## Radio Propagation in a Magnetized Plasma

Before proceeding with a discussion of the Appleton (mag – netoionic) equations, we need to define two quantities con­tained explicitly in the equations. The first is v, the number of collisions per second (collision frequency) between electrons and heavier particles (ions and neutrals). Another quantity, the gyromagnetic frequency or gyrofrequency, is the natural frequency (Hz) of gyration of an ion or electron in a magnetic field of strength B0 (Wb/m2) and is given by

f

J0

dz

max

h (f) —

(6)

l(f, z)

where z is the true height, Zmax is the maximum height reached by the frequency f, and n is the refractive index at Zmax for the frequency f. A good discussion of the relation be­tween true height and virtual height is given in Ref. 19.

## The Virtual Height Concept

If we consider an RF pulse traveling vertically upward into the ionosphere at the speed of light, v = c, it will be reflected

at the virtual height, h’. The time required for the pulse to be reflected from an ionospheric layer and return to the earth is space velocity c. Referring to the geometry shown in Fig. 6, we can write the expression

 2 fh dz C Jo M

 t ‘ ^X c JtER sin Фо

 4 c Jti

f — (4)

J0

then the virtual height can be found from h'( f) = і ct, or

, h

h'(f) = -=

J0 J1

 D. = — sin ф0 c TE + ER

 (8)

 dz

 (5)

 л/1 – fn/f2

 Martyns theorem may be written concisely as

Since the pulse always travels more slowly in the layer than in free space, the virtual height of a layer is always greater than the true height. The true height and virtual height are related by the integral equation

 h’ob — К

 (9)

Smith (20) devised a set of logarithmic transmission curves, parametric in range, for the curved earth and iono­sphere. They are shown in Fig. 7 and are sufficiently accurate for the distances shown.

## PHYSICAL PRINCIPLES AND MATHEMATICAL DESCRIPTION OF ELECTROMAGNETIC INTERACTION WITH THE IONOSPHERE

Because of the complexity of the terrestrial ionosphere (a weakly ionized plasma with a superimposed magnetic field in which electric currents flow), we must utilize the magne – toionic theory to quantify the ionosphere physical parameters. The most successful formulation of the appropriate magne- toionic theory was derived by Appleton and others in the mid – 1920s (15-17). We can obtain some first-order properties of the ionosphere by ignoring the magnetic field (18). A simple dispersion equation for electromagnetic (EM) waves in the ionosphere is

fl — t 1 –

where

U = refractive index of the ionosphere (real part of the com­plex refractive index n)

N = electron number density of the ionosphere (e/cm3 or

e/m3)

e = electronic charge = 1.6 X 10~19 C m = mass of the electron = 9.1 X 10~31 kg f = frequency of the radio wave in the ionosphere (Hz)

For reflection at vertical incidence, u = 1 and

N — mn f2 /e2

— 1.24 x 104f2 e/cm3 (f in MHz) (2)

— 1.24 x 1010f2e/m3 (f in MHz)

Another useful quantity is the plasma frequency,

fn = j —

V n m

= 9VNkHz (N in cm-3) (3)

= 9 x lO^V^MHz (N in e/cm3)

## Extrahigh Frequencies

At EHF and above, propagation is primarily LOS, and be­cause of the higher frequencies (f a 300 MHz), these signals are less affected by the ionosphere than lower frequencies. On earth-space paths that traverse the equatorial and/or high – latitude ionosphere, however, the signal quality can be sig­nificantly degraded. These effects will be described below.

To summarize, the radio services most affected by the iono­sphere lie in the frequency range of «1 MHz to 150 MHz [fixed communication services, AM (amplitude modulation) and SW (shortwave) broadcasting, amateur radio]. To a lesser degree, services in the 20 kHz to 300 MHz region (mainly some of the navigation services] suffer some ionospheric per­turbation effects.

There is a plethora of radio instrumentation currently de­ployed globally that operates routinely or on a campaign basis to measure characteristics of the terrestrial ionosphere. It is beyond the scope of this article to describe these techniques, but they have been described in considerable detail in the lit­erature (2-4).

## Very High Frequencies

Propagation in the VHF band (30 MHz to 300 MHz) is pri­marily by line of sight (LOS) to the optical horizon, so if the antenna patterns direct most of the RF power in the hori­zontal plane, there are essentially no ionospheric effects. For earth-space propagation paths, however, the ionosphere can affect the signal adversely by refraction, diffraction, scatter­ing, or reflection. These effects can be especially important when the path traverses the equatorial, auroral, and polar ionosphere. The amplitude, phase, and polarization of the sig­nal may change measurably. These effects will be quantified in the following section.