Geoscience Reference
In-Depth Information
5. At low latitudes the basic source of IAR excitation is believed to be the ULF
electromagnetic noise produced by random lightning discharges due to the
global thunderstorm activity. However, at middle latitudes far from tropical
thunderstorm centers, the regional thunderstorms can make a main contribution
to the observed IAR power spectra. The solitary CG lightning discharge in the
vicinity of ground-recording station may result in the impulse IAR excitation
which is capable of producing observable SRS signature on the ground.
Additionally, the IAR excitation at mid-latitudes can be associated with the
turbulent motions of the neutral winds. At high latitudes other mechanisms can
play a key role in the generation of IAR eigenmodes. Among them are the
magnetospheric convective flow and the fast feedback instability induced by the
precipitating energetic electrons.
Appendix C: Vector and Scalar Potentials
of Electromagnetic Field
General Description
In this section we introduce the standard vector and scalar potentials of the
electromagnetic field in a conducting medium immersed in the external magnetic
field
B
0
. To treat the electric and magnetic fields, we need Maxwell's equations,
which, in their full form, are given by Eqs. (
1.1
)-(
1.4
). If we seek for the solution of
these equations in the form
B
D
B
0
C
ı
B
, where ı
B
is the small variation of
B
0
,the
electromagnetic field can be represented through the vector potential,
A
, and scalar
potential, dž, as follows (Jackson
2001
)
ı
B
Dr
A
;
(5.73)
E
Dr
dž
@
t
A
:
(5.74)
Considering two important cases when the external field
B
0
is a constant value
or when
B
0
denotes the Earth's magnetic field in the dipole approximation given by
Eq. (
1.32
), we have the condition
r
B
0
D
0. Taking the notice of this condition
and substituting the field presentation given by Eqs. (
5.73
) and (
5.74
) into Maxwell
equations (
1.2
) and (
1.3
) converts these equations into identities.
Let
z
axis be positive parallel to the external/unperturbed magnetic field
B
0
and
O
z
D
B
0
=B
0
be a unit vector parallel to
B
0
. In this notation the total vector potential
can be written as
A
D
A
O
z
C
A
?
, where the second term represents the perpendicular
component of the vector potential. We choose the calibration equation for the vector
potential in the form
r
?
A
?
D
0;
(5.75)
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