Study of the electric field in a diffuse nanosecond positive ionization wave generated in a pin-to-plane geometry in atmospheric pressure air

The dynamics of a nanosecond positive ionization front generated in a pin-to-plane geometry in atmospheric pressure air is simulated using a 2D axisymmetric drift-diffusion fluid model. For a 16 mm gap and a sharp pin electrode, the plateau of the applied voltage is varied between 40 and 60 kV and the rise time is varied between 0.5 and 1.5 ns or a DC voltage is applied. The discharge ignition time and the voltage at ignition are shown to depend mostly on the voltage rise time. The connection time, i.e. the time for the ionization wave to ignite, propagate and connect to the plane is shown to strongly depend on both the values of the voltage plateau and rise time. For all cases, the discharge has a conical shape with a maximal radius of about 8 mm as it connects to the grounded plane. The average propagation velocity of the ionization front is found to vary in the range 3.1 to 8.5 mm ns-1. These values are in rather good agreement with experiments. Temporal evolutions of the electric field are recorded on the symmetry axis at different positions in the gap. At each location, an increase and decrease of the electric field is observed as the ionization front, propagating from the pin to the plane, passes the studied point, in accordance with experimental observations. Finally, for a voltage plateau of 55 kV and a rise time of 0.5 ns, a temporal sampling of 100 ps is shown to be sufficient to capture the dynamics of the electric field during the ionization front propagation when it passes close to the middle of the gap. Conversely, a temporal sampling of 10 ps is required when the ionization wave is close to both electrodes, or during the fast redistribution of the electric field after the connection of the ionization front at the cathode.