Conditions for inception and propagation of negative streamers

Negative streamers play an important part in propagation of a negative stepped leader. They are emitted from the tip of a space stem or, as a streamer burst, from the tip of the space leader right after its attachment to the main leader.

In the laboratory conditions, it was shown that negative streamers need a significantly higher voltage for inception than positive streamers [e.g., Briels et al, 2008, doi:10.1088/0022-3727/41/23/234004]. The higher negative threshold is in agreement with the higher field measured inside streamer channels, namely 13±2 kV/cm for negative streamers versus 5 kV/cm for positive streamers.

We obtain the conditions for propagation of negative streamers using the Streamer Parameter Model (SPM) [Lehtinen, 2021, doi:10.1007/s11141-021-10108-5]. In this model, we calculate various streamer parameters from relationships between them, with the assumption of maximization of streamer velocity. This model, in the positive streamer case, was shown to agree well with both experimental measurements and hydrodynamic simulation results [Lehtinen and Marskar, 2021, doi:10.3390/atmos12121664]. In the negative streamer case, we show that the parameter equations have no solution below certain background electric fields. The threshold at which the negative streamer appears is around 12-14 kV/cm for 5-10 cm streamer length, which agrees with the experimental data. We also perform hydrodynamic simulations of negative streamers as another way to calculate the conditions for negative streamer propagation.

There is an important difference from positive streamers, for which the propagation threshold is determined by the rate of free electron removal from the streamer channel (i.e., attachment): namely, we find that the negative streamer threshold field is finite even in the absence of the electron removal.