## 4 Discussion  
### Relationship Between Restrike Current Pulse Peak and Relaxation Time  
In long-air-gap discharges, when the rate of rise in the electric field applied to the HV electrode is lower than the rate of rise in the space charge electric field generated by the ionization in the streamer region near the leader tip, the activity level of the streamer region will significantly weaken or prevent ionization. In addition, when the ambient humidity is relatively high, the ionization efficiency of the streamer region also decreases significantly, due to the strong affinity of water molecules for electrons. In the experiments described herein, a switching pulse with a wavefront of 1 ms was applied to the gap, and the corresponding voltage rise rate was relatively low. Coupled with the relatively high ambient humidity, the frequency of restrike during the discharge process was high. When the streamer region at the leader head gradually weakens until ionization stops, it can no longer continue to inject electrons into the leader channel. In addition, the high-temperature gas molecules in the channel continuously undergo convection with the gas  
Figure 5: High-speed photographs and the corresponding discharge current before and after the fourth (**a**) and seventh (**b**) restrikes when the gap was broken down.  
molecules in the surrounding environment, causing the temperature of the channel to continuously decrease. This process additionally leads to a decrease in or the cessation of thermal dissociation within the channel, resulting in the discharge current of the leader dropping to zero and entering the relaxation stage.  
Statistical analysis of the experimental observation results showed that the luminous phenomenon at the leader head could not be clearly seen on all occasions in the relaxation process. A total of 18 discharges were carried out in this experiment, and the number of restrikes in each discharge varied from one to seven times. In total, about 74 relatively obvious restricle current pulses were generated 18 times during discharge. Based on the photographs of the discharge process taken by the high-speed camera, 34 discharges exhibited luminescence at the head of the leader channel during the relaxation process before the occurrence of restricle. The relationship between the peak values of these 34 restricle current pulses and the duration of the relaxation phase before the occurrence of restricle is shown in Figure 6.  
It can be seen from Figure 6 that, due to the high dispersion of long-gap discharges, when there is luminescence at the head of the leader channel during the relaxation process, there is no obviously linear relationship between the corresponding relaxation time and the peak value of the restricle current pulse that follows immediately. However, when examining the overall trend of change, it can be concluded that as the relaxation time increases, the peak value of the restricle current pulse shows a relatively obvious increasing trend. Under the experimental conditions described in this paper, when the peak value of the current pulse exceeds 5 A and the duration of the relaxation stage is greater than 40-50 us, the frequency of the luminescence occurring at the head of the leader channel before the restricle is relatively high. Based on the corresponding high-speed optical photographs, when the relaxation time is relatively short (<40 us), the luminescence at the head of the leader channel is not obvious. Relatively speaking, when the relaxation time is longer, the luminescence at the head of the channel is more obvious, and the luminous intensity increases significantly with the passage of the relaxation time, with the peak value of the restricle current pulse also being larger.  
Figure 6: The relationship between the relaxation time before restricle and the peak value of the current upon the occurrence of restricle.