Method Of Smooth Perturbations Research Articles

Scintillation Level of Scattered Radio Waves in the Equatorial Ionosphere

Scintillation effects of propagating and scattered radio waves (RWs) are considered analytically and numerically in the equatorial terrestrial ionosphere applying the statistical characteristics. Analytical calculations of the second-order statistical moments of the phase fluctuations of the ordinary and extraordinary RWs in the conductive collision ionospheric magnetoplasma (COCOIMA) are carried out for the first time using the Wentzel-Kramers-Brilluen method and the modified smooth perturbation method in consideration of the diffraction effects. Polarization coefficients of these waves in the equatorial ionosphere have been derived for the first time. The scintillation level includes the variance and the correlation functions of scattered RWs. Statistical moments contain complex refractive index, anisotropy coefficient characterizing irregular plasmonic structures, tilt angle of prolate irregularities concerning to the external magnetic field, permittivity components of the equatorial ionosphere, Hall's, Pedersen and longitudinal conductivities. A new feature of the "Fountain Effect" has been discovered in the equatorial ionosphere at weak and moderate scintillations caused due to anisotropy parameters of electron density fluctuations. Anisotropy parameters of electron density inhomogeneities influence the scintillation index of both the ordinary and extraordinary radio waves shifting maximums of the curves in the opposite directions at weak and moderate scintillations. Numerical calculations are carried out using the hybrid anisotropic correlation function of electron density fluctuations containing both exponential and power-law spectral functions having arbitrary spectral index, applying the experimental data.

Структурно-многолучевой подход к разработке пространственно-временной модели одномодового декаметрового канала связи с диффузной многолучевостью

A structural-multipath approach has been developed for constructing a spatiotemporal model of a single-mode decameter communication channel, which makes it possible to determine the two-frequency spatial correlation function of a single-mode decameter communication channel and to establish the dependences of frequency and spatial correlation intervals of fading on the operating frequency, diffuse ionosphere parameters, and radio link geometry. The method for constructing this model of a communication channel using the structural multipath approach includes four stages: 1) development of a multibeam spatiotemporal decameter model of a communication channel; 2) development of a radiophysical space-time model of radio wave propagation in a decameter radio link, taking into account the influence of inhomogeneities (diffusion) of the ionosphere based on the method of smooth perturbations; 3) identification of multipath and radiophysical models to determine the two-frequency spatial correlation function of the decameter of the communication channel; 4) determining the dependence of frequency and spatial correlation intervals of fading in a single-mode decameter communication channel on the choice of operating frequency, diffuse ionosphere parameters, and radio link geometry.

Influence Characteristics of Laser Transmission Amplitude Fluctuation Based on Turbulent Medium

In order to study the transmission characteristics of laser in atmospheric turbulent medium and understand the influence degree of various factors on amplitude fluctuation, by means of smooth perturbation method, this paper establishes a theory model of amplitude fluctuation of laser propagation in turbulent medium by using the smooth perturbation method and reflects the amplitude fluctuation degree, carries out specific discussion on each influence factor. The results show that the larger the wavelength, the more stable the amplitude fluctuation. With the increase of laser section radius, the amplitude fluctuates sharply and then decreases slowly after reaching the peak. Transmission distance is the main influence factor of amplitude fluctuation. With the increase of transmission distance, the amplitude fluctuation will become more obvious. The amplitude acquisition can be comprehensively modulated in a specific transmission distance by wavelength and section ra-dius, so as to ensure the stability of the received laser and provide a theoretical basis for the interferometry technology.

Sharp-interface approach for simulating solid-state dewetting in two dimensions: A Cahn–Hoffman [formula omitted]-vector formulation

By using a Cahn–Hoffman ξ-vector formulation, we propose a sharp-interface approach for solving solid-state dewetting problems in two dimensions. First, based on the thermodynamic variation and smooth vector-field perturbation method, we rigorously derive a sharp-interface model with weakly anisotropic surface energies, and this model describes the interface evolution which occurs through surface diffusion flow and contact line migration. Second, a parametric finite element method in terms of the ξ-vector formulation is proposed for numerically solving the sharp-interface model. By performing numerical simulations, we examine several specific evolution processes for solid-state dewetting of thin films, e.g., the evolution of small islands, pinch-off of large islands and power-law retraction dynamics of semi-infinite step films, and these simulation results are consistent with experimental observations. Finally, we also include the strong surface energy anisotropy into the sharp-interface model and design its corresponding numerical scheme via the ξ-vector formulation.

