Ionospheric Alfvén Resonator (IAR) - Ultra and Extremely Low Frequency Electromagnetic Fields - page 175

0.18

5

0.16

4

0.14

3

0.12

0.1

2

0.08

0.06

1

0.04

0.02

0

0.5 1 1.5 2 2.5 3 3.5 4

f , Hz

Fig. 5.14 A model calculation of the nighttime IAR spectra due to a solitary lightning discharge at

distance r D 300 km. The component b x is shown with lines 1-5, which correspond to the angles

' D 0, =8, =4, 3=8 and =2, respectively. Taken from Surkov et al. ( 2006 )

b x D b ' sin ' b r cos ' ; and
b y D b ' cos ' b r sin ' :

(5.62)

On the ground surface at z D z 0 D d the components b r and b ' are random values,
which depend on polar radius r and the time interval t t n .
Experimental recordings of the horizontal field contain a certain mixture of
both resonant, b r , and non-resonant, b ' , components. The observations depend
on the angle ' between the direction to lightning flash and to the x axis
(Fig. 5.13 ). To illustrate this, we have calculated the spectra of a single CG
discharge at fixed distance r D 300 km and different angles. The lines 1-
5 in Fig. 5.14 correspond to the angles ' D 0, =8, =4, 3=8, and =2,
respectively. Not surprisingly, the most distinct signature of the SRS is expected
for the angle ' D 0 when the signal is dependent on only the radial field in
contrast to the case of ' D =2 when the signal contains only perpendicular, b ' ,
component.
As is seen from Eqs. ( 5.54 ) and ( 5.55 ), the magnetic field of the single lightning
discharge is proportional to the current moment magnitude, M n , and thus can be

written similarly to Eq. ( 4.42 ), i.e., b r ;t t n D M n G r ;t t n , where

M n is a random value whereas G D G r ;G ' ;G z are deterministic functions,
describing the shape of single lightning discharge. The Fourier transform of these