ELF-VLF atmospheric waveforms under night-time ionospheric conditions

Tweek atmospherics generated by lightning discharges and propagated in the night-time Earth-ionosphere waveguide, have often very pronounced dispersive features near the first few waveguide cut-off frequencies (f_cmsimmdot{s}f_c1, f_c1sim1.6-1.9 kHz, m=1, 2, ...,), being very extended in time, and have rather large amplitudes of oscillations with periods corresponding to the narrow vicinity of the cut-off frequencies. In this paper an analytical approach is developed to describe the waveform of distant tweeks. It is based on the solving of the Maxwell equations in two qualitatively different regions, whose changes are related in the first instance to the changes in the relative magnitudes of the displacement current and components of the conduction currents, and the following asymptotic matching of the solutions in the transitional region. The analytical night-time waveguide model accounts for both anisotropy and vertical inhomogeneity of the low ionosphere. The model is valid for upper ELF - lower VLF range and is well suitable for the analysis of the QTE_m modes in the cut-off frequency regions, which determine the most important part of the tweek spectra and tweek amplitudes. The influence of the different ionospheric heights on the tweek characteristics is determined. The efficiency of the tweek generation by cloud-to-cloud discharge is also evaluated.