Streamer Branching Research Articles

Streamer branching on clusters of solid particles in air and air bubbles in liquids

We present the results from a two-dimensional computational investigation of the intersection of a streamer with solid particles and density fluctuations and gas bubbles filled with air and immersed in liquids. We consider the evolution of a streamer propagating along the vector of the applied external electric field. The clusters of particles in air or bubbles in liquids have a symmetric form with branches elongated either in horizontal or vertical direction. The orientation of the cluster determines the branching patterns. We show that clusters having the prevailing horizontal branches facilitate streamer branching in liquids, while clusters in gases with vertical branches promote the splitting or reinitiating of a discharge filament. The phenomenon is mainly due to different polarization patterns of vertical or horizontal clusters in air and liquids and the ratio of dielectric permittivity of medium/particle or medium/bubble.

Studying branching of a cathode-directed streamer in air by means of 3D modeling

A cathode-directed streamer in air is modeled using the hypothesis that branching is initiated by large electron avalanches that develop in a strong electric field in the front of streamer head. A series of streamer discharge simulations are carried out using a three-dimensional numerical model. The possibility of streamer branching is shown as a result of the interaction with two electron avalanches that arise in front of its head. They are directed to the sides from streamer propagation direction. Such a mechanism of branching is brought about by the fact, that at the moment of contact with the streamer, the avalanches have already undergone an avalanche–streamer transition or are close to it. The equality of the number of electrons in these avalanches at the moment of contact is not important. If this equality is violated, branching is asymmetric. If one of the avalanches interacting with the streamer is far from the avalanche–streamer transition, it does not trigger perfect branching, but it may produce an underdeveloped branch that does not evolve further. The streamer trajectory then deviates toward a larger avalanche, interacting with it.

Gas heating effects on the formation and propagation of a microwave streamer in air

The development of microwave plasma streamers at 110 GHz in atmospheric pressure air is numerically investigated taking into account the intense gas heating and its effects on the plasma formation and dynamics. The simulations are based on an implicit finite difference time domain formulation of Maxwell's equations coupled with a simple plasma fluid model and a real gas Euler equation solver. The numerical results show how the formation of a shock wave due to the large microwave power absorbed by the plasma and converted into gas heating strongly modifies the streamer elongation and dynamics. A microwave streamer filament stretches along its axis because of ionization-diffusion mechanisms in the enhanced electric field at the streamer tips. The change in the gas density distribution associated with the formation of shock wave due to gas heating strongly modifies the ionization and diffusion mechanisms and tends to limit the on-axis microwave streamer elongation by enhancing resonance effects. The simulations suggest that gas heating effects also play an important role in the observed bending or branching of microwave streamers after they have reached a critical length.

Streamer formation and branching from model hydrometeors in subbreakdown conditions inside thunderclouds

AbstractElectric field values measured inside thunderclouds have consistently been reported to be up to an order of magnitude lower than the value required for the conventional electrical breakdown of air. This result has made it difficult to explain how lightning frequently occurs in thunderclouds. A few different theories have been offered to explain the lightning initiation process, one of them being the theory of lightning initiation from hydrometeors. According to this theory, lightning can be initiated from electrical discharges originating around thundercloud water or ice particles in the measured thundercloud electric field. These particles, called hydrometeors, are believed to cause significant enhancement of the thundercloud electric field in their vicinity and then initiate streamers that are the precursor discharges for the hot lightning leader channel. Previously, Liu et al. (2012a) reported streamer formation from a model hydrometeor in an electric field value of half of the conventional breakdown threshold (Ek) for air. In this paper, we present modeling results for streamer formation in electric fields as low as one third of the breakdown threshold. According to our results, initiation of stable streamers from thundercloud hydrometeors in a 0.3Ek electric field is possible, only if enhanced ambient ionization levels (e.g., the ionization created by corona discharges around the same or other nearby hydrometeors) are present ahead of the streamer. The magnitude and distribution of this ambient density may be a determining factor on whether the streamer branches, recovers after the prebranching stage, or continues propagating stably. We investigate the streamer branching behavior and characteristics and test a theory that has recently been proposed to explain this phenomenon. We find that the geometry of the streamer head plays an important role in the streamer branching phenomena. The fast radial movement of the maximum streamer head curvature, combined with the slow reduction of the maximum curvature value, eventually leads the streamer head to branching. Finally, we compare our modeling results with laboratory experiments and realistic thundercloud conditions and discuss the implications of this study to lightning initiation and other lightning‐related phenomena.

