Geoscience Reference
In-Depth Information
If the electric field
E
?
is parallel to
k
?
, such a polarization is referred to as the
shear Alfvén wave as shown in Fig.
1.15
. The dispersion relation of the Alfvén mode
can be derived from Eq. (
2.24
) under the requirement that the latter equation has a
nonzero solution whence it follows that
!
2
V
A
k
2
k
2
?
D
:
(2.25)
On account of the relation k
2
k
D
k
2
cos
2
this dispersion relation
coincides with Eq. (
1.59
) for Alfvén mode of the MHD waves. As it follows from
k
2
?
D
k
2
Eq. (
2.22
), the magnetic field perturbation, ı
B
D
k
k
E
?
=!, is perpendicular
to the parallel wave vector that means ı
B
is perpendicular to both the electric field
and
B
0
.
Conversely, if the electric field
E
?
is perpendicular to
k
?
,Eq.(
2.24
) reduces to
the dispersion relation
k
2
D
!
2
=V
A
;
(2.26)
which describes the compressional/FMS wave. This equation is compatible with
Eq. (
1.69
) describing the dispersion relation for the FMS waves in the extreme
case V
A
c
s
. The polarization of the electric and magnetic components of the
compressional wave is the same as shown in Fig.
1.16
.
Finally we note that the dispersion relations for the shear Alfvén and the
compressional waves in the collisionless magnetized plasma are practically the same
as the dispersion relations under MHD approach.
References
Chapman S (1956) The electric conductivity of the ionosphere: a review. Nuovo Cimento
5(Suppl.):1585-1412
Ginzburg VL (1970) The propagation of electromagnetic waves in plasmas. Pergamon Press,
Oxford
Ginzburg VL, Rukhadze AA (1972) Waves in magnetoactive plasma. Hand physics, vol. 49.
Springer, New York
Hines CO (1974) The upper atmosphere in motion: a selection of papers with annotation.
Geophysical monograph, vol 18. American Geophysical Union, Washington, DC
Johnson FS (ed) (1961) Satellite environment handbook. Stanford University Press, Stanford
Kelley MC (1989) The earth's ionosphere. Academic, New York
Search WWH ::
Custom Search