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.     

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.     

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.     

On fractal structure of large-scale electron-density inhomogeneities of traveling disturbances in the midlatitude ionosphere

We present the results of studies of the multifractal structure of slow (of duration τ ≈ 10 s) fluctuations of the received-signal amplitudes in special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2004–2006. It is shown, in particular, that the method of multifractal analysis of amplitude records of the received signals yields information on the spectrum of large-scale ionospheric inhomogeneities, which is inaccessible for the classical method of radio scintillations. From the results of measurements with the use of multifractal processing of experimental data, we found that large-scale (tens of kilometers) quasiregular electron-density inhomogeneities of traveling ionospheric disturbances (TIDs) have a power-law spectrum. It is exactly the power-law form of the spatial spectrum of large-scale inhomogeneities of TIDs that can be the reason for the observed multifractal structure of the intermittency of slow fluctuations of the received-signal amplitudes. However, under conditions of a developed small-scale turbulence of TIDs, the observed multifractal structure of the received signals is, as a rule, stipulated by the spatial inhomogeneity of the variance of the integral electron-density fluctuations of small-scale inhomogeneities on scales comparable with the sizes of large-scale inhomogeneities of TIDs. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 3, pp. 191–198, March 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.     

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.     

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.     

Restoration of spectral characteristics of ionospheric wave disturbances

The problem of short-wave radio-signal reflection from a parabolic ionospheric layer with traveling ionospheric disturbances (TID) in the form of density waves is solved in an approximation of geometrical optics. Formulas that relate the arrival angle and Doppler shift of a radio signal to the TID parameters are derived by the small-perturbation method for the characteristic function. The inverse problem of determination of the TID spectral characteristics is solved. The amplitude, dispersion law, and propagation direction of ionospheric irregularitiesare restored.     

Fractal analysis of RF signals scattered by small-scale ionospheric irregularities

The fractal dimension as a characteristic of an experimental data series is considered. The correlation integral method is used for dimension calculation. It is shown that by the fractal dimension one can identify a variety of ionospheric processes even when the conventional spectral analysis fails. It is found that the realizations corresponding to volume scattering by natural and artificial irregularities have finite dimension, which is significantly different. A technique for preparing experimental data to be processed by the correlation integral method is developed. The influence of the data sampling rate and signal-to-noise ratio on the dimension is analyzed.Radioastronomical Institute, Ukrainian Academy of Sciences, Khar'kov. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 6, pp. 557–565, June, 1995.     

On fractal nature of the structure of nanoporous carbon obtained from carbides

The curves describing small-angle x-ray scattering at npor-C nanoporous carbon samples obtained from polycrystalline α-SiC, TiC, and Mo₂C and a 6H-SiC single crystal have been analyzed. An algorithm is developed for taking into account the corrections to experimental curves for the intensity of the primary beam transmitted through the sample and the height of the inlet slit in these measurements. Two systems of nanoclusters observed in the npor-C structure differ in the type of stacking of structural elements: small-scale mass fractals of a dimension 1<D ₂<3 and a size L ₂=50–90 Å, which depend on the type of the initial carbide, and large-scale nanoclusters having a size L ₁>550 Å. In most samples, large-scale nanoclusters can be regarded as objects with a fractal surface and a dimension 2<D ₁<13, which also depends on the type of the initial carbide. Large-scale nanoclusters in npor-C obtained from Mo₂C prove to be mass fractals with a dimension D ₁>2. Peculiarities of the structure formation of nanoporous carbon obtained from various carbides are discussed.     

Radio-frequency radiation energy transfer in an ionospheric layer with random small-scale inhomogeneities

Conclusion The equation of the energy balance for the radiation in a randomly inhomogeneous planestratified plasma layer is derived in this paper based on the phenomenological approach. This equation can be transformed, thanks to the use of invariant ray variables, into a drift-type equation which describes deformation of the spatial distribution of the radio-frequency radiation resulting from the multiple scattering. Two related effects are studied numerically: the variations in the radiowave arrival angles for the slightly oblique propagation and variation in the intensity of the radio-frequency radiation reflected from the plasma layer. Their practical value is associated with such fields as radio homing at short paths, SW radars, the interpretation of results of vertical sounding of the ionosphere, as well as diagnostics of the inhomogeneous structure of the plasma in plasma-like media.The procedure suggested can be used for the study of scattering effects for radiowaves crossing the plasma layer (e.g., in transionospheric sounding), or oblique propagation (e.g., in the vicinity of the maximum frequency). This will be the subject of papers to follow, as well as analysis of the complete solution of the equation of energy balance in a plane-stratified layer.Scientific-Research Institute of Physics, Rostov University. Translated from Izvestiya Vysshikh Uchebnykh Zavednii, Radiofizika, Vol. 36, No. 12, pp. 1075–1088, December, 1993.     

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.     

Some distinctive features in the behavior of small-scale artificial ionospheric irregularities at mid-and high latitudes

We present the results of experimental studies of some features in the behavior of small-scale artificial irregularities (SSAIs) at mid-and high latitudes based on the “Sura” and EISCAT/HEATING HF facilities. Observations were performed by the method of aspect scattering using a network of diagnostic paths having a common reception point located near St. Petersburg. We found that an extremely long duration of the second (slow) stage of SSAI relaxation of up to 5 min occurs in the evening hours when the ionosphere above the “Sura” facility is illuminated by the Sun, but the solar terminator travels through the magnetically conjugated ionosphere. The conjecture is made that the processes initiated by the terminator are mostly responsible for secondary ionospheric turbulence maintaining the irregularities above “Sura.” A drastic increase in the Doppler spectra width of the scattered signals is revealed when the magnetically conjugate point of the ionosphere is located on the shade side of the terminator, but the ionosphere above the “Sura” facility is still lighted. It is assumed that the “ run away” of photoelectrons from the day to the night side could reduce the threshold of excitation of artificial irregularities, leading to an increase in their intensity. The presence of fairly intense scattered signals was detected from the “Sura” and EISCAT/HEATING experimental results both under conditions of pulsed HF heating after continuous heater-on periods and cycled HF heating by short pulses. In the case of pulsed heating by short pulses with duration τ_p < 100 ms and average radiated power P_a below the threshold power P_thr of the SSAI generation cutoff the irregularities can be maintained due only to striction parametric instabilities. The excitation of irregularites under the cycled HF pumping with the pulse duration τ_p = 384 ms for P_a comparable with P_thr was detected. The aspect-angle dependence, or the so-called magnetic zenith effect, was found in the SSAI intensity. The residual turbulence aftereffects played a significant role in the SSAI development. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 8, pp. 678–694, August 2007.