## 1 Introduction  
Partial discharge (PD) is one of the main factors affecting the stable operation of high-voltage electrical equipment, and surface discharge is a common type of PD. In high-voltage electrical equipment, when the surface of the insulator is discharged, a streamer develops along the surface of the insulator, which may eventually cause flashover on the surface of the insulator. Therefore, it is of great significance to study the mechanism and influencing factors of surface discharge. In the process of partial discharge, acoustic, optical, electrical, and thermal signals are often generated [1]. With advantages such as anti-electromagnetic interference, anti-mechanical vibration, and the high sensitivity and fast response of optical detection [2], partial-discharge-detection technology based on optical signals is an important research direction in the field of partial discharge in the future. Currently, SF\({}_{6}\) is a widely used insulating gas in high-voltage electrical equipment, but SF\({}_{6}\) has a strong ability to absorb infrared radiation, and its global warming potential (GWP) is 23,900 times that of CO\({}_{2}\)[3, 4], so it cannot meet the requirements of environmentally friendly power system development. Therefore, the search for an alternative to SF\({}_{6}\) gas has become a research hotspot in recent years. At present, alternative gases have been found, including SF\({}_{6}\)/N\({}_{2}\), SF\({}_{6}\)/CO\({}_{2}\) and other sulfur hexafluoride mixture gases [5, 6], as well as C\({}_{4}\)F\({}_{7}\)N, C\({}_{5}\)F\({}_{10}\)O, and other new insulation gases. Studies have demonstrated that the insulation strength of C\({}_{4}\)F\({}_{7}\)N is about twice that of pure SF\({}_{6}\). It is colorless, tasteless, and chemically stable at 700 \({}^{\circ}\)C, with liquefaction temperature at a standard atmospheric pressure of \(-\)4.7 \({}^{\circ}\)C and a GWP of only 2400 [7, 8]. However, it also has some problems as an insulating medium, such as a high price and high toxicity. At present, these problems are mainly solved by mixing C\({}_{4}\)F\({}_{7}\)N with CO\({}_{2}\)N\({}_{2}\), as well as other gases with lower liquefaction temperatures. In recent years, domestic and foreign scholars have carried out a lot of research on the insulation performance of C\({}_{4}\)F\({}_{7}\)N and gases mixed with it, which mainly focuses on the saturation vapor pressure of C\({}_{4}\)F\({}_{7}\)N [9], critical breakdown field strength, effective ionization coefficient [10], and the comparison of dielectric strength with SF\({}_{6}\)[11], but few people study the surface discharge mechanism and variation law of C\({}_{4}\)F\({}_{7}\)N and its mixture. The theory of streamer discharge was first proposed by [PERSON] [12], who believed that the separation of positive and negative charges in a streamer would shield the external electric field and cause a sharp enhancement of the electric field in a limited area outside the streamer head. The initial electrons needed for the streamer to move forward usually come from the photoionization of the streamer head, and whether the streamer can reach the cathode depends on the strength of the applied electric field. From the perspective of surface discharge, the authors of [13] carried out a simulation study on the surface discharge process in a SF\({}_{6}\)/N\({}_{2}\) mixture and compared the influence of the dielectric constant of insulators on the surface charge density of insulators. In [14], air-gap discharge and surface discharge in the air were compared, and the processes of charge generation, electric field variation, and charge accumulation in surface discharge were studied. The surface charge characteristics of surface discharge were investigated in [15]. At present, there are limited studies on the mechanism and variation law of the discharge along the surface of C\({}_{4}\)F\({}_{7}\)N and the mixture with it. Table 1 shows the comparison between the existing research and this research.