Nonplanar Waves Research Articles

Time evolution of nonplanar dust ion-acoustic solitary waves in a charge varying dusty plasma with superthermal electrons

A theoretical study on the nonlinear propagation of nonplanar (cylindrical and spherical) dust ion-acoustic solitary waves (DIASW) is carried out in a dusty plasma, whose constituents are inertial ions, superthermal electrons, and charge fluctuating stationary dust particles. Using the reductive perturbation theory, a modified Korteweg-de Vries equation is derived. It is shown that the propagation characteristics of the cylindrical and spherical DIA solitary waves significantly differ from those of their one-dimensional counterpart.

A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution

In the present work, we consider the propagation of nonlinear electron-acoustic non-planar waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical coordinates through the use reductive perturbation method in the long-wave approximation. The modified cylindrical Korteweg–de Vries equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, which is fractional, this evolution equation cannot be reduced to the conventional Korteweg–de Vries equation. An analytical solution to the evolution equation, by use of the method developed by Demiray [Appl. Math. Comput. 132, 643 (2002); Comput. Math. Appl. 60, 1747 (2010)] and a numerical solution by employing a spectral scheme are presented and the results are depicted in a figure. The numerical results reveal that both solutions are in good agreement.

Nonplanar ion-acoustic shock waves in a multi-ion plasma with nonextensive electrons and positrons

The basic features of ion-acoustic shock waves (IASHWs) in a multi-ion nonextensive plasma (containing positive light ions, negative heavy ions, as well as nonextensive electrons and positrons) have been rigorously investigated in a nonplanar geometry. The standard reductive perturbation method has been employed to derive the Modified Burgers (MB) equation. The combined effects of the electron and positron nonextensivity, and the ion kinematic viscosity significantly have been found to modify the basic properties of these electrostatic shock structures. The properties of the cylindrical and the spherical IASHWs are observed to differ significantly from those of onedimensional planar waves. The findings obtained from this theoretical investigation may be useful in understanding the characteristics of IASHWs both in space and laboratory plasmas.

Instability of nonplanar modulated dust acoustic wave packets in a strongly coupled nonthermal dusty plasma

Cylindrical and spherical amplitude modulations of dust acoustic (DA) solitary wave envelopes in a strongly coupled dusty plasma containing nonthermal distributed ions are studied. Employing a reductive perturbation technique, a modified nonlinear Schrödinger equation including the geometrical effect is derived. The influences of nonthermal ions, polarization force, and the geometries on the modulational instability conditions are analyzed and the possible rogue wave structures are discussed in detail. It is found that the spherical DA waves are more structurally stable to perturbations than the cylindrical ones. Possible applications of these theoretical findings are briefly discussed.

Nonplanar Ion-acoustic Waves in a Relativistically Degenerate Quantum Plasma

Nonplanar Ion-acoustic Waves in a Relativistically Degenerate Quantum Plasma

The analysis of plane discontinuities in offset cylindrical waveguides.

This paper applies the re-expansion method for analyzing the effects on the sound field due to planar discontinuities at the junction of two offset circular acoustic waveguides. The normal modes in the two waveguides are expanded at the junction plane into a system of functions accounting for velocity singularities at the corner points. As the new expansion has a high convergence order, only a few terms have to be considered for obtaining the solution of most practical problems. This paper gives the equivalent impedance accounting for nonplanar waves into a plane-wave analysis. The last section of the paper applies the re-expansion technique to the case of two offset pipes (step discontinuity) and to that of an offset aperture in a cylindrical pipe (diaphragm-type discontinuity). The plots of the discontinuity inductance, characterized by Karal's factor, are quite similar but the values in the second case are 1.5-2 times larger, showing that the diaphragm-type discontinuity excites much more nonplanar evanescent modes than the step discontinuity.

