Depolarization of the electromagnetic field scattered by a three-dimensional large-scale irregularity of the lower ionosphere

This paper develops analytical and numerical methods for the solution of three-dimensional problems of radio wave propagation. We consider a three-dimensional vector problem for the electromagnetic field of a vertical electric dipole in a planar Earth-ionosphere waveguide with a largescale local irregularity of negative characteristics at the anisotropic ionospheric boundary. The field components at the boundary surfaces obey the Leontovich boundary conditions. The problem is reduced to a system of two-dimensional integral equations taking into account the overexcitation and depolarization of the field scattered by the irregularity. Using asymptotic (with respect to the parameter kr≫1, where r is the distance from the source or receiver to the nearest point of the irregularity, k=2π/λ, and λ is the radio wavelength) integration over the direction perpendicular to the ray path, we transform this system to one-dimensional integral equations where integration contours represent the geometric contour of the irregularity. The system is numerically solved in the diagonal approximation, combining direct inversion of the Volterra integral operator and subsequent iterations. The proposed numerical algorithm reduces the computer time required for the solution of this problem and is applicable for studying both small-scale and large-scale irregularities. We obtained novel estimates for the field components that are not excited by the source but result entirely from scattering by the sample three-dimensional ionospheric irregularity.     

Depolarization of the electromagnetic field in a locally inhomogeneous earth-ionosphere waveguide

This paper presents a further development of the numerical-analytical method for the solution of three-dimensional problems in the theory of radio wave propagation. We consider a vector problem of the electromagnetic field of a vertical electric dipole in a plane Earth-ionosphere waveguide with a local large-scale irregularity on the anisotropic ionosphere wall. The possibility of lowering (elevating) of the local region of the upper waveguide wall with respect to the regular ionosphere level is taken into account. The field components on the boundary surfaces obey the Leontovich impedance conditions. The problem is reduced to a system of two-dimensional integral equations taking into account the overexcitation and depolarization of the field scattered by the irregularity. Using asymptotic (with respect to the parameter kr ≫1) integration along the direction perpendicular to the ray path, we transform this system to a system of one-dimensional integral equations. The system is solved numerically in the diagonal approximation, combining direct inversion of the Volterra integral operator and the subsequent iterations. The proposed method reduces the computer time required for solving the problem and is useful for the study of both small-scale and large-scale irregularities. We obtained estimates of the TE field components that are not excited by the source considered and originate entirely from field scattering by a three-dimensional irregularity disturbing the geometric regularity of the ionospheric waveguide wall. State University of St. Petersburg, Russia Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 7, pp. 617–629, July, 2000.     

Estimation of field in plane impedance waveguide with local geometrical irregularity. II

The author investigates effect on the field of a point source in a plane impedance waveguide of an irregularity in the form of spherical surface that projects from (or is embedded into) the plane of the, ionospheric wall of the waveguide. In a scalar approximation, the problem is reduced to a two-dimensional integral equation over the surface of the irregularity. A solution is constructed by successive approximations, for which the solution of the problem for a regular impedance waveguide is used as the initial approximation. Numerical results are given for estimation of the effect of a local ionospheric irregularity on the field of an electric dipole in the earth-ionosphere waveguide.St. Petersburg State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 6/7, pp. 569–578, June–July, 1992.     

Nonlinear resonance of plasma waves in the thermal irregularities of ionospheric plasma

We study the effect of striction plasma density disturbances on the generation intensity of longitudional cold and plasma oscillations due to polarization of the magnetic field-aligned ionospheric plasma irregularities with δN_o<0 by a powerful radio wave. It is assumed that the plasma density level inside the irregularity intersects the upper-hybrid resonance level, in the vicinity of which the cold oscillations excited directly by a powerful radio wave are transformed to shorter-wave plasma oscillations. We consider the short plasma wave limit to reduce the problem to a system of two coupled equations for the cold wave induction and plasma wave electric field. The first equation is supplemented by a local source equal to the integral of the plasma wave electric field in the resonance region. The second equation involves the cold wave induction at the resonance point and describes the electric field of interacting waves in the resonance vicinity. We use simplifications connected with the small absorption of plasma waves propagating inside the irregularity and weak radiation of these waves outside the irregularity. These conditions correspond to the generation of eigenmodes of plasma oscillations trapped in the irregularity. We have obtained a resonance-type nonlinear equation for the electric field intensity (or energy flux) of eigenmode plasma waves with allowance for striction disturbances of the plasma density profile in the resonance region. It is shown that the striction expulsion of plasma is responsible for the occurrence of coefficients describing the change in the intensity of excitation and radiation of plasma waves at the irregularity boundary. Such an expulsion leads to variations of the efficient generation band of plasma eigenmodes with the total phase increment of the wave in the irregularity. It also leads to a change in the phase shift of the plasma wave reflected from the resonance. These coefficients and the nonlinear phase shift are expressed in terms of real wave functions of the nonlinear Airy equation which describes the electric field of the excited waves in the resonance vicinity when the dissipation is absent. Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow region, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 3, pp. 270–297, March, 1998.     

