arXiv subjects

Ute Ebert

Publications and source records attributed to Ute Ebert.

At least 55 records · Page 3Linked to original sources

arXiv2009

Moving boundary approximation for curved streamer ionization fronts: Numerical tests

Recently a moving boundary approximation for the minimal model for negative streamer ionization fronts was extended with effects due to front curvature; this was done through a systematic solvability analysis. A central prediction of this analysis is the existence of a nonvanishing electric field in the streamer interior, whose value is proportional to the front curvature. In this paper we compare this result and other predictions of the solvability analysis with numerical simulations of the minimal model.

physics.plasm-ph↗

arXiv2008

Streamers, sprites, leaders, lightning: from micro- to macroscales

"Streamers, sprites, leaders, lightning: from micro- to macroscales" was the theme of a workshop in October 2007 in Leiden, The Netherlands; it brought researchers from plasma physics, electrical engineering and industry, geophysics and space physics, computational science and nonlinear dynamics together around the common topic of generation, structure and products of streamer-like electric breakdown. The present cluster issue collects relevant articles within this area; most of them were presented during the workshop. We here briefly discuss the research questions and very shortly review the papers in the cluster issue, and we also refer to a few recent papers in other journals.

physics.plasm-ph↗

arXiv2008

Positive streamers in air and nitrogen of varying density: experiments on similarity laws

Positive streamers in ambient air at pressures from 0.013 to 1 bar are investigated experimentally. The voltage applied to the anode needle ranges from 5 to 45 kV, the discharge gap from 1 to 16 cm. Using a "slow" voltage rise time of 100 to 180 ns, the streamers are intentionally kept thin. For each pressure p, we find a minimal diameter d_{min}. To test whether streamers at different pressures are similar, the minimal streamer diameter d_{min} is multiplied by its pressure p; we find this product to be well approximated by p*d_{min}=0.20 \pm 0.02 mm*bar over two decades of air pressure at room temperature. The value also fits diameters of sprite discharges above thunderclouds at an altitude of 80 km when extrapolated to room temperature (as air density rather than pressure determines the physical behavior). The minimal velocity of streamers in our measurements is approximately 0.1 mm/ns = 10^5 m/s. The same minimal velocity has been reported for tendrils in sprites. We also investigate the size of the initial ionization cloud at the electrode tip from which the streamers emerge, and the streamer length between branching events. The same quantities are also measured in nitrogen with a purity of approximately 99.9 %. We characterize the essential differences with streamers in air and find a minimal diameter of p*d_{min}=0.12 \pm 0.02 mm*bar in our nitrogen.

physics.plasm-ph↗

arXiv2008

Positive and negative streamers in ambient air: measuring diameter, velocity and dissipated energy

Positive and negative streamers are studied in ambient air at 1 bar; they emerge from a needle electrode placed 40 mm above a planar electrode. The amplitudes of the applied voltage pulses range from 5 to 96 kV; most pulses have rise times of 30 ns or shorter. Diameters, velocities and energies of the streamers are measured. Two regimes are identified; a low voltage regime where only positive streamers appear and a high voltage regime where both positive and negative streamers exist. Below 5 kV, no streamers emerge. In the range from 5 to 40 kV, positive streamers form, while the negative discharges only form a glowing cloud at the electrode tip, but no streamers. For 5 to 20 kV, diameters and velocities of the positive streamers have the minimal values of d=0.2 mm and v \approx 10^5 m/s. For 20 to 40 kV, their diameters increase by a factor 6 while the voltage increases only by a factor 2. Above the transition value of 40 kV, streamers of both polarities form; they strongly resemble each other, though the positive ones propagate further; their diameters continue to increase with applied voltage. For 96 kV, positive streamers attain diameters of 3 mm and velocities of 4*10^6 m/s, negative streamers are about 20 % slower and thinner. An empirical fit formula for the relation between velocity v and diameter d is v=0.5 d^2/(mm ns) for both polarities. Streamers of both polarities dissipate energies of the order of several mJ per streamer while crossing the gap.

physics.plasm-ph↗

arXiv2008

Experiments on propagating and branching positive streamers in air

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 electrode distance. While next to the emitting anode tip, a similar number of streamers seems to emerge due to multiple branching, more streamers seem to survive over a fixed distance, when the gap is shorter. When lowering the voltage, streamers branch less at all distances from the anode tip or do not branch at all beyond a certain distance.

