Numerical simulation of the penetration and reflection of a whistler beam incident on the lower ionosphere at very low latitude

By the full-wave algorithm with Fourier synthesis, 3-D propagation of a whistler beam incident on the pre-dawn lower ionosphere at very low latitude is numerically investigated. Processes of transmission, reflection, and coupling with the Earth-ionosphere waveguide are discussed via the wave energy and polarisation distributions and their dependence on the wave parameters and the ionospheric profile (such as the E_s-layer). It is shown that the dominant wave above 90 km altitude has the propagation characteristics of the magneto-ionic whistler mode, and absorption, spreading, reflection and mode conversion mainly occur at, and are greatly affected by, the bottom of the ionosphere. It is found that the transmitted energy density along the Earth's surface is reduced by 20 dB or more. Beam transmission loss varies asymmetrically with the incident angle, but changes little with the frequency. In the region 150 km (for 5 kHz) away from the ‘exit area’ where whistlers emerge, the bearing measurements using ground-based VLF direction-finders may be in error because direction-finding algorithms assume plane wave propagation. Only a small portion (about −25 dB at 5 kHz) of the incident energy is reflected up to an altitude of 150 km, and major reflection takes place in a small range of altitude at the bottom of the ionosphere with little spreading and lateral shift with respect to the incident beam. Reflection is enhanced considerably at lower frequency. Our results also suggest that an E_s-layer or an ionospheric gradient refracting waves to higher latitudes would be favorable factors for multi-hop echoes to be received on the ground.