Dielectric Ellipsoids Research Articles

Modeling of a New Electron Acceleration Mechanism Ahead of Streamers

AbstractHead‐on collisions between negative and positive streamers have been proposed as a mechanism behind X‐ray emissions by laboratory spark discharges. Recent simulations using plasma fluid and particle in cell models of a single head‐on collision of two streamers of opposite polarities in ground pressure air predicted an insignificant number of thermal runaway electrons >1 keV and hence weak undetectable X‐ray emissions. Because the current available models of a single streamer collision failed to explain the observations, we first use a Monte Carlo model coupled with multiple static dielectric ellipsoids immersed in a subbreakdown ambient electric field as a description of multiple streamer environment and we investigate the ability of multiple streamer‐streamer head‐on collisions to accelerate runaway electrons >1 keV up to energies ∼200–300 keV instead of just one single head‐on collision. The results of simulations show that the streamer head‐on collision mechanism fails to accelerate electrons; instead, they decelerate in the positive streamer channel. In a second part, we use a streamer plasma fluid model to simulate a new streamer‐electron acceleration mechanism based on a collision of a large negative streamer with a small neutral plasma patch in different Laplacian electric fields |E0|= (35, 40, 45) kV/cm, respectively. We observe the formation of a secondary short propagating negative streamer with a strong peak electric field >250 up to 378 kV/cm over a time duration of ∼0.16 ns at the moment of the collision. The mechanism produces up to 106 runaway electrons with an upper energy limit of 24 keV.

Near-field inverse electromagnetic scattering problems for ellipsoids

The scattering problems of time-harmonic electromagnetic plane waves by a penetrable or an impenetrable ellipsoidal scatterer are considered. A low-frequency formulation of the corresponding direct scattering problems using the Rayleigh approximation is described. A method for solving inverse electromagnetic scattering problems for ellipsoids using near-field data is presented. A finite number of measurements of the zeroth low-frequency approximation of the electric scattered field lead to specify the orientation as well as the size of the ellipsoids. This method is applied for the cases of the perfectly conductive, the impedance, the lossless dielectric and the lossy dielectric ellipsoids. Especially for the case of penetrable ellipsoids, using additionally the leading order term of the low-frequency expansion of the magnetic scattered field, the physical parameters of the ellipsoids are also specified. Corresponding results for spheres and spheroids considering them as geometrically degenerate forms of the ellipsoid are presented.

Optically driven oscillations of ellipsoidal particles. Part II: ray-optics calculations.

We report numerical calculations on the mechanical effects of light on micrometer-sized dielectric ellipsoids immersed in water. We used a simple two-dimensional ray-optics model to compute the radiation pressure forces and torques exerted on the object as a function of position and orientation within the laser beam. Integration of the equations of motion, written in the Stokes limit, yields the particle dynamics that we investigated for different aspect ratios k. Whether the beam is collimated or focused, the results show that above a critical aspect ratio k(C), the ellipsoids cannot be stably trapped on the beam axis; the particle never comes to rest and rather oscillates permanently in a back-and-forth motion involving both translation and rotation in the vicinity of the beam. Such oscillations are a direct evidence of the non-conservative character of optical forces. Conversely, stable trapping can be achieved for k < k(C) with the particle standing idle in a vertical position. These predictions are in very good qualitative agreement with experimental observations. The physical origin of the instability may be understood from the force and torque fields whose structures greatly depend on the ellipsoid aspect ratio and beam diameter. The oscillations arise from a non-linear coupling of the forces and torques and the torque amplitude was identified as the bifurcation control parameter. Interestingly, simulations predict that sustained oscillations can be suppressed through the use of two coaxial counterpropagating beams, which may be of interest whenever a static equilibrium is required as in basic force and torque measurements or technological applications.

