Streamers In Air Research Articles

Calculating Radio Emissions of Positive Streamer Phenomena Using 3D Simulations

AbstractWe study radio emissions from positive streamers in air using 3D simulations, from which the radiated electric field is computed by solving Jefimenko’s equations. The simulations are performed at using two photoionization methods: the Helmholtz approximation for a photon density and a Monte Carlo method using discrete photons, with the latter being the most realistic. We consider cases with single streamers, streamer branching, streamers interacting with preionization and streamer‐streamer encounters. We do not observe a strong VHF radio signal during or after branching, which is confirmed by lab experiments. This indicates that the current inside a streamer discharge evolves approximately continuously during branching. On the other hand, stochastic fluctuations in streamer propagation due to Monte Carlo photoionization lead to more radio emission being emitted at frequencies of 100 MHz and above. Another process that leads to such high‐frequency emission is the interaction of a streamer with a weakly preionized region, which can be present due to a previous discharge. In agreement with previous work, we observe the strongest and highest‐frequency emission from streamer encounters. The amount of total energy that is radiated seems to depend primarily on the background electric field, and less on the particular streamer evolution. Finally, we present approximations for the maximal current along a streamer channel and a fit formula for a streamer's current moment.

The Prospects of Theoretical Lines for Studying Streamers in Air (Review)

The Prospects of Theoretical Lines for Studying Streamers in Air (Review)

3D simulations of positive streamers in air in a strong external magnetic field

We study how external magnetic fields from 0 to 40 T influence positive streamers in atmospheric pressure air, using 3D PIC-MCC (particle-in-cell, Monte Carlo collision) simulations. When a magnetic field B is applied perpendicular to the background electric field E , the streamers deflect towards the +B and −B directions which results in a branching into two main channels. With a stronger magnetic field the angle between the branches increases, and for the 40 T case the branches grow almost parallel to the magnetic field. Due to the E×B drift of electrons we also observe a streamer deviation in the opposite −E×B direction, where the minus sign appears because positive streamers propagate opposite to the electron drift velocity. The deviation due to this E×B effect is smaller than the deviation parallel to B . In both cases of B perpendicular and parallel to E , the streamer radius decreases with the magnetic field strength. We relate our observations to the effects of electric and magnetic fields on electron transport and reaction coefficients.

3D modeling of positive streamers in air with inhomogeneous density

We study the effect of an inhomogeneous gas density on positive streamer discharges in air using a 3D fluid model with stochastic photoionization, generalizing earlier work with a 2D axisymmetric model by Starikovskiy and Aleksandrov (2019 Plasma Sources Sci. Technol. 28 095022). We consider various types of planar and (hemi)spherical gas density gradients. Streamers propagate from a region of density towards a region of higher or lower gas density , where corresponds to and . We observe that streamers can always propagate into a region with a lower gas density. When streamers enter a region with a higher gas density, branching can occur at the density gradient, with branches growing in a flower-like pattern over the gradient surface. Depending on the gas density ratio, the gradient width and other factors, narrow branches are able to propagate into the higher-density gas. In a planar geometry, we find that such propagation is possible up to a gas density slope of , although this value depends on a number of conditions, such as the gradient angle. Surprisingly, a higher applied voltage makes it more difficult for streamers to penetrate into the high-density region, due to an increase of the primary streamer’s radius.

A kinetic Monte Carlo study of positive streamer interaction with complex dielectric surfaces

We present a computational study of positive streamers in air propagating over dielectric plates with square channels running orthogonal to the propagation direction. The study uses a newly developed non-kinetic Particle-In-Cell model based on Îto diffusion and kinetic Monte Carlo, which does not introduce artificial smoothing of the plasma density or photo-electron distributions. These capabilities permit the computational study to use high-resolution grids with large time steps, and also incorporates geometric shielding for particle and photon transport processes. We perform Cartesian 2D simulations for channel dimensions ranging from 250 µm to 2 mm, and track streamers over a distance of 4 cm and times ranging up to 300 ns, for various voltages ranging from 15 kV to 30 kV. These baseline simulations are supplemented by additional studies on the effects of transparency to ionizing radiation, streamer reignition, dielectric permittivity, and 3D effects. The computer simulations show: 1) Larger channels restrict streamer propagation more efficiently than narrow channels, and can lead to arrested surface streamers. 2) Geometric shielding of ionizing radiation substantially reduces the number of starting electrons in neighboring channels, and thus also reduces the onset point of streamer reignition. 3) Decreasing the streamer channel separation leads to slower streamers. 4) Increasing the dielectric permittivity increases the discharge velocity. The results are of generic value to fields of research involving streamer-dielectric interactions, and in particular for high-voltage technology where streamer termination is desirable.

Quantitative modeling of streamer discharge branching in air

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.

On propagation of positive and negative streamers in air in uniform electric fields

Recently published results of numerical simulations of positive and negative streamers propagating in uniform applied electric fields in air are analyzed in the framework of an analytical approach. It is shown that obtained approximate relations between the streamer radius, velocity and length, depending on the value of applied electric field, are in reasonable agreement with the computational data.

