## 3 Results and Discussion
### Effect of Nozzle on Arc Characteristic Parameters
The air gap breakdown-arc stretching-arc extinction is defined as a period, and the corresponding frequency is recorded as the frequency of the arc regeneration. The variation trend is similar to that of arc length. When the size of discharge cone is larger than a certain value, the frequency begins to decrease sharply. This can be seen from Figure 9 where the frequency of the arc regeneration without the extension tube was nearly four times as high as that with the extension tube. When the No. 6 discharge cone was used in assembling the extension tube, the regeneration frequency of the extension tube was recorded as 0 because the arc could not extend beyond the extended tube. Combined with Figure 8, it can be seen that the arc length of the No. 4 discharge cone and No. 5 discharge cone was the same, but the regeneration frequency was different. The regeneration frequency was more sensitive to the discharge spacing when the discharge cone became thicker and the gap spacing decreased, and the change trend obviously changed in advance. The possible reason is that as the gap becomes smaller, the equivalent resistance of the gap becomes smaller, and the breakdown of the gap becomes easier. In addition, once the air gap breaks down, the discharge current is much larger than that of the small discharge cone, which leads to a larger arc stiffness and a longer time-consuming process of arc stretching and deformation. Finally, although the arc length remains unchanged, the arc stretching period prolongs, that is, the regeneration frequency decreases. For the circumferential rotation of the arc taken from the front, the case of the No. 5 discharge cone was used as an example. As shown in Figure 10, the arc rotated uniformly along the circumference when the extension tube was installed. From the perspective of the orthographic projection plane, the arc shape was basically along the radial direction, and the bending direction in the middle of the arc was the tangential direction of the air swirl. As the arc extended out of the extension tube, its cathode discharge point was located at the end of the extension tube. Therefore, in Figure 11, thick and bright spots appeared at the cathode discharge points. In the case of no extension tube, the position of the  
Figure 8: Effect of discharge cone size on arc length. cathode discharge point was basically unchanged in a rotating period, and the arc bent sharply under the action of the rotating airflow. Combined with the analysis of the arc axial tension in Figure 4 above, it can also be seen that the arc was prone to short circuit regeneration, corresponding to 1.07 ms, 2.13 ms, and 3.2 ms in Figure 10, respectively. When the rotating gliding arc was applied to fuel pyrolysis, the discharge advantage with the extended tube was more obvious. On the one hand, due to the long arc stretching, the area of fuel treated by plasma will be greatly increased; on the other hand, because of the stable circumferential rotation of the arc, the pyrolysis fuel will be more uniform and stable. Figure 11: Distribution uniformity of the rotating gliding arc under different experimental conditions. Figure 10: Comparison of the development and evolution of the gliding arc circumferential rotation. Figure 9: The influence of the discharge cone size on the regeneration frequency. Figure 11 visualizes the distribution of the rotating gliding arcs. Short-time Fourier transform was performed on the same pixel in all photos in each experimental condition to obtain the corresponding intensity value of the rotating principal frequency of each pixel, and finally the rotating gliding arc distribution cloud map was produced. The legend on the right side of Figure 11 shows the gray value, which represents the strength of the gliding arc. It can be seen from the figure that the distribution of the cathode discharge points was extremely non-uniform in the circumferential direction without the extension tube. When the No.