Multifractal Structure of Intermittency in a Developed Ionospheric Turbulence

We present the results of studying the multifractal structure of intermittency in a developed ionospheric turbulence during special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2005–2006. It is shown, in particular, that the determination of multidimensional structural functions of the energy fluctuations of received signals permits one to obtain the necessary information on multifractal spectra of the studied process of radio-wave scattering in the ionosphere. Experimental data on multifractal spectra of slow fluctuations in the received-signal energy under conditions of a developed small-scale turbulence are compared with the existing concept of the radio-wave scattering within the framework of the statistical theory of radio-wave propagation in the ionosphere. It is inferred that under conditions of a developed ionospheric turbulence, the multifractal structure of the intermittency of slow fluctuations in the received-signal energy is a consequence of the intermittency of small-scale fluctuations in the electron number density of the ionospheric plasma on relatively large spatial scales of about several ten kilometers. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 6, pp. 485–493, June 2008.     

Some features of the fractal structure of the developed small-scale ionospheric turbulence

We present the results of the first studies of the fractal structure of the developed small-scale ionospheric turbulence (SSIT) during special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2005–2006. It is established that under conditions of developed turbulence, typical values of the fractal dimension of the space occupied by natural SSIT inhomogeneities are, as a rule, close to the topological dimension of their embedding space, and the true values of the spectral index of isotropic SSIT only slightly differ from the corresponding generally accepted nominal values in the embedding space. Nevertheless, even small differences in the mentioned parameters detected in the experiment witness a sharply nonuniform distribution of the local fractal structures of the developed SSIT in space. We propose a stochastic model of the nonstationary process for fast amplitude fluctuations of signals during their propagation in the ionosphere with nonuniform spatial distribution of small-scale electron-density fluctuations. Eventually, namely this nonuniform distribution of small-scale electron-density fluctuations leads to the specific multifractal structure of the amplitude records of received signals. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 287–294, April 2008.     

Multipower spectrum of small-scale ionospheric turbulence

We consider the problem of diagnostics of the local structure of small-scale ionospheric turbulence using the multifractal analysis of received signals from the Earth’s orbital satellites after the radio sounding of the inhomogeneous ionosphere by these signals. In particular, it is shown that analysis of the multifractal structure of the received-signal amplitude records by the method of multidimensional structural functions allows one to determine the indices of the multipower local spectra of the small-scale ionospheric turbulence, which are inherent in it due to the nonuniform spatial distribution of small-scale fluctuations of the electron number density. It is noted that information on the multipower spectrum of small-scale ionospheric turbulence is not available for the conventional radio scintillation method based on the classical spectral analysis of received signals during the remote radio sounding of the ionosphere. At the same time, the method of multidimensional structural functions is efficient under conditions of actual nonstationarity of the process of scattering of the HF radio waves by the randomly inhomogeneous ionospheric plasma. The method of multidimensional structural functions is used for the multifractal processing of received signals of orbital satellites during special experiments on radio sounding of the midlatitude ionosphere under natural conditions and its modification by high-power HF radio waves. First data on the indices of the multipower local spectra of small-scale ionospheric turbulence are obtained. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 1, pp. 14–22, January 2009.     

On the fractal structure of small-scale traveling ionospheric disturbances

We present the results of the studies of fractal properties of the small-scale inhomogeneities of traveling ionospheric disturbances in special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2004–2006. Along with the conventional correlation processing of the received signals, we performed their multifractal analysis, as well as fractal processing of signals by the correlation-integral method. Important information on fractal properties of the small-scale turbulence for the least studied part of the upper-ionosphere inhomogeneity spectrum in the interval of characteristic scales l ≈ 1–10 km is obtained. In particular, it is noted that the fractal structure of these inhomogeneities can be originated from the nonlinear “destruction” of several large-scale sinusoidal structures in a quasistable traveling disturbance. It is also noted that the multifractal spectra of amplitude fluctuations of the received signals obtained in the experiments in different years, in different time of the day, and in different seasons of the observations are quite similar. This is evidence that intermittency is a universal property of the plasma turbulence, at least for the midlatitude upper ionosphere. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 1, pp. 22–30, January 2008.     

Fractal structure of artificial ionospheric turbulence

We show the results of the first experimental studies of the multifractal structure of the developed artificial ionospheric turbulence. As a result of the special multifractal analysis of the recorded amplitudes of signals from the orbital satellites, which were obtained during the experiments on radio tomography of the irregularities excited in the ionosphere by the powerful mid-latitude heating facility “Sura,” it is found that the characteristic multifractal structure of these records is caused by the nonuniform spatial distribution of the small-scale fluctuations of the electron number density in the artificial irregularities of the ionospheric plasma. Comparative analysis is performed for the multifractal spectra of fluctuations of both the amplitudes and energies of signals received from the orbital satellites upon radio transmission probing of the region of artificial ionospheric turbulence by these signals at three observation points located near the “Sura” heating facility and spaced apart to a distance of about 100–150 km. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 11, pp. 970–976, November 2008.     

