FLR in Plasma Configurations - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 172

400

6

b

a

5

300

4

1 1

200

3

2

2

2

100

1

3 3

0

0

2

3 4 5 6 2 3 4 5 6

L − shell L − shell

Fig. 6.6. (a) The FLR-period and (b) relative decrement versus L . Exponent p =6
in (6.76) describing the field-aligned plasma distribution. Indexes refer to the 1-st,
2-nd and 3-rd harmonics

L pp . These results for δ i do not contradict the ones
obtained from the experimental data.
The resonance periods T res (left frame) and decrements γ (right frame)
as functions of the L -shell for the first three harmonics are shown in Fig. 6.6
for the cold plasma distribution (6.76) with p = 6. Figure 6.7 represents the
half-widths δ L ( L ) of three harmonics for the distributions with exponent
p = 6 (left frame) and p = 3 (right frame). At p = 3 the harmonics are not
equidistant and it is possible to use this fact in sounding the magnetosphere
by estimating the parameter p . The decrement and the resonance half-width
in the regions 2

∼

10 km at L

about

4 . 5 for the 3-rd
harmonic are almost constant and the resulting shape of the resonance curve
changes weakly in these ranges of L .
Note also that γ decreases in the thin ionosphere with harmonic number.
Contrary, the finite ionospheric thickness leads to the growth of the relative

L 4 . 5 for the 2-nd harmonic and 3 L

× 10 2

× 10 2

2 2

1,2,3 1,2,3

0 0

3

3

2

2

− 2 − 2

2

1

1

1

−4 1 −4

2

−6 −6

2 3 4 5 6 2 3 4 5 6

L - shell L - shell

Fig. 6.7. The half-widths δ L in the magnetosphere for the first three resonance
harmonics functioning L . The curves are calculated for the field-aligned plasma
distributions with exponent p = 6 (left panel) and p = 3 (right panel) of (6.76)