This paper contains the foundation for a new Particle-In-Cell model for gas discharges, based on Îto diffusion and Kinetic Monte Carlo (KMC). In the new model the electrons are described with a microscopic drift-diffusion model rather than a macroscopic one. We discuss the connection of the Îto-KMC model to the equations of fluctuating hydrodynamics and the advection-diffusion-reaction equation which is conventionally used for simulating streamer discharges. The new model is coupled to a particle description of photoionization, providing a non-kinetic all-particle method with several attractive properties, such as: 1) Taking the same input as a fluid model, e.g. mobility coefficients, diffusion coefficients, and reaction rates. 2) Guaranteed non-negative densities. 3) Intrinsic support for reactive and diffusive fluctuations. 4) Exceptional stability properties. The model is implemented as a particle-mesh model on cutcell grids with Cartesian adaptive mesh refinement. Positive streamer discharges in atmospheric air are considered as the primary application example, and we demonstrate that we can self-consistently simulate large discharge trees.
We study positive streamers in air propagating along polycarbonate dielectric plates with and without small-scale surface profiles. The streamer development was documented using light-sensitive high-speed cameras and a photo-multiplier tube, and the experimental results were compared with 2D fluid streamer simulations. Two profiles were tested, one with 0.5 mm deep semi-circular corrugations and one with 0.5 mm deep rectangular corrugations. A non-profiled surface was used as a reference. Both experiments and simulations show that the surface profiles lead to significantly slower surface streamers, and also reduce their length. The rectangular-cut profile obstructs the surface streamer more than the semi-circular profile. We find quantitative agreement between simulations and experiments. For the surface with rectangular grooves, the simulations also reveal a complex propagation mechanism where new positive streamers re-ignite inside the surface profile corrugations. The results are of importance for technological applications involving streamers and solid dielectrics.
We investigate the propagation of positive streamers along a profiled dielectric surface in air at atmospheric pressure. Results from experiments and two-dimensional planar low-temperature plasma fluid simulations are presented and analysed. The test object consists of a disk-shaped high voltage electrode and a dielectric slab with 0.5 mm deep corrugations. The corrugated surface has a 47% larger surface area than the smooth reference surface. The experiments and simulations are performed at voltage levels that lead to either gap-bridging or arrested streamers. In both experiments and simulations, the streamers take a longer time to reach the ground electrode when propagating along the profiled surface than along the smooth reference surface. Also, arrested streamers stop closer to the high voltage electrode when a profiled surface is used. Streamers propagate closely along the surface profile in the simulations, which suggests that the observed surface profile effect is mainly a result of elongated streamer channels. Compared to the streamers propagating along the smooth surface, the elongated streamers on the profiled surface have less residual voltage at the streamer front to drive the streamer advancement.
A compact numerical method for simulating ultrafast pulse interaction with inhomogeneously broadened multi-level media is reported. We use a low-dispersion pseudospectral scheme with fourth order time stepping for Maxwell's equations, and a weakly coupled operator splitting method for the Bloch equations where inhomogeneous broadening and relaxations are also taken into account. The underlying physics is briefly discussed with emphasis on the formalism used.
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