Magnetospheric MHD Resonances and ULF Pulsations - Ultra and Extremely Low Frequency Electromagnetic Fields - page 239

An important example of internal sources is the global lightning activity,
considering that there is about 2 10 3 thunderstorm in progress around the world at
any time.
The sources of natural ULF noise covering the frequency range 10 4 -10 2 Hz
have not yet been adequately explored. It is customary to conjecture that the MHD
waves traveling through the magnetosphere can transfer a variety of electromagnetic
noises from the outer regions of the magnetosphere towards the Earth. The high
frequency region of the noise spectrum is lost in the conducting E layer of the
ionosphere. In this picture the E layer plays a major role in formation of the ULF
noise in the neutral atmosphere. Furthermore, the ionospheric current variations due
to fluctuations of the ionospheric plasma conductivity and of neutral wind velocity
can produce an additional random perturbation in the ULF region.

6.4.2 Model and Basic Equations

In what follows we focus our attention on the two possible sources, which are
the incident MHD waves and the ionospheric current fluctuations originated from
variation of the neutral gas flow in the altitude range of the ionospheric E layer.
The field fluctuations in the magnetosphere and ionosphere can excite a random
electromagnetic field in the atmosphere and on the ground surface. At first we
consider the fields of the MHD wave and of the wind-driven currents in the
ionosphere as given deterministic functions, which play a role of forcing functions.
Solving this problem we can find the transfer matrices, which relate the fields in
the ionosphere and magnetosphere with the fields in neutral atmosphere. Since the
characteristic spatial size of the ULF variations is supposed to be smaller than the
Earth radius, the curvature of the magnetic field lines is disregarded. This implies
that the undisturbed geomagnetic field is considered as a homogeneous one.
To approximate the actual variation of medium parameters with altitude, we
consider a plane-stratified medium model, which consists of the magnetosphere,
conducting ionosphere, neutral atmosphere and conducting earth, as shown in
Fig. 6.12 . Consider first the conducting E layer of the ionosphere. We use a
traditional coordinate system in which the y axis is directed westward, the x axis
to the north, and z axis vertically upward. The origin of the local coordinate system
is situated on the boundary between the bottom of the ionosphere and the neutral
atmosphere. The vector of the Earth magnetic field is situated at the meridional x; z
plane and makes an angle with respect to the horizontal axis x. The inclination
angle is chosen in such a way that is positive for the northern hemisphere.
Let ı B be a small perturbation of the geomagnetic field B 0 , i.e., ıB B 0 .
In the frequency range of interest the conduction current is much greater than the
displacement one so the Ampere's law ( 1.5 ) holds at the E-layer. The Ohm's law
for the ionospheric plasma of the E-layer is given by Eq. ( 2.6 ). Combining these
equations we get