Estimating the properties of single positive air streamers from measurable parameters

We develop an axial model for single steadily propagating positive streamers in air. It uses observable parameters to estimate quantities that are difficult to measure. More specifically, for given velocity, radius, length and applied background field, our model approximates the ionization density, the maximal electric field, the channel electric field, and the width of the charge layer. These parameters determine the primary excitations of molecules and the internal currents. Our approach is to first analytically approximate electron dynamics and electric fields in different regions of a uniformly-translating streamer head, then we match the solutions on the boundaries of the different regions to model the streamer as a whole, and we use conservation laws to determine unknown quantities. We find good agreement with numerical simulations for a range of streamer lengths and background electric fields, even if they do not propagate in a steady manner. Therefore quantities that are difficult to access experimentally can be estimated from more easily measurable quantities and our approximations. The theoretical approximations also form a stepping stone towards efficient axial multi-streamer models.

A computational study on the energy efficiency of species production by single-pulse streamers in air

We study the energy efficiency of species production by streamer discharges with a single voltage pulse in atmospheric dry air, using a 2D axisymmetric fluid model. Sixty different positive streamers are simulated by varying the electrode geometry, the pulse duration and the applied voltage. Between these cases, the streamer radius and velocity vary by about an order of magnitude, but the variation in the maximal electric field is significantly smaller, about 30%. We find that G-values for the production of N(4S), O(3P), NO and N2O, which have relatively high activation energies, vary by about 30% to 60%. This variation is mainly caused by two factors: differences in the fraction of energy deposited in the streamer head region, and differences in the maximal electric field at the streamer head. When accounting for both factors, our computed G-values are in good agreement with an analytic estimate proposed by Naidis (2012 Plasma Sources Sci. Technol. 21 042001). We also simulate negative streamers and find that their production of N(4S), O(3P) and NO is less energy efficient. The results suggest that energy efficiency can be increased by reducing Joule heating in the streamer channel and by increasing the maximal electric field at the streamer head, for example by using short voltage pulses with a high applied voltage.

Positive and negative streamers in air and nitrogen in a sharply inhomogeneous electric field under conditions of runaway electron generation

AbstractThe development of positive and negative streamers in a point‐to‐plane gap filled with air and nitrogen at various pressures (50–200 kPa) and voltages (8–25 kV) was studied. A four‐channel intensified charge‐coupled device (ICCD) and a streak‐camera were used. Electrical parameters were measured with high resolution (10 GHz). An original method of measuring a displacement current caused by a streamer was applied. As was expected, positive streamer branches in nitrogen at low voltages and/or elevated pressures while a large‐diameter streamer is formed in air. However, at high voltages or negative polarity, the large‐diameter streamer is formed both in nitrogen and air in the entire pressure range. It was found that runaway electrons (REs) are generated in the very first picoseconds of gas ionisation near the pointed cathode. It was assumed that REs can be generated near the pointed anode and produce bremsstrahlung radiation due to a sharply inhomogeneous distribution of electrical potential. It was found that in the final stage of negative streamer development in air and nitrogen, the gas between the streamer front and the opposite electrode is ionised almost simultaneously in the entire volume when the streamer diameter is almost equal to the interelectrode gap.

Studying the Features of Streamer Formation and Development in Air by Using Computation Experiments

The aim of the work is to estimate the relevance and current state of the problem of mathematical modeling of streamer discharges in air, as well as to identify the features pertinent to formation and initial development stage of two-head streamers in air by using computational experiments. The streamer discharge mathematical model developed at the National Research University Moscow Power Engineering Institute Department of High Voltage Engineering and Electrophysics was used as the research tool. It is shown that mathematical modeling of a streamer discharge can be effectively used in its studies and in training specialists in the field of electric power engineering and high-voltage electrical technologies. The article presents the results of computational experiments on studying the occurrence of streamers in a discharge gap filled with dry air with a uniform electric field (EF) under standard atmospheric conditions. The initial conditions were chosen so that a single-avalanche-streamer formation mechanism was realized. It is shown that in the considered range of initial conditions, the distance between the anode and initial inhomogeneity has a weak, within 1%, influence on the minimum and maximum values of electric field strength in the streamer. A different picture is observed on the anode surface. When a two-head streamer is formed in the discharge gap depth, the field strength at the anode remains close to the average strength in it. As the negative streamer head approaches the anode, the field strength on its surface increases to values close to those achieved in the positive head. After that, the field at the anode weakens rapidly to a level at which effective impact ionization becomes impossible. The article will be of interest for specialists and graduate students working in the field of electric power engineering and high-voltage electrical technologies.

