We use numerical simulations to study the dynamics of surface discharges, which are common in high-voltage engineering. We simulate positive streamer discharges that propagate towards a dielectric surface, attach to it, and then propagate over the surface. The simulations are performed in air with a two-dimensional plasma fluid model, in which a flat dielectric is placed between two plate electrodes. Electrostatic attraction is the main mechanism that causes streamers to grow towards the dielectric. Due to the net charge in the streamer head, the dielectric gets polarized, and the electric field between the streamer and the dielectric is increased. Compared to streamers in bulk gas, surface streamers have a smaller radius, a higher electric field, a higher electron density, and higher propagation velocity. A higher applied voltage leads to faster inception and faster propagation of the surface discharge. A higher dielectric permittivity leads to more rapid attachment of the streamer to the surface and a thinner surface streamer. Secondary emission coefficients are shown to play a modest role, which is due to relatively strong photoionization in air. In the simulations, a high electric field is present between the positive streamers and the dielectric surface. We show that the magnitude and decay of this field are affected by the positive ion mobility.

We compare simulations and experiments of single positive streamer discharges in air at 100 mbar, aiming toward model validation. Experimentally, streamers are generated in a plate–plate geometry with a protruding needle. We are able to capture the complete time evolution of reproducible single-filament streamers with a ns gate-time camera. A 2D axisymmetric drift-diffusion-reaction fluid model is used to simulate streamers under conditions closely matching those of the experiments. Streamer velocities, radii and light emission profiles are compared between model and experiment. Good qualitative agreement is observed between the experimental and simulated optical emission profiles, and for the streamer velocity and radius during the entire evolution. Quantitatively, the simulated streamer velocity is about 20% to 30% lower at the same streamer length, and the simulated radius is about 1 mm (20% to 30%) smaller. The effect of various parameters on the agreement between model and experiment is studied, such as the used transport data, the background ionization level, the photoionization rate, the gas temperature, the voltage rise time and the voltage boundary conditions. An increase in gas temperature due to the 50 Hz experimental repetition frequency could probably account for some of the observed discrepancies.

Both fluid and particle models are commonly used to simulate streamer discharges. In this paper, we quantitatively study the agreement between these approaches for axisymmetric and 3D simulations of positive streamers in air. We use a drift–diffusion–reaction fluid model with the local field approximation and a particle-in-cell, Monte Carlo collision particle model. The simulations are performed at 300 K and 1 bar in a 10 mm plate–plate gap with a 2 mm needle electrode. Applied voltages between 11.7 and 15.6 kV are used, which correspond to background fields of about 15–20 kV cm ⁻¹ . Streamer properties like maximal electric field, head position and velocity are compared as a function of time or space. Our results show good agreement between the particle and fluid simulations, in contrast to some earlier comparisons that were carried out in 1D or for negative streamers. To quantify discrepancies between the models, we mainly look at streamer velocities as a function of streamer length. For the test cases considered here, the mean deviation in streamer velocity between the particle and fluid simulations is less than 4%. We study the effect of different types of transport data for the fluid model, and find that flux coefficients lead to good agreement whereas bulk coefficients do not. Furthermore, we find that with a two-term Boltzmann solver, data should be computed using a temporal growth model for the best agreement. The numerical convergence of the particle and fluid models is also studied. In fluid simulations the streamer velocity increases somewhat using finer grids, whereas the particle simulations are less sensitive to the grid. Photoionization is the dominant source of stochastic fluctuations in our simulations. When the same stochastic photoionization model is used, particle and fluid simulations exhibit similar fluctuations.

Streamer discharges are the primary mode of electric breakdown of air in lightning and high voltage technology. Streamer channels branch many times, which determines the developing tree-like discharge structure. Understanding these branched structures is for example important to describe streamer coronas in lightning research. We simulate branching of positive streamers in air using a 3D fluid model where photoionization is included as a discrete and stochastic process. The probability and morphology of branching are in good agreement with dedicated experiments. This demonstrates that photoionization indeed provides the noise that triggers branching, and we show that branching is remarkably sensitive to the amount of photoionization. Our comparison is therefore one of the first sensitive tests for Zheleznyak’s photoionization model, confirming its validity.

In this paper, we address two main topics: steady propagation fields for positive streamers in air and streamer deceleration in fields below the steady propagation field. We generate constant-velocity positive streamers in air with an axisymmetric fluid model, by initially adjusting the applied voltage based on the streamer velocity. After an initial transient, we observe steady propagation for velocities of 3 × 10 ⁴ m s ⁻¹ to 1.2 × 10 ⁵ m s ⁻¹ , during which streamer properties and the background field do not change. This propagation mode is not fully stable, in the sense that a small change in streamer properties or background field eventually leads to acceleration or deceleration. An important finding is that faster streamers are able to propagate in significantly lower background fields than slower ones, indicating that there is no unique stability field. We relate the streamer radius, velocity, maximal electric field and background electric field to a characteristic time scale for the loss of conductivity. This relation is qualitatively confirmed by studying streamers in N ₂ –O ₂ mixtures with less oxygen than air. In such mixtures, steady streamers require lower background fields, due to a reduction in the attachment and recombination rates. We also study the deceleration of streamers, which is important to predict how far they can propagate in a low field. Stagnating streamers are simulated by applying a constant applied voltage. We show how the properties of these streamers relate to the steady cases, and present a phenomenological model with fitted coefficients that describes the evolution of the velocity and radius. Finally, we compare the lengths of the stagnated streamers with predictions based on the conventional stability field.