## 3 Results and Discussion
### Effect of Nozzle on Arc Characteristic Parameters  
In this paper, the data were processed frame by frame. First, the image was transformed into a gray format, and 150,000 pictures of storage time (5 s) were superimposed. Then, the data collected from the three repeated experiments under each condition were averaged, and finally, the arc length images under each condition (Figure 7) were obtained. It can be seen from the figure that the arc outside the nozzle exit was conical convergence and backward extension after adding the extension tube, while the plasma torch expanded first and then converged at the nozzle exit without the extension tube. This phenomenon was caused by the annular convergence channel that formed between the discharge cone at the nozzle exit and the grounding nozzle (in the case without the extension tube), and the air flow at different angular positions impacted on the central axis and collided with each other. The turbulence of flow at the nozzle outlet was severe, resulting in a pressure drop gradient along the radial direction from the center, resulting in a larger radial velocity of air flow, which made the arc bend outward. Finally, the plasma torch appeared to expand after leaving the nozzle outlet. The effect of the extension tube on arc length is shown in Figure 8. On the whole, with the increase in the discharge cone diameter, the discharge gap decreases, and the arc length basically remains unchanged. When the discharge gap is less than the critical value, the arc length will be greatly reduced. For the discharge structure in this paper, the critical value was between 2.5 mm and 3.0 mm. The results showed that the average arc length without the extension tube was 10 mm longer than that with the extension tube. However, it should be considered that the arc length described in this paper was the arc length outside the nozzle. Considering that the arc will undergo a 100 mm extension tube when the nozzle is lengthened, it can be concluded that the length of the rotating gliding arc in the direction of the airflow can be effectively extended by lengthening the nozzle. It should be noted that the arc extension is only unilateral. Generally, the arc shape is \"C\". The arc is divided by the farthest point to which the arc extends. The side connected with the high voltage electrode is called the high voltage side, and the side connected to the ground terminal is called the low voltage side. For the discharge with the extended tube in this paper, the arc extension was mainly attributed to the  
Figure 6: Contrast of arc growth process with or without extension tube. Figure 7: Comparison of arc profiles with different discharge cones. extension of the high voltage side. As the nozzle was a metal conductor, the extension tube acted as the grounding electrode, and the arc root of the low voltage side was directly connected with the end of the extension tube. From Figure 6, it can be seen that the brightness at the root of the low voltage side was enhanced and recorded as the cathode discharge point. At this time, the arc shape was similar to the slender \"L\" shape. When the discharge gap is less than the critical value, the breakdown voltage will decrease dramatically. After the air gap breakdown at the smallest gap between the discharge cone and grounding nozzle, under the action of the axial flow, the high voltage side extends backward, and the cathode discharge point moves downstream along the inner wall of the extension tube. When the arc is extended to the point where the required voltage to maintain the arc exceeds the breakdown voltage, the gliding arc will be extinguished and re-breakdown will occur at the minimum gap. In this case, the cathode discharge point has not yet moved to the end of the extension tube, and the high voltage side of the gliding arc has not been fully extended, which ultimately leads to a sharp reduction in the length of the plasma torch outside the nozzle.