Branching and path-deviation of positive streamers resulting from statistical photon transport

The branching and change in direction of propagation (path-deviation) of positive streamers in molecular gases such as air likely require a statistical process which perturbs the head of the streamer and produces an asymmetry in its space charge density. In this paper, the mechanisms for path-deviation and branching of atmospheric pressure positive streamer discharges in dry air are numerically investigated from the viewpoint of statistical photon transport and photoionization. A statistical photon transport model, based on randomly selected emitting angles and mean-free-path for absorption, was developed and embedded into a fluid-based plasma transport model. The hybrid model was applied to simulations of positive streamer coaxial discharges in dry air at atmospheric pressure. The results show that secondary streamers, often spatially isolated, are triggered by the random photoionization and interact with the thin space charge layer (SCL) of the primary streamer. This interaction may be partly responsible for path-deviation and streamer branching. The general process consists of random remote photo-electron production which initiates a back-traveling electron avalanche, collision of this secondary avalanche with the primary streamer and the subsequent perturbation to its SCL. When the SCL is deformed from a symmetric to an asymmetric shape, the streamer can experience an abrupt change in the direction of propagation. If the SCL is sufficiently perturbed and essentially broken, local maxima in the SCL can develop into new streamers, leading to streamer branching. During the propagation of positive streamers, this mechanism can take place repetitively in time and space, thus producing multi-level branching and more than two branches within one level.

Abrupt Changes in Streamer Propagation Velocity Driven by Electron Velocity Saturation and Microscopic Inhomogeneities

Causes of streamer acceleration caused by electron velocity saturation at intense electric fields are investigated in liquid dielectrics. Findings of this paper explain regimes of higher positive streamer velocity using a nonlinear electric-field-dependent electron velocity model that describes the streamer velocity more accurately when compared with the experimental results in the literature. Streamer branching in inhomogeneous transformer oil is also studied as an alternative cause of sudden changes in streamer velocity magnitude and direction, because after branching, the velocities of the born branches are significantly higher than the main streamer column velocity. In this paper, a 3-D model is established to incorporate nonsymmetrical variations in the streamer shape. The modeling results show that the streamer branching has both stochastic and deterministic origins. The stochastic parameters are determined by the content of inhomogeneity in the liquid and the deterministic origins of branching are defined by the structure of the volume charge layer at the streamer head. The results indicate that the sudden changes in streamer velocities are due to the electric-field-dependent electron mobility, electric-field-dependent ionization potential of dielectric molecules, and the branching capability of streamers even in extremely homogeneous liquid bulk.

Infrasonic acoustic waves generated by fast air heating in sprite cores

Acceleration, expansion, and branching of sprite streamers can lead to concentration of high electrical currents in regions of space, that are observed in the form of bright sprite cores. Driven by this electrical current, a series of chemical processes take place in the sprite plasma. Excitation, followed by quenching of excited electronic states leads to energy transfer from charged to neutral species. The consequence is heating and expansion of air leading to emission of infrasonic acoustic waves. Results indicate that Pa pressure perturbations on the ground, observed in association with sprites, can only be produced by exceptionally strong currents in sprite cores, exceeding 2 kA.

Growing discharge trees with self-consistent charge transport: the collective dynamics of streamers

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 dielectric breakdown models that the electric fields inside all streamers are equal to the so-called stability field and we even find cases of local field inversion. We also find that, counter-intuitively, the inner branches of a positive-streamer tree are negatively charged, which provides a natural explanation for the observed reconnections of streamers in laboratory experiments and in sprites. Our simulations show the structure of an overall ‘streamer of streamers’ that we name collective streamer front, and predict effective streamer branching angles, the charge structure within streamer trees and streamer reconnection.

Electron acceleration above thunderclouds

The acceleration of electrons results in observable electromagnetic waves which can be used for remote sensing. Here, we make use of ∼4 Hz–66 MHz radio waves emitted by two consecutive intense positive lightning discharges to investigate their impact on the atmosphere above a thundercloud. It is found that the first positive lightning discharge initiates a sprite where electrons are accelerated during the exponential growth and branching of the sprite streamers. This preconditioned plasma above the thundercloud is subsequently exposed to a second positive lightning discharge associated with a bouncing-wave discharge. This discharge process causes a re-brightening of the existing sprite streamers above the thundercloud and initiates a subsequent relativistic electron beam.

