general principles of propagation in the ionosphere

8/12/2019 General Principles of Propagation in the Ionosphere

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General Principles of Propagation in the Ionosphere

The presence of the free electrons in the ionosphere is what effects radio signalsacross several bands of the spectrum from 3kHz to 30GHz. The alternating electricfield of the radio wave causes the motion in the free electrons. Depending upon the

density of the electrons and their range of movement and the frequency andamplitude of the radio wave, the effects range from total absorption of the radiowaves to selective reflection and phase delays. Leading to distortions in thecommunications or complete failures.

The proximity of the transmitted radio wave to the local resonant frequency, orplasma frequency, in the ionosphere determines many aspects of how theelectromagnetic wave propagates, i.e. what fraction of the energy is refracted,reflected, transmitted or absorbed.

The ionosphere is a plasma of freely moving electrons and ions. Plasmas are notrigid structures, the electromagnetic force creates organisation upon the collection ofcharges particles. Once an electron is displaced from the fairly uniform backgroundof ions, by say the alternating field of a passing electromagnetic wave, then thedisplacement of the electron creates an electric field which attempts to restore theneutrality of the plasma by returning the electron to its original position. However,because of inertia the electron overshoots and then proceeds to oscillate about itsequilibrium position with a characteristic frequency known as the plasma

frequency, p.

The relationship between the density of electrons and the plasma frequency can be

shown to be:

Equation 1

Here p is the angular plasma frequency and f p the plasma frequency, N is thedensity of electrons and e the charge on the electron with me equal to the electron

mass and o is the permittivity of free space. Since the electron density varies with

altitude, N(h), then so does the plasma frequency, p(h). So the electron densityprofile in Figure 1 could be shown as either density of electrons or plasma frequency.

For typical ionospheric electron densities of between 1x1011 to 1x1012 electrons persquare meter the plasma frequency, f p, is between 1 to 10MHz, which is in the HFband. This is why HF is the band most significantly affected by the ionosphere.

The plasma frequency plays a fundamental role in the refractive index and hencepropagation in the ionosphere.

Without going into the derivation, which is covered in many text books (Davis 1990,

Chen 1984, Budden 1985), the phase refractive index of the ionosphere, p, in its

simplest case is given by:



Equation 2

Where is the angular frequency of the transmitted radio wave, c , the speed of light

in a vacuum and v p the phase speed of the radio wave.

This equation serves to illustrate some of the unique features of propagation inionised media compared to non-ionised media such as in the lower atmosphere.

When the transmitted radio frequency equals the local plasma frequency, = p , therefractive index is then 0. This means that the radio wave is evanescent and doesnot propagate. The energy of the wave is absorbed because it is in resonance withthe local natural vibrational frequency of the free electrons at the plasma frequency.

If the frequency of the radio wave is greater than the plasma frequency, > p

, thenthe refractive index is less than 1 and phase velocity, v p, of the radio wave would begreater than the speed of light, c . This is allowed because the group velocity of awave packet, v g , would be correspondingly less than c , and it is the group velocitythat carries the information and energy in an electromagnetic wave (Budden 1985).This aspect is illustrated in practical terms in the next section.

When the frequency of the radio wave is less than the plasma frequency, < p thenthe refractive index is complex and radio wave experiences absorption which

increases as approaches p. But this is only one form of signal loss that the radiowave can experience.

The simple expression in Equation 2 for the phase refractive index assumes thatthere is no effect of the Earth's magnetic field and no effect from the presence of theneutral atmosphere and the ions in which the free electrons are embedded. In realityboth these factors significantly effect the propagation of radio waves in theionosphere and are some of the causes of signal distortion.

With magnetic field but no collisional absorption the expression for the phaserefractive index for radio waves perpendicular to the magnetic field direction,becomes (Budden 1985):

Equation 3

Where c is the electron cyclotron frequency. This is the frequency a free electronwould naturally gyrate about a magnetic field line.

The consequences of this are to illustrate how radio propagation in the ionosphere isbirefringent, which is to say that different polarisations of radio waves propagatedifferently. This is because the Earth's magnetic field in the ionosphere has a definite

direction, which varies according to latitude and radio signals with componentsparallel and perpendicular to the Earth's magnetic field propagate differently. This is

general principles of propagation in the ionosphere

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