The Earth–ionosphere waveguide refers to the phenomenon in which certain radio waves can propagate in the space between the ground and the boundary of the ionosphere. Because the ionosphere contains charged particles, it can behave as a conductor. The earth operates as a ground plane, and the resulting cavity behaves as a large waveguide.
Extremely low frequency (ELF) (< 3 kHz) and very low frequency (VLF) (3–30 kHz) signals can propagate efficiently in this waveguide. For instance, lightning strikes launch a signal called radio atmospherics, which can travel many thousands of kilometers, because they are confined between the Earth and the ionosphere. The round-the-world nature of the waveguide produces resonances, like a cavity, which are at ~7 Hz.
Introduction
Radio propagation within the ionosphere depends on frequency, angle of incidence, time of day, season, Earth's magnetic field, and solar activity. At vertical incidence, waves with frequencies larger than the electron plasma frequency ( in Hz) of the F-layer maximum
( in is the electron density) can propagate through the ionosphere nearly undisturbed. Waves with frequencies smaller than are reflected within the ionospheric D-, E-, and F-layers. is of the order of 8–15 MHz during day time conditions. For oblique incidence, the critical frequency becomes larger.
Very low frequencies (VLF: 3–30 kHz), and extremely low frequencies (ELF: <3 kHz) are reflected at the ionospheric D- and lower E-layer. An exception is whistler propagation of lightning signals along the geomagnetic field lines.
The wavelengths of VLF waves (10–100 km) are already comparable with the height of the ionospheric D-layer (about 70 km during the day, and 90 km during the night). Therefore, ray theory is only applicable for propagation over short distances, while mode theory must be used for larger distances. The region between Earth's surface and the ionospheric D-layer behaves thus like a waveguide for VLF- and ELF-waves.
In the presence of the ionospheric plasma and the geomagnetic field, electromagnetic waves exist for frequencies which are larger than the gyrofrequency of the ions (about 1 Hz). Waves with frequencies smaller than the gyrofrequency are called hydromagnetic waves. The geomagnetic pulsations with periods of seconds to minutes as well as Alfvén waves belong to that type of waves.
Transfer function
The prototype of a short vertical rod antenna is a vertical electric Hertz dipole in which electric alternating currents of frequency f flow. Its radiation of electromagnetic waves within the Earth-ionospheric waveguide can be described by a transfer function T(ρ,ω):
where Ez is the vertical component of the electric field at the receiver in a distance ρ from the transmitter, Eo is the electric field of a Hertzian dipole in free space, and the angular frequency. In free space, it is . Evidently, the Earth–ionosphere waveguide is dispersive because the transfer function depends on frequency. This means that phase- and group velocity of the waves are frequency dependent.
Ray theory
In the VLF range, the transfer function is the sum of a ground wave which arrives directly at the receiver and multihop sky waves reflected at the ionospheric D-layer (Figure 1).
For the real Earth's surface, the ground wave becomes dissipated and depends on the orography along the ray path. For VLF waves at shorter distances, this effect is, however, of minor importance, and the reflection factor of the Earth is , in a first approximation.
At shorter distances, only the first hop sky wave is of importance. The D-layer can be simulated by a magnetic wall () with a fixed boundary at a virtual height h, which means a phase jump of 180° at the reflection point. In reality, the electron density of the D-layer increases with altitude, and the wave is bounded as shown in Figure 2.
The sum of ground wave and first hop wave displays an interference pattern with interference minima if the difference between the ray paths of ground and first sky wave is half a wavelength (or a phase difference of 180°). The last interference minimum on the ground (z = 0) between the ground wave and the first sky wave is at a horizontal distance of
with c the velocity of light. In the example of Figure 3, this is at about 500 km distance.