Fractal Analysis of Positive Pulsed Streamer Patterns in Supercritical Carbon Dioxide

A positive pulsed prebreakdown in a needle-to-plane gap at CO
₂
phases up to supercritical (SC) condition was observed by means of Schlieren imaging method. Our observations confirmed that the pattern of positive prebreakdown discharge was a treelike streamer independent of medium phase and that the SC phase led to streamer branches of higher complexity than those in the gas and liquid phases. Both streamer branches' complexity and fractal dimension variation of the developing streamer were quantitatively assessed by means of fractal analysis. Experimental results are summarized as follows: 1) SC carbon dioxide (SCCO
₂
) led to the greatest complexity of streamer branching in comparison with gas and liquid phases; 2) the fractal dimensions of gas, liquid, and SC phases of CO
₂
were estimated to around D = 1.47, 1.60, and 1.73 with a coefficient of determination R
²
>; 0.99; and 3) the fractal dimension D in SCCO
₂
stayed constant at around D = 1.7 during the streamer growth phase.