Spontaneous branching of discharge channels is frequently observed, but not well understood. We recently proposed a new branching mechanism based on simulations of a simple continuous discharge model in high fields. We here present analytical results for such streamers in the Lozansky-Firsov limit where they can be modelled as moving equipotential ionization fronts. This model can be analyzed by conformal mapping techniques which allow the reduction of the dynamical problem to finite sets of nonlinear ordinary differential equations. The solutions illustrate that branching is generic for the intricate head dynamics of streamers in the Lozansky-Firsov-limit.
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…
We recently have shown that a negative streamer in a sufficiently high homogeneous field can branch spontaneously due to a Laplacian instability, rather than approach a stationary mode of propagation with fixed radius. In our previous simulations, the streamer started from a wide initial ionization seed on the cathode. We here demonstrate in improved simulations that a streamer emerging from a single electron branches in the same way. In fact, though the evolving streamer is much more narrow, it branches after an even shorter propagation distance.
In sufficiently large gaps and electric fields, discharge streamers do branch. In [Arrayas et al., PRL 88, 174502 (2002)], we observed streamer branching numerically within a deterministic particle density model and explained it as a Laplacian instability of a thin space charge layer. Our numerical results were criticized in [Kulikovsky, PRL 89, 229401 (2002)]. We here present an adaptive grid refinement method for streamer simulations, and we carry out the first conclusive investigation on the effect of the numerical grid on streamer branching in different fields. On stepwise finer grids the …
Non-ionized media subject to strong fields can become locally ionized by penetration of finger-shaped streamers. We study negative streamers between planar electrodes in a simple deterministic continuum approximation. We observe that for sufficiently large fields, the streamer tip can split. This happens close to Firsov's limit of `ideal conductivity'. Qualitatively the tip splitting is due to a Laplacian instability quite like in viscous fingering. For future quantitative analytical progress, our stability analysis of planar fronts identifies the screening length as a regularization mechanism…
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…
Previous studies of streamer discharge branching mechanisms have mainly been generative other than predictive. To predict or even control branching, a reliable connection between experimental conditions and streamer branching needs to be established. As an important step toward the goal, in this work, a 2D deterministic model of negative streamers in air is numerically solved with the ionization seeds assumed as the superposition of Gaussians. The "indicative profiles approach" developed here can consistently relate the change in a quantitative measure of geometrical irregularity of the seed p…
This proceedings paper from 2004 contains figures of discharges in different gap lengths at the same potential that are not available elsewhere. The 2004 abstract: The evolution of streamers is known to depend on gas composition and electrode geometry, on polarity and size of the voltage and also on the electric circuit that produces the high voltage pulse. To characterize the phenomena better and to compare with theory, a new larger experimental setup with vacuum enclosure has been built. We here present first results in this setup on positive streamers in air at fixed voltage and varying ele…
In dielectric breakdown, the phenomena of streamers formation and spontaneous branching is commonly observed. A deterministic negative streamer model is reviewed in this article. We recently have proposed that this reduced model is able to explain the branching phenomena, due to a Laplacian instability quite like in viscous fingering. Particular attention is paid to the physical interpretation of the model.
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…
Streamers are a generic mode of electric breakdown of large gas volumes. They play a role in the initial stages of sparks and lightning, in technical corona reactors and in high altitude sprite discharges above thunderclouds. Streamers are characterized by a self-generated field enhancement at the head of the growing discharge channel. We briefly review recent streamer experiments and sprite observations. Then we sketch our recent work on computations of growing and branching streamers, we discuss concepts and solutions of analytical model reductions, we review different branching concepts and…
We present an open-source plasma fluid code for 2D, cylindrical and 3D simulations of streamer discharges, based on the Afivo framework that features adaptive mesh refinement, geometric multigrid methods for Poisson's equation, and OpenMP parallelism. We describe the numerical implementation of a fluid model of the drift-diffusion-reaction type, combined with the local field approximation. Then we demonstrate its functionality with 3D simulations of long positive streamers in nitrogen in undervolted gaps, using three examples. The first example shows how a stochastic background density affects…
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…
Standard photographs of streamer discharges show a two-dimensional projection. We here present stereo-photographic images that resolve their three-dimensional structure. We describe the stereoscopic set-up and evaluation, and we present results for positive streamer discharges in air at 0.2 - 1 bar in a point plane geometry with a gap distance of 14 cm and a voltage pulse of 47 kV. In this case an approximately Gaussian distribution of branching angles of 43 degrees is found; these angles do not significantly depend on the distance from the needle or on the gas pressure.
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, …
We present the first analytical and numerical studies of the initial stage of the branching process based on an interface dynamics streamer model in the fully 3-D case. This model follows from fundamental considerations on charge production by impact ionization and balance laws, and leads to an equation for the evolution of the interface between ionized and non-ionized regions. We compare some experimental patterns with the numerically simulated ones, and give an explicit expression for the growth rate of harmonic modes associated with the perturbation of a symmetrically expanding discharge. B…
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 …
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…
Controlling streamer morphology is important for numerous applications. Up to now, the effect of the voltage rise rate was only studied across a wide range. Here we show that even slight variations in the voltage rise can have significant effects. We have studied positive streamer discharges in a 16 cm point-plane gap in high-purity nitrogen 6.0, created by 25 kV pulses with a duration of 130 ns. The voltage rise varies by a rise rate from 1.9 kV/ns to 2.7 kV/ns and by the first peak voltage of 22 to 28 kV. A structural link is found between smaller discharges with a larger inception cloud cau…
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…
