On the generation of ELF/VLF waves for long‐distance propagation via steerable HF heating of the lower ionosphere

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Abstract
ELF/VLF radio waves (300 Hz to 30 kHz) have been successfully generated via modulated HF (3–10 MHz) heating of the lower ionosphere in the presence of natural currents, most recently with the HAARP facility in Alaska. Generation is possible via amplitude modulation or via two techniques involving motion of the HF beam during the ELF/VLF cycle, known as beam painting and geometric modulation, described and measured by Cohen et al. (2010b). In this paper, we describe a theoretical model describing the HF heating and ionospheric responses, followed by a full‐wave calculation of ELF/VLF propagation, and utilize this end‐to‐end model to derive the predicted radiated ELF/VLF pattern up to 1000 km from the HF heater in the Earth‐ionosphere waveguide. We quantitatively compare the generated ELF/VLF signals on the ground from various generation techniques and find it to be generally in agreement with earlier measurements. We apply a simplified ELF/VLF propagation model to quantify the contribution of the ELF/VLF phased array in the radiation pattern resulting from geometric modulation and find this contribution to be significant. We also use a limited HF heating model to quantify the degree to which the current power level of HAARP is sufficient for the beam painting technique, since this technique requires high HF power densities at high altitudes.

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