Ionospheric Alfvén Resonator (IAR) - Ultra and Extremely Low Frequency Electromagnetic Fields - page 172

Fig. 5.12 A model calculation of the nighttime IAR spectra excited by a solitary CG lightning
discharge. The radial/resonant component ıB r on the ground is shown with lines 1-4,which
correspond to the distances r 100, 300, 1;000,and10;000 km, respectively. The approximate

analytical solution (Eqs. ( 5.59 )and( 5.60 )) at distance r

D

300 km is shown with dotted line 2 0 .

D

Taken from Surkov et al. ( 2006 )

† P D 0:2 1 and † H D 0:3 1 (nighttime conditions). In this figure the lines
1-4 correspond to the distances r D 100, 300, 1;000, and 10;000 km, respectively.
It is obvious from Fig. 5.12 that the spectra exhibit distinct resonance structure in
such a way that the resonance frequencies are close to the IAR eigenfrequencies. By
symmetry of the problem the radial component of the magnetic perturbation must
tend to zero when r ! 0. The calculations have shown that the spectrum magnitude
reaches a peak at the distance of about 300 km.
If the thunderstorm activity occurs at the distance r 10 3 km, that is far away
from the ground-recording station, then Eqs. ( 5.54 )-( 5.57 ) are simplified since the
integrands include the rapidly oscillating function J 1 .kr/ with the short period k
r 1 10 3 km 1 . The other slowly varying functions under the integral sign may

be moved through the integral at k D 0 to yield

0 Ǜ H LMF .!/ 1 .!/
2rd Œ1 C 1 .!/dq 1 .!/ ;

ıB r .!;r; d/ D Mg r

(5.59)

where 1 D . i 0 !/ 1=2 , and

i 1 .!/L
1 C 1 .!/d C x 0 f LJ 1 .!/ C Ǜ P g

f LJ 1 .!/ C Ǜ P gC x 0 Ǜ 2 H : q 1 D (5.60)