George Jandieri

A physical mechanism for the generation of slow and fast electromagnetic-type planetary waves due to standing factor—latitude variation of geomagnetic field—in the dissipative E-region of the ionosphere is suggested. It has been shown that slow waves are generated due to the dynamo-field in the ionosphere, and fast waves by the vortical electric field. The slow electromagnetic wave is analog to the Rossby planetary wave; the fast electromagnetic wave is a new mode of natural oscillations of the E-region of the ionosphere. Linear waves propagate along the parallel west and east directions in the dynamo-region of the ionosphere against a background of the mean zonal flow. Phase velocity of the fast waves is a few , oscillation frequencies are in the frequency band of 10−2– and the wavelength is of the order of and higher. Phase velocities of the slow waves and local winds are at the same order of magnitude, the frequency band is 10−4– and wavelength is of and higher order. Fast waves generate intense magnetic fields in order of a few hundred nanotesla (nT); slow waves—a few tens of nT.

In this paper the nonlinear theory of both fast and slow planetary electromagnetic waves in the E-region of the ionosphere is investigated for the first time. It was established that these perturbations are self-localized as nonlinear solitary vortical structures in the dynamo-region of the ionosphere move to the west (fast) and to the east (slow) against a background of the mean zonal flow. The nonlinear structure consists of cyclone–anticyclone-type mutual counter-clockwise-rotating vortices, which capture medium particles. Energy and enstrophy of these large-scale vortices are weakly attenuated and are long-lived. Vortical structures generate magnetic fields, which are an order of magnitude larger than those generated by the corresponding linear waves. Features and parameters of electromagnetic wavy structures are theoretically investigated and are in good agreement with the experimental data of large-scale ULF wavy perturbations observable in the ionosphere.

A mechanism is proposed for the generation of a vortex electric field in the ionospheric E-region. It is shown that long-scale (with a wavelength of L>103 km) synoptically short-period (from several minutes to several hours) fast (with a propagation velocity higher than 1 km/s) processes excite a vortex electric field that may be much higher than the dynamo field generated in this region by ionospheric winds.

The propagation of radiation from a point source through a plane layer of an absorbing medium with smooth random permittivity inhomogeneities is considered for the case in which the source and a receiver are spaced by different distances from the layer boundaries. The angular power spectra of the scattered radiation are calculated by the method of statistical modeling for different values of the layer thickness, positions of the source and the receiver relative to the layer, and absorption in the layer. The results for the moments of the angular power distribution obtained earlier in the small-angle approximation are fully confirmed. The transformation of the angular power spectrum upon variation of the source or receiver position with respect to the layer is analyzed for the first time.

Using an analogy method the frequencies of new modes of the electromagnetic planetary-scale waves (with a wavelength of 103 km or more), having a weather forming nature, are found at different ionospheric altitudes. This method gives the possibility to determine spectra of ionospheric electromagnetic perturbations directly from the dynamic equations without solving the general dispersion equation. It is shown that the permanently acting factor-latitude variation of the geomagnetic field generates fast and slow weakly damping planetary electromagnetic waves in both the L73E- and F-layers of the ionosphere. The waves propagate eastward and westward along the parallels. The fast waves have phase velocities (1–5) km s−1 and frequencies (10−1– 10−4 ), and the slow waves propagate with velocities of the local winds with frequencies (10−4–10−6 ) s−1 and are generated in the E-region of the ionosphere. Fast waves having phase velocities (10–1500) km s−1 and frequencies (1–10−3) s−1 are generated in the F-region of the ionosphere. The waves generate the geomagnetic pulsations of the order of one hundred nanoTesla by magnitude. The properties and parameters of the theoretically studied electromagnetic waves agree with those of large-scale ultra-low frequency perturbations observed experimentally in the ionosphere

A mechanism is proposed for the generation of a vortex electric field in the ionospheric E-region. It is shown that long-scale (with a wavelength of L>103 km) synoptically short-period (from several minutes to several hours) fast (with a propagation velocity higher than 1 km/s) processes excite a vortex electric field that may be much higher than the dynamo field generated in this region by ionospheric winds.

