Inception voltage of positive streamer and its length on PMMA in air

A positive surface discharge on a solid insulator in air consists of many branched streamers. The length of the streamers is controlled by the applied voltage at the instant when the streamers occur. The relationship between the inception voltage and the streamer length depends on the thickness of the solid insulator and the number of streamer branches. At a low voltage, the length of a streamer decreases with increasing the thickness of the insulator, but at a high voltage, it increases with thickness. The length of a streamer with a large number of branches is shorter than that with a few branches. This phenomenon can be explained as follows: the electrons generated in each branch flow into a positive high-potential electrode through the stem of the streamer, and the potential drop in the stem is enhanced due to this electron flow