Determination of in-duct sound power beyond the plane wave range using wall-mounted microphones

When studying the acoustic wave propagation in a duct, the frequency range can be divided into the low frequency plane wave range and the high frequency range with non-plane waves. In the low frequency range, the wave propagation is one-dimensional and the governing equations are rather simple. The larger the duct, the lower the frequency limit of the non-plane waves. Therefore, also taking into account the three-dimensional acoustic wave propagation is important, especially when considering the duct systems used in large machines. In practice often a harsh environment and immobile structures restrict the use of standardized noise measuring methods. For instance to characterize the exhaust noise of medium speed internal combustion engines (IC-engines) in situ, the in-duct sound pressures are measured using wall-mounted microphones. Then the low frequency range source sound power can be estimated by wave decomposition (“two-microphone method”). Often a three-microphone array is used to cover a sufficiently large frequency range. One way to formulate the sound pressure and sound power relationship in the high frequency range is to weight the sound pressures at the duct wall in one-third octave bands. The aim of this study is to extend the classical plane wave formulation by determining these weighting factors, so that a three-microphone array also can be used beyond the plane wave range. The results from numerical approach are compared to experimental data.

The free surface influence on blast vibration

When a charged blasthole initiates it typically radiates P waves and shear-vertical (SV) waves. Furthermore, dependent upon the velocity of detonation (VoD), P-Mach and/or SV-Mach waves will form, which will contain a significant proportion of the blast vibrational energy. It is important to understand the influence of the free surface on such wave radiation when considering near field vibration monitoring for material damage/fragmentation and far field surface vibration monitoring for statutory compliance. The reflection characteristics of plane P- and SV-waves incident on a free surface are given by the well-known Zoeppritz equations. However, it is much more difficult to derive the reflection characteristics for the non-planar waves radiated from a blasthole. This work describes an analytical model in which the non-planar incident radiation from a blasthole is given by the Heelan solution and its reflection from the free surface is approximated using the Zoeppritz equations. Predictions of the free surface influence using this analytical model are in good agreement with the predictions from a dynamic finite element model. The analytical model also shows that as the VoD increases, the reflected vibrational energy is channelled further away from the near field. Thus the model predicts that the explosive VoD can be altered to control damage in specific near-field regions. In this regard, the present analytical method produces a complete near field vibration damage model in which the VoD and the free surface play crucial roles. At high VoD, the radiation approaches grazing incidence at the surface in the far field. This phenomenon is relevant to monitoring far field vibration.

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

This paper presents a parameter-free perfectly matched layer (PML) method for the finite-element-based solution of the Helmholtz equation. We employ one of Bermúdez et al.'s unbounded absorbing functions for the complex coordinate mapping underlying the PML. With this choice, the only free parameter that controls the accuracy of the numerical solution for a fixed numerical cost (characterised by the number of elements in the bulk and the PML regions) is the thickness of the perfectly matched layer, δPML. We show that, for the case of planar waves, the absorbing function performs best for PMLs whose thickness is much smaller than the wavelength. We then perform extensive numerical experiments to explore its performance for non-planar waves, considering domain shapes with smooth and polygonal boundaries, different solution types (smooth and singular), and a wide range of wavenumbers, k, to identify an optimal range for the normalised PML thickness, kδPML, such that, within this range, the error introduced by the presence of the PML is consistently small and insensitive to change. This implies that if the PML thickness is chosen from within this range no further PML optimisation is required, i.e. the method is parameter-free. We characterise the dependence of the error on the discretisation parameters and establish the conditions under which the convergence of the solution under mesh refinement is controlled exclusively by the discretisation of the bulk mesh.

Optical chirality exhibited by two axially propagating electromagnetic waves in counter-rotations

The optical chirality of two axially propagating electromagnetic waves is investigated. These two waves of different nature are in counter-rotations, thereby being non-plane waves. From the resulting spatial distributions of energy and chirality, we find not only enhancements but also cancellations due to the interferences in these hybrid waves. In addition, the roles of the axial wave number and interference phase are illustrated by introducing a proper figure of merit for relevant device performances.

Near-Field Image Restoration for Rotman Lens by Localized Angle-Time Spread Function-Based Filtering Method

Rotman lens is a prospective device for real-time microwave/millimeter-wave imaging by virtue of its parallel multibeam functionality. For imaging purposes, a Rotman lens intrinsically requires that the scattered waves arriving at the array be plane waves. However, this requirement cannot be met in near-field imaging applications, as the scattered waves from targets in the near field defocus at the beam ports of the lens because of the nonplane wave scattering. As a result, out-of-focus blurs appear in the near-field images, thus leading to degradation of picture quality. To address this problem, we propose a localized angle-time spread function (ATSF)-based filtering method to reduce out-of-focus blurs. With the proposed method, the deblurring process becomes simple for a Rotman lens. Both simulations and experiments were performed. The results show that the proposed method significantly improves the quality of near-field images with enhanced resolutions in both angular and radial directions.

