Effects of VLF heating of ionosphere on the transmission cone of MF waves propagating from ground to space

Global maps of VLF-MF waves observed by the low-altitude (~700 km) DEMETER satellite (Parrot et al., 2009) have pointed out localized enhancements of wave energy above the most powerful VLF transmitters and their conjugate regions, both in the 18-25 kHz frequency range (VLF transmitters) and in the 2.-2.5 MHz frequency range (emissions associated with lightning discharges). Under hypothesis made for the computation of the refractive index by the Appleton-Hartree formula, simulations are conducted to estimate the effect of VLF heating on the transmission cone of MF waves propagating from ground to space. The method used consists in the computation of the vertical variations of the Real part of the refractive index n and of the α attenuation factor (α = ω. Imag(n)/c), with an IRI electron density profile derived from the geophysical parameters of a DEMETER orbit and an hybrid collision frequency model taking into account of theoretical and experimental data. Half-angles of the transmission cone are estimated: first, at the X=1 (X=fpe2/f2) low altitude boundary (where Ordinary mode waves may be converted into Extraordinary mode waves), and second, at the high-altitude X=1 boundary (where Extraordinary mode waves may be converted into Ordinary mode waves). It is shown that enhancements in the collision frequencies, produced by VLF heating at altitudes where the product of the collision frequency ν by the electronic density Ne is maximum (i.e. at altitudes including the low-altitude and the high-altitude X=1 boundaries), open the half angle of the transmission cones for MF waves which cross the ionosphere, and so explain enhancements of wave energy observed in the 2. - 2.5 MHz band above the powerful VLF transmitters and their conjugate regions.