180 both in the daytime and at night. The use of the
approximate formula for
Rm is reasonable at frequencies of
0.5-2 kHz at altitudes of 100-500 km and 200-500 km in the
daytime ( em<2% ) and at night ( em<10% ),
respectively.[30] Using the generalized reciprocity theorem, the expressions relating the components of the fields generated in the anisotropic ionosphere by various emitters located in the Earth-ionosphere waveguide and also the relations between field components excited in the waveguide by emitters located in the ionosphere are derived.
[31] In the frequency range 0.5-5 kHz in the scope of a regular terrestrial waveguide, parameters of the efficiency of the waveguide excitation by horizontal and radial electric and magnetic dipoles located in the ionosphere are studied. The analysis was performed using the numerical methods that allow us to derive the field components with the given accuracy and the approximate analytical formulae. The latter are valid in the case of the emitters location in the region of applicability of the quasi-longitudinal approximation.
[32] The analysis of the frequency dependencies of the
Rm parameter
characterizing the efficiency of waveguide excitation by magnetic
dipoles showed that for the midlatitude ionosphere ( I=36o )
in the considered ranges of frequencies and heights
( H=100-500 km and 200-500 km in the daytime and at night, respectively), a
horizontal magnetic dipole is more efficient than a vertical one.
The
Rm parameter at a frequency of 0.5 kHz for
H=300 km is
Rm 180 both in the daytime and at night. The use of the
approximate formula for
Rm is reasonable at frequencies of
0.5-2 kHz at altitudes of 100-500 km and 200-500 km in the
daytime ( em<2% ) and at night ( em<10% ),
respectively.
[33] The form of the
Rm dependencies on the emitter height is
determined by the features of the electron concentration profiles.
In particular, the positions of the maxima in the dependencies
Rm(H) and
N(H) coincide at all latitudes. At a frequency of
0.5 kHz the efficiency parameter
Rm reaches its maximum at all
latitudes at
H 250 and
H 300 km in the daytime
and at night, respectively. The value of
Rm in the maximum can
reach 350-370 (at a latitude of 10o). The accuracy of the
approximate formula
m is high enough: for all considered
latitudes at
H> 250 km,
em is not more than
2% both in the daytime and nighttime conditions.
[34] The error of the approximate formula for the efficiency parameter Re characterizing excitation of the waveguide by electric dipoles does not exceed 5% in the considered frequency range for the daytime and nighttime midlatitude ionosphere and dipole location heights of 200-500 km. In this case the efficiency of waveguide excitation by electric dipoles is determined mainly by the geomagnetic field.
[35] In the scope of an irregular waveguide, the diurnal dependencies of Rm(t) are calculated using the algorithm taking into account geomagnetic and geographic coordinates, solar zenith angle, azimuth, and local time. For the midlatitudinal path at the location of the transmitters at altitude of 200 km and at a frequency of 0.5 kHz, the daytime values ( t=12 h) of Rm exceed considerably the nighttime values ( t=1 h) (by about an order of magnitude). This excess is much less at altitudes of 400-500 km.
[36] Concluding, we note that in the ELF range, the approximate formulae for the efficiency parameters make it possible, without calculating the fields in the ionosphere, with sufficiently high degree of accuracy to estimate the efficiency of the Earth-ionosphere waveguide excitation by emitters located at altitudes of 200-500 km both in the daytime and nighttime ionosphere.
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