Stochastic and deterministic causes of streamer branching in liquid dielectrics

Streamer branching in liquid dielectrics is driven by stochastic and deterministic factors. The presence of stochastic causes of streamer branching such as inhomogeneities inherited from noisy initial states, impurities, or charge carrier density fluctuations is inevitable in any dielectric. A fully three-dimensional streamer model presented in this paper indicates that deterministic origins of branching are intrinsic attributes of streamers, which in some cases make the branching inevitable depending on shape and velocity of the volume charge at the streamer frontier. Specifically, any given inhomogeneous perturbation can result in streamer branching if the volume charge layer at the original streamer head is relatively thin and slow enough. Furthermore, discrete nature of electrons at the leading edge of an ionization front always guarantees the existence of a non-zero inhomogeneous perturbation ahead of the streamer head propagating even in perfectly homogeneous dielectric. Based on the modeling results for streamers propagating in a liquid dielectric, a gauge on the streamer head geometry is introduced that determines whether the branching occurs under particular inhomogeneous circumstances. Estimated number, diameter, and velocity of the born branches agree qualitatively with experimental images of the streamer branching.

Streamers in air splitting into three branches

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 and after a branching event is roughly the same.

Reasons for branching of a positive streamer in a non-uniform field

The stage of streamer branching initiation in a nonuniform electric field (the point-plane electrode system) is analyzed in a drift-diffusion approximation. A chain of cause-and-effect relations is analyzed using a sufficiently simplified model of a semi-ellipsoidal ideally conductive streamer head. It is found that the bluntness of the head may occur even if the maximum of the electric field intensity is located in the center of the head (on the “pole”) if the maximum is feebly marked. The electric field distribution on the streamer head depends on both the potential and the form of the head and on the adjacent charged objects, in particular, on the active electrode. The electric field minimum in the area of the electrode-streamer contacts makes the maximum of the field intensity on the head to be sharper and prevents branching. When the streamer head moves away from the active electrode, the maximum of the field intensity gets less sharp. It makes the head blunter; due to this, the maximum of the electric field shifts from the pole and branching starts. Thus, it is found that, under certain conditions, a streamer can branch even in an entirely determinated model where all the fluctuations are neglected.

Low frequency electromagnetic radiation from sprite streamers

Sprites are mesospheric discharges that carry significant electrical currents and produce electromagnetic radiation observed typically in the extremely low (ELF) to ultra low (ULF) frequency bands. In this letter, we present the first theoretical estimates of the electromagnetic radiation produced by individual sprite streamers using simulation results from a plasma fluid model. It is demonstrated that the spectral content of the radiation produced by sprite streamers is a function of the air density Nand the lightning‐induced quasi‐static ambient electric fieldE in the regions of space where the sprite streamers are propagating. We demonstrate that the exponential growth of the current in sprite streamers at 75 km would be preferentially associated with electromagnetic radiation in the frequency range from 0 and up to ∼3 kHz, whereas the growth of the streamer current at 40 km could produce radiation with frequencies up to ∼300 kHz, consistently with the scaling of atmospheric air density. We further conjecture that the periodic branching of streamers may lead to a radiation spectrum enhancement in the very low (VLF) to low frequency (LF) range.

Fractal Analysis of Positive Pulsed Streamer Patterns in Supercritical Carbon Dioxide

A positive pulsed prebreakdown in a needle-to-plane gap at CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> phases up to supercritical (SC) condition was observed by means of Schlieren imaging method. Our observations confirmed that the pattern of positive prebreakdown discharge was a treelike streamer independent of medium phase and that the SC phase led to streamer branches of higher complexity than those in the gas and liquid phases. Both streamer branches' complexity and fractal dimension variation of the developing streamer were quantitatively assessed by means of fractal analysis. Experimental results are summarized as follows: 1) SC carbon dioxide (SCCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) led to the greatest complexity of streamer branching in comparison with gas and liquid phases; 2) the fractal dimensions of gas, liquid, and SC phases of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> were estimated to around D = 1.47, 1.60, and 1.73 with a coefficient of determination R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> >; 0.99; and 3) the fractal dimension D in SCCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stayed constant at around D = 1.7 during the streamer growth phase.

Influence of impurities and additives on positive streamers in paraffinic model oil

This paper presents an experimental study of positive streamers in paraffinic model oil in a point-plane gap. The investigation was performed concerning the influence of voltage, impurities and additives. It was seen how increased voltage changes streamer shape and speed resulting in different propagation modes. Carbon particles markedly reduce inception, breakdown and acceleration voltages, while dissolved gases/air have little effect on these voltages. A low ionization potential additive decelerates the streamers, while an electron scavenger shows an increase in streamer velocity. The correlation between propagation velocity and streamer's branching is discussed.

Investigation of Three-Dimensional Characteristics of Underwater Streamer Discharges

We have developed a new three-dimensional (3D) observation method suitable for studying the structure of streamer discharges. Using this method we investigated the propagation of underwater streamer discharges generated in a nozzle-plate electrode system. As a result, the streamer branching angle was found to take a bell-shaped distribution having a mean value in the range of 65–75° with a standard deviation of about 20°. Moreover, we confirmed that the mean branching angle is a physical quantity that increases with water conductivity. The propagation velocity of the underwater streamer was estimated to be (2–3) ×104 m/s.