On fractal properties of small-scale ionospheric irregularities

We consider the problem of relating the local structure of small-scale ionospheric turbulence to the measured frequency-spectrum indices and fractal dimensions of amplitude records of the signals received on the Earth during remote sensing of the ionosphere onboard the satellites. It is shown that knowledge of these parameters permits one to determine the true values of the local-spectrum indices of the electron-density fluctuations for isotropic small-scale turbulence of the ionosphere both under natural conditions and during its modification by high-power short-wave radiation as well as to specify fractal dimensions of space filled by small-scale irregularities of the turbulent structures in the ionosphere. We show the necessity of detailed experimental studies of the fractal properties of small-scale ionospheric irregularities of both natural and artificial origin by using a multifractal analysis in combination with the synchronous correlation processing of received signals during remote sensing of the ionosphere. This will give important information on the local structure of small-scale ionospheric turbulence inaccessible for studies within the framework of the classical method of radio scintillation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 4, pp. 300–308, April 2007.     

Magnetic zenith effect and some features of the multifractal structure of the small-scale artificial ionospheric turbulence

We present the results of the experiment on studying the multifractal structure (with inhomogeneity sizes from tens to hundreds of meters across the Earth’s magnetic field) of the artificial ionospheric turbulence when the midlatitude ionosphere is affected by high-power HF radio waves. The experimental studies were performed on the basis of the “Sura” heating facility with the help of radio sounding of the disturbed region of the ionospheric plasma by signals from the Earth’s orbital satellites. The influence of the magnetic zenith effect on measured multifractal characteristics of the small-scale artificial turbulence of the midlatitude ionosphere was examined. In the case of vertical radio sounding of the disturbed ionosphere region, the measured multipower and generalized multifractal spectra of turbulence coincide well with similar multifractal characteristics of the ionospheric turbulence under natural conditions. This result is explained by the fact that the scattering of signals by weak quasi-isotropic small-scale inhomogeneities of the electron number density in a thick layer with a typical size of several hundred kilometers above the region of reflection of high-power HF radio waves gives the major contribution to the observed amplitude fluctuations of received signals. In the case of oblique sounding of the disturbance region at small angles between the line of sight to the satellite and the direction of the Earth’s magnetic field, the nonuniform structure of the small-scale turbulence with a relatively narrow multipower spectrum and small variations in the generalized multifractal spectrum of the electron number density was detected. Such a fairly well ordered structure of the turbulence is explained by the influence of the magnetic zenith effect on the generation of anisotropic small-scale artificial turbulence in a thin layer having a typical size of several ten kilometers and located below the pump-wave reflection height in the upper ionosphere.     

On small-scale plasma inhomogeneities of the traveling ionospheric disturbances

We report on the results of the first special experiment on radio sounding of the midlatitude ionosphere by signals from in-orbit satellites at a frequency of 150 MHz under quiet geophysical conditions. Along with the conventional correlation processing, fractal processing of the received signals was also performed. Using the fractal approach, we obtained first data on the sources and generation mechanisms of small-scale plasma inhomogeneities of the traveling ionospheric disturbances (TIDs) in the upper ionosphere. It is noted that the phenomenon of nonlinear “ breaking” of the acoustic-gravity waves entering the ionosphere from the underlying atmosphere plays the crucial role in the formation of plasma inhomogeneities of the TIDs. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 7, pp. 561–569, July 2006.     

Anisotropic Structure of Small-Scale Ionospheric Turbulence

We consider various theoretical models for the spectrum of small-scale ionospheric turbulence. The particular role of the generalized model of the ionospheric-turbulence spectrum, which takes into account that the anisotropy (extension) of small-scale irregularities of the upper ionosphere along the Earth's magnetic field direction depends on the transverse scale of those irregularities, is emphasized. The results of the. rst target experiments on radio sensing of the midlatitude ionosphere by signals from on-orbit satellites at frequencies 150 and 400 MHz under conditions of increased solar activity are presented. The experiments were performed at the radiophysical facility in the Nizhny Novgorod region in 2003. We studied statistical characteristics of the amplitude fluctuations of the received signals for different angles ϑ between the line of sight from a satellite to a ground-based reception point and the Earth's magnetic field direction. It was found in the course of the experiments that the spectrum slope of amplitude fluctuations of the received radiation is a function of the angle ϑ. The obtained result agrees with the generalized model of the ionospheric-turbulence spectrum and can be an argument in favor of the pronounced anisotropic structure of small-scale electron-density irregularities of the midlatitude ionosphere under disturbed geophysical conditions. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 5, pp. 382–387, May 2005.     