Statistical Moments and Scintillation Level of Scattered Electromagnetic Waves in the Magnetized plasma

Statistical characteristics of scattered ordinary and extraordinary electromagnetic waves in the magnetized plasma are considered using the smooth perturbation method. Diffraction effects and polarization coefficients are taken into account. Second order statistical moments of scattered radiation are obtained for arbitrary correlation function of electron density fluctuations. Broadening of the spatial power spectrum and displacement of its maximum, wave phase structure function and the angle-of-arrivals are obtained for three-dimensional spectral function containing anisotropic Gaussian and power-law spectral functions. Scintillation level of scattered radiation is analyzed for different parameters characterizing anisotropic plasma irregularities for the ionospheric F-region. The spectral widths (first and second moments) of the power spectrum and scintillation periods are calculated for “frozen-in” drifting elongated plasma irregularities using the experimental data.

Features of interferometry of small-sized plasma channels obtained during nanosecond discharge

The applicability of the method of smooth perturbations for processing interferograms of small (5–100 μm) objects by taking into account the diffraction is investigated. The test problems showed the consistency of the method to the range of parameters that are interesting for us. The requirements for preliminary processing of experimental data are determined, adhering to which it is possible to improve the accuracy of the final results. The analysis of experimental interferograms by assuming the cylindrical symmetry of the plasma object is carried out: the two-dimensional map of the electron density for the plasma object formed at the initial stage of nanosecond discharge was obtained from the phase map.

Statistical Characteristics and Scintillation Level of Scattered Radio Waves in the Magnetized Plasma

Second order statistical moments of scattered radiation in the magnetized plasma is considered using modified smooth perturbation method taking into account both diffraction effects and polarization coefficients of both the ordinary and extraordinary waves. The broadening of the spatial spectrum and displacement of its maximum are obtained. Scintillation level of scattered waves is analyzed for different parameters characterizing anisotropic irregularities for the ionospheric F-region.

STATISTICAL MOMENTS AND SCINTILLATION LEVEL OF SCATTERED ELECTROMAGNETIC WAVES IN THE MAGNETIZED PLASMA

Statistical characteristics of scattered ordinary and extraordinary electromagnetic waves in the magnetized plasma are considered using the smooth perturbation method. Diffraction effects and polarization coefficients are taken into account. Second order statistical moments of scattered radiation are obtained for arbitrary correlation function of electron density fluctuations. Broadening of the spatial power spectrum and displacement of its maximum, wave phase structure function and the angle-of-arrivals are obtained for three-dimensional spectral function containing anisotropic Gaussian and power-law spectral functions. Scintillation level of scattered radiation is analyzed for different parameters characterizing anisotropic plasma irregularities for the ionospheric F-region. The spectral widths (first and second moments) of the power spectrum and scintillation periods are calculated for “frozen-in” drifting elongated plasma irregularities using the experimental data.

SCINTILLATION EFFECTS AND THE SPATIAL POWER SPECTRUM OF SCATTERED RADIO WAVES IN THE IONOSPHERIC F REGION

Differential equation for two-dimensional spectral function of the phase fluctuation is derived using the modify smooth perturbation method. Second order statistical moments of the phase fluctuations are calculated taking into account polarization coefficients of both ordinary and extraordinary waves in the turbulent collision magnetized plasma and the diffraction effects. Analytical and numerical investigations in the ionospheric F region are based on the anisotropic Gaussian and power law spectral functions of electron density fluctuations including both the field-aligned anisotropy and field-perpendicular anisotropy of the plasma irregularities. Scintillation effects in this region are investigated for the small-scale ionospheric irregularities. The large-scale background plasma structures are responsible for the double-humped shape in the spatial power spectrum taking into account diffraction effects. Numerical calculations are based on the experimental data of the navigation satellites.Â

Second Order Statistical Moments of the Power Spectrum of Ionospheric Scintillation

Paper considers some aspects of the relationship between scintillation level of scattered radiation and anisotropic plasma irregularities in the collision turbulent magnetized plasma. Analytical calculations are carried out using modify smooth perturbation method taking into account both diffraction effects and polarization coefficients of both ordinary and extraordinary waves. Correlation function and the wave structure function of the phase fluctuations are obtained for arbitrary correlation function of electron density fluctuations. Analytical and numerical calculations of the second order statistical moments are carried out for the anisotropic Gaussian correlation function taking into account both anisotropy factor and the inclination angle of the elongated plasma irregularities with respect to the external magnetic field. Scintillation level and the power spectrum of the intensity fluctuations are analyzed for different parameters characterizing anisotropic irregularities.

