated during the preceding breakdown due to the strong electronegativity of SF\({}_{6}\) gas molecules. SF\({}_{6}\) negative ions have a relatively long lifetime (hundreds of milliseconds) and can provide numerous initial electrons for subsequent breakdown through collision-induced de-attachment [14; 24; 32]. This greatly increases the probability of subsequent breakdown initiation, resulting in a lower breakdown voltage and poor insulation recovery of the switch.  
The stability of gas switches with highly inhomogeneous fields is better under the same conditions because residual space charges play a different role in the breakdown process compared to homogeneous gap breakdown. Local corona discharge occurs prior to complete breakdown in the gap with a highly inhomogeneous field. The residual SF\({}_{6}\) negative ions do not directly contribute to the complete breakdown of the gap by providing initial electrons through collision detachment. Instead, they preferentially participate in corona discharge, enhancing the corona-stabilization effect and improving the repetitive breakdown stability of the switch [13; 14]. Therefore, switches with highly inhomogeneous electric field gaps exhibit better stability in repetitive breakdown and insulation recovery rate than those with uniform or slightly non-uniform electrode gaps due to their coronal-stabilization effect under the same experimental conditions.  
The field inhomogeneity of corona-stabilized switches using rod electrodes increases as the electrode radius decreases. A higher level of field inhomogeneity results in accelerated insulation recovery and enhanced stability of repetitive breakdowns due to the intensified field intensity surrounding the rod electrode during subsequent pulsed voltage. The electrons in neutral gas molecules and SF\({}_{6}\) negative ions are more easily desorbed, resulting in a larger number of initial free electrons. This leads to a stronger corona discharge [33; 34; 35]. The corona space charges provide better shielding for the rod electrode and a stronger corona stabilization effect, resulting in improved repetitive breakdown stability and insulation recovery of the switch.  
When the field inhomogeneity of the corona-stabilized switch is low, its repetitive breakdown voltage hardly recovers within 10-100 ms. This phenomenon, known as the \"plateau\" of insulation recovery, means that the withstand voltage level does not recover significantly over time, as shown in Figure 15. This is because when the inhomogeneityof the electric field is low, the intensity of corona discharge and the accumulation of space charges weaken, and the corona-stabilization effect during the breakdown is very weak or even negligible. In this case, the initial electrons provided by the residual space charge will directly serve the subsequent complete breakdown rather than the corona activity. Therefore, the relative difficulty of subsequent breakdown mainly depends on the concentration of residual space charges. As a result, during the residual SF\({}_{6}\) negative ions existing, the relative breakdown difficulty will remain at a nearly constant level, corresponding to the \"plateau\" in the insulation recovery curve. As the recovery time increases, the residual space charge dissipates, and its impact on the subsequent breakdown weakens until it disappears. Consequently, the insulation ability of the switch continues to recover.