Magneto-optical effect in a system of colloidal particle having anisotropic dielectric property

Spherical, non-cubic crystal nanoparticles with an anisotropic dielectric constant and a weak intrinsic magnetic moment, such as goethite nanoparticles, can be considered to be equivalent to a magnetic dielectric ellipsoid. For colloids based on such ellipsoids, the dielectric constant is isotropic in zero magnetic field. However, when a magnetic field is applied, the moments’ Brownian rotation, which is connected with the rotation of the ellipsoids themselves, will induce order in the orientation of the dielectric ellipsoids, so that the dielectric constant of the colloids becomes anisotropic to exhibit magneto-optical effect. As the orientation of the dielectric ellipsoids has been ordered by the magnetic field, the mechanism of optical effects is different from general ferrofluids and liquid crystals, and can be viewed as an optically anisotropic action which results from the coupling of both the magnetic and dielectric properties, i.e. the optical effects only come up when a magnetic field is applied because all the dielectric ellipsoids become aligned. It is confirmed from theory and experiment that for magnetic colloid based on spherical nanoparticles with cubic crystal structure, the magneto-optical effects cannot be due to the reaction of single particles.

Computational study of the optical trapping of ellipsoidal particles

Ellipsoidal dielectric particles may be trapped in a linearly polarized Gaussian beam such that they are harmonically bound with respect to each of their rotational and translational degrees of freedom. The ellipsoid belongs to the highest symmetry class for which this is possible. Typically, the longest axis of the ellipsoid aligns itself with the incident beam axis and the second longest with the polarization direction. We investigate this special property by evaluating the trap stiffness matrix for dielectric ellipsoids with aspect ratios (largest:smallest dimension) in the range 1--10, using the discrete dipole approximation. The results are interpreted using a simple phenomenological model and conclusions are drawn concerning optimization of the trap stiffness for specific applications.

Localized plasmons at pores and clusters within inhomogeneous indium nitride films

We report on reproducibly observed enhancement of luminescence within inhomogeneous InN films near both In clusters and pores. Low-temperature absorption in these films deviates from that expected for a conventional semiconductor. The enhancement of emission is discussed in terms of coupling of excited radiative states with localized particle plasmons. It implies concentration of an electric field near the pores and clusters, which are considered, respectively, as metallic and dielectric ellipsoids within a semiconductor matrix. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Control of spontaneous emission by complex nanostructures.

Spontaneous emission in the presence of complex nanostructures is discussed by use of a calculational scheme that permits us to deal with interfaces of arbitrary shape. Control over the field associated with the emission is shown to be attainable. In particular, decay rates are offered for geometries that lead to focusing and collimation of near- and far-field distributions. Emission from axially symmetric gratings is shown to lead to narrow angular distributions of emission, and focusing at the foci of dielectric ellipsoids is achieved for dimensions comparable with the wavelength. In the latter case the total emission rate for two atoms in an ellipsoidal cavity is shown to be enhanced in a way that deviates from the predictions of the Dicke effect by means of intermediate- and far-field contributions.

Effective medium theory for dispersions of dielectric ellipsoids

A material composed of a mixture of distinct homogeneous media can be considered as a homogeneous one at a sufficiently large observation scale. In literature, a widely dealt topic is that of calculating the overall permittivity of a dispersion of dielectric spheres in a homogeneous matrix: the well-known Maxwell formula solves the problem in the case of very diluted suspensions. Moreover, this relationship has been adapted, to yield correct results even if the dispersion in not strongly diluted, by means of the so-called Bruggeman's procedure. In this paper, we apply this technique to perform a complete study on the equivalent permittivity of a dispersion of ellipsoids. The obtained solutions allow us to evaluate the effects of the shape of the inclusions on the overall electric behaviour of the mixture. In particular we find explicit expressions, which give the equivalent permittivity of the medium in terms of the eccentricities of the embedded ellipsoids and of some stoichiometric parameters. The treatment is carried out both for aligned ellipsoidal inclusions and for randomly oriented ellipsoids. In particular, new explicit relationships have been derived for dispersions of generally shaped randomly oriented ellipsoids.

