LDI DIGISONDE 4D - Chapter 2 _ Methodology, Theoretical Basis, and Implementation; Background: Ionospheric Propagation of Radio Waves

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DIGISONDE-4D
SYSTEM MANUAL
VERSION 1.2.11
1-12 SECTION 1 - GENERAL SYSTEM DESCRIPTION
CHAPTER 2
METHODOLOGY, THEORETICAL BASIS, AND IMPLEMENTATION
BACKGROUND: IONOSPHERIC PROPAGATION OF RADIO WAVES
1:14. An ionospheric sounder uses basic radar techniques to detect the electron density (equal to the ion den-
sity since the bulk plasma is neutral) of ionospheric plasma as a function of height. The ionospheric plasma is
created by energy from the sun transferred by particles in the solar wind as well as direct radiation (especially
ultra-violet and x-rays). Each component of the solar emissions tends to be deposited at a particular altitude or
range of altitudes and therefore creates a horizontally stratified medium where each layer has a peak density
and to some degree, a definable width, or profile. The shape of the ionized layer is often referred to as a
Chapman Function [Davies, 1989] which is a roughly parabolic shape somewhat elongated on the top side.
The peaks of these layers usually form between 70 and 300 km altitude and are identified by the letters D, E, F1
and F2, in order of their altitude.
1:15. By scanning the transmitted frequency from 1 MHz to as high as 40 MHz and measuring the time delay
of any echoes (i.e., apparent or virtual height of the reflecting medium) a vertically transmitting sounder can
provide a profile of electron density vs. height. This is possible because the relative refractive index of the ion-
ospheric plasma is dependent on the density of the free electrons (N
e
), as shown in Equation 1-1 (neglecting
the geomagnetic field):

2
(h) = 1 – k (N
e
/f
2
)
1-1
where k = 80.5, N
e
is electrons/m
3
, and f is in Hz [Davies, 1989; Chen, 1987].
1:16. The behavior of the plasma changes significantly in the presence of the Earth’s magnetic field. An ex-
haustive derivation of m [Davies, 1989] results in the Appleton Equation for the refractive index, which is one
of the fundamental equations used in the field of ionospheric propagation. This equation clearly shows that
there are two values for refractive index, resulting in the splitting of a linearly polarized wave incident upon the
ionosphere, into two components, known as the ordinary and extraordinary waves. These propagate with a dif-
ferent wave velocity and therefore appear as two distinct echoes. They also exhibit two distinct polarizations,
approximately right hand circular and left hand circular, which aid in distinguishing the two waves.
1:17. When the transmitted frequency is sufficient to drive the plasma at its resonant frequency there is a to-
tal internal reflection. The plasma resonance frequency (f
p
) is defined by several constants, e – the charge of an
electron, m – the mass of an electron, ε
o
– the permittivity of free space, but only one variable, N
e
– electron
density in electrons/m
3
[Chen, 1987]:
f
p
2
= (N
e
e
2
/4
o
m) = kN
e
1-2
A typical number for the F-region (200 to 400 km altitude) is 10
12
electrons/m
3
, so the plasma resonance fre-
quency would be 9 MHz. The value of  in Equation 1-2 approaches 0 as the operating frequency, f, ap-
proaches the plasma frequency. The group velocity of a propagating wave is proportional to  so  = 0 implies