Fractal characteristics of simulated electrical discharges

Abstract

A two dimensional stochastic dielectric breakdown model was utilized to study the fractal properties of simulated lightning discharges and surface discharges. The fractal dimension of the simulated growth patterns varied depending on the cell configuration chosen for the breakdown. The inclusion of the cells in the diagonals with reference to the growth site produced less branched trees with smaller fractal dimensions. The production of branches in the electrical tree growth depends highly on 'η', which is the exponent of the breakdown probability distribution. For small η values, highly complex tree patterns with many branches were observed. By controlling the value of η, growth patterns similar to the experimental observations could be produced. The average fractal dimension estimated through the Correlation Function method when η=1 for simulated lightning discharges and surface discharges were 1.56±0.01 and 1.68±0.01 respectively. When η>4 the growth patterns effectively lose their fractal structure and became a curve with dimension 1.