physics.plasm-ph↗

arXiv2008

Moving boundary approximation for curved streamer ionization fronts: Solvability analysis

The minimal density model for negative streamer ionization fronts is investigated. An earlier moving boundary approximation for this model consisted of a "kinetic undercooling" type boundary condition in a Laplacian growth problem of Hele-Shaw type. Here we derive a curvature correction to the moving boundary approximation that resembles surface tension. The calculation is based on solvability analysis with unconventional features, namely, there are three relevant zero modes of the adjoint operator, one of them diverging; furthermore, the inner/outer matching ahead of the front has to be performed on a line rather than on an extended region; and the whole calculation can be performed analytically. The analysis reveals a relation between the fields ahead and behind a slowly evolving curved front, the curvature and the generated conductivity. This relation forces us to give up the ideal conductivity approximation, and we suggest to replace it by a constant conductivity approximation. This implies that the electric potential in the streamer interior is no longer constant but solves a Laplace equation; this leads to a Muskat-type problem.

physics.plasm-ph↗

arXiv2008

Laplacian instability of planar streamer ionization fronts - an example of pulled front analysis

Streamer ionization fronts are pulled fronts propagating into a linearly unstable state; the spatial decay of the initial condition of a planar front selects dynamically one specific long time attractor out of a continuous family. A transverse stability analysis has to take these features into account. In this paper we introduce a framework for this transverse stability analysis, involving stable and unstable manifolds in a weighted space. Within this framework, a numerical dynamical systems method for the calculation of the dispersion relation as an eigenvalue problem is defined and dispersion curves for different values of the electron diffusion constant and of the electric field ahead of the front are derived. Numerical solutions of the initial value problem confirm the eigenvalue calculations. The numerical work is complemented with analytical expressions for the dispersion relation in the limit of small and large wave numbers and with a fit formula for intermediate wave numbers. This empirical fit supports the conjecture that the smallest unstable wave length of the Laplacian instability is proportional to the diffusion length that characterizes the leading edge of the pulled ionization front.

nlin.PS↗

arXiv2008

Saffman-Taylor streamers: mutual finger interaction in an electric breakdown

Bunches of streamers form the early stages of sparks and lightning but theory presently concentrates on single streamers or on coarse approximations of whole breakdown trees. Here a periodic array of interacting streamer discharges in a strong homogeneous electric field is studied in PDE approximation in two dimensions. If the period of the streamer array is small enough, the streamers do not branch, but approach uniform translation. When the streamers are close to the branching regime, the enhanced field at the tip of the streamer is close to $2 E_{\infty}$, where $E_{\infty}$ is the homogeneous field applied between the electrodes. We discuss a moving boundary approximation to the set of PDEs. This moving boundary model turns out to be essentially the same as the one for two-fluid Hele-Shaw flows. In two dimensions, this model possesses a known analytical solution. The shape of the 2D interacting streamers in uniform motion obtained from the PDE simulations is actually well fitted by the analytically known ``selected Saffman-Taylor finger''. This finding helps to understand streamer interactions and raises new questions on the general theory of finger selection in moving boundary problems.

physics.plasm-ph↗

arXiv2008

Positive and negative streamers in ambient air: modeling evolution and velocities

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.

physics.plasm-ph↗

arXiv2008

Positive streamers in ambient air and a N2:O2-mixture (99.8 : 0.2)

Photographs show distinct differences between positive streamers in air or in a nitrogen-oxygen mixture (0.2% O2). The streamers in the mixture branch more frequently, but the branches also extinguish more easily. Probably related to that, the streamers in the mixture propagate more in a zigzag manner while they are straighter in air. Furthermore, streamers in the mixture can become longer; they are thinner and more intense.

physics.plasm-ph↗

arXiv2007

Spatial coupling of particle and fluid models for streamers: where nonlocality matters

Particle models for streamer ionization fronts contain correct electron energy distributions, runaway effects and single electron statistics. Conventional fluid models are computationally much more efficient for large particle numbers, but create too low ionization densities in high fields. To combine their respective advantages, we here show how to couple both models in space. We confirm that the discrepancies between particle and fluid fronts arise from the steep electron density gradients in the leading edge of the fronts. We find the optimal position for the interface between models that minimizes computational effort and reproduces the results of a pure particle model.

physics.plasm-ph↗

arXiv2007

Avalanche to streamer transition in particle simulations

The avalanche to streamer transition is studied and illustrated in a particle model. The results are similar to those of fluid models. However, when super-particles are introduced, numerical artefacts become visible. This underscores the need of models that are hybrid in space.

