Effect of Curvature Radius on Distribution Characteristics of Streamer Discharge Channels Based on Fractal Theory

In gas discharge, the phenomenon of discharge channel bifurcation is often observed. To further understand the characteristics of channel bifurcation, this article establishes a fractal medium breakdown simulation model for the air gap of the needle plate based on fractal theory. The spatial potential is solved using the finite element method (FEM), revealing the overall morphological changes of the channel and the distribution of the electric field during discharge. Additionally, the impact of changes in the curvature radius of the needle electrode on the discharge channel distribution characteristics is analyzed and verified through experiments. The results indicate that the formation of channel branches weakens the peak electric field, and this effect diminishes as the channel branching distance increases. When the radius of curvature of the tip ranges from 50 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$200~\mu $ </tex-math></inline-formula>m, a larger radius results in a lower electric field in the channel, a wider distribution of channel branches, an increased number of branches, and a higher fractal dimension. Conversely, when the radius of curvature of the tip ranges from 200 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$500~\mu $ </tex-math></inline-formula>m, a larger radius leads to an opposite trend in the discharge channel behavior, with a decreased fractal dimension.