Nonlinear mixing and excitation of sidebands in the ionosphere

Abstract

Two radio waves of frequencies ω1 and ω2 couple nonlinearly in the lower ionosphere to create a temperature perturbation TΔω, 2k1 (Δω = ω1 − ω2; 2k1 ≈ k1 + k2) and a density perturbation n Δω by the process of ambipolar diffusion. This perturbation couples with the ω1 frequency wave to generate electromagnetic sidebands of frequencies ω1 ± nΔω (n = 1, 2, ⋯ ) as observed in a recent experiment. The field of the sideband wave near the turning point has an Airy function dependence while away from the turning point it has a WKB sinusoidal solution. The power of the sideband decreases with increasing Δω. It also falls almost exponentially with the order of the sideband. The existence of a turning point for the pump waves is essential for efficient nonlinear coupling.