Geoscience Reference
In-Depth Information
low frequency limit, when !< j k ? j V AM , the real part of the function M becomes
negative that means that the FMS mode exponentially decreases with altitude in the
region z >L.
Inside the resonance cavity .0< z <L/ the solutions of the wave equa-
tions ( 5.12 ) and ( 5.13 ) must include both the upward and downward propagating
waves, which arise due to the wave reflection from the lower . z D 0/ and upper
boundaries . z D L/ of the IAR. These solutions should be matched at this boundary
under the requirement of continuity of the magnetic field components and transverse
electric field e ? at z D L . Whence there follows the requirement of continuity of
the potentials dž and ‰ and their derivatives, @ z dž and @ z ‰,at z D L. The solution
of the problem derived in Appendix D can be written as
dž D dž.0/ cos ! z
:
V AI C 1 sin ! z
(5.18)
V AI
D ‰.0/ cosh I z
:
L C LJ 2 sinh I z
(5.19)
L
Here we made use of the following abbreviations
I D k 2
L 2
x 0
(5.20)
?
1 C .1 / exp .2ix 0 /
1 C C .1 / exp .2ix 0 / ;
LJ 1 D
(5.21)
I C M . I M / exp .2 I /
I C M C . I M / exp .2 I / :
LJ 2 D
(5.22)
where D V AI =V AM 1 is the ratio of the Alfvén velocity in the IAR to that in
the magnetosphere.
5.1.5
Boundary Conditions at the
E
Layer of the Ionosphere
At altitudes of the E-layer the electron gyrofrequency, ! H , is much greater than the
sum, e , of electron-ion and electron-neutral collision frequencies. In contrast, the
ion gyrofrequency, H , is much smaller than the sum, i , of ion-electron and ion-
neutral collision frequencies. This means that inside the E-layer the collisions play
a crucial role in the behavior of ions whereas the electrons are guided by the Earth's
magnetic field lines since they are magnetized. The tensor of plasma conductivity
by Eq. ( 2.5 ) describes this kind of the anisotropy in the plasma conductivity which
occurs in the E-layer of the ionosphere. Furthermore, in the ULF range the tensor
components are nearly independent of the wave frequency, !, because the value of
! is much smaller than all the collision frequencies and gyrofrequencies entering the
tensor. In this case the components of the tensor can be expressed through Pedersen,
 
Search WWH ::




Custom Search