DBD surface streamer expansion described using nonlinear diffusion of the electric potential over the barrier

The plasma sheet in a surface dielectric barrier discharge (SDBD) is formed by transient surface streamers (SSs). In this article, we report on our investigations of SS development using a 1D numerical simulation. The SS dynamics were investigated for negative pulsed SDBDs in Ar at atmospheric pressure in pin-to-plane and strip-on-plane geometries. Reducing the simulations to 1D allowed us to include a much larger set of plasma species (12) and elementary processes (28) than would have been possible in 2D or 3D simulations. It was discovered that stepwise ionization of high energy Ar levels plays a crucial role in sustaining the conductivity of the plasma sheet. The SS propagation velocity, V-SS, is not determined by the fast process of direct ionization at the SS front but rather by the slow process of electric charge deposition onto the barrier. Expansion of the area occupied by surface charge can be described using a diffusion equation. The expansion velocity obeys the parametric dependence VSS similar to delta/epsilon, where delta and epsilon are the thickness and dielectric permittivity of the dielectric barrier. The results of calculations compare well with both our own experiments and published data.