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is small in comparison with
v
n
. From (14.15) we obtain
∂N
∂t
+
∇
·
(
N
v
n
)=0
.
From the above, it is also clear that the charged particles are completely
dragged, i.e. without slipping, by the neutral flow. For their part, closed cur-
rents due to Pedersen conductivity, while not small, do not change the charged
particles concentration
N
.
At the second stage when
ν
em
ω
ci
, electrons are magne-
tized but ions move together with neutrals. The charges separation produces
an electric field, which in turns excites an electric current. In this case, the Hall
conductivity is defined by electrons. The dynamo field and the Hall conduc-
tivity produce a radial current, causing perturbations of the charged particles
concentration
N
.
At the third stage electrons and ions are both magnetized, and neutral
component continues to extend. The Pedersen conductivity is small, the elec-
tron and ion Hall conductivities are equal in magnitude and opposite in sign.
As a result, the expression in the parentheses of (14.15) vanishes:
∂N/∂t
=0,
i.e. the ionized component concentration is almost constant.
Let us consider (14.15) for an axially symmetric emission, neglecting ex-
ternal electric field effects
E
0
.
In the cylindrical coordinate system (
ρ, ϕ, z
),
the radial and azimuthal fluxes of charged components are
ω
ce
and
ν
in
J
ρ
=
NU,
U
=
αv
n
,
(14.16)
J
ϕ
=
σ
eP
−
σ
iP
2
eN
v
n
c
B
0
,
(14.17)
where
σ
eH
−
σ
iH
2
eN
B
0
c
α
=1
−
.
The Pedersen flux forms a ring and
∂J
ϕ
/∂ϕ
=0
,
therefore the Pedersen
flux does not contribute to the perturbation of
N.
Then (14.15) is
∂N
∂t
∂
∂ρ
(
ρNU
)=0
.
+
1
ρ
(14.18)
with the initial condition
|
t
=0
=
N
0
,
ρ
n
(0)
,
N
0
,
ρ > R
n
(0)
.
Let
i
0
(
t
)=
dR
i
(
t
)
dt
R
i
(
t
)
,
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