Calculation of VLW fields in a waveguide with A 3-D local inhomogeneity

The problem of a point-source field in an irregular impedance waveguide is solved. The 3-D inhomogeneity of one of the walls of the waveguide is given by an area-inhomogeneous impedance. To obtain a solution within the framework of the method of integral equations, we develop a procedure for asymptotic transformation of the 2-D equation into an 1-D equation with allowance for the waves reflected from all the inhomogeneity boundaries. The obtained 1-D integral equation for points that belong to both the path line and boundary contour of the inhomogeneity is solved numerically using an original algorithm. The results of model calculations in a near-earth waveguide for the case of ionospheric perturbations that are large on the wavelength scale are given.State University, St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 12, pp. 1312–1322, December, 1995.     

Influence of ionospheric irregularities on the form of radio signal scattering spectrum in over-the-horizon radar sounding of the rough sea surface

Abstract

This paper is concerned with the backscattering of HF radio waves from the rough sea surface, which have propagated through the ionosphere with random large-scale irregularities.

For the sake of simplicity, it is assumed in calculations that the rough sea surface is a perfectly conducting surface with the known Philips power spectrum of irregularities. Ionospheric irregularities of a random medium that are isotropic and single-scale ones, with a Gaussian spectrum, are considered within the limits of the hypothesis of frozen-in irregularities.

Within the first approximation of perturbation theory, using, as the incident wave and the Green function, their geometrical-optics approximations, we obtained the expression for the backscattering spectrum of the ionospheric chirp radio signal with a Gaussian envelope. The expression involves the parameters of the receive–transmit antenna, the signal, the propagation medium, and of the scattering surface. Numerical simulation was used to investigate the influence of all the above-mentioned parameters on the backscattering spectrum. It is shown that travel of ionospheric irregularities has the largest influence on the scattering spectrum, the signal parameters mainly determine the size of the scattering area in the range, and the form of the coherent integration window determines the form of the received signal and can distort it.     

On solution of the vector 3-D locally irregular waveguide problem

The vector 3-D problem of a point-source field in a plane waveguide with a large-scale local inhomogeneity on one of its walls is considered. The field components on the boundary surfaces comply with the Leontovich conditions, which are used as a basis for obtaining expressions for the derivatives of the field vectors normal to the boundaries; these expressions reflect the 3-D nature of the inhomogeneity. The problem is reduced to a system of 2-D integral equations allowing for overexcitation and depolarization of the field scattered by the irregularity. The system of 2-D integral equations is asymptotically transformed over the inhomogeneity region on the surface of the walls bounding the waveguide space into a system of linear integral equations, for which the integration contour is represented by the line between the source and observation point, as well as by the linear geometric contour of the irregularity.State University, St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 8, pp. 785–803, August, 1995.     

Influence of ionospheric irregularities on the form of radio signal scattering spectrum in over-the-horizon radar sounding of the rough sea surface

This paper is concerned with the backscattering of HF radio waves from the rough sea surface, which have propagated through the ionosphere with random large-scale irregularities.

For the sake of simplicity, it is assumed in calculations that the rough sea surface is a perfectly conducting surface with the known Philips power spectrum of irregularities. Ionospheric irregularities of a random medium that are isotropic and single-scale ones, with a Gaussian spectrum, are considered within the limits of the hypothesis of frozen-in irregularities.