Cylindrical and spherical dust-acoustic wave modulations in dusty plasmas with non-extensive distributions

The nonlinear wave modulation of planar and non-planar (cylindrical and spherical) dust-acoustic waves (DAW) propagating in dusty plasmas, in the presence of non-extensive distributions for ions and electrons is investigated. By employing multiple scales technique, a cylindrically and spherically modified nonlinear Schrodinger equation (NLSE) is derived. The presence of hot non-extensive q-distributed ions and electron is shown to influence the modulational instability (MI) of the waves. It is shown that the properties of the MI of DAW in cylindrical and spherical geometry differ from those in a planar one-dimensional geometry. Furthermore, it is observed that the non-extensive distributed ions have more effect on the MI of the DAW than electrons. Also, it is found that there is a MI period for cylindrical and spherical wave modulations, which does not exist in the one-dimensional case.

A geometric calibration mehtod of hydrophone array with known sources in near field under strong multipath

In order to meet the demand of underwater acoustic array calibration in near field with strong reflection, a high-precision geometric calibration method with known sources is proposed. Colligating the principles of non-plane wave model of point source and the Taylor approximation, a two-dimensional geometry error model for near field is established. And then the line mapping relationship is obtained between geometric error of sensors and signal eigen vector. Cramer-Rao bound (CRB) of this mode is deduced and analyzed. The influence of multipath on geometric calibration is studied. The strong reflections are compared to the coherent sources at a known position, and the compensation strategy is realized. The results from theory and simulation show that the precision of geometry calibration technique with accessorial sources in near field is high and it is close to the CRB in the case of low SNR. The method has a certain tolerance for the position error of accessorial sources. And it is applicable for multipath. Pool test results further verify the correctness of these results.

Vorticity deposition, structure generation and the approach to self-similarity in colliding blast wave experiments

When strong shocks interact with transverse density gradients, it is well known that vorticity deposition occurs. When two non-planar blast waves interact, a strong shock will propagate through the internal structure of each blast wave where the shock encounters such density gradients. There is therefore the potential for the resulting vorticity to produce pronounced density structures long after the passage of these shocks. If the two blast waves have evolved to the self-similar (Sedov) phase this is not a likely prospect, but for blast waves at a relatively early stage of their evolution this remains possible. We show, using 2D numerical simulations, that the interactions of two ‘marginally young’ blast waves can lead to strong vorticity deposition which leads to the generation of a strong protrusion and vortex ring as mass is driven into the internal structure of the weaker blast wave.

Freak waves in Saturn’s magnetosphere

Properties of planar as well as nonplanar ion acoustic freak waves that propagate in a plasma composed of warm ions and two-temperature electron plasma having kappa-distribution are reported. The dynamics of the nonlinear freak waves is governed by a modified nonlinear Schrodinger equation. The possible region for the freak waves to exist is defined precisely for typical parameters of Saturn’s magnetosphere. For planar case, stability/instability analyses reveals that there is a critical value (f cr ) of f (i.e., the equilibrium density ratio of the hot-to-cold electron species) exists for low wave number k. For large wave number k, the stability domain is always a decreasing function in f. Low κ values, which indicate that an excess of suprathermal particles in the tail of the distribution, shifts f cr to higher values. Also, there exists a modulation instability period for the cylindrical and spherical envelope excitations, which does not exist in the one-dimensional case. Furthermore, cylindrical and spherical freak waves are investigated numerically. Spherical ion-acoustic freak waves are found to grow faster than the cylindrical waves.

Electron vortex beams prepared by a spiral aperture with the goal to measure EMCD on ferromagnetic films via STEM.

