Multifractal Structure of Intermittency in a Developed Ionospheric Turbulence

Abstract

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.Some structural features of a developed small-scale ionospheric turbulence (SSIT) were explored during our experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2005-2006 [1]. Emphasis was placed on a study of multidimensional structural functions of order q [∆A(τ )] q for fast amplitude fluctuations A(t) of the signals received on the Earth. This yielded important information on the local structure of the developed ionospheric turbulence which was inaccessible in the conventional remote studies of the ionosphere using the classical radio-scintillation technique [1-3]. Developed ionospheric turbulence requires the presence of a broad spectrum of inhomogeneities of the medium, whose statistical characteristics satisfy a certain scaling law. Earlier, the statistical process of ionospheric scattering of radio waves was assumed uniform, and statistical moments of the second order were used for its description [3]. Such a process is characterized by a well-defined chaotic structure of fast fluctuations in the received-signal amplitude with, as was generally assumed, uniform behavior of the scintillations [3]. Actually, the scattering of radio waves by small-scale irregularities of the ionospheric electron number density even in the case of a developed SSIT is not uniform, and the fractal method (see [2] for more detail) should be used for its correct description. In this experiment, as before, we use records of the received satellite signals with quasihomogeneous form of scintillations, but now we analyze multidimensional structural functions of the amplitude fluctuations of received signals [1]. However, by virtue of their dynamic properties, multidimensional structural functions of the amplitude fluctuations cannot be used for a sufficiently complete study of the intermittency (irregularity) of the amplit...

Fractal structure of artificial ionospheric turbulence

“…The same records of weak fluctuations of the satellite-signal amplitudes at three reception points (Ar'ya, and Sechenovo, and "Sura") in the session of August 20, 2002 were processed by the multifractalanalysis method, which was used in our studies of the multifractal structure of natural ionospheric turbulence [5,6].…”

“….) for the energy fluctuations E(t) = t 0 [∆A(t )] 2 dt of received signals for the diversity time τ by the formula [6] […”

“…where ϕ E (q) is the scaling index during approximation of the measured qth-order structural functions [∆E(τ )] q of the energy fluctuations and D E (β q ) is the fractal dimension of the energy fluctuations of received signals determined in a set of q structural fluctuations [6]:…”

“…(3)) coincided with the current energy of fluctuations of received signals: ∆E(τ ) ≈ E(τ ) = τ 0 [∆A(t )] 2 dt. In the case of weak energy fluctuations of received signals, the local value of the qth moment of E satisfies the following power-law dependence [6]:…”

“…(7) are determined by the behavior of the amplitude-fluctuation variance which, in turn, is directly related to the behavior of the variance (∆N 1 ) 2 of integral fluctuations in the electron number density for an ionospheric layer with small-scale plasma irregularities [6,7].…”