arXiv subjects

Ute Ebert

Publications and source records attributed to Ute Ebert.

At least 37 records · Page 2Linked to original sources

arXiv2014

A time scale for electrical screening in pulsed gas discharges

The Maxwell time is a typical time scale for the screening of an electric field in a medium with a given conductivity. We introduce a generalization of the Maxwell time that is valid for gas discharges: the \emph{ionization screening time}, that takes the growth of the conductivity due to impact ionization into account. We present an analytic estimate for this time scale, assuming a planar geometry, and evaluate its accuracy by comparing with numerical simulations in 1D and 3D. We investigate the minimum plasma density required to prevent the growth of streamers with local field enhancement, and we discuss the effects of photoionization and electron detachment on ionization screening. Our results can help to understand the development of pulsed discharges, for example nanosecond pulsed discharges at atmospheric pressure or halo discharges in the lower ionosphere.

physics.plasm-ph↗

arXiv2014

The inception of pulsed discharges in air: simulations in background fields above and below breakdown

We investigate discharge inception in air, in uniform background electric fields above and below the breakdown threshold. We perform 3D particle simulations that include a natural level of background ionization in the form of positive and O$_{2}^-$ ions. When the electric field rises above the breakdown and the detachment threshold, which are similar in air, electrons can detach from O$_{2}^-$ and start ionization avalanches. These avalanches together create one large discharge, in contrast to the `double-headed' streamers found in many fluid simulations. On the other hand, in background fields below breakdown, something must enhance the field sufficiently for a streamer to form. We use a strongly ionized seed of electrons and positive ions for this, with which we observe the growth of positive streamers. Negative streamers were not observed. Below breakdown, the inclusion of electron detachment does not change the results much, and we observe similar discharge development as in fluid simulations.

physics.plasm-ph↗

arXiv2014

Controlling the weights of simulation particles: adaptive particle management using k-d trees

In particle simulations, the weights of particles determine how many physical particles they represent. Adaptively adjusting these weights can greatly improve the efficiency of the simulation, without creating severe nonphysical artifacts. We present a new method for the pairwise merging of particles. Pairwise merging reduces the number of particles by combining two particles into one. To find particles that are `close' to each other, we use a k-d tree data structure. With a k-d tree, close neighbors can be searched for efficiently, and independently of the mesh used in the simulation. The merging can be done in different ways, conserving for example momentum or energy. We introduce probabilistic schemes, which set properties for the merged particle using random numbers. The effect of various merge schemes on the energy distribution, the momentum distribution and the grid moments is compared.

physics.comp-ph↗

arXiv2013

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 discuss the charge distribution inside discharge trees, 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.

physics.plasm-ph↗

arXiv2013

Angular distribution of Bremsstrahlung photons and of positrons for calculations of terrestrial gamma-ray flashes and positron beams

Within thunderstorms electrons can gain energies of up to hundred(s) of MeV. These electrons can create X-rays and gamma-rays as Bremsstrahlung when they collide with air molecules. Here we calculate the distribution of angles between incident electrons and emitted photons as a function of electron and photon energy. We derive these doubly differential cross-sections by integrating analytically over the triply differential cross-sections derived by Bethe and Heitler; this is appropriate for light atoms like nitrogen and oxygen (Z=7,8) if the energy of incident and emitted electron is larger than 1 keV. We compare our results with the approximations and cross section used by other authors. We also discuss some simplifying limit cases, and we derive some simple approximation for the most probable scattering angle. We also provide cross sections for the production of electron positron pairs from energetic photons when they interact with air molecules. This process is related to the Bremsstrahlung process by some physical symmetry. Therefore the results above can be transferred to predictions on the angles between incident photon and emitted positron, again as a function of photon and positron energy. We present the distribution of angles and again a simple approximation for the most probable scattering angle. Our results are given as analytical expressions as well as in the form of a C++ code that can be directly be implemented into Monte Carlo codes.

physics.ao-ph↗

arXiv2012

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

In the high field region at the head of a discharge streamer, the electron energy distribution develops a long tail. In negative streamers, these electrons can run away and contribute to energetic processes such as terrestrial gamma-ray and electron flashes. Moreover, electron density fluctuations can accelerate streamer branching. To track energies and locations of single electrons in relevant regions, we have developed a 3D hybrid model that couples a particle model 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 in overvolted gaps, and we show that it almost reaches the computational efficiency of a 3D fluid model. We also 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.

