Spatially hybrid computations for streamer discharges : II. Fully 3D simulations

Abstract

We recently have presented first physical predictions of a spatially hybrid model that follows the evolution of a negative streamer discharge in full three spatial dimensions; our spatially hybrid model couples a particle model in the high field region ahead of the streamer with a fluid model in the streamer interior where electron densities are high and fields are low. Therefore the model is computationally efficient, while it also follows the dynamics of single electrons including their possible run-away. Here we describe the technical details of our computations, and present the next step in a systematic development of the simulation code. First, new sets of transport coefficients and reaction rates are obtained from particle swarm simulations in air, nitrogen, oxygen and argon. These coefficients are implemented in an extended fluid model to make the fluid approximation as consistent as possible with the particle model, and to avoid discontinuities at the interface between fluid and particle regions. Then two splitting methods are introduced and compared for the location and motion of the fluid-particle-interface in three spatial dimensions. Finally, we present first results of the 3D spatially hybrid model for a negative streamer in air.

High-order fluid model for streamer discharges: I. Derivation of model and transport data

“…Furthermore, scattering is assumed to be isotropic. This can be problematic for high values of E/n 0 (generally for E/n 0 ≥ 1000 Td for electrons in N 2 ) when electrons scatter predominantly in the forward direction [24,70]. However, the errors in the calculated transport coefficients and rate coefficients are acceptable in fluid modeling for streamers in the range of the reduced electric fields E/n 0 considered in this work after appropriate renormalization of cross-sections for the scattering angle distribution [24].…”

“…The parametric dependence of the source term is open at this point; within the classical model the source term is assumed to depend on local particle densities and on the local electric field. The second approximation concerns the electron velocity v. On a time scale much larger than the collision frequency, the electron motion is overdamped, so the electrons must drift against the direction of the electric field according to the second term in (24). The stochastic and undirected motion is modeled in an ad hoc manner through the diffusion term; the fact that the diffusion correction is added to the drift term and not included in any other functional manner is not a priori clear and can actually be deduced from the above analysis.…”

High-order fluid model for streamer discharges: II. Numerical solution and investigation of planar fronts

“…The origin of, and the difference between bulk and flux transport coefficients in the context of streamer studies have been recently discussed in [19,20,47]. In this section, we consider the implications of the transport coefficient duality in the context of our high-order fluid model for streamers.…”

“…However, a full particle model long has been computationally too demanding or too inaccurate due to the used super-particle techniques, and even now the parameter range of simulations is limited. For recent progress in particle and hybrid models we refer to [18][19][20][21][22]. Due to the computational costs and limitations of particle models, up to now mainly fluid approximations have been used to model the structure and evolution of streamer discharges in two or three spatial dimensions.…”

“…We use a PIC/MC method as an alternative technique to verify our high-order fluid model. Following the recent work of Li et al [18][19][20], in section 3 we give a brief description of this method with particular emphasis on the construction of planar fronts in the particle model. The high-order fluid model is then applied in section 4 where examples of planar fronts in pure nitrogen are presented.…”