X-ray magnetic circular dichroism is a well established method to study element specific magnetic properties of a material, while electron magnetic circular dichroism (EMCD), which is the electron wave analogue to XMCD, is scarcely used today. Recently discovered electron vortex beams, that carry a discrete orbital angular momentum (OAM) L, are also predicted to reveal dichroic signals. Since electron beams can be easily focused down to sub-nanometer diameters, this novel technique promises the possibility to quantitatively determine local magnetic properties with unrivalled lateral resolution. As the spiralling wave front of the electron vortex beam has an azimutally growing phase shift of up to 2π and a phase singularity in its axial center, specially designed apertures are needed to generate such non-planar electron waves. We report on the preparation and successful implementation of spiral apertures into the condenser lens system of an aberration-corrected FEI Titan(3) 80-300 transmission electron microscope (TEM). This setup allows to perform scanning TEM (STEM) with vortex beams carrying user-selected OAM. First experiments on the interaction of the vortex beam with a poly-crystalline sample are presented. Within the achieved signal to noise ratio no EMCD signal has been detected. This finding is supported by simulations of inelastic scattering of a beam generated by spiral aperture.

Nonplanar dust acoustic solitary waves in a strongly coupled dusty plasma with superthermal ions

The nonplanar amplitude modulation of dust acoustic (DA) envelope solitary waves in a strongly coupled dusty plasma (SCDP) has been investigated. By using a reductive perturbation technique, a modified nonlinear Schrödinger equation (NLSE) including the effects of geometry, polarization, and ion superthermality is derived. The modulational instability (MI) of the nonlinear DA wave envelopes is investigated in both planar and nonplanar geometries. There are two stable regions for the DA wave propagation strongly affected by polarization and ion superthermality. Moreover, it is found that the nonlinear DA waves in spherical geometry are the more structurally stable. The larger growth rate of the nonlinear DA MI is observed in the cylindrical geometry. The salient characteristics of the MI in the nonplanar geometries cannot be found in the planar one. The DA wave propagation and the NLSE solutions are investigated both analytically and numerically.

Closed-Form Analysis of Artificial Dielectric Layers—Part I: Properties of a Single Layer Under Plane-Wave Incidence

This two-part sequence of papers deals with the analysis of artificial dielectric layers (ADLs). ADLs consist of a cascade of planar periodic surfaces designed to realize dielectric slabs with a desired equivalent permittivity. A single layer is typically composed of an array of electrically small patches periodically arranged in a rectangular lattice. In this paper we present an analytical formulation to model a single layer for arbitrary plane-wave incidence, highlighting the characteristic properties and their frequency range of validity. We derive a closed-form solution for the magnetic current distribution, including the reactive near field on the crossing slots, by expanding the total current with ad-hoc entire-domain basis functions. Simple analytical expressions are also derived for the equivalent sheet impedance of the layer. The second part of the paper extends the analysis to finite ADL slabs and nonplane wave sources.