Electrohydrodynamic instabilities and orientation of dielectric ellipsoids in low-conducting fluids.

We study the dynamics of an ellipsoidal particle in a weakly conducting dielectric liquid when submitted to a dc electric field. At low field intensities, the particle long axis is aligned in the field direction. When the field strength is increased, we show that, depending on the initial orientation of the particle, there exist two stable orientations: the one with the long axis parallel to the field direction remains possible while a spinning state with the long axis perpendicular to the field appears. This last striking orientation is due to the finite Maxwell-Wagner polarization relaxation time. For sufficiently high field intensities, each state loses its stability and the particle dynamics becomes chaotic. Those conclusions from the theoretical model are supported by experimental observations.

Integral equation model of light scattering by an oriented monodisperse system of triaxial dielectric ellipsoids: application in ectacytometry

A novel mathematical model of light scattering by an oriented monodisperse system of triaxial dielectric ellipsoids of complex index of refraction is presented. It is based on an integral equation solution to the scattering of a plane electromagnetic wave by a single triaxial dielectric ellipsoid. Both the position and the orientation of a single representative scatterer in a given coordinate system are considered arbitrary. A Monte Carlo simulation is developed to reproduce the diffraction pattern of a population of aligned ellipsoids. As an example of practical importance, light scattering by a population of erythrocytes subjected to intense shear stress is modeled. Agreement with experimental observations and the anomalous diffraction theory is illustrated. Thus a novel check of the electromagnetic basis of ektacytometry is provided. Furthermore, the versatility of the integral equation method, particularly in the advent of parallel processing systems, is demonstrated.

An Integral Equation Solution To the Scattering of Electromagnetic Radiation By a Linear Chain of Interacting Triaxial Dielectric Ellipsoids. the Case of a Red Blood Cell Rouleau

A mathematical formalism describing plane electromagnetic wave scattering by a linear chain of N triaxial dielectric ellipsoids of complex index of refraction is presented. The Fredholm integral equation theory is employed. As a first approximation, electromagnetic coupling between only neighbouring scatterers is taken into account. The case of non-negligible coupling between any pairs of scatterers is a straightforward extension of the present treatment. However, the computing time demands in that case are particularly high. The analysis is based on the Lippman-Schwinger integral equation for the electric field. The corresponding integral equation for the scattering, which contains N singular kernels, is transformed into N non-singular integral equations for the angular Fourier transform of the field indide each scatterer. The latter equations are solved by reducing them by quadrature into a matrix equation. The resulting solutions are used to calculate the scattering amplitude. As a numerical application, the case of a red blood cell rouleau consisting of three adjacent oblate spheroidal models of erythrocytes is considered. Typical values of the appropriate discretization parameters which are sufficient for achieving convergence, as well as certain validity tests are provided. The effect of electromagnetic coupling between neighbouring scatterers is demonstrated. Efficient techniques for reducing the rather high computing requirements of the analysis, such as parallel processing, are both suggested and applied.

Integral equation solution to the scattering of electromagnetic radiation by a system of two interacting triaxial dielectric ellipsoids: the case of a two red blood cell Rouleau

A mathematical formulation of the problem of electromagnetic wave scattering by a system of two homogeneous triaxial dielectric ellipsoids of complex index of refraction is presented. The analysis is based on the Lippman–Schwinger integral equation for an electric field. The corresponding integral equation for the scattering, which contains two singular kernels, is transformed into a pair of nonsingular integral equations for the angular Fourier transform of the electric field inside each scatterer. The latter equations are solved by reducing them by quadrature into a matrix equation. The resulting solutions are used to calculate the scattering amplitude. As a numerical application, the case of a two red blood cell rouleau model is considered. Typical values of the appropriate discretization parameters, which proved sufficient for achieving convergence, are presented, along with validity tests. The effect of the electromagnetic coupling of the scatterers is also illustrated. Efficient techniques, which are capable of reducing the rather high computing demands of the analysis, such as parallel processing, are both suggested and applied.