physics.plasm-ph↗

arXiv2007

Convective stabilization of a Laplacian moving boundary problem with kinetic undercooling

We study the shape stability of disks moving in an external Laplacian field in two dimensions. The problem is motivated by the motion of ionization fronts in streamer-type electric breakdown. It is mathematically equivalent to the motion of a small bubble in a Hele-Shaw cell with a regularization of kinetic undercooling type, namely a mixed Dirichlet-Neumann boundary condition for the Laplacian field on the moving boundary. Using conformal mapping techniques, linear stability analysis of the uniformly translating disk is recast into a single PDE which is exactly solvable for certain values of the regularization parameter. We concentrate on the physically most interesting exactly solvable and non-trivial case. We show that the circular solutions are linearly stable against smooth initial perturbations. In the transformation of the PDE to its normal hyperbolic form, a semigroup of automorphisms of the unit disk plays a central role. It mediates the convection of perturbations to the back of the circle where they decay. Exponential convergence to the unperturbed circle occurs along a unique slow manifold as time $t\to\infty$. Smooth temporal eigenfunctions cannot be constructed, but excluding the far back part of the circle, a discrete set of eigenfunctions does span the function space of perturbations. We believe that the observed behaviour of a convectively stabilized circle for a certain value of the regularization parameter is generic for other shapes and parameter values. Our analytical results are illustrated by figures of some typical solutions.

nlin.PS↗

arXiv2007

Construction and test of a moving boundary model for negative streamer discharges

Starting from the minimal model for the electrically interacting particle densities in negative streamer discharges, we derive a moving boundary approximation for the ionization fronts. The boundary condition on the moving front is found to be of 'kinetic undercooling' type. The boundary approximation, whose first results have been published in [Meulenbroek et al., PRL 95, 195004 (2005)], is then tested against 2-dimensional simulations of the density model. The results suggest that our moving boundary approximation adequately represents the essential dynamics of negative streamer fronts.

physics.plasm-ph↗

arXiv2007

Theory of superfast fronts of impact ionization in semiconductor structures

We present an analytical theory for impact ionization fronts in reversely biased p^{+}-n-n^{+} structures. The front propagates into a depleted n base with a velocity that exceeds the saturated drift velocity. The front passage generates a dense electron-hole plasma and in this way switches the structure from low to high conductivity. For a planar front we determine the concentration of the generated plasma, the maximum electric field, the front width and the voltage over the n base as functions of front velocity and doping of the n base. Theory takes into account that drift velocities and impact ionization coefficients differ between electrons and holes, and it makes quantitative predictions for any semiconductor material possible.

cond-mat.mtrl-sci↗

arXiv2007

Deviations from the local field approximation in negative streamer heads

Negative streamer ionization fronts in nitrogen under normal conditions are investigated both in a particle model and in a fluid model in local field approximation. The parameter functions for the fluid model are derived from swarm experiments in the particle model. The front structure on the inner scale is investigated in a 1D setting, allowing reasonable run-time and memory consumption and high numerical accuracy without introducing super-particles. If the reduced electric field immediately before the front is >= 50kV/(cm bar), solutions of fluid and particle model agree very well. If the field increases up to 200kV/(cm bar), the solutions of particle and fluid model deviate, in particular, the ionization level behind the front becomes up to 60% higher in the particle model while the velocity is rather insensitive. Particle and fluid model deviate because electrons with high energies do not yet fully run away from the front, but are somewhat ahead. This leads to increasing ionization rates in the particle model at the very tip of the front. The energy overshoot of electrons in the leading edge of the front actually agrees quantitatively with the energy overshoot in the leading edge of an electron swarm or avalanche in the same electric field.

physics.plasm-ph↗

arXiv2006

Photoionization in negative streamers: fast computations and two propagation modes

Streamer discharges play a central role in electric breakdown of matter in pulsed electric fields, both in nature and in technology. Reliable and fast computations of the minimal model for negative streamers in simple gases like nitrogen have recently been developed. However, photoionization was not included; it is important in air and poses a major numerical challenge. We here introduce a fast and reliable method to include photoionization into our numerical scheme with adaptice grids, and we discuss its importance for negative streamers. In particular, we identify different propagation regimes where photoionization does or does not play a role.

physics.plasm-ph↗

arXiv2006

The multiscale nature of streamers

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 outline a hierarchy of model reductions.

physics.plasm-ph↗