We simulate short positive and negative streamers in air at standard temperature and pressure. They evolve in homogeneous electric fields or emerge from needle electrodes with voltages of 10 to 20 kV. The streamer velocity at given streamer length depends only weakly on the initial ionization seed, except in the case of negative streamers in homogeneous fields. We characterize the streamers by length, head radius, head charge and field enhancement. We show that the velocity of positive streamers is mainly determined by their radius and in quantitative agreement with recent experimental results both for radius and velocity. The velocity of negative streamers is dominated by electron drift in the enhanced field; in the low local fields of the present simulations, it is little influenced by photo-ionization. Though negative streamer fronts always move at least with the electron drift velocity in the local field, this drift motion broadens the streamer head, decreases the field enhancement and ultimately leads to slower propagation or even extinction of the negative streamer.
Recently, a comparison of six codes for streamer discharge simulations were performed in [1]. In this comment, we discuss about the big differences between the results obtained by the different codes using the same deterministic model, and raise questions on the convergence of the codes and the minimum spatial resolution that are required for a converged results.
Positive streamer discharges have been studied and modelled extensively in air. Here we study positive streamers in CO$_2$ with and without oxygen admixtures; they are relevant for current high voltage technology as well as for discharges in the atmosphere of Venus. We discuss that no efficient photoionization mechanism is known for gases with a large CO$_2$ fraction, as photons in the relevant energy range are rapidly absorbed. Hence positive streamers can propagate only due to some other source of free electrons ahead of the ionization front. Therefore we study positive streamer propagation …
The simulation of the interaction of two simultaneously propagating air streamers of the same polarity is presented. A parametric study has been carried out using an accurate numerical method which ensures a time-space error control of the solution. For initial separation of both streamers smaller or comparable to the longest characteristic absorption length of photoionization in air, we have found that the streamers tend to merge at the moment when the ratio between their characteristic width and their mutual distance reaches a value of about 0.35 for positive streamers, and 0.4 for negative …
Branching is an essential element of streamer discharge dynamics but today it is understood only qualitatively. The variability and irregularity observed in branched streamer trees suggest that stochastic terms are relevant for the description of streamer branching. We here consider electron density fluctuations due to the discrete particle number as a source of stochasticity in positive streamers in air at standard temperature and pressure. We derive a quantitative estimate for the branching distance that agrees within a factor of 2 with experimental values. As branching without noise would o…
A 2D approach is used to simulate the properties of positive and negative streamers emerging from a high-voltage electrode in a long (14 cm) air gap for standard pressure and temperature. The applied voltage varies from 100 to 500 kV. To reveal the influence of photoionization, the calculations are made for various rates of seed electron generation in front of the streamer head. The difference between the properties of positive and negative streamers is associated with the different directions of the electron drift ahead of the streamer head. As a result, the peak electric field at the streame…
We investigate the branching of positive streamers in air and present the first systematic investigation of splitting into more than two branches. We study discharges in 100 mbar artificial air that is exposed to voltage pulses of 10 kV applied to a needle electrode 160 mm above a grounded plate. By imaging the discharge with two cameras from three angles, we establish that about every 200th branching event is a branching into three. Branching into three occurs more frequently for the relatively thicker streamers. In fact, we find that the surface of the total streamer cross-sections before an…
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 strea…
Positive streamer discharges require a source of free electrons ahead of them for their growth. In air, these electrons are typically provided by photoionization. Here we investigate how stochastic fluctuations due to the discreteness of ionizing photons affect positive streamers in air. We simulate positive streamers between two planar electrodes with a 3D plasma fluid model, using both a stochastic and a continuum method for photoionization. With stochastic photoionization, fluctuations are visible in the streamer's direction, maximal electric field, velocity, and electron density. The strea…
Streamer discharges are thin plasma channels that precede lightning and sparks. They usually evolve in bundles as stochastic tree-like structures and are inherently difficult to model due to their multiscale nature. In this paper, we perform a computer investigation of positive streamer discharges in air using contemporary photoionization models. We report on three-dimensional computer simulations under conditions that are available in laboratory spark-gap experiments. The solutions demonstrate a multiscale morphology consisting of streamer fluctuations, branching, and the formation of a disch…
We investigate streamer formation in the troposphere, in electric fields above the breakdown threshold. With fully three-dimensional particle simulations, we study the combined effect of natural background ionization and of photoionization on the discharge morphology. In previous investigations based on deterministic fluid models without background ionization, so-called double-headed streamers emerged. But in our improved model, many electron avalanches start to grow at different locations. Eventually the avalanches collectively screen the electric field in the interior of the discharge. This …
We compare simulations and experiments of single positive streamer discharges in air at 100 mbar, aiming towards 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 qualitat…
Both experimental and theoretical analysis of an {ultra-short} phenomena occurring during the positive streamer propagation in atmospheric pressure air is presented. {With tens-of-picoseconds and tens-of-microns precision, it is shown that when the streamer head passes a spatial coordinate, emission maxima from N$_2$ and N$_2^+$ radiative states follow with different delays. These different delays are caused by differences in the dynamics of populating the radiative states, due to different excitation and quenching rates.} {Associating the position of the streamer head with the maximum value o…
We simulate streamers in air at standard temperature and pressure in a short overvolted gap. The simulation is performed with a 3D hybrid model that traces the single electrons and photons in the low density region, while modeling the streamer interior as a fluid. The photons are followed by a Monte-Carlo procedure, just like the electrons. The first simulation result is present here.