Effect of the Electric Field on Wave Motion in a Thin Suspension Layer Flowing Over an Inclined Plane

Stability of surface gravity waves in an inclined layer of rheological fluid in the presence of an arbitrarily oriented electric field is considered to investigate the effect of electric fields on wave stability. Rheological equations used for a dilute suspension of the rigid dielectric ellipsoids take into account the influence of electric fields on a particular orientation. The evolution equation is derived as a long-wavelength approximation which includes a set of nondimensional parameters responsible for the behaviour of the suspension. Solution of the evolution equation is obtained in the form of a nonlinear wave with the amplitude and phase slowly varying in time in such a way as to allow determination of the curves of neutral stability, bifurcations, suband supercritical instabilities. The results of calculations show that the electric field can both stabilise or destabilise waves.

An approach to the inverse obstacle problem from the scattering Mueller matrix

A solution of the inverse obstacle problem based on the measurable Mueller matrix for randomly orientated particles is presented. The problem is ill-posed and nonlinear. It also possibly has non-unique solutions due to the rotational averaging of scattering intensity. The angular dependence of the Mueller matrix elements gives the complete linear scattering information of the scatterers at the chosen wavelength. By employing the Mueller matrix information, a better inverse solution is expected. The solution proposed here uses a statistical modelling method to build a model that correlates the size and shape of the scatterers to the calculated Mueller matrix elements. The model is then optimized for maximum prediction precision. Because no suitable set of particles was available for experimental measurement, the method was evaluated with calculated scattering data. The forward calculations were carried out with the T-matrix method for homogeneous dielectric ellipsoids, and the size and shape were characterized by the semimajor rotation axis of the ellipsoid, a and the axial ratio a/b, respectively. It was found that the usual total scattering intensity, M11, does not correlate well to the size and shape of the scatterers. The correlation is much improved when polarization information From other elements is included in to the models. It was also shown that from the models tested, no uniqueness problem was observed. The precision of the predictions was within 3% for predicted sizes and shapes which were covered by the model and from 3-4% for predictions near but outside the calibration range. This inverse solution possesses the advantages of: (1) using measurable quantities directly, (2) employing a fast and simple algorithm, and (3) excellent prediction precision. This method has also provided excellent results for the prediction of etching height and profile from Mueller matrix element measurements of gratings on semiconductor wafers.

A model for backscattering characteristics of tall prairie grass canopies at microwave frequencies

We have developed a discrete microwave scattering model, describing the radar backscattering coefficient from two treatments (burned and unburned) of tall prairie grass canopies at VV (electric field vector of the transmitted and received signals are vertically oriented) and HH (electric field vector of the transmitted and received signals and horizontally oriented) polarizations, based on the physical, biophysical, and geometrical characteristics of such canopies. Grass blades are modeled as thin and finite dielectric ellipsoids with arbitrary orientations. Scattering by an individual grass blade is formulated using a generalization of the Rayleigh—Gans approximation with a quasistatic solution for the expansion of the interior field. By associating, with each grass blade, various appropriate distribution functions, the relative orientation, location, height, cross section, and permittivity of each grass blade is taken into account. This makes for a more realistic overall description of the canopy. Kirchhoff's surface scattering is used to model the backscatter from the soil surface. An incoherent summation of the effect of grass blades and soil surface is adopted to obtain the total canopy backscattering coefficient, taking into account the attenutaion experienced by the signal as it travels through the canopy. The results of this model are given for 1.5, 5, and 10 GHz (L-, C-, and X-band). Although for the shorter wavelengths (X-band) the Rayleigh—Gans criteria is not totally satisfied, nevertheless, the limited available measured X-band data compare relatively well with the results of this model both quantitatively and qualitatively.