''DOUBLE-HUMPED EFFECT'' IN THE TURBULENT COLLISION MAGNETIZED PLASMA

Statistical moments of the spatial power spectrum of multiple scattered ordinary and extraordinary waves in the turbulent collision magnetized plasma with aligned anisotropic electron density irregularities are investigated using modify smooth perturbation method taking into account diffraction effects. Correlation function and variances of the phase fluctuations are obtained for arbitrary correlation function of the electron density fluctuations. Double-humped Effect is investigated analytically and numerically using the anisotropic Gaussian spectral function of electron density irregularities for the polar ionospheric F-region applying the experimental data. Investigation of the anisotropy of the F layer irregularities is of great interest in ionospheric physics. It is well known that the irregularities are elongated in the direction of the geomagnetic field of lines, but especially at high latitudes they are also found to be anisotropic in the plane perpendicular to the external magnetic field vector. The anisotropy is usually investigated by correlation analysis of radio signals from satellites, observed by space receiver on the ground. The fluctuations in amplitude and phase (scintillations) of radio waves passing through the ionosphere are caused by spatial irregularities in the electron density. The spatial fluctuations in phase cause fluctuations of the angle of arrival at the observation points. Broadening of the spatial power spectrum (SPS) of scattered electromagnetic (EM) waves in the turbulent collision magnetized plasma for both power-law and anisotropic Gaussian correlation functions of electron density fluctuations was analyzed in (1) using the complex ray (-optics) approximation. Double-humped Effect, the features of the SPS, spectral width and shift of its maximum of multiple scattered EM waves in the turbulent collisionless magnetized plasma were considered in (2, 3). The influence of the collision frequency between plasma particles on the statistical characteristics of scattered EM waves in the turbulent magnetized plasma with both electron density and external magnetic field fluctuations was investigated in (4). The present paper reports the results of an analysis of the SPS, which is related to fluctuations of the radio refractive index in the F region. Analytical expressions of the correlation function of phase fluctuations of scattered both ordinary and extraordinary waves are obtained for the arbitrary correlation functions of electron density fluctuation using modify smooth perturbation method taking into account the diffraction effects. The Double-humped Effect in the collision magnetized plasma with elongated electron density irregularities is considered for the first time. Formation of a gap in the SPS of scattered radiation is analyzed numerically for the polar ionospheric F -region using the anisotropic Gaussian spectral function of electron density fluctuations. This spectrum contains angle of aligned plasma irregularities to the direction of an external magnetic field and anisotropy factor. The numerical calculation is computed based on experimental data. Finally, paper concludes the obtained results and their significance.

Comparison of Kolmogorov's and coherent turbulence.

Features of optical wave fluctuations while propagating through a randomly inhomogeneous turbulent medium with a finite outer scale are considered, including conditions when areas with dominating influence of one large-scale coherent structure are observed in the atmosphere, for which the spectrum of atmospheric turbulence can differ significantly from the Kolmogorov model spectrum. Using an approximate model of the spectrum for coherent turbulence, described earlier in our works, the variance of jitter of an optical image is calculated (under the applicability condition for the smooth perturbation method). The comparison of these equations with known similar equations for Kolmogorov turbulence has shown that the variance of fluctuations is significantly weaker in coherent turbulence than in the Kolmogorov theory under similar conditions. This means that phase fluctuations of optical radiation decrease significantly in coherent turbulence. The importance of this conclusion is noted for interpretation of the results of optical sounding of atmospheric turbulence.

Features of optical image jitter in a random medium with a finite outer scale

Features of optical wave fluctuations while propagating through a randomly inhomogeneous turbulent medium with a finite outer scale are considered, including conditions when areas with dominating influence of one large scale coherent structure are observed in the atmosphere, for which the spectrum of atmospheric turbulence can differ significantly from the Kolmogorov model spectrum. Using an approximate model of the spectrum for coherent turbulence, described earlier in our works, the variance of jitter of an optical image is calculated (under the applicability condition for the smooth perturbation method). The comparison of these equations with known similar equations for Kolmogorov turbulence has shown that the variance of fluctuations is significantly weaker in coherent turbulence than in the Kolmogorov theory under similar conditions. This means that phase fluctuations of optical radiation decrease significantly in coherent turbulence. The importance of this conclusion is noted for interpretation of the results of optical sounding of atmospheric turbulence.

SOME PECULIARITIES OF THE SPATIAL POWER SPECTRUM OF SCATTERED ELECTROMAGNETIC WAVES IN RANDOMLY INHOMOGENEOUS MAGNETIZED PLASMA WITH ELECTRON DENSITY AND EXTERNAL MAGNETIC FIELD FLUCTUATIONS

Statistical characteristics of multiply scattered electro- magnetic waves in turbulent magnetized plasma with both electron density and external magnetic fleld ∞uctuations are considered. Ana- lytical expression for phase ∞uctuations of scattered radiation is derived using the smooth perturbation method. Correlation and wave struc- ture functions of the phase ∞uctuations, angle-of-arrivals are obtained for arbitrary correlation functions of ∞uctuating plasma parameters and external magnetic fleld taking into account the difiraction efiects. The evolution of a double-peaked shape in the spatial power spec- trum of scattered radiation is analyzed numerically for both anisotropic Gaussian and power-law spectra of electron density ∞uctuations using experimental data. Phase portraits of external magnetic fleld ∞uc- tuations have been constructed for difierent non-dimensional spatial parameters characterizing a given problem.

