Efficiency of the Earth--ionosphere waveguide excitation by...

4. Relations Between the Field Components Excited in the Waveguide by Ionospheric Dipoles

[19] The expressions relating the components of the fields excited in the terrestrial waveguide in point 2 with coordinates ( r, q ) by various emitters located in the ionosphere in point 1 with coordinates ( b, 0 ) can be obtained from the reciprocity theorems (1):

for the electric dipoles oriented along the unit vector e_x, x=q, j, and radial:

(33)

for magnetic dipoles oriented along the unit vector e_x, x=q, j, and radial:

(34)

Here E_z^iqx(1,2, H₀) and H_z^iqx(1,2, H₀) are the z components of the intensities of the electric and magnetic fields, respectively, excited in the waveguide at the point 2 under the given geomagnetic field H₀ by electric (q=e) or magnetic (q=m) dipoles oriented along the unit vector e_x and located in the ionosphere at point 1; E_x^qz(2,1,- H₀), H_x^qz(2,1,- H₀) are the x components of the fields excited in the ionosphere at the point 1 under the geomagnetic field - H₀ by electric or magnetic dipoles directed along e_z and located in the waveguide at the point 2. In this case z takes the values r, q, and j.

[20] It follows from expressions (33) and (34) and relations (23), (30), and (31) that the formulae relating the components of the fields excited in the waveguide cavity by emitters of different types located in the ionosphere in the region, where quasi-longitudinal approximation (22) and inequalities (27) are applicable, can be written in matrix form as

(35)

(36)

(37)

Here A^iqx ( q=e, m; x=r, q, j ) are six-element column matrices of the modules of the electric and magnetic field components and _e and _m according to formulae (30) and (31) are

(38)

(39)

Here b=a+H, where H is the height of the emitter above the surface of the ground. It is seen that (39) may be written as

where N and H_{0 L} should be given in el cm ^-3 and oersteds, respectively.

[21] In the case of an irregular waveguide, the parameters in formulae (38) and (39) describing the ionospheric properties correspond to the point at which the emitter is located.