5. Influence of IGW of a Soliton Type on the VLF Range Radio Wave Propagation
[25] In this section we will study the influence of the soliton-type
IGW on the electromagnetic field in the observational point.
Let
h (x)=h0 +h1 (x), where all terms are purely real,
h0 is a regular component, and the disturbance
h1 (x) is written in the form
Here
x0 = V0 t is the geometric center of the soliton,
V0 is the velocity of
its motion, and the horizontal scale
lg determining its width is
considerably larger than the waveguide height
h.
The conformal
transformation
x (u) is determined by the impedance of the
boundary
where the
factor
a determines the amplitude of perturbation.
Then
 | (17) |
(we should remind that
u = x + i z ). In the lower medium, in the
region
0 
z h, the function
b(x,z)=| x'(u)| is
written in the following form:
 | (18) |
In the same way as in section 4, the field of the wave reflected
from the ionosphere is taken as a product of the undisturbed
solution
P0 to the cofactor
P(x) / P0(x).
|
|
Figure 6
|
[26] Figure 6 shows the results of the numerical calculations for the
dependence of
|P/P0| on the horizontal distance
x under
the following values of the parameters: the horizontal scale of
the irregularity
lg = 500 km, time
t =1 s, and the
distance of the geometric center of the disturbance from the zero
coordinate (where the source is located)
x0 = 1500 km. The
vertical distance of the observational point to the boundary is
90 km. The regular value of impedance of the boundary
h0 =0.6 i.
Curves 1, 2, and 3
correspond to the relative amplitudes
a = 0.2,
a = 0.3, and
a = 0.4,
respectively.
|
|
Figure 7
|
[27] Figure 7 shows the dependence of the function
|P/P0 | on
the distance
x under
x0 = 1500 km,
t =1 s,
h0 = 0.6 i,
a = 0.4, and
h = 90 km. The typical
scales of the soliton are
lg = 400 km,
lg = 500 km, and
lg = 600 km for graphs 1, 2, and 3,
respectively. With an increase of the soliton scale, the
variations in the values of
| P/P0| decrease, this fact
being caused by the decrease in the impedance variations within
the zone important for the reflection.
|
|
Figure 8
|
[28] Figure 8 shows the dependence of
|P/P0| on the distance
x0 to the center of the irregularity under
h0 = 0.6 i,
lg = 400 km,
h = 90 km, and the coordinate of the
observational point
x = 850 km. In the same way as in Figure 3,
here curves 1, 2, and 3 correspond to the relative amplitude
a = 0.2,
a = 0,3, and
a = 0.4, respectively.
At such mutual position of the observational point
x and the
irregularity center
x0 that
x 
2 x0, the field at the
observational point is by the modulus close to the undisturbed
value. It is explained by the fact that in this case the ray
arriving to the observational point is reflected from the region
in the vicinity of the disturbance center where the properties of
the boundary become quasi-regular. Under the introduced
conditions, the relative dielectric permeability of the ionosphere
is negative.
[29] The performed simulations correspond to the case of purely
imaginary impedance
h (x)= i|h (x)| of the upper boundary
z=h. Because of this the reflection coefficient
V =( sin qs - h)/( sin qs + h) is by its modulus equal to
unity. Therefore the corresponding values of
|P/P0| should
tend to unity, the fact seen in the figures (see Figures 6
and 8).
|
|
Figure 9
|
[30] Bezrodny et al. [1984] for the VLF range ( f 20 kHz)
suggested similar model with the real impedance which for the
frequency
f=104 Hz has the value
h0 =0.5. The results of
simulations for this case that take into account the influence of
soliton are presented in Figure 9 for the following parameters
lg =400 km,
h=90 km,
a =0.2 (curve 1),
a =0.3 (curve 2),
a =0.4 (curve 3).
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