Phase fluctuations of optical waves in the case of cone focusing in turbulent atmosphere

Statistical parameters of phase fluctuations of optical radiation with a cone-shape wavefront propagating in turbulent atmosphere are studied. The method of smooth perturbations is used for calculation of the variance of phase fluctuations of conical optical waves formed by conical and conoidal axicons. It is found that the variance of phase fluctuations of a conical optical wave in turbulent atmosphere is less than that of a plane wave and a fundamental Bessel beam. The dependence of the variance of phase fluctuations on the parameter characterizing the cone-shape wavefront of an optical wave, is of a two-scale character for both conical and conoidal axicons. A decrease in the variance of phase fluctuations in turbulent atmosphere is more typical for the conical axicon than for the conoidal. The spatial nonuniformity of phase fluctuations, known for a fundamental Bessel beam, occurs for conic optical waves as well; however, the quantitative value of the effect differs in this case.

SPATIAL POWER SPECTRUM OF MULTIPLE SCATTERED ORDINARY AND EXTRAORDINARY WAVES IN MAGNETIZED PLASMA WITH ELECTRON DENSITY FLUCTUATIONS

Features of the spatial power spectrum (SPS) of multiple scattered ordinary and extraordinary waves in randomly inhomogeneous magnetized plasma are investigated using the smooth perturbation method taking into account difiraction efiects. Second order statistical moments are derived for arbitrary correlation function of electron density ∞uctuations at oblique illumination of magnetized plasma by mono-directed incident radiation. Numerical calculations have been carried out for anisotropic Gaussian correlation function taking into account anisotropy factor and angle of inclination of prolate irregularities with respect to the external magnetic fleld. It was shown that SPS has a double-peaked shape. External magnetic fleld narrows SPS for ordinary wave and the gap arises in the direction of prolate irregularities. For extraordinary wave the gap increases with a distance passing by the wave in anisotropic magnetized plasma, the width broadens and maximum slightly displaced.

Bessel-Gaussian beam phase fluctuations in randomly inhomogeneous media

Bessel-Gaussian beam phase fluctuations in randomly inhomogeneous media are studied. The results of calculations by the method of smooth perturbations of the variance of phase fluctuations of the above type of beams in the turbulent atmosphere are presented. The effect of the relative weakening of Bessel-Gaussian beam phase fluctuations in comparison with the case of a plane wave is revealed. A weak dependence of the phase fluctuation variance on the parameters of the Gaussian beam factor is observed. Gaussian beam phase fluctuations are spatially inhomogeneous: the ratio of the variances of the beam phase fluctuations at an out-of-optical-axis point to those at its optical axis is minimum in the Bessel beam maxima and maximum in the minima.

PECULIARITIES OF SPATIAL SPECTRUM OF SCATTERED ELECTROMAGNETIC WAVES IN ANISOTROPIC INHOMOGENEOUS MEDIUM

Features of spatial power spectrum (SPS) of scattered radiation in a randomly inhomogeneous medium with strongly prolated anisotropic inhomogeneities of dielectric permittivity are investigated. In single scattering approximation, it has been shown that a pronounced gap along a direction of prolate inhomogeneities appears in SPS. Features of SPS of multiple scattered waves at oblique illumination of a boundary of randomly-inhomogeneous medium with prolate irregularities have been analytically studied using smooth perturbation method taking into account diffraction effects. Numerical calculations have shown that with an increase of a distance passing by 192 Gavrilenko et al. the wave in random media, SPS has a double-peaked shape and a gap substantially increases. Its maximum is slightly changed and the width is broadening. The results have been obtained analytically for the first time and could find extensive practical application in optics and be useful in development of principles of remote sensing of random media.

Smooth perturbations the self–adjoint operators defined by the ℋ︁–2–construction

AbstractThe existence of the wave operators for the self–adjoint operator constructed by ℋ︁–2–construction is discussed in the abstract theory by using Kato's smooth perturbation method. Moreover, the s–matrix is calculated explicitly.

Application of the method of smooth perturbations to the solution of problems of optical tomography of strongly scattering objects containing absorbing macroinhomogeneities

It is shown that the solution of the nonstationary diffusion equation by the Rytov method of smooth perturbations can be represented in the form of a path integral taken along the mean photon trajectory. This form is convenient for the tomographic reconstruction of the distribution of macroinhomogeneities in a strongly scattering medium.