A comparison of 3D particle, fluid and hybrid simulations for negative streamers

Modeling individual free electrons can be important in the simulation of discharge streamers. Stochastic fluctuations in the electron density can accelerate the branching of streamers. In negative streamers, energetic electrons can even ‘run away’ and contribute to processes such as terrestrial gamma-ray and electron flashes. To track energies and locations of single electrons in relevant regions, we have developed a 3D hybrid model that couples a particle model for single electrons in the region of high fields and low electron densities with a fluid model in the rest of the domain. Here we validate our 3D hybrid model on a 3D (super-)particle model for negative streamers without photoionization in overvolted gaps. We show that the extended fluid model approximates the particle and the hybrid model well until stochastic fluctuations become important, while the classical fluid model underestimates velocities and ionization densities. We compare density fluctuations and the onset of branching between the models, and we compare the front velocities with an analytical approximation.

Effects of numerical and physical anisotropic diffusion on branching phenomena of negative-streamer dynamics

This paper is a contribution to the fluid modelling and simulation of the spontaneous branching of an initial mono-filamentary negative streamer propagating in molecular nitrogen at atmospheric pressure. The effects of both numerical diffusion and physical anisotropic diffusion on the branching structure are studied. We used MUSCL-type flux limiters where an artificial amount of numerical diffusion can be introduced through the choice of the value of a characteristic slope parameter. It was shown that a small amount of numerical diffusion can inhibit the spontaneous streamer branching. This means that the use of a high-order numerical scheme preventing the numerical diffusion and dispersion is a major parameter that must be taken into account in the interpretation of the simulated streamer development and splitting. This paper also clearly shows that the consideration of the anisotropy of electron diffusion affects the streamer head structure in comparison with the isotropic diffusion case. This especially occurs for electrons in gases presenting a large difference between the longitudinal and transversal diffusion coefficients as in N2 or in air.

Mechanisms behind positive streamers and their distinct propagation modes in transformer oil

Comprehensive modeling and analysis is presented for the charge generation, recombination, attachment, and transport of positive ions, negative ions, and electrons in transformer oil between a positive high voltage sharp needle electrode and a large spherical ground electrode. Case studies show that a key mechanism in streamer development is field ionization, which is the direct ionization of molecules due to action of the electric field. Due to the high mobility electrons, which are about 1 × 105 times more mobile than the positive ions, the newly generated electrons quickly exit the high field ionization zone towards the anode leading to the development of a net positive space charge peak which subsequently creates an electric field enhancement in the oil. The process is driven by the applied high voltage creating temporally dynamic space charge and electric field distributions that develop an ionizing wave that drives streamer development. The pre-breakdown modeling and analysis elucidates the development of different streamer modes in transformer oil. In particular, the analysis focuses on mechanisms driving filamentary fast mode streamers discussed in the literature. The results demonstrate that streamer modes arise in transformer oil due to the ionization of different families of hydrocarbon molecules (i.e., aromatic, naphthenic, and paraffinic) at increasing electric field levels (or applied voltages). Ionization of the low concentration aromatic molecules in transformer oil, that generally have lower ionization energies than naphthenic/paraffinic molecules, leads to the propagation of streamers with velocities on the order of 1 km/s. As the applied voltage is increased, the ionization of the main hydrocarbon molecules in transformer oil, high concentration naphthenic/paraffinic molecules, dominates producing high electric field levels and space charge at the streamer tip. This results in the propagation of a very fast streamer with velocities on the order of 10 km/s. Furthermore, these streamers have protrusion spacing in the approximate range of 20-100 μm in ~36 ns like those of electrohydrodynamic instability of charged jets that may be the origin of streamer branching. A preliminary model based on earlier electrohydrodynamic stability analysis is presented that predicts protrusion spacing in the approximate range of 7-30 μm with growth rate 2.5-5 μs.

Electron density fluctuations accelerate the branching of positive streamer discharges in air

Branching is an essential element of streamer discharge dynamics. We review the current state of theoretical understanding and recall that branching requires a finite perturbation. We argue that, in current laboratory experiments in ambient or artificial air, these perturbations can only be inherited from the initial state, or they can be due to intrinsic electron-density fluctuations owing to the discreteness of electrons. We incorporate these electron-density fluctuations into fully three-dimensional simulations of a positive streamer in air at standard temperature and pressure. We derive a quantitative estimate for the ratio of branching length to streamer diameter that agrees within a factor of 2 with experimental measurements. As branching without this noise would occur considerably later, if at all, we conclude that the intrinsic stochastic particle noise triggers branching of positive streamers in air at atmospheric pressure.