FLR in Plasma Configurations - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 173

decrement with the number beginning with the resonance period of about
20 s.
Consider the dependence of the decrement on Pedersen conductivity. At
large Σ P (dayside ionosphere), when

Σ P =4 πΣ P c A /c 2

1, the decrement

Σ P

γ 1 ∝ 1 /Σ P vanishes ( Σ P →∞ ). At 1 when the Σ P is small (night

Σ P .At Σ P →

ionosphere), the decrement γ 1 ∝ 1, the coecient of reflection

of the Alfven wave vanishes and γ 1 →∞

. This effect is connected with the
'thin' ionosphere approximation and for the 'thick' ionosphere γ is finite.

Resonance Electric and Magnetic Fields Along a Field-Line

Distribution of the electric and magnetic wave components along a resonance
field line is determined by e j ( x ) (6.79). In the dipole magnetic field the physical
components of the azimuthal magnetic field b ϕ and orthogonal to the magnetic
shells electric field E ν are determined by (6.89), (6.90). Keeping only the main
terms in (6.89), (6.90), we obtain the distribution of b ϕ and E ν along the field
line at the shell ν = ν r :

b ϕ ≈

x 2 ) − 3 / 2 e ( j 1 ( x ) ,

ν r (1 −

E ν ≈

x 2 ) − 3 / 2 (1 + 3 x 2 ) 1 / 2 e ( j 2 ( x ) , ν r (1

− (6.124)

where x =cos θ is the coordinate of a point on a field-line.
An example of the distribution of the FLR-fields for two harmonics along
a field line L = 2 is shown in Fig. 6.8. Figures 6.8a and 6.8b represent,
respectively, the fields of the 2-nd harmonic with resonance frequency ω 2 =
0 . 6136

0 . 1323 i . One can
see that ionospheric fields are larger than magnetospheric ones. The amplitude
of the magnetic field decreases steeply in the ionospheric F -layer. The electric

− 0 . 1186 i and the 3-rd harmonics with ω 3 =0 . 6336 −

1 1 2

10 10

2

0 0

4

−10 −10

3

4

3

−20 −20

−30 a −30 b

−40 −40

−50 −50

0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8

cos θ cos θ

Fig. 6.8. Field line distribution of the electric ( e 2 ) and magnetic ( e 1 ) wave com-
ponents at L =2 . a) the 2-nd FLR-harmonics with the resonance frequency
ω 2 =0 . 6136 − 0 . 1186 i ;(b)the3-rdharmonics ω 3 =0 . 6336 − 0 . 1323 i. Indexes 1
and 3 refer, respectively, to real parts of e 1 and e 2 and 2 , 4 - to their imaginary
parts. The azimuthal magnetic component b ϕ and the electric component orthogo-
nal to the E ν magnetic shell are connected with e 1 and e 2 by (6.124)