physics.plasm-ph↗

arXiv2011

Spatially hybrid computations for streamer discharges: II. Fully 3D simulations

We recently have presented first physical predictions of a spatially hybrid model that follows the evolution of a negative streamer discharge in full three spatial dimensions; our spatially hybrid model couples a particle model in the high field region ahead of the streamer with a fluid model in the streamer interior where electron densities are high and fields are low. Therefore the model is computationally efficient, while it also follows the dynamics of single electrons including their possible run-away. Here we describe the technical details of our computations, and present the next step in a systematic development of the simulation code. First, new sets of transport coefficients and reaction rates are obtained from particle swarm simulations in air, nitrogen, oxygen and argon. These coefficients are implemented in an extended fluid model to make the fluid approximation as consistent as possible with the particle model, and to avoid discontinuities at the interface between fluid and particle regions. Then two splitting methods are introduced and compared for the location and motion of the fluid-particle-interface in three spatial dimensions. Finally, we present first results of the 3D spatially hybrid model for a negative streamer in air.

physics.plasm-ph↗

arXiv2011

Simulated avalanche formation around streamers in an overvolted air gap

We simulate streamers in air at standard temperature and pressure in a short overvolted gap. The simulation is performed with a 3D hybrid model that traces the single electrons and photons in the low density region, while modeling the streamer interior as a fluid. The photons are followed by a Monte-Carlo procedure, just like the electrons. The first simulation result is present here.

physics.plasm-ph↗

arXiv2010

Comment on "NOx production in laboratory discharges simulating blue jets and red sprites" by H. Peterson et al

Peterson et al. [2009] intend to determine the NOx production of sprites and blue jets from laboratory experiments. Sprite discharges are known to be physically similar to streamer discharges at standard temperature and pressure. However, streamer experiments that simulate geophysical discharges require voltage pulses of one polarity, in contrast to the oscillating voltages of Peterson et al. Furthermore, Peterson et al. make errors in their comparison of current densities, sprite volumes and gas densities. Finally, there is a calculation error of 6 orders of magnitude in an important result.

physics.geo-ph↗

arXiv2010

Density models for streamer discharges: beyond cylindrical symmetry and homogeneous media

Streamer electrical discharges are often investigated with computer simulations of density models (also called drift-diffusion-reaction models). We review these models, detailing their physical foundations, their range of validity and the most relevant numerical algorithms employed in solving them. We focus particularly on schemes of adaptative refinement, used to resolve the multiple length scales in a streamer discharge without a high computational cost. We then report recent results from these models, emphasizing developments that go beyond cylindrically symmetrical streamers propagating in homogeneous media.

physics.plasm-ph↗

arXiv2010

Probing photo-ionization: simulations of positive streamers in varying N2:O2 mixtures

Photo-ionization is the accepted mechanism for the propagation of positive streamers in air though the parameters are not very well known; the efficiency of this mechanism largely depends on the presence of both nitrogen and oxygen. But experiments show that streamer propagation is amazingly robust against changes of the gas composition; even for pure nitrogen with impurity levels below 1 ppm streamers propagate essentially with the same velocity as in air, but their minimal diameter is smaller, and they branch more frequently. Additionally, they move more in a zigzag fashion and sometimes exhibit a feathery structure. In our simulations, we test the relative importance of photo-ionization and of the background ionization from pulsed repetitive discharges, in air as well as in nitrogen with 1 ppm O2 . We also test reasonable parameter changes of the photo-ionization model. We find that photo- ionization dominates streamer propagation in air for repetition frequencies of at least 1 kHz, while in nitrogen with 1 ppm O2 the effect of the repetition frequency has to be included above 1 Hz. Finally, we explain the feather-like structures around streamer channels that are observed in experiments in nitrogen with high purity, but not in air.

physics.plasm-ph↗

arXiv2010

Sprite discharges on Venus and Jupiter-like planets: a laboratory investigation

Large sprite discharges at high atmospheric altitudes have been found to be physically similar to small streamer discharges in air at sea level density. Based on this understanding, we investigate possible sprite discharges on Venus or Jupiter-like planets through laboratory experiments on streamers in appropriate CO2-N2 and H2-He mixtures. First, the scaling laws are experimentally confirmed by varying the density of the planetary gasses. Then streamer diameters, velocities and overall morphology are investigated for sprites on Venus and Jupiter; they are quite similar to those on earth, but light emissions in the visible range are fainter by two orders of magnitude. The discharge spectra are measured; they are dominated by the minority species N2 on Venus, while signatures of both species are found on Jupiter-like planets. The spectrum of a fully developed spark on Venus is measured. We show that this spectrum is significantly different from the expected sprite spectrum.

physics.ao-ph↗

arXiv2010

Review of recent results on streamer discharges and discussion of their relevance for sprites and lightning