An experimental study of the effect of laminar airflow on positive self-pulsating streamer coronas in a needle-to-plate geometry is presented. The experiments are performed in an open return wind tunnel with winds up to 30 m/s orthogonal to the needle. The experimental data is presented in terms of statistical properties of the discharge, inferred from high resolution, large sample-size current waveforms. The key properties of the current pulsations, namely inter-pulse period, peak current, deposited energy, and pulse width are analyzed as a function of wind speed and applied DC voltage. All p…
We discuss spatially and temporally adaptive implicit-explicit (IMEX) methods for parallel simulations of three-dimensional fluid streamer discharges in atmospheric air. We examine strategies for advancing the fluid equations and elliptic transport equations (e.g. Poisson) with different time steps, synchronizing them on a global physical time scale which is taken to be proportional to the dielectric relaxation time. The use of a longer time step for the electric field leads to numerical errors that can be diagnosed, and we quantify the conditions where this simplification is valid. Likewise, …
Streamer discharges can be used as a primary source of reactive species for plasma-assisted combustion. In this research we investigate positive streamers in a stoichiometric air-methane mixture at 1 bar and 300 K with a three-dimensional particle-in-cell model for the electrons. We first discuss suitable electron scattering cross sections and an extension of the photoionization mechanism to air-methane mixtures. We discuss that the addition of 9.5% methane leaves electron transport and reaction coefficients essentially unchanged, but it largely suppresses photoionization and shortens the phot…
To find a viable alternative to SF6 with growing climate change regulations, proper evaluation of alternatives such as compressed air ought to be done. For medium voltage applications, the withstand voltage is used as the dimensioning criteria and this is dependent on the initiation and propagation of streamers which are precursors to electrical breakdown. For design optimization, a thorough understanding of the initiation and propagation mechanisms of such electrical discharges under different stresses, pressure etc. ought to be studied experimentally and numerically also via a predictive mod…
The dynamics of positive and negative streamers is numerically simulated in atmospheric pressure air. It is shown that positive and negative streamers behave in radically different ways when decelerating and stopping. When the head potential drops, the negative streamer transits to the mode in which the propagation is due to the forward electron drift. In this case, the radius of the ionization wave front increases, whereas the electric field at the streamer head decreases further and the streamer stops. The only advancement mechanism for a positive streamer with decreasing head potential is a…
Photo-ionization is the accepted mechanism for the propagation of positive streamers in air though the parameters are not very well known; the efficiency of this mechanism largely depends on the presence of both nitrogen and oxygen. But experiments show that streamer propagation is amazingly robust against changes of the gas composition; even for pure nitrogen with impurity levels below 1 ppm streamers propagate essentially with the same velocity as in air, but their minimal diameter is smaller, and they branch more frequently. Additionally, they move more in a zigzag fashion and sometimes exh…
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 PIC-MCC (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 to 20 kV/cm. …
We here propose a model to capture the complexity of the streamer corona adjacent to leader stepping and relate it to the production of energetic electrons serving as a source of X-rays and $γ$-rays, manifesting in terrestrial gamma-ray flashes (TGFs). During its stepping, the leader tip is accompanied by a corona consisting of multitudinous streamers perturbing the air in its vicinity and leaving residual charge behind. We explore the relative importance of air perturbations and preionization on the production of energetic run-away electrons by 2.5D cylindrical Monte Carlo particle simulation…
It is by now well understood that large sprite discharges at the low air densities of the mesosphere are physically similar to small streamer discharges in air at standard temperature and pressure. This similarity is based on Townsend scaling with air density. First the theoretical basis of Townsend scaling and a list of six possible corrections to scaling are discussed; then the experimental evidence for the similarity between streamers and sprites is reviewed. We then discuss how far present sprite and streamer theory has been developed, and we show how streamer experiments can be interprete…
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 $3\times10^4$ m/s to $1.2\times10^5$ m/s, during which streamer properties and the background field do not change. This propagation mode is not fully stable, in the sense that a small chan…
