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 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.     

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.     

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.     

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.     

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.     

Structure and dynamics of the ionospheric region with artificial small-scale irregularities according to complex measurements of the scattered radio-signal characteristics

We present the results of complex measurements of characteristics of HF radio signals scattered by artificial small-scale irregularities by means of oblique sounding using a chirp signal and by direction finding. On the basis of comparison of the experimental data and the calculations of aspect scattering of radio waves, the conclusion on the patch structure of an artificially disturbed ionosphere filled with small-scale field-aligned irregularities is drawn. The sizes of the patches amount to several ten kilometers, and they are separated by 100 or more kilometers. The drift speed of irregularities in the direction of the scattering vector in the plane perpendicular to the magnetic field is determined for several patches. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 12, pp. 1011–1025, December 2008.     

Trapping of plasma waves in small-scale cylindrical irregularities

We consider the efficiency of trapping of short plasma waves excited by a high-power radio wave inside the magnetic field-aligned small-scale cylindrical irregularities with low density. It is shown that in the case of cylindrical irregularities the reflection of a plasma wave from the points of its transformation into cold plasma oscillations is sufficiently large. Therefore, this process must be taken into account in the calculation of heating of irregularities in the field of a high-power radio wave. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 3, pp. 181–195, March 2007.     

Probable mechanism of change in the spectral index of ionospheric irregularities

A probable cause of variability in the spectral index of ionospheric irregularities is discussed, based on the ability of intense longitudinal plasma waves to generate density disturbances with steep fronts. The results are experimentally confirmed.Institute of Space Research, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 2, pp. 131–135, February, 1991.     

Influence of atomic-scale irregularities in fractal analysis of electrode surfaces

To clarify the vague points appeared in the literature, it was discussed that fractal analysis of electrode surfaces based on the concept of ‘diffusion toward electrode surfaces’ is only able to monitor surface roughness in scales larger than 10 nm. When inspecting fractality in atomic scale (and even up to 10 nm), electrochemical measurements are not reliable due to the presence of surface defects, which affect the electrochemical reaction. In other words, for fractal analysis of electrode surfaces, the diffusion layer width which acts as yardstick length, should be sufficiently large, incomparable to the scale of atomic inhomogeneities. To this aim, the experiment time should be sufficiently long or the diffusion coefficient should be sufficiently large.     

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

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

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

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