A study is made of oblique incidence of a small-amplitude plane electromagnetic wave on a semi-infinite slab of a collisional turbulent plasma in an external uniform magnetic field. In the small-angle scattering approximation, the condition for neutralizing the effects of oblique incidence and plasma anisotropy on the statistical properties of radiation multiply scattered in the absorbing plasma medium is determined by using the methods of geometrical optics. The validity of this condition was confirmed by numerical calculations based on the statistical modeling technique. The effect of the shape of the spectrum of the electron density fluctuations on the shape of the angular power distribution of a multiply scattered radiation is investigated.

In the present article, the results of theoretical investigation of the dynamics of generation and propagation of planetary (with wavelength 103 km and more) ultra-low frequency (ULF) electromagnetic wave structures in the dissipative ionosphere are given. The physical mechanism of generation of the planetary electromagnetic waves is proposed. It is established, that the global factor, acting permanently in the ionosphere—inhomogeneity (latitude variation) of the geomagnetic field and angular velocity of the earth's rotation—generates the fast and slow planetary ULF electromagnetic waves. The waves propagate along the parallels to the east as well as to the west. In E-region the fast waves have phase velocities (2–20) km s−1and frequencies (10−1–10−4) s−1; the slow waves propagate with local winds velocities and have frequencies (10−4–10−6) s−1. In F-region the fast ULF electromagnetic waves propagate with phase velocities tens–hundreds km s−1 and their frequencies are in the range of (10–10−3) s−1. The slow mode is produced by the dynamoelectric field, it represents a generalization of the ordinary Rossby-type waves in the rotating ionosphere and is caused by the Hall effect in the E-layer. The fast disturbances are the new modes, which are associated with oscillations of the ionospheric electrons frozen in the geomagnetic field and are connected with the large-scale internal vortical electric field generation in the ionosphere. The large-scale waves are weakly damped. The features and the parameters of the theoretically investigated electromagnetic wave structures agree with those of large-scale ULF midlatitude long-period oscillations (MLO) and magnetoionospheric wave perturbations (MIWP), observed experimentally in the ionosphere. It is established, that because of relevance of Coriolis and electromagnetic forces, generation of slow planetary electromagnetic waves at the fixed latitude in the ionosphere can give rise to the reverse of local wind structures and to the direction change of general ionospheric circulation. It is considered one more class of the waves, called as the slow magnetohydrodinamic (MHD) waves, on which inhomogeneity of the Coriolis and Ampere forces do not influence. These waves appear as an admixture of the slow Alfven- and whistler-type perturbations. The waves generate the geomagnetic field from several tens to several hundreds nT and more. Nonlinear interaction of the considered waves with the local ionospheric zonal shear winds is studied. It is established, that planetary ULF electromagnetic waves, at their interaction with the local shear winds, can self-localize in the form of nonlinear solitary vortices, moving along the latitude circles westward as well as eastward with velocity, different from phase velocity of corresponding linear waves. The vortices are weakly damped and long lived. They cause the geomagnetic pulsations stronger than the linear waves by one order. The vortex structures transfer the trapped particles of medium and also energy and heat. That is why such nonlinear vortex structures can be the structural elements of strong macroturbulence of the ionosphere.

A rigorous electromagnetic theory is developed to analyze multiport waveguide junctions with artificial inclusions made of cylindrical rods and placed in the main arm. The scattering characteristics of a 3-port junction are discussed with the numerical examples for the SWR maps, the power reflection and transmission coefficients, and the 3D plots of near fields inside the junction area. A strategy to optimize matching properties of the 3-port waveguide junctions is also described.

The strategy of optimising parameters of artificial discontinuities in multiport waveguide junctions is presented. This strategy is numerically illustrated for different canonical types of discontinuities, including conducting diaphragm, strip and circular rod. The numerical results for scattering characteristics of 3-port waveguide junctions with different types of discontinuities are discussed and optimal parameters of these discontinuities are predicted.

