Electron density fluctuations accelerate the branching of positive streamer discharges in air

Abstract

Branching is an essential element of streamer discharge dynamics. We review the current state of theoretical understanding and recall that branching requires a finite perturbation. We argue that, in current laboratory experiments in ambient or artificial air, these perturbations can only be inherited from the initial state, or they can be due to intrinsic electron-density fluctuations owing to the discreteness of electrons. We incorporate these electron-density fluctuations into fully three-dimensional simulations of a positive streamer in air at standard temperature and pressure. We derive a quantitative estimate for the ratio of branching length to streamer diameter that agrees within a factor of 2 with experimental measurements. As branching without this noise would occur considerably later, if at all, we conclude that the intrinsic stochastic particle noise triggers branching of positive streamers in air at atmospheric pressure.

Radio Frequency Electromagnetic Radiation From Streamer Collisions

“…Typically, the radiation diameter (as measured in experiments) is around half of the electrodynamic diameter so in our simulations it is around 5 mm. This is somewhat larger than the diameters shown by Kochkin et al (2014), probably due to the streamer branching present in experiments which is absent in our deterministic simulations (the role of random fluctuations in branching processes was discussed by Luque and Ebert, 2011). As the two streamers get closer they also become wider, presumably because they experience an electric field enhanced by the opposite streamer.…”

Growing discharge trees with self-consistent charge transport: the collective dynamics of streamers

“…On the one hand, we are now reaching a very detailed knowledge of their microphysics; this includes models of electron energy distributions [5], and of transport coefficients and cross-sections of the main reactions, at least for air and other common gas compositions. This knowledge translates into sophisticated and reasonably accurate models of single streamers [6][7][8][9][10][11], the initiation of the streamer branching [5,[11][12][13], the merging of two nearby streamers [14,15] and the influence of surrounding mesoscopic inhomogeneities [16,17]. On the other hand, we barely understand most macroscopic processes in a fully developed corona or streamer tree involving hundreds or thousands of mutually interacting plasma filaments.…”

“…Therefore the growth at least of positive streamers can be modeled as the growth of a conducting channel at its tip only. While streamer propagation has a long history of experimental and theoretical investigations, streamer branching and streamer interaction are now being investigated as well by experiments [45,[51][52][53] and theory [12,13,54]. Leader dynamics, though investigated in less detail up to now, is believed to evolve in a similar manner through field enhancement at the channel tip-however, its conductivity is maintained over longer times by Ohmic heating and its trajectory is paved by a streamer corona.…”

“…For branching of the channel tip, an appropriate distribution as a function of the head parameters has to be found. For positive streamers in air, both experimental [45,[51][52][53] and theoretical [12] studies have been presented; they constitute the start of quantitative investigations.…”

On the spatial scale of streamers

“…In particular, the branching of streamers in the presence of only the electron drift mechanism in a two-dimensional cylindrically-symmetric system was demonstrated by [3], whose work was expanded by [4] with inclusion of diffusion and photoionization mechanisms. Currently, there are also other extensive three-dimensional streamer branching modeling efforts [5].…”