Polarizability and Effective Permittivity of Layered and Continuously Inhomogeneous Dielectric Ellipsoids

In this paper, the polarizabilities of partially and continuously inhomogeneous dielectric ellipsoids are analyzed. Multilayer inclusions where the boundaries between the layers are confocal ellipsoids, are solved in a static field. Transmission line analogy is applied, resulting in matrices with which the field components and the polarizability can be solved. In case of the continuous permittivity profile, a differential equation is derived for the scattered potential, and from the amplitude of this function, the polarizability results. The limitation in the continuous case is that the permittivity function of the ellipsoid depend only on one coordinate (ξ) in the ellipsoidal coordinate system. The theory is applied to calculating the microwave attenuation of melting hail at the frequency of 1 GHz, where the hydrometeors are modeled as two-layer ellipsoids.

Radar Backscatter from a Vegetation Layer with Rough Ground Boundary

The problem of radar backscattering from a vegetation layer with a smooth or a rough ground boundary is formulated by a Monte Carlo method. The vegetation layer is assumed to contain a mixture of randomly distributed dielectric discs and thin prolate ellipsoids whose phase matrices are known and whose distributions of angular orientations can be prescribed independently. The ground boundary is modelled by a Fresnel reflection coefficient for a plane lossy surface or a Kirchhoff lossy surface as the case may be. Results from the Monte Carlo simulations are compared with calculations of a matrix-doubling method by [9], and also with measurements from fields of wheat, soyabean, milo and corn [7,20]. The results indicate that the Monte Cario method presented in this paper can give a good fit with experimental data, using parameters which are believed to be reasonable.

Polarizability and Effective Permittivity of Layered and Continuously Inhomogeneous Dielectric Spheres

In this paper, the polarizabilities of partially and continuously inhomogeneous dielectric ellipsoids are analyzed. Multilayer inclusions where the boundaries between the layers are confocal ellipsoids, are solved in a static field. Transmission line analogy is applied, resulting in matrices with which the field components and the polarizability can be solved. In case of the continuous permittivity profile, a differential equation is derived for the scattered potential, and from the amplitude of this function, the polarizability results. The limitation in the continuous case is that the permittivity function of the ellipsoid depend only on one coordinate (ξ) in the ellipsoidal coordinate system. The theory is applied to calculating the microwave attenuation of melting hail at the frequency of 1 GHz, where the hydrometeors are modeled as two-layer ellipsoids.

Differential scattering of circularly polarized light by chromatin modeled as a helical array of dielectric ellipsoids within the born approximation.

AbstractTheoretical predictions within the Born approximation of the expected differential light scattering of circularly polarized light (CIDS) were made for the 300‐Å chromatin fiber, modeled as a helical array of dielectric ellipsoids. Computed CIDS values were strongly dependent on the exact geometry of the solenoid model, depending particularly on parameters relaed to the chiral nature of the fiber and the orientation of the nucleosomes within the helix, in contrast to the values of the total light scattering, which mainly probed size and shape. In particular, both a superbead model and a strict linear 110‐Å nucleosome filament would be predicted as giving rise to zero CIDS (in disagreement with the finite values observed). At the same time, helical models in which the normal vectors to the nucleosome faces were exactly parallel to the helical axis also yielded zero CIDS. Confirming earlier expectations, CIDS values were significantly less dependent on helical length than total light scattering. Finally, comparison of these calculated results from those extrapolated from available experimental data indicates that predicted CIDS values, based on currently accepted models of solenoid structure, are within an order of magnitude of those experimentally observed. Together, these results indicate the potential of differential light scattering measurements as a probe of chromatin higher‐order structure, complementary to existing scattering measurements.

Dielectric and crystal-optic properties of lithium ammonium tartrate mono-hydrate ferro-elastic crystal under mechanic stress: Piezo-dielectric and piezooptic effects at the phase transition

Abstract Dielectric constants, birefringence and rotation of optical and dielectric ellipsoids in LAT vs temperature and mechanic stress are studied