## 1 Introduction  
Positive leader discharge of a long spark generally originates from an energized anode. Before the spark bridges the cathode, four main processes occur: initial corona formation, streamer-to-leader transition, leader development, and the final jump [1, 2, 3]. In general, as the voltage applied to the gap increases, the leader propagates forward continuously, with minute changes in current and velocity, until the gap is broken down. However, the leader often demonstrates noticeable discontinuous development with a relatively long front time of the applied voltage or at a high ambient humidity, and the leader channel brightens and elongates abruptly with a powerful glaring corona streamer burst at its tip [4, 5], associated with a sharp current pulse. This phenomenon is often referred to as restrike or re-illumination [3, 6]. Discontinuous development of the positive leader occurs both in the discharge process of natural lightning and in long-air-gap discharges under laboratory conditions [7, 8]. Although long-air-gap discharges have been studied for a number of years, few researchers have focused on restrike, with its physical mechanisms difficult to explain. In the field of electrical engineering, an air gap is usually used as the main external insulation method for UHV transmission and transformation systems, and the front time of switching overvoltage generated during operation can reach more than 1 ms [9]. When overvoltage accumulates, the flashover of air gaps with a gap distance of several meters is often accompanied by restrike, which, in turn, affects the flashover characteristics of air gaps in UHV transmission and transformation systems [10; 11]. It is therefore of significant value in engineering research to clarify the physical process and mechanism of positive restrike in a long-air-gap discharge or to improve existing positive leader development models and refine the design of external insulation in ultra-high-voltage transmission projects. Since the 1970s, scholars around the world have conducted numerous theoretical or experimental studies on positive leader restrike. The Les Renardieres Group team in France found that the probability of restrike occurring during discharge significantly increased as the humidity exceeded 8-10 g/m\({}^{3}\) in a laboratory environment [3]. A restrike phenomenon often occurs with sudden elongation of the leading channel, a sudden increase in the discharge current, and sudden enhancement of channel luminescence. [PERSON] and [PERSON] classified the restrike phenomenon into two types, \"bell shaped\" and \"steep rise\", based on the similarity between the channel discharge current waveform and the channel emission pulse that takes place when restrike occurs [12; 13]. In 1986 [14], the Les Renardieres Group used a schlieren system and conducted a \"simulated\" experimental study on the restrike phenomenon by applying positive and negative switching-impulse voltages of opposite polarity to a 6 m rod-plate air gap at different time points. Dissipation and activation of the leader channel during discharge relaxation were observed, and the experimental results indicated that there was no luminescence in the leader channel during the discharge relaxation stage. Furthermore, during the discharge relaxation stage, the original channel was reactivated as the electrode applied a negative voltage impulse. This phenomenon is very similar to the restrike observed in long-air-gap discharge; as a result, this experiment was also referred to as \"artificial restrike\" by the authors of Ref. [15]. In Ref. [15], [PERSON] et al. observed restrike by applying a positive impulse to a 16.7 m rod-plate air gap; they found that the discharge current always disappeared for a certain period of time before the discharge activity resumed. This finding is consistent with the observation results of the \"steep\"-type restrike phenomenon [3]. In a similar vein, [PERSON] et al.