The conductivity profile of the ionosphere and the exponential model

The behavior of the cavity is governed by the height profile of the conductivity of the lower ionosphere. To a first approximation the conductivity grows approximately exponentially with height: with each height step of a fixed characteristic scale (on the order of a few km) the conductivity increases by a constant factor. One can therefore write roughly \sigma(z) \propto e^{z/\zeta}, where \zeta is the characteristic height of the profile, of the order of a few km.

This exponential growth is important because the ELF wave penetrates the ionosphere only to a depth where the conductivity reaches a critical value; above that the field is rapidly attenuated. The profile thus defines the effective "ceiling" of the cavity and, together with it, the losses that shift the frequencies (see #18) and lower the Q-factor (see #19).

Because the electric and magnetic components of the field "feel" the ionosphere at different heights, a single exponential is not sufficient for an accurate description; two characteristic heights are therefore introduced (see #21) and refined two-exponential ("knee") models (see #22).