Geoscience Reference
In-Depth Information
N
n
(
r, t
)=
N
0
(
t
)
f
r
R
n
(
t
)
,
(14.2)
where
f
(
ξ
) is normalized by the condition
1
f
(
ξ
)
ξ
2
dξ
=1
.
4
π
0
and
f
(
ξ
)=0for
ξ>
1.
We neglect the change of concentration of neutral gas due to processes
of ionization and recombination. The total number of injected particles be
N
T
=const
.
This allows us to find a relation between
N
0
(
t
)and
R
n
(
t
)
.
The
total number of particles is
≥
R
n
(
t
)
1
N
n
(
r, t
)4
πr
2
dr
=4
πN
0
(
t
)
R
n
(
t
)
f
(
ξ
)
ξ
2
dξ.
N
T
=
0
0
The last equation and the normalization requirement yield
N
T
R
n
(
t
)
.
N
0
(
t
)=
(14.3)
Equation (14.3) and dependencies
R
n
(
t
) allow us to study the time depen-
dencies of electron and ion magnetization parameters,
β
e
=
ω
ce
/ν
em
and
β
i
=
ω
ci
/ν
im
. Initially the neutral density in the cloud is so strong that the
electron-neutral collision frequencies exceed
ω
ce
and
ω
ci
considerably, and so
β
e
1. As the cloud continues to expand, the neutral density
drops and electrons become completely frozen that is
β
e
1and
β
i
1. At this time
the ions move together with the neutral gas. With the further expansion, both
electrons and ions become frozen into the magnetic field. For emission at 150-
210 km electrons are frozen after
τ
e
∼
10 ms and ions are frozen after
τ
i
∼
0.5-1 s.
The basic conclusion is that virtually instantly after emission electrons
become magnetized and ions remain non-magnetized until
0
.
5 s. The hydro-
magnetic pulse, radiated due to the dynamo field, has a characteristic duration
of 0
.
5 s. The time change of
β
e
and
β
i
defines three stages in ionized compo-
nent dynamics: non-magnetized electrons and ions, magnetized electrons and
non-magnetized ions and electrons and ions frozen into the magnetic field.
∼
Ionized Cloud Component Dynamics
The feedback action of charged components on neutral-gas motion can be
ignored at times
τ
10
3
s. Let (14.1) be valid for the neutral gas speed,
v
n
.
For emissions time-scale of
1 s it is possible to neglect the electron/ion
inertia in the equations of motion for electrons/ions in crossed electric and
∼
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