A rigorous electromagnetic theory is developed to analyze multiport waveguide junctions with artificial inclusions formed of the conducting strips and dielectric layers. The method is based on the Fourier transform technique combined with the mode matching method technique that takes into account the edge conditions in vicinity of the strip edges. The scattering characteristics of a 3-port junction are discussed with the numerical examples for the SWR maps, the power reflection and transmission coefficients, and the 2D plots of near fields distributions inside the junction area. A strategy of optimize matching properties of the 3-port waveguide junctions is also presented.

The strategy of optimising parameters of artificial discontinuities in multiport waveguide junctions is presented. This strategy is numerically illustrated for different canonical types of discontinuities, including conducting diaphragm, strip and circular rod. The numerical results for scattering characteristics of 3-port waveguide junctions with different types of discontinuities are discussed and optimal parameters of these discontinuities are predicted.

The propagation of acoustic-gravity, magnetonydrodynamic and planetary waves in the upper atmosphere is considered. The general dispersion equation for magneto-acoustic and magneto-gravity waves, as well as planetary waves, is derived in E and F ionospheric regions. Peculiarities of propagation of these waves are revealed in a weakly- ionized ionospheric plasma.

The problem of generation and existence conditions of both large-scale ultra-low-frequency wavy structures and large-scale vortices in the ionosphere is considered. Some exact solutions of magnetohydrodynamic equations are found, and new invariants allowing to reveal generation mechanisms of large-scale vortices and planetary waves in the ionosphere under the effect of nonconservative Coriolis and Ampere forces constructed. This method seems to be important and original in solving the most complicated nonlinear problems of the magnetohydrodynamics of compressible, inhomogeneous, baroclinic liquid being, in the general case, under non-conservative forces. Unfortunately, it is poorly known for a wide circle of investigators in magnetohydrodynamics and plasma physics.

Publication:

Radio Physics and Radio Astronomy, Vol. 12, p. 135

 Pub Date: June 2007 Bibcode: 

Electromagnetic waves scattering in turbulent anisotropic collision magnetized ionospheric plasma is investigated using complex geometrical optics approximation. Correlation function of the phase fluctuations of scattered radiation is obtained taking into account both electron density and magnetic fields fluctuations. The features of the angular power spectrum of scattered radiation are investigated analytically and numerically. The expressions of broadening of the spatial spectrum have been obtained for both powerlaw and anisotropic Gaussian correlation functions of electron density fluctuations. Gaussian spectral function takes into account the axial ratio of the field-aligned irregularities and the angle of inclination of prolate irregularities with respect to the external magnetic field. The variance of the phase and scintillation level of scattered radiation are calculated numerically for F-region irregularities of the ionosphere. The conditions of non-fully and fully developed diffraction patterns have been determined.

The effect of the Ampére force on inertio-gravity (IG) waves in the partially ionized ionospheric E-layer is considered. Electromagnetic IG waves are then studied. It is shown that the free energy necessary for linear instability of electromagnetic IG waves arises from the field-aligned current. Furthermore, it is found that atmospheric vortex motions can induce substantial variations in the geomagnetic field and field-aligned currents. 

Taking into account nonlinear interaction of magnetized Rossby waves with zonal shear flow in the Earth's ionospheric E-layer modified by inhomogeneous geomagnetic field and sheared zonal flow Charney equation is obtained. The appropriate region of linear phase velocities is analyzed and the stability condition of zonal flows is obtained. In case of nonlinear regime the appropriate compatibility condition is obtained and its independence on zonal shear flows is shown. It is shown that zonal shear flow may support the existence of solitary vortical structures. Owing to carried out analysis different from dipole structures new class of nonlinear solitary vortical structures is found.

