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integration of Eqs. ( 11.36 ) and ( 11.37 ) over z from zero to " and then assuming
" ! 0 we come to the following boundary conditions at z D 0
B 'a B 'i D 0 bJ H ; B ra B ri D 0 bJ P ; B z a D B z i ;
(11.39)
where the subscripts a and i are related to the atmosphere and ionosphere,
respectively. The extrinsic current densities, J H D H V r B 0 and J P D P V r B 0 ,
are assumed to be given functions.
Equations ( 11.36 ) and ( 11.37 ) can be solved for E r and E ' . Substituting these
components of electric field into Maxwell equation r E D @ t B and rearranging
yields
r @ r r@ z B ' ;
D H
2 B z
@ t B z D D P r
(11.40)
@ t B r D D P
B r
r 2
2 B r
C D H @ zz B ' ;
r
(11.41)
2 B ' D H
;
B r
r 2
2 B r
@ t B ' D D P r
r
(11.42)
where
P
0 P C H
H
0 P C H
D P D
; D H D
;
(11.43)
2 is
are the coefficients of diffusion in a gyrotropic medium and the operator r
given by
2
D r 1 @ r C @ rr C @ zz :
r
(11.44)
The set of Eqs. ( 11.40 )-( 11.42 ) can be solved with respect to each component of the
magnetic perturbation. For example, excluding B ' from Eq. ( 11.40 ) gives (Surkov
1996 )
@ t @ t B z D P r
2 B z D @ zz ǚ D p @ t B z D P C D H r
2 B z B z =r 2 : (11.45)
Applying Eq. ( 11.36 ) to the atmosphere and taking into account that the compo-
nents of the conductivity tensor are equal to zero, we obtain that B ' D 0 everywhere
in the atmosphere. Other components of the GMP can be determined from the
Laplace equation:
2 B r D B r =r 2 ; r
2 B z D 0:
r
(11.46)
Suppose that the acoustic wave reaches the lower boundary of the ionosphere at
the moment t D 0. The region of interaction between the wave and ionosphere
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