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where a, b, and c are the correlation scales of the uctuations of the dielectric permittivity along the corresponding coordinate axes. From geometry shown in Figures 7.18 and 7.19 we get jABj  l2 l1 2 m2 m1 2 n2 n1 2 1=2 # # 2 sin n2 n1 2 4 sin2 sin2 c 2 2
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7:117
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Assuming that the inhomogeneity is symmetric with respect to the longitudinal axis QS (along z-axis), we set a b l and c ljj , where l is the transverse and ljj is the longitudinal correlation scales of the uctuations of the plasma density (or plasma permittivity). For the small angles c, that is, for the quasi-specular scattering, and for strong anisotropy of inhomogeneities (ljj ) l ) from (7.115) (7.117) we get e 2p s
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*  + & ' & ' N1 2 8p2 2 8p2 2 2 2 # 2 2# exp 2 ljj c sin ljj l exp 2 l sin N0 2 2 l l 7:118
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Here lN is the plasma wavelength; the above formula was obtained keeping in mind  e  4  N 2  4 e  1 ; N1 that j~e1 j2 1 ll for an ionized medium and that j~e1 j2 ll ~ ~ N0 N N is the density of the plasma disturbances with respect to the ambient ionospheric plasma density N0. The Power of The Scattered Signal. The power of the forward scattered signal at the receiving antenna input can be determined by the following formula [44 46] P R PT l2 4p
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GT GR edv s 2 2 rT rR
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7:119
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where GT and GR are the transmitting and receiving antenna gain factors, respectively. For suf ciently long radio paths, when the working volume of scattering 2 2 is not too large with respect to radio path, that is, V 1=3 ( rT ; rR , the product rT rR 4 can be replaced by r . Where r is the distance from the receiver and transmitter along the straight line TOR (see Fig. 7.19), so that P R PT l2 4p 2 r 4 GT GR edv s 7:120
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The power of quasi-continuous scattered signals can be determined by numerical integration of (7.120) where e is determined from (7.118). Here, we note that the s
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p 2 factor l2 exp 8p2 l2 sin2 # has a maximum for lopt l= 2 2p sin #=2 . As this 2 l factor decreases fairly sharply for values l other than lopt , we can assume that those inhomogeneities are mainly involved in the scattering process for which l lopt . In 8p2 2 this case, factor exp l2 l sin2 # exp 1 . Taking the foregoing into account 2 and introducing notation a ljj =l, we nally get the power of scattered quasicontinuous HE -signals PR P T al2 32e 2p 1=2 r 4 * N1 N0 2 +
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& ' GT GR sin2 w # dv exp 8p2 a2 c2 sin2 2 sin2 #=2 7:121
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For the practical use of this formula, one must determine the parameters #, w and c at the center of each element of volume of scattering using the geometry and geophysical parameters of the radio trace and allow for the gain factors of the transmitting and receiving antennas for the corresponding directions. This procedure for the concrete middle-latitude radio trace is fully described in Reference [46]. We do not enter into details of the problem presented in Figure 7.20. To limit the working volume in the numerical integration, it is convenient to plot the isolines of the quantity of angle g c sin #=2 given in Figure 7.20, at the left side of each isoline. The numbers in decibel at the right side of each isoline in Figure 7.20 indicate the decrease of the power received due to p exponential factor the exp 8p2 a2 g2 . Here, the rst number is for a ljj =l 10 % 3:16, the second is for a 10. We can see that for a 3:16 integration can be con ned to within the volume of scattering between the isolines g 3 and for a 10 between the lines
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