Geoscience Reference
In-Depth Information
This parameter is principal in the Alfven wave-ionosphere interaction.
Thus, we give it in SI, as well:
Σ P = [ Σ P ] SI
1
µ 0 [ c A ] SI ,
[ Σ A ] SI ,
[ Σ A ] SI =
where [ Σ P ] SI is the integral ionospheric conductivity in SI, [ Σ A ] SI is the wave
conductivity of the magnetosphere in SI, µ 0 =4 π
10 7 H/A 2 is the magnetic
×
permeability.
Plasma oscillations can be excited by sources located both inside and out-
side the box. In the first case, the oscillations are described by (4.42a) with
uniform boundary conditions which are supplemented by extraneous currents
caused by field sources. In the latter case, following Southwood (1974), let us
consider excitation of FLR-oscillations by external sources, setting the field
on the outer boundary of the magnetosphere.
Boundary Conditions
If there are no sources of magnetic field near the ionospheres, then the hor-
izontal electric and magnetic components are in linear ratio. Let X =
4 πΣ P /c and X + =4 πΣ P /c . Then the impedance boundary conditions at
the ionosphere can be written as
E x =
b y /X , E y =
±
b x /X .
So, on the box faces z =0 ,l z , the conditions reduce to
{
b x
X E y } z =0; l z =0 ,
{
b y ±
X E x } z =0; l z =0 ,
(5.2)
where the upper sign corresponds to the southern ionosphere ( z = 0) and the
lower sign corresponds to the northern ionosphere ( z = l z ). Σ P is assumed
to be constant at each ionosphere. Let us assume that the magnetospheric
waves are forced by monochromatic sources
exp(
iωt ). Combining (4.17d),
(4.18), (4.20), and (5.2) gives
∂ξ
∂z ±
i ω
c X ξ
=0 .
(5.3)
z =0 ,l z
We consider the equatorial ionosphere ( x = 0) free from the sources. Since
the fields produced by sources near the outer magnetospheric boundary decay
exponentially when penetrating into the magnetosphere, a specific form of the
boundary conditions is not important. For definiteness, let
E y
ξ x =0
or b =0 .
(5.4)
At the 'magnetospheric' boundary ( x = l x ) let us put inhomogeneous bound-
ary conditions, for example
ξ x = ξ 0 ( y, z ) r b = b 0 ( y, z ) .
(5.5)
 
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