Non-linear resonant excitation of whistler mode waves in the Earth's ionosphere

We examine the resonant non-linear interaction in the Earth's ionosphere of two powerful high frequency radio beams with frequencies f ₁ and f ₂ (both larger than the plasma frequency at F2_max) and wave numbers k ₁ and k ₂ such that a whistler mode wave can be excited with a frequency f ₃ = f ₁ — f ₂ and a wave number k ₃ = k ₁ – k ₂. The feasibility of an effective ground based installation, sited at low latitudes, is discussed and the field strength of the wave emerging from a 10 km wide ionospheric region illuminated by the beams is evaluated for a range of transmitted frequencies, beam orientations and plasma frequencies in the interaction region. It is suggested that the longitude dependence of the enhancement of VLF noise bands detected by the Ariel 3 satellite may be due to a non-linear interaction of this type between any two or more medium wavelength signals from areas where there is a high concentration of commercial broadcasting stations, such as the NE region of the U.S.A.