## 2 Experimental Set-Up and Conditions  
The experimental set-up for the synchronous observation of long-air-gap discharge performed in this study is presented in Figure 1. In order to generate a restrike during the discharge process, it is necessary to apply a voltage impulse with a long front time to the air gap. Therefore, by precisely calculating the resistance and capacitance parameters within the synthetic circuit of a Marx generator and implementing optimized selection of wavefront resistors, we achieved reliable generation of a switching impulse voltage with a wavefront of 1 ms, which was then directly delivered to the rod-plate gap with a gap distance of 6 m. The anode terminal was a 10 cm long copper electrode with a hemispherical tip with a 1 cm radius, and the electrode itself was a cylindrical rod with a diameter of 2 cm. The plate electrode was composed of aluminum, with a size of 30 m \(\times\) 30 m, and was effectively grounded. For safety reasons, during the experiment, the voltage and current waveforms, in addition to trigger signals, were all isolated and converted by electrical-to-optical converters (E/O) or optical-to-electrical converters (O/E) during transmission. Among these, the data obtained at high potential were transmitted through optical fibers, whereas those obtained at low potential were transmitted through signal cables. It should be mentioned that the upper end of the rod electrode was a hollow cylinder, in which a transient current acquisition system was installed. The structure and principle of this acquisition system were consistent with those described in Ref. [19]. It could achieve discharge transient current acquisition with a peak current of 600 A, a bandwidth of 0-70 MHz, and a time resolution of up to 2 ns [20], and it could sensitively and accurately reflect the current characteristics during the discharge process. The output voltage impulse of the Marx generator was sent to an oscilloscope of the Tektronix DPO-4104B model (made in Beaverton, Oregon, USA) through a capacitor divider with a voltage division ratio of 1:5358. After capturing the switching-wave voltage pulse, the oscilloscope output a synchronous trigger signal [21], which was then sent to the current acquisition device and the CCD high-speed camera, separately, through an E/O, in order to achieve synchronous acquisition of the discharge voltage, current, and optical morphology of the leader channel during the discharge process. Figure 1: The experimental layout of the synchronous observation platform for long-air-gap discharge. In positive long-gap discharges, the leader channel propagates stably at approximately 1-2 cm/us [1,3,5], with its development time ranging from hundreds of microseconds to milliseconds under varying gap configurations and applied voltages [17,18]. Capturing the optical morphology evolution of the leader channel necessitates a high-speed imaging system equipped with a \(\upmu\)m-scale spatial resolution, a \(\upmu\)s-level temporal resolution, and an ms-range recording capacity, coupled with high-sensitivity photosensitive characteristics. Through systematic evaluation, a Photron FASTCAM SA5 (12-bit CMOS, 20 \(\upmu\)m pixel pitch, made by Photron Limited, Tokyo, Japan) high-speed camera was ultimately selected as the primary imaging device to capture the optical evolution of leader channels during discharge, which could operate at 1,000,000 fps with 1 \(\upmu\)s exposure to resolve discharge transients. With an ISO sensitivity of 25,000 and 32 GB of onboard memory, this set-up enabled 1.5 s continuous capture of leader propagation dynamics, satisfying \(\upmu\)s-scale temporal resolution requirements for leader channel characterization.