5. Efficiency of the Waveguide Excitation: Numerical
Results and Interpretations
[22] The efficiency parameters of the waveguide excitation will be
defined as
 | (40) |
 | (41) |
where
Erieq and
Erier are the radial components
of the electric field excited on the surface of the ground by the
ionospheric electric dipoles oriented along the unit vector
eq and radial, respectively. Similar values for magnetic
dipoles are designated as
Erimq and
Erimr. The
field components in expressions (40) and (41) were calculated by
the method described by
Rybachek [1995] and
Rybachek et al. [1997a, 1997b],
and in the scope of the problem in question
may be computed with any given accuracy. The values of
Re and
Rm which in this sense may be called "accurate," as well as
the approximate expressions for the efficiency parameters
e (38) and
m (39), following from (36) and (37), characterize
the efficiency of excitation of the waveguide by horizontal and
radial dipoles located in the ionosphere.
[23] The region where approximate expressions (38) and (39) are valid,
is roughly described by inequalities (22) and (27). One can obtain
more exact estimation introducing the relative errors
 | (42) |
 | (43) |
[24] In the case if the waveguide is a regular one on the coordinate
q the daytime and nighttime models of the electron
concentration
N(H) [Prikner, 1980]
and effective collision
frequency of electron with neutral particles and ions
ne(H) [Fatkullin et al., 1981]
were used for the calculations. The
electrical properties of the ground correspond to the seawater
(the specific conductivity is 4 mho m
-1 ).
The calculations were
performed for the frequencies of 0.5-5 kHz, the distance from the
projection of the emitter onto the ground surface to the
ground-based receiver of 500 km, the emitter location heights from
50 to 500 km, and latitudes
I=10-80o.
|
|
Figure 1
|
|
|
Figure 2
|
[25] The frequency dependencies of the efficiency parameter
Rm (41)
for various heights
H of emitter location for the daytime and
nighttime propagation conditions are shown in Figures 1 and 2, respectively ( I=36o ).
It follows from Figures 1 and 2 that
at the heights of 100-500 km in the daytime and 200-500 km at
night, the horizontal magnetic dipole is more effective than the
vertical one
(Rm>1). Calculations show that for the heights of
50-60 km in the daytime and 50-80 km at night,
Rm may be less
than unity. In the daytime in the frequency range 2-3 kHz and at
night at frequencies below 2 kHz, a nonmonotonic dependency
Rm(f) is observed. This is due to the presence of the so-called
waveguide minima in the frequency dependencies of the field
component modules. The position of the minima depends on the state
of the ionosphere (day, night) and is different for different
components of the fields. The efficiency parameter reaches the
highest value
Rm 
180 in the daytime at a frequency of
0.5 kHz and
Rm 250 at night at a frequency of
f 1.5 kHz (at the source height of 300 km).
|
|
Figure 3
|
|
|
Figure 4
|
[26] Now we consider possibilities of using the approximate formula
(39). For this purpose we calculated the frequency dependencies of
the relative errors
em (43) for the daytime (Figure 3) and
night (Figure 4). In the daytime at heights of 100-500 km,
formula (39) is the most accurate at frequencies of 0.5-2 kHz
(here
em<2% ). At night, the use of approximation
(39) is reasonable at the heights of 200-500 km and the same as
for the daytime frequencies. That gives
em<10%.
|
|
Figure 5
|
|
|
Figure 6
|
|
|
Figure 7
|
[27] The dependencies of the efficiency parameter
Rm on the height
of the emitter locations ( H=50-500 km) for various latitudes
I
and a frequency of 0.5 kHz are shown in Figures 5 and 6 for
the daytime and nighttime conditions, respectively. The ratio
Rm reaches a maximum at all latitudes at
H 250 and
H 300 km in the daytime and at night, respectively. The
ratio
Rm takes the peak values of 350-370 at a latitude
I=10o
. The corresponding daytime and nighttime dependencies
of the relative error
em (43) on
H for
I=60o are shown in Figure 7. In the daytime at
H
100 km and at
night at
H 250 km, the values of
em do not
exceed 1%. The calculations show that for all considered
latitudes in the daytime under
H 100 km,
em does not exceed 2%. At night under
H 250 km, the values
of
em do not exceed 2%, whereas under
H 200 km,
em
12%. This fact makes it possible to use
for interpretation of the results presented in Figures 5 and 6 approximate
formula (39). According to this formula, the form of
the
Rm(H) dependencies is determined by the features of the
N(H) profiles having a maximum at
H 250 km in the
daytime and two maxima at
H 100 and 300 km at night.
|
|
Figure 8
|
|
|
Figure 9
|
[28] The calculated by exact formulae dependences of the efficiency
parameter
Re (40) on latitude
I for the daytime and nighttime
ionosphere, at a frequency of 0.5 kHz and altitudes of 100-500 km
are described by the same curve in Figure 8. It follows from
Figure 8 that at latitudes
I > 25o the horizontal electric
dipole is more effective than the radial dipole, and the ratio
Re 11.5 at a latitude of
80o. The latitudinal
dependencies of the relative errors
ee (42) for
altitudes of 100 and 500 km are shown in Figure 9 (solid lines
correspond to the daytime values). In the daytime for all
considered latitudes and emitter heights, it is valid:
ee<0.2%.
At night we have the same result for
H=500 km, whereas for
H=100 km at all latitudes
ee<1.2%. Such small errors make it possible to use
for interpretation of the results presented in Figure 8 approximate
formula (38). According to this formula, the values of
the efficiency parameters are determined only by the geomagnetic
field, so we have one curve in Figure 8. This result qualitatively
is true at an increase of the frequency in the considered range.
The calculations show that in this case for the daytime and
nighttime midlatitude ionosphere and dipole location heights of
200-500 km,
ee<5%.
|
|
Figure 10
|
[29] Similar results of calculations for an irregular waveguide are
presented in Figure 10 in the form of the diurnal variations of
the
Rm parameter for a frequency of 0.5 kHz and the path with
the emitter and receiver coordinates 30o N, 30o E
and 60o N, 30o E, respectively. The data are obtained
with the help of the algorithm
[Rybachek et al., 1997a, 1997b]
taking into account the geomagnetic and geographic
coordinates, solar zenith angle, azimuth, and local time. The path
was approximated by seven regular parts. The
N(H)
and
ne(H) profiles from
Rawer et al. [1978] and
COSPAR [1990]
and Fatkullin et al. [1981],
respectively, were used in the
calculations. It follows from Figure 10 that at the location of
the transmitter at a height of 200 km, the daytime values of
Rm
( t=12 h) exceed considerably the nighttime values ( t=1 h) (by
about an order of magnitude). The excess is much less at altitudes
of 300-500 km, this fact agreeing to the presented
in Figures 1 and 2 results of calculations of the
Rm parameter for the
nighttime and daytime regular waveguide.
Powered by TeXWeb (Win32, v.2.0).