Wave Structure Functions of Multiply Scattered Electromagnetic Waves by Anisotropic Magnetized Turbulent Plasma Layer

Abstract

Wave structure functions of both phase and logarithmic relative amplitude, their mutual wave structure functions for two plane electromagnetic waves with difierent frequencies are studied. Besides, features of intensity of frequency ∞uctuations of multiply scattered radiation by flnite thickness of anisotropic magnetized plasma layer are investigated in complex geometrical optics approximation. Source and receiver are assumed to be located on opposite sides with respect to turbulent plasma layer. Numerical calculations have been carried out for F-region of the ionosphere using satellite data of ionospheric plasma parameters. Wave structure functions for plane, spherical waves and Gaussian beams have been investigated in (1{4). Evolution of the angular power spectrum of scattered electromagnetic radiation and features of its statistical characteristics, broadening and displacements of its maximum has been studied in geometrical optics approximation (5{8). High-frequency monochromatic EM wave scat- tered on electron density ∞uctuations of ionospheric plasma lead to distortion of the observable angular power spectrum. Wave propagation in turbulent plasma with electron density ∞uctua- tions is usually accompanied by ∞uctuations of its parameters | amplitude, phase, intensity and so on. Investigation of peculiarities of frequency and frequency-spatial correlation functions are under the particular interest in satellite communications. It enables to deflne frequency band that could be transferred through statistically inhomogeneous medium without distortion of the form of signal spectrum. Determination of the frequency band demands the knowledge of frequencyspatial correlations of ∞uctuated fleld in the aperture plane of a highly directional antenna. In satel- lite communications, the ability to transmit a wideband data is closely related to the frequency correlation of the signal. Information about the frequency and spatial correlation of the signal is essential in designing and analyzing frequency and/or spatial diversity schemes. Therefore, in this paper, statistical characteristics: the log-amplitude and the phase wave structure functions, of frequency-spaced plane EM waves are computed. Complex geometrical optics approximation is applied taking into account multiple scattering efiects. Numerical calculations have been carried out utilizing satellite data of F-region ionospheric plasma parameters. 2. CORRELATION FUNCTION OF THE PHASE A point source, located in vacuum at a terminal distance l1 above from the plane boundary of random magnetized plasma, irradiate high-frequency electromagnetic waves. Thickness of the scat- tered layer is equal to l2, receiver is located in vacuum below the layer at a distant l3 in the XZ plane (principle plane) and the length of line-of-sight connecting the source and the receiver is L0 = l1 + l2 + l3. The imposed magnetic fleld makes an angle µ0 between Z axis and angle µ with the direction of a wavevector of the incident wave. The plasma concentration in the layer is: N(r) = N0 + N1(r); where N0-is the constant term, N1(r) is a random function of the spatial coordinates describing concentration ∞uctuations. We shall suppose that the inequalities are sat- isfled for magnetized plasma: !B ? !, !B ? eff, !B ? !p, where ! is the angular frequency, eff is the efiective collision frequency of electrons with other particles, !p = (4…e 2 N=m) 1=2 is the plasma frequency and !B = eB0=mc is the angular gyro-frequency for magnetic fleld; e and m are the charge and the mass of an electron, respectively, c is the speed of light in the vacuum. Plasma is considered as a uniaxial crystal having permittivity tensor components: ~