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 interpreted as sprite simulations. We review those results of recent streamer research that are relevant for sprites and other forms of atmospheric electricity and discuss their implications for sprite understanding. These include the large range of streamer diameters and velocities and the overall 3D morphology with branching, interaction and reconnection, the dependence on voltage and polarity, the electron energies in the streamer head and the consecutive chemical efficiency and hard radiation. New theoretical and experimental results concern measurements of streamer spectra in air, the density dependence of streamer heating (hot leaders are unlikely at 80 km altitude and cold streamers are unlikely in liquids), and a discussion of the influence of magnetic fields on thermal electrons or on energetic electrons in streamers or sprites.

physics.ao-ph↗

arXiv2009

A moving boundary model motivated by electric breakdown: II. Initial value problem

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a Laplacian growth model regularized by a 'kinetic undercooling' boundary condition. Using this model we study both the linearized and the full nonlinear evolution of small perturbations of a uniformly translating circle. Within the linear approximation analytical and numerical results show that perturbations are advected to the back of the circle, where they decay. An initially analytic interface stays analytic for all finite times, but singularities from outside the physical region approach the interface for $t\to\infty$, which results in some anomalous relaxation at the back of the circle. For the nonlinear evolution numerical results indicate that the circle is the asymptotic attractor for small perturbations, but larger perturbations may lead to branching. We also present results for more general initial shapes, which demonstrate that regularization by kinetic undercooling cannot guarantee smooth interfaces globally in time.

nlin.PS↗

arXiv2009

3D hybrid computations for streamer discharges and production of run-away electrons

We introduce a 3D hybrid model for streamer discharges that follows the dynamics of single electrons in the region with strong field enhancement at the streamer tip while approximating the many electrons in the streamer interior as densities. We explain the method and present first results for negative streamers in nitrogen. We focus on the high electron energies observed in the simulation.

physics.plasm-ph↗

arXiv2009

A study of the possibility of sprites in the atmospheres of other planets

Sprites are a spectacular type of transient luminous events (TLE) which occur above thunderstorms immediately after lightning. They have shapes of giant jellyfish, carrots or columns and last tens of milliseconds. In Earth's atmosphere, sprites mostly emit in red and blue wavelengths from excited N2 and N2+ and span a vertical range between 50 and 90 km above the surface. The emission spectra, morphology and occurrence heights of sprites reflect the properties of the planetary atmosphere they inhabit and are related to the intensity of the initiating parent lightning.. This paper presents results of theoretical calculations of the expected occurrence heights of sprites above lightning discharges in the CO2 atmosphere of Venus, the N2 atmosphere of Titan and the H2-He atmosphere of Jupiter. The expected emission features are presented and the potential of detecting sprites in planetary atmospheres by orbiting spacecraft is discussed.

physics.ao-ph↗

arXiv2009

Spatially hybrid computations for streamer discharges with generic features of pulled fronts: I. Planar fronts

Streamers are the first stage of sparks and lightning; they grow due to a strongly enhanced electric field at their tips; this field is created by a thin curved space charge layer. These multiple scales are already challenging when the electrons are approximated by densities. However, electron density fluctuations in the leading edge of the front and non-thermal stretched tails of the electron energy distribution (as a cause of X-ray emissions) require a particle model to follow the electron motion. As super-particle methods create wrong statistics and numerical artifacts, modeling the individual electron dynamics in streamers is limited to early stages where the total electron number still is limited. The method of choice is a hybrid computation in space where individual electrons are followed in the region of high electric field and low density while the bulk of the electrons is approximated by densities (or fluids). We here develop the hybrid coupling for planar fronts. First, to obtain a consistent flux at the interface between particle and fluid model in the hybrid computation, the widely used classical fluid model is replaced by an extended fluid model. Then the coupling algorithm and the numerical implementation of the spatially hybrid model are presented in detail, in particular, the position of the model interface and the construction of the buffer region. The method carries generic features of pulled fronts that can be applied to similar problems like large deviations in the leading edge of population fronts etc.

physics.plasm-ph↗

arXiv2009

A moving boundary problem motivated by electric breakdown: I. Spectrum of linear perturbations

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be written as a Laplacian growth model regularized by a `kinetic undercooling' boundary condition. We study the linear stability of uniformly translating circles that solve the problem in two dimensions. In a space of smooth perturbations of the circular shape, the stability operator is found to have a pure point spectrum. Except for the zero eigenvalue for infinitesimal translations, all eigenvalues are shown to have negative real part. Therefore perturbations decay exponentially in time. We calculate the spectrum through a combination of asymptotic and series evaluation. In the limit of vanishing regularization parameter, all eigenvalues are found to approach zero in a singular fashion, and this asymptotic behavior is worked out in detail. A consideration of the eigenfunctions indicates that a strong intermediate growth may occur for generic initial perturbations. Both the linear and the nonlinear initial value problem are considered in a second paper.

nlin.PS↗