Prediction of Lightning Inception by Large Ice Particles and Extensive Air Showers.

We derive that lightning can start if the electric field is 15% of the breakdown field, and if elongated ice particles of 6 cm length and 100 free electrons per cm3 are present. This is one particular example set from a parameter range that we discuss as well. Our simulations include the permittivity ε(ω) of ice.

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.

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.

Saffman-Taylor streamers: mutual finger interaction in spark formation.

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 density or fluid approximation in two dimensions. If the period of the streamer array is small enough, the streamers do not branch, but approach uniform translation.

How do sinking phytoplankton species manage to persist?

Phytoplankton require light for photosynthesis. Yet, most phytoplankton species are heavier than water and therefore sink. How can these sinking species persist? Somehow, the answer should lie in the turbulent motion that redisperses sinking phytoplankton over the vertical water column.

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

Starting from the minimal model for the electrically interacting densities of electrons and ions in negative streamer discharges, we derive a moving boundary approximation for the ionization fronts. Solutions of the moving boundary model have already been discussed, but the derivation of the model was postponed to the present paper. The key ingredient of the model is the boundary condition on the moving front.

Spatiotemporal patterns in a dc semiconductor-gas-discharge system: stability analysis and full numerical solutions.

A system very similar to a dielectric barrier discharge, but with a simple stationary dc voltage, can be realized by sandwiching a gas discharge and a high-ohmic semiconductor layer between two planar electrodes. In experiments this system forms spatiotemporal and temporal patterns spontaneously, quite similarly to, e.g.

Numerical convergence of the branching time of negative streamers.

Discharge streamers in experiments branch frequently. Arrayás [Phys. Rev.

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions.

Oscillations in dc driven barrier discharges: numerical solutions, stability analysis, and phase diagram.

A short gas-discharge layer sandwiched with a semiconductor layer between planar electrodes shows a variety of spatiotemporal patterns. We focus on the spontaneous temporal oscillations that occur while a dc voltage is applied and while the system stays spatially homogeneous; the results for these oscillations apply equally to a planar discharge in series with any resistor with capacitance. We define the minimal model, identify its independent dimensionless parameters, and then present the results of the full time-dependent numerical solutions of the model as well as of a linear stability analysis of the stationary state.

Period doubling cascade in glow discharges: local versus global differential conductivity.

Short planar glow discharges coupled to a resistive layer exhibit a wealth of spontaneous spatiotemporal patterns. Due to similarities with other pattern forming systems that are described by reaction-diffusion models, several authors have tried to derive such models from discharge physics. We investigate the temporal oscillations of the discharge system and find a cascade of period doubling events.

Dependence of the transition from Townsend to glow discharge on secondary emission.

, (1991)]]. Sijacić and Ebert stated that this transition strongly depends on secondary emission gamma from the cathode. We show here that the earlier results of von Engel and Raizer on the small current expansion about the Townsend limit actually are the limit of small gamma of the Sijacić and Ebert expression, and that for larger gamma the old and the Sijacić and Ebert new results vary by no more than a factor of 2.

Streamer branching rationalized by conformal mapping techniques.

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 modeled as moving equipotential ionization fronts.

Stability of negative ionization fronts: Regularization by electric screening?

We recently have proposed that a reduced interfacial model for streamer propagation is able to explain spontaneous branching. Such models require regularization. In the present paper we investigate how transversal Fourier modes of a planar ionization front are regularized by the electric screening length.

Transition from Townsend to glow discharge: subcritical, mixed, or supercritical characteristics.

The transition from Townsend to glow discharge is investigated numerically in one space dimension in full parameter space within the classical model: with electrons and positive ions drifting in the local electric field, impact ionization by electrons (alpha process), secondary electron emission from the cathode (gamma process) and space charge effects. We also perform a systematic analytical small current expansion about the Townsend limit up to third order in the current that fits our numerical data very well. Depending on the two determining parameters gamma and system size pd, the transition from Townsend to glow discharge can show the textbook subcritical behavior, but for smaller values of pd, we also find supercritical or some unexpected intermediate "mixed" behavior.

Branching of negative streamers in free flight.

We have recently 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.

Coherent scattering function in the reptation model: analysis beyond asymptotic limits.

We calculate the coherent dynamical scattering function S(c)(q,t;N) of a flexible chain of length N, diffusing through an ordered background of topological obstacles. As an instructive generalization, we also calculate the scattering function S(c)(q,t;M,N) for the central piece of length M View Article and Find Full Text PDF

Spontaneous branching of anode-directed streamers between planar electrodes.

Nonionized 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.

Diffusion coefficient of propagating fronts with multiplicative noise.

Recent studies have shown that in the presence of noise, both fronts propagating into a metastable state and so-called pushed fronts propagating into an unstable state, exhibit diffusive wandering about the average position. In this paper, we derive an expression for the effective diffusion coefficient of such fronts, which was motivated before on the basis of a multiple scale ansatz. Our systematic derivation is based on the decomposition of the fluctuating front into a suitably positioned average profile plus fluctuating eigenmodes of the stability operator.