Geoscience Reference
In-Depth Information
magnetic fields ((1.44)-(1.45) and restrict our consideration to the quasi sta-
tionary approximation. Then for the electron and ion drift velocities we have
σ
e
eN
e
E
0
,
v
e
0
=
v
n
−
σ
i
eN
i
E
0
.
v
i
0
=
v
n
+
(14.4)
Here
σ
e
and
σ
i
are tensors of the electron and ion conductivities (see electron
and ion parts of (1.86)-(1.87) for
ω
= 0). The sum of the external field
E
0
and dynamo-field is
E
0
=
E
0
+
1
c
v
n
×
B
0
.
(14.5)
Perturbations of the electron and ion concentrations are connected with
the corresponding fluxes through the equations of a continuity
∂N
e
∂t
+
∇
·
J
e
=
q,
(14.6)
∂N
i
∂t
+
∇
·
J
i
=
q,
(14.7)
where
J
e
=
N
e
v
e
,
J
i
=
N
i
v
i
are the electron and ion fluxes;
q
is defined by the processes of the ion pro-
duction, recombination etc.
In an inhomogeneous plasma, the internal concentration gradients, among-
st others, create particle flows that in turn produce electric and magnetic
fields. Moreover, an inhomogeneity placed in an external field of any kind (i.e.
temperature, electric, etc.) produces polarization electric fields. Upon emis-
sion, electron-ion gas pressure is significantly lower than magnetic pressure
and all velocities are substantially lower than the Alfven velocity. In such
conditions, motion of the ionized gas is unaffected by the magnetic perturba-
tions.
The electric field
E
p
caused by the plasma inhomogeneity is given by
∇
·
−
4
πe
(
N
e
−
N
i
)
.
E
p
=
(14.8)
The electron and ion fluxes are
σ
e
E
p
e
J
e
=
N
e
v
e
0
−
,
(14.9)
J
i
=
N
i
v
i
0
+
σ
i
E
p
e
.
(14.10)
B
0
is so strong that the charged particles cannot move in the transverse
direction and transport across
B
0
is small. This is why the fluxes proportional
to
∇
⊥
N
e,i
and
∇
⊥
T
e,i
in (14.9) and (14.10) are not included.
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