ОТКРЫТЫЙ РЕЗОНАТОР С ОТРЕЗКОМ ПРЯМОУГОЛЬНОГО ВОЛНОВОДА

A hemispherical open resonator with a rectangular waveguide section mounted at the center of the open resonator plane mirror is considered. A theoretical analysis has been made to find out that the excitation efficiency of the waveguide wave TE 10 excited by the open resonator oscillation TEM 0 0 q can reach 90 % for some certain cross-sectional dimensions of the waveguide. To this end, a hemispherical open resonator with a superdimensional rectangular waveguide section was experimentally studied in the 4 mm wave region. The cross-sectional dimensions were chosen under the condition of obtaining maximum excitation efficiency of the fundamental waveguide wave. The study shows that the excitation of the fundamental mode alone holds in this resonant system across the whole tuning range. Comparison of reflection coefficients of a waveguide-loaded resonator either with or without a reflecting diffraction grating at the waveguide section bottom indicates that both of the electrodynamic systems have nearly equal losses. Key words: excitation efficiency, open resonator, overmoded rectangular waveguide, diffraction grating Manuscript submitted 29.04.2014 Radio phys. radio astron. 2014, 19(3): 249-257 REFERENCES 1. MIROSHNICHENKO, V. S., SENKEVICH, E. B., PIVOVAROVA, A. G., and YUDINTSEV, D. V., 2010. Excitation of oscillations in a generator of diffraction radiation with multistage space interaction. Izv. vuzov . Radiofizika. vol. 53, no. 3, pp. 200–209 (in Russian). 2. RUSIN, F. S. and BOGOMOLOV, G. D., 1968. Orotron as millimeter-wave generator. 3. SHESTOPALOV, V. P. (ed.), VERTII, A. A., and ERMAK, G. P., 1991. Diffraction radiation oscillators . Kyiv: Naukova Dumka Publ. (in Russian). 4. MYASIN, E. A., EVDOKIMOV, V. V., and IL'IN A. Yu., 2011. Orotron with double periodic structure range 140 ... 300 GHz. Radiotekhnika i Elektronika , vol. 56, no. 4, pp. 454–467 (in Russian). 5. MIROSHNICHENKO, V. S., DUDKA, V. G., YUDINTSEV, D. V., 2010. Shaping of Extended Fields in the Open Resonator with Trapezoidal Mirrors. Radiophysics and Electronics , vol. 15, no. 2. pp. 16–21 (in Russian). 6. SHESTOPALOV, V. P., 1976. Diffraction electronics . Kharkov: Kharkiv University Publishers. 7.KUZ'MICHEV, I. K. and HLOPOV, G. I. 1989. Consistent stimulation Quasi-optical Open Resonator. In: Quasi-optical equipment in the millimeter and submillimeter waves . Kharkiv, Ukraine: IRENASU Publ. pp. 149–156 (in Russian). 8. BURSHTEIN, E. L., 1958. On the power received by the antenna in the fall at her non-planar wave. Radiotekhnika I Elektronika , vol. 3, no. 2, pp. 186–189 (in Russian). 9. KAY, A. F., 1960.Near-field gain of aperture antennas. IEE Trans. Antennas Propag. vol. 8, no. 6, pp. 586–593. DOI: https://doi.org/10.1109/TAP.1960.1144905 10. KUZMICHEV, I. K., 2009. Exitation efficiency of quasioptical resonancesystems. Telecommunications and Radio Engineering. vol. 68, no. 1, pp. 49–63. DOI:10.1615/TelecomRadEng.v68.i1.30 11. KUHN, R., 1967. Microwave antenna. Leningrad. USSR: Sudostroenie Publ. (in Russian). 12. SUHU, R. F., 1963. Non confocal multi-wave resonators for quantum-mechanical oscillator. Proc. IEEE , vol. 51, no.1, pp. 106–111 (in Russian). 13. SHESTOPALOV, V. P., 1985. Physical basis for millimeter- and submillimeter-wave equipmen . Vol. 2 (Sources. Element base. Radio Systems), Kyiv: Naukova dumka Publ. (in Russian). 14. FRAIT, Z. and PATTON, C. E., 1980. Simple analytic method formicrowave cavity Q determination. Rev. Sci. Instrum . vol. 51, no. 8, pp. 1092–1094. DOI: https://doi.org/10.1063/1.1136368 15. VALITOV, R. A. (ed.), DYUBKO, S. P., and KAMYSHAN, V. V., 1969. Technique submillimeter waves . Moskow: Sov. radio Publ. (in Russian). 16. ANDROSOV, V. P. and KUZ'MICHEV, I. K., 1987. The influence of internal irregularities open cavity to communicate with its oscillation waveguide lines . Kharkiv, Ukraine: IRENASU Publ. (in Russian). 17. TARASOV, L, V., 1981. The physics of the processes in generators of coherent optical radiation . Moskow: Rasio i Svyaz' Publ. (in Russian).

Nonplanar ion-acoustic shock waves in degenerate plasmas with positively charged heavy ions

The theoretical and numerical study on the nonlinear propagation of heavy-ion-acoustic (HIA) shock waves has been carried out in an unmagnetized, collisionless dense plasma system (containing degenerate electron and inertial light ion fluids, and positively charged static heavy ions). The normal mode analyse is used to investigate the linear wave properties. Reductive perturbation technique is used to derive the Burgers equation which admits a localized wave solution for the shock profile. It is seen that the shock wave characteristics have been influenced significantly for the non-relativistic as well as for the ultra-relativistic limits. It has also been found that the effect of degenerate pressure and number density of electron and inertial light ion fluids, and positively charged static heavy ions significantly modify the basic features (speed, amplitude, width, etc.) of HIA shock waves. The relevance of our results in astrophysical objects (like white dwarfs and neutron stars), which are of scientific interest, is briefly discussed.