Feature of the multifractal structure of small-scale ionospheric turbulence during the solar eclipse of August 1, 2008

Using the method of radio sounding of the mid-latitude ionosphere by the satellite signals, we study the multifractal structure of small-scale ionospheric turbulence during a solar eclipse. The measured multipower and generalized multifractal spectra of small-scale ionospheric turbulence at the initial and closing stages of the eclipse turn out to be almost identical on the space radio paths with different orientations. This is indicative of a sufficiently high stability of the nonuniform spatio-temporal distribution of small-scale fluctuations of the ionospheric electron number density under conditions of geophysical disturbances due to global physical processes in the ionospheric plasma during a solar eclipse. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 4, pp. 302–306, April 2009.     

On the Problem of True Values of the Spectrum Indices for Small-scale Ionospheric Turbulence

We consider the problem of obtaining reliable values of the local-spectrum indices of the electron number density fluctuations for small-scale ionospheric turbulence. It is shown that the use of a multifractal analysis in combination with the synchronous correlation processing of the received signals in the experiments on remote radio sounding of the ionosphere by satellite signals permits one to solve the posed problem. In this case, the true values of the local-spectrum indices of small-scale ionospheric turbulence, which are measured in such specialized experiments under natural conditions and during modification of the ionosphere by high-power HF radio emission, can differ notably from their standard values obtained within the framework of the classical method of radio scintillations, in which only correlation processing of the data is used. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 7, pp. 571–574, July 2008.     

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.     

Generation of ionospheric irregularities upon propagation of solitary internal gravity wave during the major magnetic storm of October 29–31, 2003

Using the technique of global detection of ionospheric disturbances, based on processing the data of the global GPS-receiver network, we obtain experimental proof of the existence of a solitary wave (soliton) in the atmosphere during the main phase of the major magnetic storm of October 30, 2003. The soliton with a characteristic duration of about 40 min and a relative amplitude of up to 40%, originated at the moment of the maximum disturbance of the Earth’s magnetic field, traveled without changing its shape at a distance of up to 4500 km with a velocity of 1400 m/s, which exceeded the atmospheric sound velocity at the heights of the main electron-density maximum in the ionosphere (about 300 km) by a factor of 1.5. The intensity of variations in the total electron content in the period range 1–10 min increases by an order of magnitude as the soliton propagates from the North-East to the South-West of the USA in the regions with the maximum amplitude of the large-scale disturbance. This corresponds to enhancement of ionospheric irregularities with scales from 10 to 100 km, and also of small-scale irregularities (SSI) with scales of 100 to 1000 m, since the spectrum of the ionospheric irregularities has a power-law shape. Spatio-temporal characteristics of the density distribution of phase slips of GPS signals are close to the corresponding characteristics of the SSI intensity. This agrees with the existing concept that the phase slips result from scattering of GPS radio signals by SSIs. Both the SSI amplitude and the density of phase slips decrease as the soliton decays in amplitude. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 2, pp. 89–104, February 2006.     

On the reflection of a radiowave beam from a plasma layer with large-scale inhomogeneities

Using the method of parabolic equation (MPE), we obtain transfer equations for the mean field, the space-coherence function, and the ray intensity of a radiowave beam as it is reflected from a plasma layer with random inhomogeneities. The general solutions of these equations are found. Special attention is given to the case of radiowave beam reflection from a linear plasma layer with large-scale electron-density inhomogeneities. If a weakly directed transceiving SW antenna is used, the shortwave scattering can lead to a pronounced (of the order of 3 dB) decrease in the intensity of a vertical-sounding signal reflected from the ionospheric F2 layer only under the conditions of abnormally strong ionospheric electron-density perturbations. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 8, pp. 955–965, August, 1998.     

Some results of synchronous experimental study of artificial F-spread at radiophysical test sites in nizhny novgorod province

We show some results of experiments on synchronous sounding of the ionosphere by short-wave signals at the Radiophysical Research Institute’s test site in Zimenki and Vasil’sursk, Nizhniy Novgorod province, during ionospheric modification by high-power short radiowaves from transmitters of the “Sura” facility in Vasil’sursk. In the course of experiments we proved directly the decisive role of large-scale inhomogeneities of the ionospheric plasma with dimensions of from several kilometers to several dozens of kilometers in the formation of artificial F- spread. The small-scale inhomogeneities with dimensions smaller than 1 km, which are localized in a relatively thin layer near the reflection level of a high-power short radiowave, emerged only at sounding waves, propagating (reflected) in the immediate vicinity of the center of the heating region. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 6, pp. 688–692, June, 1997.     

