The onset of tree-like patterns in negative streamers

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. By means of full numerical simulation, the splitting and formation of characteristic tree-like patterns of electric discharges is observed and described

Contour dynamics model for electric discharges

A contour dynamics model for electrical discharges is obtained and analyzed. The model is deduced as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, in the limit of small electron diffusion. The dispersion relation for a non planar 2-D discharge is calculated. The development and propagation of finger-like patterns are studied and their main features quantified.Comment: 4 pages, 2 fi

Impact ionization fronts in Si diodes: Numerical evidence of superfast propagation due to nonlocalized preionization

We present numerical evidence of a novel propagation mode for superfast impact ionization fronts in high-voltage Si $p^+$-$n$-$n^+$ structures. In nonlinear dynamics terms, this mode corresponds to a pulled front propagating into an unstable state in the regime of nonlocalized initial conditions. Before the front starts to travel, field-ehanced emission of electrons from deep-level impurities preionizes initially depleted $n$ base creating spatially nonuniform free carriers profile. Impact ionization takes place in the whole high-field region. We find two ionizing fronts that propagate in opposite directions with velocities up to 10 times higher than the saturated drift velocity.Comment: 3 pages, 4 figure

Electric discharge contour dynamics model: the effects of curvature and finite conductivity

In this paper we present the complete derivation of the effective contour model for electrical discharges which appears as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, when the electron diffusion is small. It consists of two integro-differential equations defined at the boundary of the plasma region: one for the motion and a second equation for the net charge density at the interface. We have computed explicit solutions with cylindrical symmetry and found the dispersion relation for small symmetry-breaking perturbations in the case of finite resistivity. We implement a numerical procedure to solve our model in general situations. As a result we compute the dispersion relation for the cylindrical case and compare it with the analytical predictions. Comparisons with experimental data for a 2-D positive streamers discharge are provided and predictions confirmed.Comment: 23 pages, 3 figure

Optomagnetic composite medium with conducting nanoelements

A new type of metal-dielectric composites has been proposed that is characterised by a resonance-like behaviour of the effective permeability in the infrared and visible spectral ranges. This material can be referred to as optomagnetic medium. The analytical formalism developed is based on solving the scattering problem for considered inclusions with impedance boundary condition, which yields the current and charge distributions within the inclusions. The presence of the effective magnetic permeability and its resonant properties lead to novel optical effects and open new possible applications.Comment: 48 pages, 13 figures. accepted to Phys. Rev. B; to appear vol. 66, 200

Dipole Response of Spaser on an External Optical Wave

We find the conditions upon the amplitude and frequency of an external electromagnetic field at which the dipole moment of a Bergman-Stockman spaser oscillates in antiphase with the field. For these values of the amplitude and frequency the losses in metal nanoparticles is exactly compensated of by gain. This shows that spasers may be used as inclusions in designing lossless metamaterials

A generalization of Snoek's law to ferromagnetic films and composites

The present paper establishes characteristics of the relative magnetic permeability spectrum $\mu$(f) of magnetic materials at microwave frequencies. The integral of the imaginary part of $\mu$(f) multiplied with the frequency f gives remarkable properties. A generalisation of Snoek's law consists in this quantity being bounded by the square of the saturation magnetization multiplied with a constant. While previous results have been obtained in the case of non-conductive materials, this work is a generalization to ferromagnetic materials and ferromagnetic-based composites with significant skin effect. The influence of truncating the summation to finite upper frequencies is investigated, and estimates associated to the finite summation are provided. It is established that, in practice, the integral does not depend on the damping model under consideration. Numerical experiments are performed in the exactly solvable case of ferromagnetic thin films with uniform magnetization, and these numerical experiments are found to confirm our theoretical results. Microwave permeability measurements on soft amorphous films are reported. The relation between the integral and the saturation magnetization is verified experimentally, and some practical applications of the theoretical results are introduced. The integral can be used to determine the average magnetization orientation in materials with complex configurations of the magnetization, and furthermore to demonstrate the accuracy of microwave measurement systems. For certain applications, such as electromagnetic compatibility or radar absorbing materials, the relations established herein provide useful indications for the design of efficient materials, and simple figures of merit to compare the properties measured on various materials