Study on discharge phenomena of short-air-gap in needle-plate electrode based on fractal theory

Abstract

The process of gas discharge is very complicated and experimental observations indicate that streamers in short gap under non-uniform electric fields always exhibit irregularity and self-similarity, so a dielectric breakdown model, which is the combination of the random fractal method and the traditional streamer theory, can simulate this phenomenon.In this paper, a stochastic model with the growth probability index at any point proportional to the power of the electric field is utilized to quantify the channel tortuosity, and the space charge effect is taken into account as well. The potential distribution is solved by the Poisson's equation which is calculated iteratively by finite difference method; and the box counting method is used to characterize the channel tortuosity and estimate the fractal dimensions of the discharge channels. Based on this, an idea is proposed that the analysis of the experimental results, which in turn provide the appropriate parameters for the model, can better elucidate this phenomenon.The growth probability index can always get from the previous data, but the range of the will change under different experimental condition and there will exist differences in simulation results on fractal dimensions for different , so the limitation of the previous studies is its possible lack of generalizability. In order to define the range of the growth probability index in this model, the bifurcation phenomenon of plasma channels generated by the discharge, affected by HVDC (high-voltage direct current) of short-air-gap in a needle-plate electrode, is captured by ICCD. Before estimating the fractal dimensions of discharge channels, experimental images are saved as a binarized (black and white) image, and the gray-level transformation and boundary identification algorithm will be conducted to remove the apparent thickness of the discharge channel caused by the magnitude of the flowing currents through different branches. Experimental results show that the range of fractal dimensions in the box counting method for the discharge channel is 1.40-1.55. Under the same condition that other factors remain the same but the adjusted growth probability index in this simulation model should accord with the experimental results, all the facts demonstrate that the value of must lie between 0.04 and 0.05.