Fractal analysis of the treeing process from luminous discharge image and measurement of discharge magnitude

The purpose of this study is to analyze the growth of trees generated in PMMA from the apex of a void created by a needle tip. The analysis was based on fractal theory. In the measurement system, PMMA blocks were used with electrodes consisting of a needle and a plate. One cycle of an applied ac voltage was divided into twenty successive phase angle sections, labeled φ1, φ2, ..., φ20, from one negative peak to the next negative peak of the applied voltage. The quantitative evaluation of the fractal dimension D of the luminous discharge pattern was performed for each section, particularly, for the sections φ7, 8, 9, 17, 18 and 19 where the discharge luminescence reached around the tip of the tree. It was noted that some samples revealed substantially different tree patterns even under the same measurement conditions. The reasons for the different trees have been investigated by determining D and attempting to correlate tree growth and the change of tree length with aging. When D of the discharge luminescence at φ7, 8, 9, 17, 18 and 19 were large, luminescence with complex branches were generated. The present results indicate that tree growth and branching depend on the discharge at φ7, 8, 9,17, 18 and 19