The propagation of positive streamers in a weak and uniform background electric field

The results of numerical simulations of a positive streamer development in air in a weak and uniform electric field are presented. Streamer dynamics is considered in an electrode gap of 33 mm in length and the configuration was `protrusion on a plate-plate'. This particular configuration was chosen in order to perform direct comparison between simulated results and experimental data. The electrostatic field in such a system decreases rapidly with increase of the distance from the protrusion (anode) and the region with a weak and uniform background field covers ~30 mm of the gap. The parameters of the propagating streamer are studied at six different values of the background field strength: 0.24; 0.30; 0.345; 0.37; 0.43 and 0.50 MV m^-1. Stable streamer development (with constant velocity) takes place in a field of 0.5 MV m^-1 (the stability field) but the streamer is able to cross the gap in a background field of 0.3 MV m^-1. These values are in excellent agreement with experimental data. During the stable streamer propagation, the electron density and plasma conductivity in the discharge channel and the electric field at its front remain constant. In a background field lower than 0.5 MV m^-1, the discharge front velocity and the electric field at the front decrease linearly with an increase of streamer length. The discharge propagation in the stability field is associated with an increase of electrostatic energy at the streamer front but it decreases if the streamer develops in a weaker electric field. This behaviour is accompanied by a constant Joule dissipation at 0.5 MV m^-1 and decreasing energy losses at the streamer front in a weaker background electric field.