The effect of the stochasticity of photoionization on 3D streamer simulations

Abstract

Positive streamer discharges require a source of free electrons ahead of them for their growth. In air, these electrons are typically provided by photoionization. Here we investigate how stochastic fluctuations due to the discreteness of ionizing photons affect positive streamers in air. We simulate positive streamers between two planar electrodes with a 3D plasma fluid model, using both a stochastic and a continuum method for photoionization. With stochastic photoionization, fluctuations are visible in the streamer's direction, maximal electric field, velocity, and electron density. The streamers do not branch, and we find good agreement between the averaged stochastic results and the results with continuum photoionization. The streamers stay roughly axisymmetric, and we show that results obtained with an axisymmetric model indeed agree well with the 3D results. However, we find that positive streamers are sensitive to the amount of photoionization. When the amount of photoionization is doubled, there is even better agreement between the stochastic and continuum results, but with half the amount of photoionization, stochastic fluctuations become more important and streamer branching starts to occur.

Simulation of positive streamers in CO2 and in air: the role of photoionization or other electron sources

“…Having the UV photon source term calculated, we evaluate the integral in equation ( 6) by using a set of Helmholtz differential equations [33,34] with Bourdon's three-term parameters [33]. Besides to the original papers, the reader is referred to [35] and the appendix of [36] for more details.…”

“…Conversely, this location depends logarithmically on the seed density. However, it should be noted that the morphology of the discharge can change, when a particle model is used, as discussed in [35].…”

On the Emergence Mechanism of Carrot Sprites

“…Our 3-D model is implemented in Afivo-streamer code (Bagheri & Teunissen, 2019;Teunissen & Ebert, 2017), which is based on the Afivo framework (Teunissen & Ebert, 2018). This framework includes geometric multigrid methods to solve Poisson's equation, octree-based adaptative mesh refinement, and OpenMP parallelism.…”

Adaptive Strategies to Fast Multipole Method in Photoionization Calculations

“…A coarser grid was introduced in [31,40] to compute the integral and then the interpolation was taken to get the photoionization rate on the original grid, which could be regarded as picking y j on a coarser grid. The stochastic version of (1) in [20,41] can also be viewed as picking up y j by a prescribed distribution.…”

“…In air or other oxygen-nitrogen mixtures, the free electrons are provided by photoionization [15,16], which makes the photoionization significant in the propagation of positive streamers. Moreover, the photoionization has an impact on streamers in their velocities [17,18] and branching behaviors [19,20,21].…”