The problem of propagation of ultralong planetary waves in the Earth’s upper atmosphere is considered. A new exact solution to the MHD equations for the ionosphere is obtained in spherical coordinates with allowance for the geomagnetic field and Earth’s rotation. A general dispersion relation is derived for planetary waves in the ionospheric E and F regions, and the characteristic features of their propagation in a weakly ionized ionospheric plasma are discussed.

Statistical characteristics of the angular power spectrum (broadening and displacement of its maximum) of multiply scattered electromagnetic waves by plane layer of turbulent anisotropic magnetized collisional plasma are considered. The influence of distances between the emitter as well as the receiver (they are located in opposite sides with respect to scattered layer) and layer’s boundaries is analyzed for anisotropic Gaussian correlation function describing the irregularities of electron density fluctuations with various parameter of anisotropy and the angle of inclination of prolate irregularities with respect to the external magnetic field. Numerical calculations have been carried out for F region of the ionosphere.

A general dispersion relation for three-dimensional electromagnetic planetary waves from which, as a particular case, follow the Khantadze results (onedimensional case) is obtained. It is shown that a partially frozen-in geomagnetic field, like in the one-dimensional case, leads to generation of "fast" and "slow" planetary waves being in a two-liquid approximation (i.e., with complete ion drag by neutrals) oscillations of magnetized electrons and partially magnetized ions in the E-region of ionosphere. In the F-region in a one-liquid approximation, only the "fast" planetary wave being oscillation of the environment as a whole is generated.

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 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.

A new branch of planetary Rossby waves is found taking into account latitudinal gradient of horizontal component of the earth rotation's angular velocity. Frequencies of a new branch and ordinary Rossby waves numerically coincide but strongly differ on character of dispersion. The general condition naturally “filtering” planetary waves in the long-wave approximation and internal inertial waves in the short-wave approximation was established.

The influence of non-monochromaticity on low-frequency, large-scale zonal-flow nonlinear generation by small-scale magnetized Rossby (MR) waves in the Earth's ionospheric E-layer is considered. The modified parametric approach is used with an arbitrary spectrum of primary modes. It is shown that the broadening of the wave packet spectrum of pump MR waves leads to a resonant interaction with a growth rate of the order of the monochromatic case. In the case when zonal-flow generation by MR modes is prohibited by the Lighthill stability criterion, the so-called two-stream-like mechanism for the generation of sheared zonal flows by finite-amplitude MR waves in the ionospheric E-layer is possible. The growth rates of zonal-flow instabilities and the conditions for driving them are determined. The present theory can be used for the interpretation of the observations of Rossby-type waves in the Earth's ionosphere and in laboratory experiments.

The features of angle-of-arrival (AOA) of scattered radiation using the geometrical optics approximation and statistical simulation (Monte Carlo method) are studied in the paper. Analytical expressions are derived for the power law spectrum of electron density fluctuations and numerically calculated at different angles of inclination of geomagnetic field with respect to the layer boundary, at different parameters of anisotropy and different locations of a point source with respect to the layer having a finite thickness. Analyses show that the proposed theory in a small angle approximation quite well describes experimental data of satellite observations and the behaviour of the AOA is in a good agreement with statistical simulation using the Monte Carlo method. The proposed theory could be applied to remote sensing problems at microwaves propagation in the low turbulent atmospheric layers. Index terms: turbulent plasma layer, angle-of-arrival, Monte Carlo method.

The problem of generation and existence of large-scale vortices in the ionosphere is analyzed in this paper. Some exact solutions of the magneto-hydrodynamic (MHD) equations have been found and new invariants have been constructed allowing to descover mechanisms of generation of large-scale vortices and planetary waves in the electroconducting atmosphere under the action of non-conservative Coriolis and Ampere forces.

The problem of propagation of large-scale vortices in the ionosphere is investigated. Permanently acting fundamental factors have been discovered making it possible to reveal the mechanisms of generation of large-scale vortices and planetary waves in conductive atmosphere.

