Self‐focusing of radio waves in an underdense ionosphere

Abstract

The theory of self‐focusing instabilities in the ionosphere is developed emphasizing the critical parameters required to obtain sufficiently fast temporal and spatial growth rates so that the instability may be observed. It is shown that self‐focusing will not occur unless 2cf/πfp²l <1, where f is the radio wave frequency, fp a typical ionospheric plasma frequency, and l the spatial growth length. (In the F region, l ≈ 25 km is used, while in the E region l ≈ 1 km.) In the F region, the threshold power flux Pc is Pc,F ≈ (1.5 µW/m²) (f/15 MHz)³ (Te/1000 °K)4 × (106 cm−3/ne)³CF, where ne and Te are typical electron densities and temperatures, and CF ∼1 depends on spatial and temporal growth rates. In the E region, the result is Pc,E ≈ (1 mW/m²) (f/15 MHz)³ (105 cm−3/ne)CE, where CE ≈ 1 again depends on growth rates. Dimensional analysis indicates nonlinear saturation will set in when variations of order unity occur in the radio wave intensity. The corresponding relative electron density fluctuations are given by δn/n ∼πcf/fp²l. Applications to planned ionospheric heating experiments and ionospheric modification by the microwave beam from a satellite power station are discussed.