Fractal analysis of positive streamer branching produced with field ionization in gaseous, liquid, and supercritical CO 2

Field ionization is adopted as a streamer initiation mechanism in highly pressurized CO 2 , using a 3D particle model. The field ionization is implemented into the 3D model through Zener’s model. Streamer evolution is classified into three stages; inception cloud formation, main streamer channels, and subsequent streamer branching independent of the medium state. The comparison of average electron density, electric field, and the length of streamer in three thermodynamic states of CO 2 is presented. Box counting method is used to calculate the fractal value (D) for positive streamer pattern in gaseous, liquid, and supercritical (SC) CO 2 . The figures of streamer discharge obtained from the 3D simulation model are fractal with fractal dimension for gaseous, liquid phase, and SC- CO 2 as 1.577, 1.578, and 1.587. The results of fractal analysis of positive streamer branching in this paper are consistent with the fractal values of streamer in the SC-CO 2 through experiments in literature.