We propose a new approach to unambiguous determination of parameters of positive and negative electric streamer discharges. From hydrodynamic equations, in the assumption of a solution in the shape of a streamer, it is possible to derive several relations between streamer parameters, which form a system of algebraic equations (SAE). Because of the made approximations, the error in the solution of this system is expected to be probably up to a few tens of percent. Solving the SAE allows us to express all streamer parameters in terms of the streamer length $L$, the constant uniform external electric field $E_e$, and the streamer radius. The solutions with different radii are valid solutions of the hydrodynamic equations, and are analogous to the propagation modes of flat-front perturbations with different transverse wavelengths. We interpret the streamer as a nonlinear instability, whose behavior is determined by choosing the radius at which the velocity is maximized, because, as we show, the velocity plays the same role as the exponential growth rate in the case of linear instabilities.
Thus, streamer behavior is unambiguously determined by $E_e$ and $L$, in a relatively computationally economical way. In contrast, numerical methods of solving the microscopic equations, such as hydrodynamic simulations, are more computationally demanding, and the preferred solution in them arises automatically because of numerical fluctuations. The calculations for air at sea level conditions produce reasonable values for commonly observed streamer parameters. The calculated positive streamer velocities and negative threshold fields are compatible with experimental measurements. The physical reason for the positive threshold fields is also discussed. A much simplified analytical model (Appendix B) reproduces many of the presented results, at least qualitatively.
In this paper we study the lateral instability of streamer discharges using a continuum discharge model. We observe similarities to Kelvin-Helmholz instability in fluids. In strong electric fields, lateral long wave length perturbations can grow while small wave length perturbations diminish during the discharge evolution. We perform numerical simulations and carry out asymptotic analysis of the instability. Our results could explain the growth observed in experimental discharges.
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…
Streamers, thin, ionized plasma channels, form the early stages of lightning discharges. Here we approach the study of extraterrestrial lightning by studying the formation and propagation of streamer discharges in various nitrogen-methane and nitrogen-oxygen mixtures with levels of nitrogen from 20% to 98.4%. We present the friction force and breakdown fields Ek in various N2:O2 (Earth-like) and N2:CH4 (Titan-like) mixtures. The strength of the friction force is larger in N2:CH4 mixtures whereas the breakdown field in mixtures with methane is half as large as in mixtures with oxygen. We use a …
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…
Radiation is important for the propagation of streamers in dielectric liquids. Photoionization is a possibility, but the effect is difficult to differentiate from other contributions. In this work, we model radiation from the streamer head, causing photoionization when absorbed in the liquid. We find that photoionization is local in space (μm-scale). The radiation absorption cross section is modeled considering that the ionization potential (IP) is dependent on the electric field. The result is a steep increase in the ionization rate when the electric field reduces the IP below the energy of t…
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…
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…
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…
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…
We present a software to simulate the propagation of positive streamers in dielectric liquids. Such liquids are commonly used for electric insulation of high-power equipment. We simulate electrical breakdown in a needle-plane geometry, where the needle and the extremities of the streamer are modeled by hyperboloids, which are used to calculate the electric field in the liquid. If the field is sufficiently high, electrons released from anions in the liquid can turn into electron avalanches, and the streamer propagates if an avalanche meets the Townsend-Meek criterion. The software is written en…
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…
A simulation model for second mode positive streamers in dielectric liquids is presented. Initiation and propagation is modeled by an electron-avalanche mechanism and the Townsend--Meek criterion. The electric breakdown is simulated in a point-plane gap, using cyclohexane as a model liquid. Electrons move in a Laplacian electric field arising from the electrodes and streamer structure, and turn into electron avalanches in high-field regions. The Townsend--Meek criterion determines when an avalanche is regarded as a part of the streamer structure. The results show that an avalanche-driven break…
We use a three-specie fluid model of electric discharge in air to simulate streamer evolution from the avalanche-to-streamer transition to the collision of opposite-polarity streamers. We estimate the upper limit on the production of thermal runaway electrons, which is dominant during the second of these processes. More thermal runaways are produced if the ionization due to natural background and photoionization is reduced, due to possibility of creation of higher electric fields at streamer tips. The test-particle simulation shows, however, that these thermal runaway electrons have insufficie…
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 the emergence of space stems ahead of negative leaders. These are luminous spots that appear ahead of an advancing leader mediating the leader's stepped propagation. We show that space stems start as regions of locally depleted conductivity that form in the streamers of the corona around the leader. An attachment instability enhances the electric field leading to strongly inhomogeneous, bright and locally warmer regions ahead of the leader that explain the existing observations. Since the attachment instability is only triggered by fields above 10 kV/cm and internal electric fie…
We investigate the launch of negative upward streamers from sprite glows. This phenomenon is readily observed in high-speed observations of sprites and underlies the classification of sprites into carrot or column types. First, we describe how an attachment instability leads to a sharply defined region in the upper part of the streamer channel. This region has an enhanced electric field, low conductivity and strongly emits in the first positive system of molecular nitrogen. We identify it as the sprite glow. We then show how, in the most common configuration of a carrot sprite, several upward …
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 …
Behavior of the potential and electric field intensity at the front of a lightning leader channel taking into account the influence of space charges injected by the streamers is investigated theoretically. Analytical solutions of Poisson equation are found for different laws of charge density distribution in the streamer zone. Influence of the streamer zone parameters on the formation of final jump phase of a leader is investigated.
Transmission and multiple reflection mechanisms of guided streamers propagating through grounded annular electrode and interacting with grounded surface electrode
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…
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…
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…
The numerical simulation of the development of a streamer discharge in a gap with an external longitudinal magnetic field was used to demonstrate the self-focusing of such discharges. Self-focusing is caused by a sharp deceleration of the radial ionization wave due to a change in the electron energy distribution function, a decrease in the average electron energy, the rate of gas ionization and the electron mobility in crossed electric and magnetic fields as compared to the case of the discharge development without a magnetic field. The self-focusing effect of a streamer discharge in an extern…
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, …
