Streamer discharges play a central role in electric breakdown of matter in pulsed electric fields, both in nature and in technology. Reliable and fast computations of the minimal model for negative streamers in simple gases like nitrogen have recently been developed. However, photoionization was not included; it is important in air and poses a major numerical challenge. We here introduce a fast and reliable method to include photoionization into our numerical scheme with adaptice grids, and we discuss its importance for negative streamers. In particular, we identify different propagation regimes where photoionization does or does not play a role. More precisely, when a high voltage pulse is applied to a gap of insulating matter, conducting streamer channels grow through the gap. Streamer propagation is characterized by a strong field enhancement at the channel tip. This field enhancement is created by a thin curved space charge layer around the streamer tip as many computations show. Such computations are quite challenging due to the multiple inherent scales of the process.Recent streamer research largely concentrates on positive streamers in air or other complex gases for industrial applications [2]. This is because positive streamers emerge from needle or wire electrodes at lower voltages than negative ones [1]. Natural discharges such as sprites [3], on the other hand, occur in both polarities [4], in particular, when they are not attached to an electrode and therefore double ended. Photoionization (or alternatively background ionization) is essential for positive streamers: as their tips propagate several orders of magnitude faster than positive ions drift in the local field, a nonlocal photon-mediated ionization reaction is thought to cause the fast propagation of the positive ionization front. Negative streamers, on the other hand, have velocities comparable to the drift velocity of electrons in the local field, therefore a local impact ionization reaction can be sufficient to explain their propagation. This is why photoionization in negative streamers has received much less attention, most recent work concentrating on sprite conditions with relatively low electric fields [5].The nonlocal photoionization reaction depends strongly on gas composition and pressure [6], in particular, it is much more efficient in air than in pure gases. Furthermore, in air its relative importance saturates for pressures well below 60 Torr (≈ 0.1 bar), while it is suppressed like ≈ 60 Torr/p at atmospheric pressure and above. In this paper we study the effects of photoionization on the propagation of negative streamers by means of efficient computations with adaptive grids.Streamer model. Streamer models always contain electron drift and diffusion, space charge effects and the generation of electron ion pairs by essentially local impact ionization. We will use a fluid model in local field approximation as described, e.g., in Refs. [7,8]. A numerical code with adaptive grid refinement was introduced in [8] to investigate negativ...

Streamers are a generic mode of electric breakdown of large gas volumes. They play a role in the initial stages of sparks and lightning, in technical corona reactors and in high altitude sprite discharges above thunderclouds. Streamers are characterized by a self-generated field enhancement at the head of the growing discharge channel. We briefly review recent streamer experiments and sprite observations. Then we sketch our recent work on computations of growing and branching streamers, we discuss concepts and solutions of analytical model reductions, we review different branching concepts and outline a hierarchy of model reductions.

The evolution of negative streamers during electric breakdown of a non-attaching gas can be described by a two-fluid model for electrons and positive ions. It consists of continuity equations for the charged particles including drift, diffusion and reaction in the local electric field, coupled to the Poisson equation for the electric potential. The model generates field enhancement and steep propagating ionization fronts at the tip of growing ionized filaments. An adaptive grid refinement method for the simulation of these structures is presented. It uses finite volume spatial discretizations and explicit time stepping, which allows the decoupling of the grids for the continuity equations from those for the Poisson equation. Standard refinement methods in which the refinement criterion is based on local error monitors fail due to the pulled character of the streamer front that propagates into a linearly unstable state. We present a refinement method which deals with all these features. Tests on one-dimensional streamer fronts as well as on three-dimensional streamers with cylindrical symmetry (hence effectively 2D for numerical purposes) are carried out successfully. Results on fine grids are presented, they show that such an adaptive grid method is needed to capture the streamer characteristics well. This refinement strategy enables us to adequately compute negative streamers in pure gases in the parameter regime where a physical instability appears: branching streamers.

Space-charge dominated streamer discharges can emerge in free space from single electrons. We reinvestigate the Raether-Meek criterion and show that streamer emergence depends not only on ionization and attachment rates and gap length, but also on electron diffusion. Motivated by simulation results, we derive an explicit quantitative criterion for the avalanche-to-streamer transition both for pure non-attaching gases and for air, under the assumption that the avalanche emerges from a single free electron and evolves in a homogenous field.

In sufficiently large gaps and electric fields, discharge streamers do branch. In [Arrayas et al., PRL 88, 174502 (2002)], we observed streamer branching numerically within a deterministic particle density model and explained it as a Laplacian instability of a thin space charge layer. Our numerical results were criticized in [Kulikovsky, PRL 89, 229401 (2002)]. We here present an adaptive grid refinement method for streamer simulations, and we carry out the first conclusive investigation on the effect of the numerical grid on streamer branching in different fields. On stepwise finer grids the branching time converges, hence streamer branching is for the first time predicted quantitatively.Comment: 4 pages, 7 figures, submitted to Phys Rev E, Rapid Com