Earth–ionosphere waveguide

Low-frequency electromagnetic waves ( <30 kHz ) propagate in the region between Earth's surface and the ionospheric D- layer ( <90 km altitude) similar to a micro - optic cables made. The waves are so concentrated that they are guided in the waveguide. The ray- optical approach loses its validity. This propagation region is therefore called ionospheric waveguide.

Introduction

The radio wave propagation in the ionosphere depends on the frequency, angle of incidence of the day and year, the Earth's magnetic field and the solar activity. For vertical incident waves may be larger than the electron plasma frequency of the F -layer maximum with a frequency

(Ne in cm -3 is the electron density ) summarizes the ionosphere undisturbed penetrate. Waves with frequencies below fe other hand, are reflected in the ionospheric D-, E- and F- layers. fe is less on the day of the order of 8-15 MHz, at night. For oblique incidence, this critical frequency is greater.

Long waves (3-30 kHz, very low frequencies, VLF ) and extremely long waves (<3 kHz, extremely low frequencies, ELF ) are already reflected in the ionospheric E- and D- layer. An exception is the Whistler propagation of lightning signals along the geomagnetic lines of force in the magnetosphere.

The dimensions of the wavelengths of VLF waves (10-100 km ) are already comparable to the height of the ionospheric D- layer (about 70 km during the day and 90 km during the night). Therefore, the radiation- optical approach has only limited validity, and the wave-optical method (at least for longer distances ) are required. The area between the ground and ionospheric D- layer behaves as a waveguide compared to VLF and ELF waves.

Electromagnetic waves in the earth's magnetic field in the presence of ionospheric plasma cease to exist if their frequency is less than the Gyrofrequenz the ions ( about 1 Hz). Waves with lower frequencies are called hydro- magnetic waves. The geomagnetic pulsations with periods of seconds to minutes, and the Alfven waves belong to this wave type.

Transfer function

The prototype of a vertical rod antenna is a vertical Hertzian dipole in which an alternating electric current of frequency flows. His radiation of electromagnetic waves in the waveguide between the earth and ionosphere can be described by a transfer function:

Wherein the vertical component of the electric field at the receiver at a distance ρ from the transmitter, the electric field of the Hertzian dipole in free space and the circular frequency. Is in free space. Seen the waveguide is dispersive, as the transfer function depends on the frequency. This means that the phase and group velocity are frequency dependent.

Ray theory

In the VLF range the transfer function is the sum of ground wave and of multiply reflected from the ionospheric D- layer beams ( Fig. 1).

On the ground, the ground wave ( Sommerfeld ground wave ) is attenuated. This energy loss depends on the orography along the beam path. VLF waves, however, this effect is relatively low at short intervals between the transmitter and receiver, so that in a first approximation, the reflection coefficient of the ground.

At shorter distances are only ground wave and the singly reflected sky wave of importance. The D layer behaves for VLF waves in a first approximation as a magnetic wall () with a sharp boundary in height. This means a phase shift of 180 ° at the reflection point. In fact the electron density of the layer D to the height increases, and the true optical path is curved.

The sum of the ground wave and the reflected wave is a simple minimum interference, where the difference of the beam paths amounts to half a wavelength (or a phase difference of 180 °). The last measured on the ground interference minimum is located at a distance of

The transmitter ( with c the speed of light ). In the example of Figure 2, these are about 500 km.

Wave-optical theory

For VLF waves, the ray theory is at a longer distance between transmitter and receiver no longer usable due to too many multiple reflected waves are involved, and the sum diverges. Here you can apply the wave-optical theory. In this theory, it is also possible to take into account the curved earth. The wave modes are the eigenmodes in the waveguide between the earth and ionosphere. These wave modes have individual vertical structures of their electric field strengths in the waveguide with maximum amplitudes on the ground and vanishing amplitude at the top ( of the ionospheric D- layer). In the case of the fundamental mode, this is a first quarter-wave length. With increasing frequency, the eigenmodes are evanescently. This occurs at the cutoff frequency fco. This is for the first mode

At lower frequency, this mode can not propagate more ( Fig. 3).

The damping of the modes increases with the wave number. Therefore, substantially only the first and the second mode is important. The first interference minimum of the two modes is in the same distance as in the ray optics theory ( Eq. 2 ), which illustrates the equivalence of both theories. Wave and ray- theory are two approximations of the transfer function in Eq. 1 with two different convergence areas. From Figure 2 it is clear that the distance between the interference minima of the two modes is equal to; in the example of Figure 2 about 1,000 km. The first mode is dominant at distances greater than about 1500 km, since the second mode is stronger than the first mode damped.

In the ELF range, the wave- optical solution is still possible. The fundamental mode is the zeroth mode ( Fig. 3). The D layer behaves here as a first approximation as an electrical wall with the reflection factor. For the zero mode, the vertical structure of the electric field strength is a constant.

The zero mode is of particular importance for the Schumann resonances. Their wavelengths are the m-th part of the earth's circumference. They have the frequency

With a the radius of the earth. The first resonance frequencies are at 7.5, 15 and 22.5 Hz Schumann resonances are excited by lightning, the spectral amplitudes are reinforced in this frequency range.

Properties of the waveguide

The above presentation of the waveguide are of course represents only an extremely simplified picture. For a more detailed approach to numerical models are necessary. It is particularly difficult to introduce horizontal and vertical inhomogeneities. Due to the finite size of the waveguide, the field strength is amplified at the antipodes points. Under the influence of the earth's magnetic field of iononosphärische reflection factor is a matrix. This means that a vertically polarized wave, after reflection on the ionosphere is split into a vertically polarized and horizontally polarized wave. Finally, the Earth's magnetic field is responsible for this, that in the spread from west to east, the waves are less attenuated than in the spread from east to west. A further non-reciprocity is performed in the vicinity of the minimum interference depth of the Eq. 2 During the time of sunrise and sunset, there is a temporary phase gain or loss from 360 ° because of the irreversible behavior of the reflected wave at the ionosphere.

The dispersion property of the ionospheric waveguide allows detection of thunderstorm cells. A flash emits a broad spectrum of VLF and ELF waves, called spherics. The difference between the group propagation delays of adjacent frequencies of such Sferics is directly proportional to the distance ρ between the transmitter and receiver. Along with a direction determination of the incoming signal gets you a local determination of its origin from a single station with a range of several 1000 km ( Atmospheric disturbances ). Using the measurement of Schumann resonances at a few stations, the global thunderstorm activity can be determined