Radiation Theory of VLF Waves Generated by Beating HF Waves in the Anisotropic Ionosphere

Ionospheric heating by high-power high frequency (HF: 3–30 MHz) electromagnetic waves has been an emerging technique to generate very low frequency (VLF: 3–30 kHz) signals in recent decades. In this article, we propose an analytical method to calculate the VLF field generated by electrojet-independent beat-wave heating in an anisotropic ionospheric plasma. By considering the effects of both the extraordinary wave and ordinary wave, the kernels of the virtual ionospheric antenna are derived under the anisotropic condition and are further combined with the nonlinear modulation current induced by beating two HF heaters to evaluate the VLF radiation directly. Computations show that a lower heater frequency would give rise to stronger radiation and the generated VLF radio waves always propagate along the background magnetic field regardless of the dip angle of the heater induced current source. The results manifest that the intensity of VLF radiation due to beat-wave modulation may still increase with the radiation frequency within a certain frequency range, and the predicted fields using the presented theory are found to be in good agreement with the observations in previous HAARP experiments.