Zdenek Bonaventura

Derivation of a merging condition for two interacting streamers in air

The simulation of the interaction of two simultaneously propagating air streamers of the same polarity is presented. A parametric study has been carried out using an accurate numerical method which ensures a time-space error control of the solution. For initial separation of both streamers smaller or comparable to the longest characteristic absorption length of photoionization in air, we have found that the streamers tend to merge at the moment when the ratio between their characteristic width and their mutual distance reaches a value of about 0.35 for positive streamers, and 0.4 for negative ones. Moreover it is demonstrated that these ratios are practically independent of the applied electric field, the initial seed configuration, and the pressure.

Sub-nanosecond delays of light emitted by streamer in atmospheric pressure air: Analysis of N2(C3Πu) and N2+(B2Σu+) emissions and fundamental streamer structure

Theoretical analysis of ultra-short phenomena occurring during the positive streamer propagation in atmospheric pressure air is presented. Motivated by experimental results obtained with tens-of-picoseconds and tens-of-microns precision, it is shown that when the streamer head passes a spatial coordinate, emission maxima from N2 and N2+ radiative states follow with different delays. These different delays are caused by differences in the dynamics of populating the radiative states, due to different excitation and quenching rates. Associating the position of the streamer head with the maximum value of the self-enhanced electric field, a delay of 160 ps was experimentally found for the peak emission of the first negative system of N2+. A delay dilatation was observed experimentally on early-stage streamers and the general mechanism of this phenomenon is clarified theoretically. In the case of the second positive system of N2, the delay can reach as much as 400 ps. In contrast to the highly nonlinear behavio...

A numerical strategy to discretize and solve the Poisson equation on dynamically adapted multiresolution grids for time-dependent streamer discharge simulations

We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used to solve hyperbolic and parabolic time-dependent PDEs. Such an approach guarantees a numerical solution of the Poisson equation within a user-defined accuracy tolerance. Most adaptive meshing approaches in the literature solve elliptic PDEs level-wise and hence at uniform resolution throughout the set of adapted grids. Here we introduce a numerical procedure to represent the elliptic operators on the adapted grid, strongly coupling inter-grid relations that guarantee the conservation and accuracy properties of multiresolution finite volume schemes. The discrete Poisson equation is solved at once over the entire computational domain as a completely separate process. The accuracy and numerical performance of the method are assessed in the context of streamer discharge simulations.