Sounding of an artificially perturbed ionosphere by means of an ionosonde/position finder with chirp modulation of the signal

We describe the operation of an ionosonde/position finder with chirp modulation of the signal. The first results of measuring the characteristics of short-wave radio signals scattered by artificial small-scale inhomogeneities, which were obtained by means of an ionosonde/position finder on the IZMIRAN—“SURA”—Rostov-on-Don path are presented. It was found that under certain ionospheric conditions, the angular and frequency selection of the scattered signals take place, in which case the signals are observed simultaneously in several frequency intervals (mainly, in three, namely, 6–9.5 MHz, 10–12 MHz, and 15–18 MHz) with different angles of incidence of radio waves in the vertical plane. In this case, the incidence angles were 20◦–35◦, 18◦–32◦, and 10◦–20◦ from the horizon for the first, second, and third frequency interval, respectively. Ionograms of oblique sounding were modeled allowing for the scattering of radio waves by artificial small-scale inhomogeneities. It is shown that at frequencies from 10 to 12 MHz, aspect conditions are fulfilled for the signals ducting along the high-angle beam (Pedersen mode). At frequencies 15–18 MHz (higher than the maximum observable frequency of the forward signal on the path IZMIRAN—Rostov-on-Don), aspect scattering conditions are fulfilled for the signals incident on a scattering area in the ascending part of the trajectory. At low frequencies 6–9.5 MHz (below the maximum observed frequency of the forward signal on the IZMIRAN—Rostov-on-Don path), the observable additional signals are caused by the scattering of radio waves by artificial inhomogeneities with subsequent relfection of the scattered signal from the Earth on the “SURA”—Rostov-on-Don path. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 4, pp. 267–278, April 2009.     

Information entropy analysis of the degree of structure self-organization

Fraktal theory allows specifics of turbulence inhomogeneities of different types to be considered in the spectral theory of self-affine multifractals. Experiments demonstrate that the turbulence possesses the multifractal properties. Nowadays the multifractal analysis is widely used in various branches of modern physics. The structural elements of the homogeneous and isotropic turbulence – vortices – represent a self-similar multifractal with the same similarity coefficient for all spatial variables.     

Altitude–time variations in electron number density in the ionospheric <Emphasis Type="Italic">E</Emphasis> layer

We present the results of measuring the electron number density in the ionospheric E layer by a method based on the creation of artificial periodic irregularities of the ionospheric plasma with two different spatial scales. Artificial periodic irregularities were created by the radiation of the Sura heating facility at frequencies 4.7 and 5.6 MHz. The electron number density was determined by the ratio of relaxation times of the signals backscattered by artificial periodic irregularities during their sounding by probing radio waves at the mentioned frequencies. Features of the electron-density profiles obtained in 2006 and 2007 in the altitude range 95–115 km are discussed and their altitude–time variations are analyzed.     

Characteristics of the spatial spectrum of plasma irregularities excited at mid-latitudes by the high-power “Sura” facility

We present the results of analysis of the spectra of amplitude scintillations at a frequency of 150 MHz and a difference phase at frequencies of 150 and 400 MHz, which were obtained in the experiment on radio tomography of artificial ionospheric turbulence (AIT) excited by the mid-latitude high-power “Sura” heating facility [1]. We used the data on radio probing of the AIT region at a frequency of 150 MHz by signals from artificial satellites in near-polar circular orbits at altitudes of 1000 km above the Earth’s surface. The signals were received simultaneously at three spaced apart points located at distances of about 100–150 km from each other along the projection of the satellite trajectory onto the Earth’s surface. The analysis of the data shows that in the range of scales smaller than 0.5–1.0 km across the geomagnetic field, the AIT spatial spectrum can be described by the power-law function with the spectral index p_⊥ = 1.7–2.5. For irregularities with the same transverse scales, the spectral index in the direction of the magnetic field amounts to p_‖ = 5–7. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 8, pp. 722–730, August 2007     

Interferometer study of the turbulent flow by noise-signal sounding

We consider the interferometer method by which a turbulent water flow is remotely studied by sounding with a noise ultrasound signal. It is shown that the processing of signals received by two spatially separated receivers makes it possible to extract the signal phase difference caused by the concentration fluctuations of cavity air bubbles on the propagation paths. Spectral analysis of the random phase difference permitted diagnostics of the propagation medium. In particular, it is shown that the output signal of the interferometer carries information on the spatial spectrum of parameter fluctuations of the medium, and on the velocity of inhomogeneities if the interferometer base is parallel to the turbulent flow. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 2, pp. 95–103, February 2007.