FLR in Plasma Configurations - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 174

50

40

30

∝Im b ϕ

20

∝ Re b

ϕ

10

0

−10

−20 ∝Re E ν

−30 ∝Im E ν

− 40

−50

0 0.2 0.4 0.6 0.8

cos θ

Fig. 6.9. Field line distribution of the real and imaginary parts of the electric and
magnetic components of the 2-nd FLR-harmonics at field line L = 3 as a function
of colatitude θ. Point cos θ = 0 is the equatorial point and cos θ =0 . 8 is the pierce
point of the field line in the ionosphere

field varies significantly at heights about 200 km and it changes its sign at
h ≈

300 km. The relative growth of the electric field in the ionosphere results
in increasing Joule dissipation and decrement.
The same dependencies for the 2-nd harmonic at the shell L =3are
shown in Fig. 6.9. Note that the azimuthal component of the magnetic field
b ϕ ( x )

e 1 ( x ) varies rapidly in the ionospheric E -layer. It grows from zero
under the ionosphere to the maximal value above the ionosphere. On the other
hand, the component E ν ( x )

∝

e 2 ( x ) is almost constant in the E -layer.
In the above calculations the ionospheric parameters typical for the solar
maximum are used.

∝

Meridional Distribution of the FLR-Amplitudes and Phases

The meridional distribution of the FLR-amplitude and phase above the
ionosphere are determined by (6.88), (6.89) and (6.90). In order to utilize their
we need to define FLR-periods, half-widths, and coecients C 0 and Λ 0 . Res-
onance period and half-width of the FLR are determined from the dispersion
equation (6.121). C 0 and Λ 0 are given by (6.111)-(6.116). The calculations
have been carried out at Σ P =0 . 8

10 8 km/s. The equatorial distribution of
the ion concentration has been taken from Fig. 6.3 (curve 2) with plasmapause
at L pp =3 . 9 that corresponds to a mean value of the plasmapause position
at K p = 5. The calculations are performed for m = 1. Results of the calcu-
lations are shown in Fig. 6.10. Panels (a) and (b) show dependencies of the
FLR-period and half-width against L -shell, and (c) and (d) show abs C 0 ( L )
and abs Λ 0 ( L ).
Let us now find the meridional distribution of the wave field produced by
a driver of period T . From 6.10a follows that there are two fundamentally

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