We investigate discharge inception in air, in uniform background electric fields above and below the breakdown threshold. We perform 3D particle simulations that include a natural level of background ionization in the form of positive and O$_{2}^-$ ions. When the electric field rises above the breakdown and the detachment threshold, which are similar in air, electrons can detach from O$_{2}^-$ and start ionization avalanches. These avalanches together create one large discharge, in contrast to the `double-headed' streamers found in many fluid simulations. On the other hand, in background field…
We investigate structure and evolution of long positive spark breakdown; and we study at which stage pulses of hard X-rays are emitted. Positive high-voltage pulses of standardized lightning impulse wave form of about 1 MV were applied to about 1 meter of ambient air. The discharge evolution was imaged with a resolution of tens of nanoseconds with an intensified CCD camera. LaBr3(Ce+) scintillation detectors recorded the X-rays emitted during the process. The voltage and the currents on both electrodes were measured synchronously. All measurements indicate that first a large and dense corona o…
The spatial non-uniformity of the electric field in air discharges, such as streamers, can influence the accuracy of spectroscopic diagnostic methods and hence the estimation of the peak electric field. In this work, we use a self-consistent streamer discharge model to investigate the spatial non-uniformity in streamer heads and streamer glows. We focus our analysis on air discharges at atmospheric pressure and at the low pressure of the mesosphere. This approach is useful to investigate the spatial non-uniformity of laboratory discharges as well as sprite streamers and blue jet streamers, two…
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 fie…
We study the development of a negative discharge driven by a Marx generator of about 1 MV in an air gap of 1 up to 1.5 meter, at standard temperature and pressure. We show the evolution of the discharge with nanosecond-fast photography together with the electrical characteristics. The negative discharge develops through four well-distinguished streamer bursts. The streamers have different velocities and life times in different bursts. The last burst triggers a positive inception cloud on the positive grounded electrode and a burst of positive counter-streamers emerges. The pre-discharge then b…
We introduce the generic structure of a growth model for branched discharge trees that consistently combines a finite channel conductivity with the physical law of charge conservation. It is applicable, e.g., to streamer coronas near tip or wire electrodes and ahead of lightning leaders, to leaders themselves and to the complex breakdown structures of sprite discharges high above thunderclouds. Then we implement and solve the simplest model for positive streamers in ambient air with self-consistent charge transport. We demonstrate that charge conservation contradicts the common assumption of d…
The propagation mechanisms of plasma streamers have been observed and investigated in a surface dielectric barrier discharge (SDBD) using 2D particle in cell simulations. The investigations are carried out under a simulated air mixture, 80\% N$_2$ and 20\% O$_2$, at atmospheric pressure, 100$\,$kPa, under both DC conditions and a pulsed DC waveform that represent AC conditions. The simulated geometry is a simplification of the symmetric and fully exposed SDBD resulting in the simultaneous ignition of both positive and negative streamers on either side of the Al$_2$O$_3$ dielectric barrier. In …
We investigate the dynamics of negative surface discharges in air through numerical simulations with a 2D fluid model. A geometry consisting of a flat dielectric embedded between parallel-plate electrodes is used. Compared to negative streamers in bulk gas, negative surface streamers are observed to have a higher electron density, a higher electric field and higher propagation velocity. On the other hand, their maximum electric field and velocity are lower than for positive surface streamers. In our simulations, negative surface streamers are slower for larger relative permittivity. Negative c…
We recently have presented first physical predictions of a spatially hybrid model that follows the evolution of a negative streamer discharge in full three spatial dimensions; our spatially hybrid model couples a particle model in the high field region ahead of the streamer with a fluid model in the streamer interior where electron densities are high and fields are low. Therefore the model is computationally efficient, while it also follows the dynamics of single electrons including their possible run-away. Here we describe the technical details of our computations, and present the next step i…
Positive streamers need a source of free electrons ahead of them to propagate. A streamer can supply these electrons by itself through photo-ionization, or the electrons can be present due to external background ionization. Here we investigate the effects of background ionization on streamer propagation and morphology by changing the gas composition and the repetition rate of the voltage pulses, and by adding a small amount of radioactive Krypton 85. We find that the general morphology of a positive streamer discharge in high purity nitrogen depends on background ionization: at lower backgroun…
