Ionospheric waveguide

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Low-frequency electromagnetic waves (<30 kHz) propagate in the area between the earth's surface and the ionospheric D-layer (<90 km height) similar to a micro- waveguide . The waves are bundled in such a way that they are guided in the waveguide. The ray-optical approach loses its validity. This range is therefore called ionospheric waveguide .

introduction

The propagation of radio waves in the ionosphere depends on the frequency, the angle of incidence , the time of day and season, the earth's magnetic field , and solar activity . With vertical incidence, waves can have a frequency greater than the electron plasma frequency of the F-layer maximum

(N e in cm −3 is the electron density) the ionosphere can penetrate undisturbed. Waves with frequencies less than f e , however, are reflected in the ionospheric D, E and F layers. f e is of the order of 8–15 MHz during the day, less at night. At an oblique incidence, this critical frequency increases.

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

The dimensions of the wavelengths of the 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, the ray-optical approach is only valid to a limited extent, and the wave-optical method becomes necessary (at least for larger distances). The area between the earth and the ionospheric D-layer behaves like a waveguide towards VLF and ELF waves.

Electromagnetic waves in the ionospheric plasma in the presence of the earth's magnetic field cease to exist if their frequency is less than the gyrofrequency of the ions (about 1 Hz). Waves with lower frequencies are called hydromagnetic waves. The terrestrial magnetic pulsations with periods from seconds to minutes as well as the Alfvén waves belong to this type of wave.

Transfer function

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

(1)

where 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 angular frequency are. In free space is . The waveguide can be seen to be dispersive , since the transfer function depends on the frequency. This means that phase and group speed are frequency dependent.

Radiation theory

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

The ground wave ( Sommerfeld 's ground wave) is dampened on the ground. This energy loss depends on the orography along the beam path. For VLF waves, however, this effect is relatively small at shorter distances between transmitter and receiver, so that the reflection factor of the ground is a first approximation .

Figure 1. Geometry of the radiation paths within the ionospheric waveguide. The ground wave and two reflected sky waves are shown

For shorter distances, only the ground wave and the simply reflected sky wave are important. As a first approximation, the D-layer behaves for VLF waves like a magnetic wall ( ) with a sharp limit in height . That means a phase jump of 180 ° at the reflection point. In fact, the D-layer electron density increases with height, and the true ray path is curved.

The sum of the ground wave and the simply reflected wave shows an interference minimum where the difference between the beam paths is half a wavelength (or a phase difference of 180 °). The last interference minimum measured on the ground is at a distance of

(2)

from the transmitter (with c the speed of light). In the example in Fig. 2, this is around 500 km.

Figure 2. Normalized vertical field strength E z (transfer function) as a function of the distance ρ between transmitter and receiver according to amount (full line; left ordinate) and phase (dashed line; right ordinate). The transmitter is a vertical Hertzian diploma with a frequency of f = 15 kHz. The virtual reflection height is 70 km. This corresponds to daytime conditions in mid-latitudes. The amplitude minimum at a distance of about ρ = 500 km is the last interference minimum between the ground wave and the simply reflected wave in ray-optical theory and the first interference minimum in wave-optical theory (mode theory)

Wave-optical theory

For VLF waves, the ray theory is no longer usable at greater distances between transmitter and receiver, since too many multiply reflected waves are involved and the sum diverges. The wave-optical theory can be applied here. In this theory it is also possible to take the curved earth into account. The wave modes are the eigenmodes in the waveguide between the earth and the ionosphere. These wave modes have individual vertical structures of their electric field strengths in the waveguide with maximum amplitudes on the ground and vanishing amplitudes at the upper edge (the ionospheric D-layer). In the case of the fundamental first mode, this is a quarter wavelength. With increasing frequency, the eigenmodes become evanescent. This happens at the cutoff frequency f co . This is for the first time fashion

At a lower frequency, this mode can no longer propagate (Fig. 3).

The attenuation of the modes increases with the wave number . Therefore, essentially only the first and the second mode are of importance. The first interference minimum of both modes is at the same distance as in the ray-optical theory (Eq. 2), which illustrates the equivalence of both theories. Wave and ray-optical theory are two approximations of the transfer function in Eq. 1 with two different convergence areas. From Fig. 2 it is clear that the distance between the interference minima of the two modes is the same; in the example in Fig. 2 about 1,000 km. The first mode dominates at distances greater than about 1500 km, since the second mode is more attenuated than the first mode.

Figure 3. Amplitude of the transfer function of the first and the zeroth mode as a function of the frequency at intervals of 1,000, 3,000 and 10,000 km per day

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

Mode zero is of particular importance for the Schumann resonances . Their wavelengths are the m-th part of the earth's circumference. You own the frequency

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

Properties of the waveguide

The above representation of the waveguide is of course only an extremely simplified picture. For a more detailed approach, numerical models are necessary. Taking horizontal and vertical inhomogeneities into account is particularly difficult. Due to the finite expansion of the waveguide, the field strength at the antipode points is increased. Under the influence of the earth's magnetic field, the iononospheric reflection factor becomes a matrix. This means that a vertically polarized wave after reflection at the ionosphere splits into a vertically polarized and a horizontally polarized wave. After all, the earth's magnetic field is responsible for the fact that the waves are less dampened when they spread from west to east than when they spread from east to west. Another non-reciprocity occurs in the vicinity of the low interference minimum in Eq. 2. During the time of sunrise and sunset, there is a temporary gain or loss of 360 ° due to the irreversible behavior of the wave reflected from the ionosphere.

The dispersion property of the ionospheric waveguide allows the location of thunderstorm cells. A flash emits a wide range of VLF and ELF waves Spherics called. The difference in the group delay delays of neighboring frequencies of such a sferic is directly proportional to the distance ρ between transmitter and receiver. Together with a determination of the direction of the incoming signal, you get a position determination of its origin from a single station with a range of several 1000 km ( atmospheric disturbances ). The global thunderstorm activity can be determined by measuring Schumann resonances at a few stations.

Individual evidence

  1. a b c d K. Davies: Ionospheric Radio . Peregrinus, London 1990.
  2. ^ K. Rawer: Wave Propagation in the Ionosphere . Kluwer Publ., Dordrecht 1993.
  3. ^ Robert A. Helliwell: Whistlers and Related Ionospheric Phenomena . Dover Publications, 2006, ISBN 0-486-44572-0 (Originally published by Stanford University Press, Stanford, California, 1965).
  4. a b c d e J. R. Wait: Electromagnetic Waves in Stratified Media . McMillan, New York 1979.
  5. ^ KG Budden: The Propagation of Radiowaves . Cambridge University Press, Cambridge 1985.
  6. ^ A b H. Volland: Atmospheric Electrodynamics. Springer, Heidelberg 1984.
  7. AP Nickolaenko, M. Hayakawa: Resonances in the Earth-ionosphere cavity . Kluwer Academic Publishers, Dordrecht / Boston / London, 2002.
  8. Christoph Grandt: Thunderstorm Monitoring in South Africa and Europe by Means of Very Low Frequency Sferics . In: Journal of Geophysical Research . tape 97 , D16, 1992, pp. 18215-18226 , doi : 10.1029 / 92JD01623 .
  9. ^ SJ Heckman, E. Williams ,: Total global lightning inferred from Schumann resonance measurements . In: JGR . 103, No. D24, 1998, pp. 31775-31779. bibcode : 1998JGR ... 10331775H . doi : 10.1029 / 98JD02648 .