Within the first approximation of perturbation theory, using, as the incident wave and the Green function, their geometrical-optics approximations, we obtained the expression for the backscattering spectrum of the ionospheric chirp radio signal with a Gaussian envelope. The expression involves the parameters of the receive-transmit antenna, the signal, the propagation medium, and of the scattering surface. Numerical simulation was used to investigate the influence of all the above-mentioned parameters on the backscattering spectrum. It is shown that travel of ionospheric irregularities has the largest influence on the scattering spectrum, the signal parameters mainly determine the size of the scattering area in the range, and the form of the coherent integration window determines the form of the received signal and can distort it.     

Estimation of field in plane impedance waveguide with local geometrical inhomogeneity. I

The effect of an inhomogeneity in the form of a circular cylinder the properties of whose base are described by a certain impedance and whose lateral surface is ideally conducting on the field of a point source in a plane impedance waveguide is studied. In a scalar approximation, the problem is reduced to a two-dimensional integral equation over the surface of the inhomogeneity. A solution is constructed by the method of successive approximations; the solution of the problem for a regular impedance waveguide is used as an initial approximation. The effect of a local ionospheric inhomogeneity on the field of an electrical dipole in the earth-ionosphere waveguide is estimated.Leningrad State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 8, pp. 908–918, August, 1991.     

Influence of ionospheric irregularities on decameter radio wave propagation: Mathematic modeling

Based on numerical simulation and using the Monte Carlo method, an investigation is carried out of the influence of random irregularities in the ionospheric F-region on short-wave propagation along one-hop radio paths.Irkutsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 11, pp. 1439–1446, November, 1994.     

Radiative transfer in a layer of magnetized plasma with random irregularities

The problem of radio wave reflection from an optically thick plane uniform layer of magnetized plasma is considered in the present work. The plasma electron density irregularities are described by a spatial spectrum of arbitrary form. The small-angle scattering approximation in invariant ray coordinates is proposed as a technique for the analytical investigation of the radiation transfer equation. The approximate solution describing the spatial and angular distribution of radiation reflected from a plasma layer is obtained. The solution obtained is investigated numerically for the case of ionospheric radio wave propagation. Two effects occur as a consequence of multiple scattering: a change in the reflected signal intensity and an anomalous refraction.     

Numerical investigation of characteristics of laser radiation scattered in an integrated optical waveguide with three-dimensional inhomogeneities

Specifics of theoretical analysis of wave phenomena in irregular integrated optical waveguides are investigated. The object of the investigation and the main types of irregularities (smooth, statistical, and sharp) are described. The goals of the numerical modeling are formulated. The structure of the program and the general structure of the algorithm allowing numerical investigation of guided modes’ scattering from 3D-irregularities of an integrated optical waveguide are described. The dispersion relations of the TE and TM modes of the integrated optical waveguide under investigation, as well as field patterns of the radiating TE modes of the substrate and the laser radiation scattered from the three-dimensional guiding-layer inhomogeneities of an integrated optical waveguide, are presented. The results are analyzed in detail. The methods developed can be used for numerical investigation of the characteristics of laser radiation scattered in various optical waveguides with three-dimensional irregularities.     

Round-the-clock measurements of absorption and motions in the lower atmosphere for diversity reception of signals from LF broadcasting stations

The computer Doppler filtering of a ground wave is proposed for diversity reception of signals from LF broadcasting stations with a high-stability master oscillator. This method can be employed in round-the-clock measurements of the motion characteristics, absorption, and angles of arrival of radio waves. The method was implemented in a LF receiving complex. First results on the dynamics of ionospheric irregularities and radio wave absorption at ionospheric D-layer heights are presented. Institute of Solar-Terrestrial Physics, Siberian Branch of the Russian Academy of Sciences, Iskutsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 7, pp. 836–844, July, 1997.     

On the problem of coastal refraction in an impedance waveguide

The problem of wave propagation in an irregular plane impedance waveguide is considered. This problem is similar to the classical coastal refraction problem with arbitrary geometry of the coastline. The two-dimensional integral equation is converted asymptotically in the large parameter kr1 to a one-dimensional equation, which contains, besides the conventional terms, a curvilinear integral taken along the interface (coastline). A convenient formula is obtained for the case of a straight coastline. The results of numerical calculations are presented.State University, St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 11, pp. 1168–1176, November, 1995.     