Statistical characteristics of scattered electromagnetic waves by turbulent magnetized plasma slab with electron density and magnetic field fluctuations are considered via the perturbation method and boundary conditions. Magnetic field fluctuates both in magnitude and direction. Analytical expressions for the component of scattered electric field, correlation functions of the amplitude and phase fluctuations, and also the phase structure function for arbitrary correlation functions of fluctuating plasma parameters are derived. The obtained results are valid for near and far zones. Under equal conditions, at strong magnetic fields, electron density fluctuations play the important role and in this case the imposed magnetic field decreases fluctuation intensity of the ordinary and extraordinary waves. Numerical calculations of statistical characteristics of scattered radiation were carried out for anisotropic Gaussian correlation function for electron density fluctuation and correlation tensor of the second order for the fluctuation of an external magnetic field. The phase portraits of correlation functions of the amplitude and phase fluctuations are constructed 

 A complete theory of low-frequency MHD oscillations of the Earth's weakly ionized ionosphere is formulated. Peculiarities of excitation and propagation of electromagnetic acoustic-gravity, MHD and planetary waves are considered in the Earth's ionosphere. The general dispersion equation is derived for the magneto-acoustic, magneto-gravity and electromagnetic planetary waves in the ionospheric E- and F-regions. The action of the geomagnetic field on the propagation of acoustic-gravity waves is elucidated. The nature of the existence of the comparatively new large-scale electromagnetic planetary branches is emphasized. 

Numerical modeling and studies of the wind fields at the junction of three continents: over the complex terrains of the South-east Europe, Asia Minor, Middle East, Caucasus and over the Black, Caspian and Mediterranean seas have been carried out for the first time. Traveling synoptic scale vortex wave generation and subsequent evolution of orographic vortices are discovered. Wind fields, spatial distribution of the coefficients of subgrid scale horizontal and vertical turbulence and the Richardson number are calculated. It is shown that the local relief, atmospheric hydrothermodynamics and air-proof tropopause facilitate the generation of -mesoscale vortex and turbulence amplification in the vicinity of the atmospheric boundary layer and tropopause. Also turbulence parameters distribution in the troposphere has the same nature as in the stratosphere and mesosphere: turbulence coefficients, stratification of the vertical profiles of the Richardson number, thickness of the turbulent and laminar layers.

 Keywords: Numerical Modeling, Complex Terrain, Characteristics of Atmospheric Turbulence, Wind Field, Mesoscale Vortex, Bulk Richardson Number 

The mutual correlation function of the phase fluctuations of scattered ordinary and extraordinary waves by the magnetized plasma slab with electron density fluctuations and the variance of the Faraday angle is calculated by the perturbation method. Analytical expression of broadening of the spatial spectrum of scattered radiation is obtained for arbitrary fluctuation spectrum. Numerical calculations are carried out for the anisotropic Gaussian fluctuation spectrum at different anisotropy factor and the angle of inclination of prolate irregularities with respect to the external magnetic field. Isolines of the normalized root mean square deviation of the Faraday angle nonlinearly depends on the angle of inclination of prolate irregularities and increases in proportion to the anisotropy factor; two receiving antennas are located in orthogonal planes. It is shown that the broadening of the spatial spectrum of scattered electromagnetic waves by turbulent magnetized plasma slab in the principle plane (location of an external magnetic field) is less than in the perpendicular one.

Metric Radio Signals and the Spatial Spectrum of Scattered

 Scattering of the electromagnetic waves by a randomly inhomogeneous electrically gyrotropic slab are studied using the perturbation method. Second order statistical moments of the ordinary and extraordinary waves scattered by the magnetized plasma slab are obtained using the boundary conditions for an arbitrary correlation function of electron density fluctuations. Normalized correlation functions at quasi-longitudinal propagation along the external magnetic field are calculated for the carrier frequency 0.1 MHz and 40 MHz.Isolines of the normalized variance of Faraday angle are constructed for the anisotropic Gaussian correlation function at various anisotropy factors of irregularities. Obtained results are in a good agreement with the experimental data.

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 diffraction effects. Second order statistical moments are derived for arbitrary correlation function of electron density fluctuations 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 field. It was shown that SPS has a double-peaked shape. External magnetic field 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.

