Geoscience Reference
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where k is the wave number and H is the ion gyrofrequency. In the coordinate
system which moves at the acoustic wave velocity, the dispersion relation is given
by (Danilov and Teselkin 1984 )
k 2 V A
H
! 0 kC a D
:
(11.60)
In the stationary problem under consideration, the frequency ! 0 D 0 whence it
follows the typical size of the precursor is about o k 1
D V A =.C a H /.We
recall that these equations are valid if the electrons are magnetized, that is, ! H
e , and the ions are not yet, that is H in . Taking into acco unt that in this
case H e 2 n=.m e ! H / D en=B 0 and substituting H D eB 0 =m i and V A D
B 0 =. 0 nm i / into the above estimate, we obtain the length of “oscillatory” portion
of the electromagnetic precursor o . 0 H C a / 1 which coincides with the above
estimate.
It appears that a high-power surface detonation can have influence not only
on the ionosphere but also on the magnetosphere. For example, the magnetic
pulses with amplitude 100 nT have been detected onboard AUREOL-3 satellite
at the altitude about 750 km several minutes after the surface detonation known
as experiment MASSA-1 (Galperin and Hayakawa 1996 ). The detonation of HE
with TNT equivalent 288 t has been performed in a sandy desert 60 km to the
north of Alma-Ata (former USSR) on November 28, 1981. In order to discuss the
plausibility of the coupling mechanisms operating between the surface detonation
and the magnetosphere, it is necessary at this point to estimate the magnitude of
the signals produced by the surface detonation at the magnetospheric altitudes.
To do this, we suppose that Eqs. ( 11.40 )-( 11.42 ) are justified in the altitude range
0< z <lwhile above this layer; that is at z >l, there take place the equations
for a cold collisionless plasma. Assuming that the field-aligned plasma conductivity
is infinite, we come to the standard equations describing Alfvén and FMS plasma
waves in this region
@ tt B z D V A r
2 B z ; tt B ' D V A @ zz B ' :
(11.61)
where V A is the Alfvén wave speed. Disregarding, as before, the derivatives of r
in the operator r
2 , we choose the solution of Eq. ( 11.61 ) in a form of upgoing
waves. The proper boundary condition at z D l is that the solution would transform
continuously into that of Eqs. ( 11.40 )-( 11.42 ).
It is easy to show that the solution of Eq. ( 11.61 ) appears as Eqs. ( 11.57 )-( 11.58 )
where z and t should be replaced by l and D t . z l/=V A , respectively. This
means that the same temporal dependence holds if we use the coordinate system
which moves at the Alfvén wave velocity. The components B z , B r , and E ' describe
Alfvén wave, while the components E r , E z , and B ' correspond to FMS wave. The
numerical modeling of the GMP in the magnetosphere versus is displayed in
Fig. 11.16 . Here we made use of Eqs. ( 11.57 )-( 11.58 ) and the typical parameters
 
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