Carolynne-Sireeh Montijn

The multiscale nature of streamers

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 and we review different branching concepts and outline a hierarchy of model reductions.

An adaptive grid refinement strategy for the simulation of negative streamers

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.

Diffusion correction to the Raether?Meek criterion for the avalanche-to-streamer transition

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 homogeneous field.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.

Numerical convergence of the branching time of negative streamers.

Discharge streamers in experiments branch frequently. Arrayás [Phys. Rev. Lett. 88, 174502 (2002)] presented simulations of branching streamers and interpreted them as physical branching events. The numerical results were criticized by Kulikovsky [Phys. Rev. Lett. 89, 229401 (2002)]. Using an adaptive grid algorithm, we here present numerical experiments on the effect of grid resolution on streamer branching. The convergence of branching time with stepwise finer grid sizes provides a quantitative correction on the earlier, low-resolution results in overvolted gaps. Furthermore, streamers can branch even in undervolted, but sufficiently long gaps, but fewer branching modes are accessible than in higher fields.