Influence of temporal fluctuations of both electron density and external magnetic field fluctuations on scattered ordinary and extraordinary waves in magnetized plasma is investigated using the ray-(optics) method. Transport equation for frequency fluctuations of scattered radiation has been derived. Broadening of the spatial power spectrum and amplification of the intensity of frequency fluctuation taking into account geometry of the task and the features of turbulent magnetized plasma is analyzed for the anisotropic Gaussian correlation function using the remote sensing data. It is shown that spatial-temporal fluctuations of electron density and external magnetic field, anisotropy and angle of inclination of prolate irregularities relative to the external magnetic field may lead to the exponential amplification of the intensity of frequency fluctuations of scattered electromagnetic waves in the collisional magnetized plasma.

Keywords: Fluctuations; Correlation function; Scattering; Magnetized Plasma; Phase portrait; Extraordinary Wave

The dispersion equation has been obtained describing propagation of very slow and long-period MHD waves in the ionospheric E-region. Statistical characteristics of the low-frequency MHD waves propagating in weakly ionized plasma are obtained for arbitrary correlation function of the particles density fluctuations. Energy exchange between “fast” and “slow” Alfven waves and the turbulent plasma flow is analyzed in the ray (optics) approximation using the stochastic eikonal equation. Correlation function of the phase fluctuations and the broadening of the temporal spectrum of scattered Alfven wave are calculated numerically for the anisotropic correlation function using the experimental data.

Keywords: Alfven wave, plasma flow, statistical characteristics, broadening, irregularities

Peculiarities of the magnetosonic waves in weakly-ionized ionospheric E-region with randomly varying spatial-temporal turbulent plasma parameters are considered. Statistical characteristics: variances of both the directional fluctuations causing curvature of the phase surface and frequency fluctuations leading to the broadening of the temporal power spectrum of scattered magnetosonic waves are investigated analytically and numerically. Energy exchange between fast and slow magnetosonic waves, and turbulent plasma is analyzed on the bases of the stochastic transport equation using the ray (- optics) approximation. Experimental data have been used in numerical calculations for the anisotropic Gaussian correlation function of the density fluctuations. It is shown that the energy balance between magnetosonic wave-nonstationary medium is different in the direction of the wave propagation and perpendicular plane leading to the compression and stretching of the ray tubes.

General dispersion equation is obtained at arbitrary inclination angles of the external magnetic field and wave vector of an incident EM wave. Statistical characteristics of the phase fluctuations of scattered high frequency EM waves in the collision magnetized plasma caused by electron density and external magnetic field fluctuations taking into account polarization coefficients for both ordinary and extraordinary waves are calculated analytically. The influence of collision frequency, anisotropy factor and angle of inclination of prolate irregularities of electron density fluctuations with respect to the geomagnetic field of lines on the broadening of the spatial power spectrum is analyzed. Phase portraits of the phase fluctuations caused by the geomagnetic field fluctuations are constructedat different spatial parameters characterizing magnetic field and electron density fluctuations. Numerical calculations are carried out for the ionospheric F-region parameters using experimental data.

The statistical model of passive impurity transfer in surface boundary layers of the turbulent atmosphere in the presence of wind is offered. Analytical expressions of the normalized concentration of impurity for arbitrary correlation tensor of the second rank of velocity pulsation when the emission source is located at a certain height over the Earth's surface are obtained. The effective coefficient of turbulent diffusion contains coefficient of molecular diffusion, longitudinal and transverse turbulent diffusion coefficients. Numerical calculations were carried out using experimental data of ground(-based) observations. The isolines describing distribution of the passive impurities at calm case are depicted at different values of a wind speed and at certain distances from a source. Dynamics of globules formation with various concentration of impurity transferred by wind is constructed. They have specific characteristic spatial scales and lifetimes.

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.

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.