Two-dimensional theory of elf electromagnetic wave propagation in the earth-ionosphere waveguide channel

We present a surface theory of the 2-D telegraph equation and describe the methods for obtaining parameters L and C of this theory from the electromagnetic field of the dominant normal wave and its propagation constant together with the first two azimuthal derivatives. To excite the waveguide by vertical and horizontal electric dipoles, we determine the external sources of the 2-D telegraph equation, which are the 2-D point external voltage and the oriented point external specific voltage, respectively. The relation between the effective and physical sources is practically independent of the ionospheric conditions. The effective source of the horizontal dipole is proportional to the earth 's surface impedance at the source location.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 9, pp. 1103–1113, September, 1996.This work was supported by grant 01.067 of the Competition Center at St. Petersburg State University.     

Ultralong-range sounding of the ionospheric HF channel using an ionosonde/direction finder with chirp modulation of the signal

We present the results of experimental studies of propagation of short radio waves on a long transequatorial path of Laverton (Australia) — Rostov-on-Don, which were obtained with the help of an ionosonde/direction finder with chirp modulation of the signal. It is shown that conditions for propagation of anomalous signals by means of sideband reflection of radio waves from the Himalayan Hills and the Plateau of Iran and also due to scattering of radio waves from the high-latitude ionosphere of the northern hemisphere are realized on the given path. The propagation of radio waves is modeled with allowance for their scattering by anisotropic magnetic field-aligned irregularities of a high-latitude ionosphere, which are located on the northern wall of the main ionospheric trough of the F layer. It is shown that the results of the experiment agree well with the calculated data.     

A Novel Three-Dimensional Wide-Angle Beam Propagation Method Based on Split-Step Fast Fourier Transform

A novel three-dimensional wide-angle beam propagation method based on the split-step fast Fourier transform is developed. The formulation is based on the three-dimensional Helmholtz wave equation. Each propagation step is performed by utilizing both the FFT and split-step scheme. The solution of Helmholtz wave equation does not make the slowly varying envelope and one-way propagation approximations. To validate the efficiency and accuracy, numerical results for a propagation beam in a tilted step-index optical waveguide are compared with other beam propagation algorithms.     

The Structure of a Chirp Signal in the Randomly Inhomogeneous Earth-Ionosphere Channel

We analyze theoretically the structure of a chirp-ionosonde signal for the cases of one- and two-hop propagation in the randomly inhomogeneous ionosphere. For the case of two-hop propagation, wave scattering by the rough ground is taken into account. Our numerical simulation showed that random ionospheric irregularities and ground roughnesses play a significant role in the formation of a signal structure. We compare numerical results with experimental data obtained at oblique ionospheric sounding.     

Turbulence spectrum of the upper ionosphere

The problem of defining the spectral form of ionospheric irregularities with dimensions from hundreds to thousands of meters is considered. A generalized model is proposed for the ionospheric turbulence spectrum, taking into account both the anisotropic properties of the large-scale fraction of irregularities and the dependence of the anisotropy (elongation) of small-scale irregularities of the upper ionosphere along the Earth magnetic field direction on the transverse scale of those irregularities. Relations have been derived to determine the basic parameters of the irregularity spectrum of the uppers ionosphere (anisotropy indices for large-scale and small-scale fractions) and the depth of a thin ionospheric layer through measurement of the spectral characteristics of amplitude and phase fluctuations of orbital satellite signals. Using this model of the plasma irregularity spectrum, we can explain consistently many well-known experimental data on spectral characteristics of the phase and amplitude fluctuations of orbital satellite signals both in the high-latitude and midlatitude ionosphere. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 4, pp. 446–456, April, 1997.     

Consistent quasi-periodic variations of the geomagnetic pulsation level and doppler frequency shift of decametric radio waves aspect-scattered by artificial field-aligned ionospheric irregularities

We present the results of experimental studies of consistent quasi-periodic variations of the geomagnetic-pulsation level and effective Doppler frequency shift of decametric radio waves aspectscattered by artificial field-aligned ionospheric irregularities. For processing of signals, we used a system spectral analysis and a correlation analysis. It is shown that quasi-periodic variations of the effective Doppler frequency shift are caused by geomagnetic-field pulsations with an amplitude of 0.5–1.0 nT and a period of 50–150 s. Estimated amplitudes of the quasi-periodic and aperiodic drift velocities of the ionospheric irregularities appeared close to 5–10 and 15–30 m/s, respectively.