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l x
C N
D N
l y
+
Northern ionosphere,
Σ P
B N
A N
z
B = B 0 (x)
C S
D S
x
y
ρ 0 =
ρ 0 (x)
c A =c A (x)
Southern ionosphere, Σ P
A S
B S
(b)
Fig. 5.1. Sketch of the transformation of the dipole geomagnetic field (a) to the
hydromagnetic 'box' model (b) in which the external magnetic field B 0 depends
only on the x -coordinate corresponding to the radial direction. Plasma density ρ
and hence the Alfven velocity c A also depend only the x -coordinate. The face x =0
corresponds to the equatorial region of the ionosphere, the face x = l x is the outer
boundary of the magnetosphere - magnetopause, the faces z = 0 and z = l z are the
'southern and northern ionospheres'. Conjugate ionospheres are characterized by the
integral Pedersen conductivities Σ P
= σ P d z . The sign '
' refers to the southern
and '+' to the northern ionospheres. Panel (a) is plotted using a Matlab code [1]
the magnetosphere-magnetopause, the faces z =0and z = l z are the 'south-
ern and northern ionospheres'. Ionospheres are characterized by the integral
Pedersen conductivity Σ P
= σ P d z . Σ P
are the integral conductivity of the
southern '
' and northern '+' ionospheres, X =4 πΣ P /c is the dimensionless
ionospheric Pedersen conductivity,
Σ A = 1 / 2
4 π = c 2
m
4 πc A
is the magnetospheric wave conductivity, ε m is the transversal dielectric per-
meability.
In this chapter two assumptions are made:
We assume that the ionosphere can be replaced by a thin conductive layer
with integral Pedersen conductivity Σ P .
The Hall conductivity Σ H is neglected because we are interested primarily
in the FLR-related effects. It will be shown later in Chapter 6 that Σ H
scarcely affect the FLR. Nevertheless, Σ H plays a significant role in field
formation near the ionosphere and on the Earth.
The interaction of the magnetospheric Alfven waves with the ionosphere
is characterized by the dimensionless parameter proportional to the ratio of
the ionospheric Pedersen conductivity to the wave conductivity of the mag-
netosphere:
Σ P = Σ P
Σ A
.
(5.1)
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