Keywords: Turbulence, Ionosphere, Irregularities, Magnetized Plasma

General dispersion equation has been obtained for three-dimensional electromagnetic planetary waves, from which follows, as particular case Khantadze results in one-dimension case. It was shown that partial magnetic field line freezing-in as in one-dimension case lead to the excitation of both fast and slow planetary waves, in two-liquid approximation (i.e. at ion drag by neutral particles) they are represent oscillations of magnetized electrons and partially magnetized ions in E region of the ionosphere. In F region of the ionosphere using one-liquid approximation only fast planetary wave will be generated representing oscillation of medium as a whole. Hence, it was shown that three-dimension magnetogradient planetary waves are exist in all components of the ionosphere, and as exact solutions, with well-known slow short-wave MHD waves, are simple mathematical consequence of the MHD equations for the ionosphere

Keywords: Electromagnetic planetary waves, irregularities, ionosphere, MHD waves

Second order statistical moments of new internal MHD wave in the ionospheric F region are investigated analytically by geometrical optics approximation. Degree of a curvature of a constant phase surface and the variance of an instant frequency measuring by experiment has been obtained for arbitrary correlation function of electron density fluctuations. Energy exchange between the internal wave and turbulent plasma flow is considered calculating the mean energy flux density in the first and second approximations. Numerical calculations are carrying out for both anisotropic Gaussian correlation function and power law-spectrum characterizing elongated plasma irregularities using experimental data of satellites and incoherent scatter radar observations.

Keywords: Ionospheric Plasma, Internal Wave, Plasma Irregularities, Statistical Moments

Statistical moments of a scattered field are calculated in the first and second approximations using modified smooth perturbation method. Analytical expressions of both the variance and correlation function are obtained in the principle plane containing wave vector of an incident wave and external magnetic field. Observation points are spaced apart at small distances taking into account diffraction effects. Numerical calculations are carried out for the anisotropic Gaussian spectral function containing both anisotropic factor and the angle of inclination of elongated anisotropic plasma irregularities using the experimental data. It was shown that 3D surface of the correlation function of the phase fluctuation oscillate and these variations are decreased increasing characteristic spatial scale of plasma irregularities. New peculiarities of the ``Double-humped Effect'' are revealed in the collisionless magnetized plasma. It was shown that spatial scale and the inclination angle of elongated anisotropic plasma irregularities play important role in formation of a gap in the spatial power spectrum. Varying the magneto-ionospheric plasma parameters and values of characteristic spatial scales of anisotropic irregularities the depth of a dip increases and oscillates.

Second order statistical moments of the phase fluctuationsare obtained taking into account the boundary condition,diffraction effects and polarization coefficients of theordinary and extraordinary waves. The variance and thecorrelation function are calculated for arbitrary 3D spectralfunction of electron density fluctuations containing bothanisotropic Gaussian and power-law spectra; anisotropycoefficient and the orientation angle of elongated plasmairregularities. The phase scintillation index and thescintillation level are analyzed numerically. Maximum ofthe scintillation index for small-scale irregularities is in theinterval 0.2-0.3 corresponding to the moderate scintillationintensity, within the weak-scatter regime. Splashes arerevealed for different anisotropy factor of elongated largescaleirregularities varying orientation angle with respect tothe lines of force of geomagnetic field. Scintillation index iscalculated for small-scale irregularities using the “frozenin”assumption and taking into account movement of rigidirregularities. Log-log plots of the power spectrum of theintensity fluctuations have the same minimums satisfyingthe “standard relationship” of scattered ordinary andextraordinary waves. It was shown that the normalizedscintillation level growth in both non-fully-developeddiffraction pattern and in transition zone increasinganisotropy factor. Rising orientation angle scintillation leveldecreases and splashes arises in fully developedscintillation 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.