Formation of wide negative streamers in air and helium: the role of fast electrons

Available experimental data show that the use of voltage pulses with subnanosecond rise times and amplitudes that essentially exceed the breakdown voltage leads to the formation of wide spherical or conical streamers. In this paper, the structure and dynamics of atmospheric pressure wide negative streamers in air and helium by applying high overvoltages with a short rise time to a sharp needle electrode are investigated experimentally and computationally. In the simulations, the two-dimensional fluid and kinetic electron Monte Carlo simulation models are used. All the streamers were simulated with the conventional photoionization term S ph that was never turned off. By including an additional source S MC, responsible for the generation of fast electrons, wide and diffuse streamers are obtained. We compare the shapes, width and velocities of conventional streamers in air and helium with those for streamers driven by fast electrons. We show that a conventional streamer in air has a cylindrical form. The conventional streamer in helium is wider than that in air and has a shape of an expanding cone. While accounting for fast electrons, different streamer shapes were obtained. In air, the gap was closed by a spherical streamer. In helium, the shape of a streamer resembles that of a pumpkin. We also demonstrate that near the flat anode, velocities of conventional streamers in air and helium were as high as 5 × 109 cm s−1 and reached values greater than 1010 cm s−1 when fast electrons were taken into account. By the application of high (by a factor of four or greater) overvoltages to a sharp needle electrode, the formation of a discharge with several parallel streamers was observed. In this regime, the trajectories of fast electrons originated not only from the cathode, but also from the region of a streamer front where the electric field is high. As a result, the so-called diffuse discharge was formed with high intensity plasma channels surrounded by an aureole of smaller electron density.

Evolution of positive streamers in air over non-planar dielectrics: experiments and simulations

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.

Streamer propagation in humid air

We investigate the effect of humidity on the propagation of streamers in air. We present a minimal set of chemical reactions that takes into account the presence of water in a nonthermal air plasma and considers ionization, attachment, detachment, recombination and ion conversion including water cluster formation. We find differences in streamer propagation between dry and humid air that we attribute mostly to an enhanced effective attachment rate in humid air, leading to higher breakdown electric field and threshold field for propagation. This higher effective attachment rate in humid conditions leads to a faster decay of the conductivity in the streamer channel, which hinders the accumulation of charge in the streamer head. In some cases a propagating streamer solution still exists at the expense of a smaller radius and lower velocity. In other cases a high humidity leads to the stagnation of the streamer. We finally discuss how all these statements may affect streamer branching and the dimensions and lifetime of a streamer corona.

A computational study of steady and stagnating positive streamers in N2–O2 mixtures

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 × 104 m s−1 to 1.2 × 105 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 N2–O2 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.

A comparison of particle and fluid models for positive streamer discharges in air

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.

Simulations of positive streamers in air in different electric fields: steady motion of solitary streamer heads and the stability field

We simulate and characterize positive streamers in ambient air in homogeneous background electric fields from 4.5 to 26 kV cm−1 in a 4 cm gap. They can accelerate or decelerate depending on the background electric field. Many experiments have shown that a streamer keeps propagating in a stable manner in the so-called stability field of 4.5 to 5 kV cm−1. Our fluid streamer simulations in STP air show that: (1) in a homogeneous field larger than 4.675 kV cm−1, a single streamer accelerates, and in a lower field, it decelerates and eventually stagnates with a small radius and very high field enhancement. (2) In a field of 4.675 kV cm−1, the streamer head propagates with an approximately constant velocity of 6.7 × 104 m s−1 and an optical radius of 55 μm over distances of several centimeters as a stable coherent structure. These values for the radius and velocity agree well with measurements of so-called minimal streamers. (3) Behind the uniformly translating streamer head, the channel conductivity decreases due to electron attachment and recombination, and the electric field returns to its background value about 1 cm behind the head. The propagation behavior of the solitary streamer agrees with the original definition of the stability field, which is the homogeneous field in which a streamer can propagate with a constant speed and shape.

Comparing simulations and experiments of positive streamers in air: steps toward model validation

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.

Formation of a Negative Streamer in a Sharply Nonuniform Electric Field and the Time of Generation of Runaway Electrons

The formation of a negative streamer in air is investigated at different pressures in a sharply nonuniform electric field under the conditions of nanosecond and subnanosecond breakdowns. The investigations are performed with a four-channel ICCD-camera and an ultrafast streak-camera. In a separate series of experiments, the generation of runaway electrons is investigated in the course of streamer formation by measuring the dynamic displacement current. It is shown that the streamer velocity changes during its motion from the electrode with a small curvature radius towards the opposite flat electrode. The data are obtained on the instantaneous streamer velocity. It is shown that runaway electrons are generated at the start of the streamer.

Characteristics of spatiotemporal variations of primary and secondary streamers under pulsed-voltage in air at atmospheric pressure

A pulsed positive streamer discharge was simulated using a two-dimensional axisymmetric model to investigate the characteristics of primary and secondary streamers in air at atmospheric pressure and ambient temperature. The spatiotemporal variations of the reduced electric field and the electron density during propagation of the primary streamer were clarified, and their relationships with the applied voltage were discussed. The phenomenon of the secondary streamer was introduced according to the previously developed “attachment instability” theory, and the spatiotemporal variations of the net-attachment frequency were presented to validate the theory. The results indicated that variations in the reduced electric field and electron density can be approximately estimated by the theory even in conditions involving a pulsed voltage and non-uniform Laplacian field. Because the primary and secondary streamers have spatiotemporal characteristics related to the chemical reactivity in the streamer discharge, understanding these characteristics is valuable for the development of atmospheric-pressure plasma applications.