## 5 Conclusions  
In this paper, the effects of crucial parameters of the corona-stabilized switch including electric field inhomogeneity, gas type, operating pressure, and gap spacing on the breakdown voltage and voltage dispersion of repetitive breakdowns were investigated. The main conclusions are as follows:  
1. The electrode with a higher field inhomogeneity results in less voltage dispersion and better stability of the switch during repetitive breakdowns. The voltage dispersion of repetitive breakdowns increases as the electric field becomes more homogeneous, and this pattern is particularly noticeable at low-repetition frequencies. The pure SF\({}_{6}\) and SF\({}_{6}\)-He mixtures had the smallest voltage dispersion and the best breakdown stability. The stability of SF\({}_{6}\) deteriorated after being diluted with air and N\({}_{2}\) and will continue  
Figure 19: Numerical simulation of different needle electrodes wrapped by a stable corona layer. to worsen as the SF\({}_{6}\) content decreases. The dispersion of the breakdown voltage increased as the operating pressure increased. The voltage dispersion changed with the gap spacing in a nonlinear trend. There was an optimal gap spacing to ensure optimal breakdown stability, as a too large or too small gap spacing will lead to poor breakdown stability. 2. The corona-stabilization effect, in general, is the core factor that determines the stability of the switch. The highly inhomogeneous field and the presence of a strong electronegative gas medium can improve the stability of the switch, as these parameters enhance the corona-stabilization effect during repetitive breakdowns. Corona stabilization can not only improve the stability during repetitive breakdowns, but also enhance the insulation recovery performance of the switch. 3. The effect of corona stabilization on insulation recovery is basically monotonic, but its impact on repetitive breakdown stability is relatively complex. For switches with different levels of electric field inhomogeneity, a better corona-stabilization effect leads to better repetitive breakdown stability. In switches with different gas media, the stronger the corona stabilization effect, the better the repetitive breakdown stability. In these two types of switches, the stronger the corona-stabilization effect, the faster the insulation recovery of the switch. However, operating at high pressures can accelerate insulation recovery in the switch, but it may also decrease its stability. For switches with different gap spacings, it is not necessary that the better the corona-stabilization effect, the better the insulation recovery and repetitive breakdown stability. Instead, there exists an optimal distance at which the switch can achieve good breakdown stability and insulation recovery performance. Therefore, considering only the intensity of corona stabilization is insufficient for understanding the underlying mechanism for repetitive breakdown in the switch. The influence of the memory effect caused by residual spatial transport characteristics must be fully considered. This view is supported by the experimental results using different needle electrodes. Conceptualization, L.L. and C.Y. ; Methodology, L.L. ; Software, Y.F. ; Validation, G.X., X.X. and B.W. ; Formal analysis, B.W. ; Investigation, L.L. ; Resources, B.W. ; Data curation, G.X. ; Writing--original draft preparation, L.L. ; Writing--review and editing, Y.F. ; Visualization, C.Y. ; Supervision, B.W. ; Project administration, X.X. ; Funding acquisition, L.L. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Natural Science Foundation of China (Program No. 62201457), the Natural Science Basic Research Program of Shaanxi (Program Nos. 2022 JQ-588 and 2022J-404 & 2023-JC-QN-0490), and the Fundamental Research Funds for the Central Universities, CHD (Program Nos. 300102322102, 300102383203). Not applicable. Data Availability Statement: Data are contained within the article.