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electrostatic forces, Earth's magnetic field and Coriolis force ( [3], [18]). The
ion and electron temperature variation along the field line and plasma dif-
fusion also have an effect on the results of the model calculations. In some
regions the anisotropy of the electron temperature is also significant.
For our purposes it is enough to use a simplified model of the cold plasma
distribution in the form
ρ ( r, L, ϕ )= ρ e ( L, ϕ ) ρ ( r, L, ϕ ) ,
where ρ e ( L, ϕ ) is the distribution in the equatorial plane and ρ ( r, L, ϕ )=
ρ ( r, L, ϕ ) e ( L, ϕ ) is the normalized distribution along a field line with the
McIllwain parameter L . ρ ( r, L, ϕ ) = 1 at the top of a field-line; ϕ is the
geomagnetic longitude; the location of a point on the field line is determined
by the geocentric distance r . Neglecting the azimuthal asymmetry, we shall
consider ρ ( r, L, ϕ ) independent on ϕ , i.e.
ρ = ρ e ( L ) ρ ( r, L ) .
(6.75)
Such a model is valid only for the MHD-disturbances localized either at the
dayside or at the nightside. Set a normalized field line distribution of plasma
density as a power function of the geocentric distance:
ρ ( r, L )= LR E
r L
p ( L )
,
(6.76)
where r L is the geocentric distance on a given field line L . Let us approximate
the equatorial distribution ρ e with the expression
ρ 1 ( L )
1 + exp 2 L
ρ 2 ( L )
1 + exp
ρ e ( L )=
+
,
L pp
∆L
2 L
L pp
∆L
ρ 1 ( L )= m p n 1 L
L 1
−s 1 ( L )
2 ( L )= m p n 2 L
L 1
−s 2 ( L )
,
.
(6.77)
Here L pp and ∆L are the position and the half-width of the plasmapause; m p is
the proton mass. We shall use two models for the plasma density distribution
in the numerical calculations. In the first model L pp =4 . 9, in the second one
L pp =4 . 4 (see Fig. 6.3).
The Dipole Dispersion Equation General Case
Let us write (6.74) for the dipole magnetic field. It is more convenient to use
a variable w defined by
w
µ
ν 2
=
(6.78)
(1
w 2 ) 2
instead of the coordinate µ =cos θ/r 2 . Substituting µ =cos θ/r 2 =(1+
νr ) 1 / 2 /r 2 into (6.78) with the branch of the root is selected according to the
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