## 3 Results
### Field Inhomogeneity
reasons for this phenomenon: (1) the insulation strength of the switch has almost fully recovered before this time interval; (2) there is a mechanism that prevents the continuous restoration of insulation capability during this interval. A detailed analysis of the reasons for the phenomena will be conducted in Section 4.1. On the other hand, as the inhomogeneity decreases, the stability of the corona-stabilized switch deteriorates. The switch that utilized electrode R1 (\(r\) = 0.5 mm) exhibited the best stability in terms of average breakdown voltage dispersion and dispersion fluctuation, while using the rod electrode R5 (\(r\) = 5.0 mm) resulted in the worst stability. This is because the electrode with a smaller radius had a more inhomogeneous electric field, resulting in stronger corona discharge activity around the high-voltage electrode and a more effective corona stabilization effect. As the radius of the rod increases, the field distribution becomes more uniform, the corona intensity during breakdown decreases, and the corona stabilization effect weakens. The effect of corona stabilization in the switch is not only influenced by the intensity of corona discharge, but also by the distribution of the stable corona layer, which provides a shielding effect on the high-voltage electrode [13; 14; 15]. Therefore, this paper also investigated the mathematical expectation and normalized breakdown voltage dispersion of needle electrodes in group N at different repetition frequencies, as illustrated in Figure 8. The rod electrode R3 (\(r\) = 1.5 mm) was compared to the electrodes in group N, considering that the electrode R3 had the same rod radius as group N but a different tip structure. The variation in the breakdown voltage of needle electrodes was generally smaller than that of the rod electrode R3, as shown in Figure 8a. Although the field inhomogeneity coefficient of needle electrodes is not very high and they all belong to slightly inhomogeneous field gaps (\(f\leq 4\)) [26], needle electrodes with different cone angles exhibit similar and excellent insulation recovery performance. The voltage dispersions of the electrodes N1, N2, and N3 were similar to those of electrode R1, which performed the best among the rod electrodes (about 4-6%). The voltage dispersion of the electrode N4 with the largest cone angle was slightly higher than that of the other needle electrodes, but it still exhibited good breakdown stability compared to electrode R3. In summary, the higher the inhomogeneity of the electric field in the corona stabilization switch, the faster its insulation recovery rate, and the better its repetitive breakdown stability. This may be due to the more effective corona stabilization effect caused by a stronger corona discharge. The effect of corona stabilization can not only improve the insulation recovery performance of the switch, but also effectively enhance the stability of repetitive breakdowns. However, to achieve an excellent corona stabilization effect, it is not  
Figure 8: The influence of tip structure on the repetitive breakdown voltage and its dispersion of the switch (SF\({}_{6}\), 0.1 MPa, gap spacing of 5 mm): (**a**) breakdown voltage; (**b**) voltage dispersion. The last column shows the results of rod electrode R3. necessary to solely rely on constantly reducing the radius of the rod electrode. Excellent repetitive breakdown stability and insulation recovery performance can also be achieved through cleverly designing the electrode structure such as using a needle electrode with multiple locations for concentrated fields.