Underlying mechanism of the stagnation of positive streamers

Several publications have shown that it is challenging to model the stagnation of positive streamers. They find that as the streamers propagate, the space charge region at the streamer tip reduces in size and that the associated electric field increases towards infinity. In a recent study on streamer propagation in unsteady airflow, we circumvented this problem by relaxing the local density and electric field approximation in the drift-diffusion model, commonly used in the past models. The results, recently published, show that the electric field remains bounded during the streamer propagation. In the present paper, we explore the process of stagnation further with a more rigorous approach. We confirm that the instability in the electric field is an immediate effect of the local density and field approximation and that an extended description of ionization stabilizes the electric field and leads to a decelerating streamer. Finally, we discuss the role of positive ions in the stagnation and we show that the stagnating streamer velocity decreases till it becomes comparable to the ion velocities in the streamer head. This causes a broadening of the streamer head which leads to a sharp decrease in the streamer tip electric field and the streamer stagnation.