Keywords: Scintillation, ionosphere, irregularities, spatial power spectrum, turbulence

Statistical characteristics of scattered electromagnetic waves in the turbulent magnetized plasma caused by electron density fluctuations are calculated using complex geometrical optics approximation taking into account both diffraction effects and polarization coefficients. Scintillation level normalized on the variance of the phase fluctuations is analyzed analytically and numerically for small-scale plasma irregularities using the experimental data. New properties of the electromagnetic wave scintillations have been revealed. It is shown that splashes arise in the ionosphere leading to the turbulence and generation of new oscillations (waves and/or Pc pulsations) propagating in space and the terrestrial atmosphere. Turbulence extending in the lower atmospheric layers can influence on the meteorological parameters leading to climate change.

Second order statistical moments of scattered electromagnetic waves in the turbulent magnetized plasma slab with electron density fluctuations are calculated applying the modify stochastic smooth perturbation theory and the boundary conditions. The obtained results are valid for arbitrary correlation function of electron density fluctuations. Stokes parameters are analyzed both analytically and numerically. The theory predicts that depolarization effect caused by second Stokes parameter may be important in scintillation effects. Numerical calculations are carried out for new spectral function of electron density fluctuations containing both anisotropic Gaussian and power-law spectral functions using the experimental data. Polarimetric parameters are calculated for different anisotropy factor and inclination angle of elongated small-scale irregularities with respect to the magnetic lines of forces. The relationship between the scintillations and the polarimetric parameters is important.

Second order statistical moments of scattered electromagnetic waves in the turbulent anisotropic conductive magnetized plasma are considered using the modify smooth perturbation method. Polarization coefficients and diffraction effect are taken into account. Broadening, displacement of the spatial power spectrum, scintillation level and the "Double-humped Effect" are investigated analytically and numerically for different anisotropy factors and inclination angles characterizing large-scale ionospheric plasmonic structures. It was shown that longitudinal conductivity and homogeneous ambient external magnetic field (in the main plane) have substantial influence on the statistical characteristics of scattered radiation in the ionospheric F-region. Increasing characteristics spatial scale of ionospheric large-scale electron density irregularities the spatial spectrum broadens, shift of the spectral maximum have opposite signs in the main and perpendicular planes. The obtained results allow to solve the reverse problem having application in the transionospheric communication and climate change. Numerical calculations are carried out using the experimental data.

Electromagnetic waves propagation in both homogeneous and random magnetized conductive plasma is considered including longitudinal, Pedersen and Hall's conductivities. The second-order statistical moments of scattered electromagnetic waves in the conductive turbulent magnetized plasma slab with electron density fluctuations are investigated on the bases of the set of stochastic differential equation. Refractive index and polarization coefficients of both the ordinary and extraordinary waves are calculated for the polar terrestrial ionosphere. Using new spectral method and the boundary conditions, transversal components of scattered electromagnetic waves are calculated. Experimentally observed Stokes parameters describing the depolarization effects are calculated for the arbitrary correlation function of electron density fluctuations. Coherent matrix describing polarization features of non-plane waves generalizing the Stokes parameters is obtained.

 Oblique incidence of small-amplitude electromagnetic wave on an anisotropic conductive collision semi-infinite turbulent plasma slab under the influence of a homogeneous magnetic field is considered. The conditions of both the ordinary and extraordinary waves’ propagation along and transversal directions with respect to the external magnetic field in a homogeneous absorbing collisional magnetoplasma are obtained. Second order statistical moments of the spatial power spectrum of a scattered radiation in the polar ionosphere are calculated for the arbitrary correlation function of electron density fluctuations using the geometrical optics approximation. External magnetic field, oblique incidence of electromagnetic wave on a plasma slab, anisotropy of both ionospheric conductivity and dielectric permittivity, also elongated plasma irregularities in the auroral region of the terrestrial atmosphere are taken into account. The direction along which these asymmetric factors compensate each other is established. The conditions of the “Compensation Effect” are obtained: the spatial power spectrum not broadens, and its maximum is not displaced. Second order statistical moments of a scattered radiation: the shift of maximum and the broadening of the spatial power spectrum in the main and perpendicular planes are investigated analytically and numerically for the power law spectrum of the anisotropic ionospheric plasmonic structures using the experimental data.