Positive streamer in gases: Physical approach from low to high energies

Approach to the breakdown theory in gases based on an energy basis has been presented. The minimum stressed volume zone (MSVZ) has been used as a concept to deal with the positive streamer process in gases. These processes start at low energy values under critical electric field (Ecr) of 4.5 kV/cm. In this MSVZ, several filament streamers spread within it with a minimum streamer filament radius (MSFR) 30μm (nearly about 400 filaments). Under Ecr, an associative detachment mechanism in these filaments starts. This detachment of electrons has occurred between O2− and O2 which leading to increase the number of electrons inside the filaments. Also, the temperature increases inside the filaments due to the exothermic reaction of O− and N2. Furthermore, increases of the temperature occurred due to the collision inside these filaments. Consequently, the filament radius enlarges too within MSVZ with a value of 120μm. This will cover the entire MSVZ with 25 filaments instead of 400 which has been considered as a new breakdown index in gases (n). Therefore, a new breakdown equation has been introduced relating energy, temperature, electric field, streamer velocity, and streamer radius with index n. At low energy level, the streamer radius changes with the stressed electrode diameter, applied field and temperature changes inside the filament till it reaches nearly 7500K. However, under high energy level when the ionized species inside filaments increase, a main ionized streamer path (leader) emanates from the MSVZ toward the opposite electrode. The increased ionized species convert the medium inside this leader streamer stem to plasma state with high temperature ≅20000K. Under arc condition, the leader streamer radius nearly becomes constant at 120μm near stressed electrode and the minimum streamer velocity at Ecr reaches a value of 105m/s and n×105m/s for higher electric fields. In addition, the calculated minimum length of initiating streamer (l0) given to be nearly 30μm which is equal to its radius. The streamer starts to branch when the calculated field (E) at its head is sufficient to supply energy eight times of Ecr value.