Ionospheric Alfvén Resonator (IAR) - Ultra and Extremely Low Frequency Electromagnetic Fields - page 174

Fig. 5.13 A schematic
drawing of reference and
local coordinate systems.
Here z and z 0 axes are “out of
paper”, b r and b ' are the
component of magnetic
variations caused by a
thunderstorm located at
r

y ′

y

N-S

E-W

x

z ′ ′

r μ

z x

˕ μ

D r

b r

b ˕

by the stroke in the atmosphere keeps on one order of magnitude greater than the TE
mode irrespective of the ionospheric parameters and the magnetic field inclination.
For example, according to Belyaev et al. ( 1990 ) the ratio ıB r =ıB ' lies in the range
of 0:08-0:5 depending on the ionosphere parameters.

5.3.5 IAR Excitation Due to Random Lightning Process

We now focus attention on ULF background electromagnetic noise originated from
lightning activity as a possible cause for the IAR excitation. On the basis of the
approach developed in Sect. 4.3 we shall treat the lightning activity as a stochastic
process. Let N be the number of thunderstorm centers simultaneously operating
around the ground-based recording station. As before we use a local coordinate
system, which has the x axis east-ward, the y axis to the north, and z axis vertically
upward. At first we are interested in solely nearby thunderstorms, so a plane-
stratified model of the medium is used. Let r and ' be the polar coordinates
of the thunderstorms epicenters, where D 1;2;:::N, as shown in Fig. 5.13 .
A typical size of the thunderstorm is assumed to be smaller than the distance from
the recording station, so that we ignore the lightning discharge distribution inside a
thunderstorm area.
Now we also introduce a reference frame x 0 ;y 0 and z 0 fixed to the thunderstorm

with number . In our model b r ;t t n denotes the random variations of the
magnetic field caused by a single lightning discharge happened at the accidental
moment t n , where n D 1;2;::: is a number of the lightning discharge.
Considering a vertical CG discharge, we use a cylindrical coordinate system in
which the lightning discharge is in the direction of the polar z 0 axis. In this case
b is independent of azimuthal angle '. As has already been stated, only radial
component, b r , among two horizontal ones contains the resonance factor, which
dominates the IAR resonance properties. In the Cartesian reference frame fixed to
the ground-recording station, the horizontal magnetic field can be expressed through
the radial and azimuthal components as follows: