Cone structure and focusing of VLF and LF electromagnetic waves at high altitudes in the ionosphere

Abstract

The frequency and angle dependencies of the electric field radiated by an electric dipole E = E 0 cos ω t are studied through numerical calculations of | E | in the VLF and LF frequency bands 0.02fnof' b ≤ F ≤ 0.5fnof; b in a model ionosphere over an altitude region of 800‐6000 km where the wave frequency and electron gyrofrequency varies between F ∼ 4 ‐ 500 kHz and fnof; b ≃ (1.1 to 0.2) MHz respectively. It is found that the amplitudes of the electric field have large maxima in four regions: close to the direction of the Earth magnetic field line B 0 (it is called the axis field E 0 ), in the Storey E St , reversed Storey E RevSt , and resonance E Res cones. The maximal values of E 0 , E Res , and E Rev.St are the most pronounced close to the lower hybrid frequency, F ∼ F L . The flux of the electric field is concentrated in very narrow regions, with the apex angles of the cones Δβ ≃ (0.1 ‐ 1) deg. The enhancement and focusing of the electric field increases with altitude starting at Z > 800 km. At Z ≥ 1000 up to 6000 km, the relative value of | E |, in comparison with its value at Z = 800 km is about (10² to 10 4 ) times larger. Thus the flux of VLF and LF electromagnetic waves generated at high altitudes in the Earth's ionosphere are trapped into very narrow conical beams similar to laser beams.