The earth‐ionosphere cavity

Abstract

To analyze ELF wave propagation in the earth‐ionosphere cavity, a flat earth approximation may be derived from the exact equations, which are applicable to the spherical cavity, by introducing a second‐order or Debye approximation for the spherical Hankel functions. In the frequency range 3 to 30 Hz, however, the assumed conditions for the Debye approximation are not satisfied. For this reason an exact evaluation of the spherical Hankel functions is used to study the effects of the flat earth approximation on various propagation and resonance parameters. By comparing the resonance equation for a spherical cavity with its flat earth counterpart and by assuming that the surface impedance Zi at the upper cavity boundary is known, the relation between the eigenvalue ν and Sν, the sine of the complex angle of incidence at the lower ionosphere boundary, is established as ν( ν + 1) = (kaSν)2. It is also shown that the approximation ν(ν + 1) ≅ (ν + ½)2 which was used by some authors is not adequate below 30 Hz. Numerical results for both spherical and planar stratification show that (1) planar stratification is adequate for the computation of the lowest three ELF resonance frequencies to within 0.1 Hz; (2) planar stratification will lead to errors in cavity Q and wave attenuation which increase with frequency; (3) computation of resonance frequencies to within 0.1 Hz requires the extension of the lower boundary of the ionosphere to a height where the ratio of conduction current to displacement current, (σ/ωε0), is less than 0.3; (4) atmospheric conductivity should be considered down to ground level in computing cavity Q and wave attenuation.