Geoscience Reference
In-Depth Information
Each species will have its own momentum equation. Although neutral fluid
dynamics on a rotating object such as the earth is strongly affected by the Coriolis
force, this velocity-dependent force has little importance in geophysical plasma
analysis, since the magnetic force (which is also velocity dependent) is much
greater. The important body forces that do act on the ionospheric plasma and
that we include in the force
F
are as follows:
Gravitational:
ρ
j
g
Electric:
n
j
q
j
E
Magnetic:
n
j
q
j
(
V
j
×
B
)
where
q
j
is the charge of the
j
th species and
E
and
B
are the electric and magnetic
fields. In addition, a frictional force is exerted on each species by collisions with
all of the other species. For example, electrons will collide with neutrals as well
as with the various ions. The force is proportional to the respective collision
frequency and to the differential velocity between the particular fluid and the
other fluids. The frictional force on each species may be written
k
ρ
j
v
jk
V
j
−
V
k
F
j
=−
k
j
=
The
v
jk
are momentum transfer collision frequencies with units of s
−
1
.We
leave any detailed discussion of the
v
jk
coefficients for other texts such as Banks
and Kockarts (1973) and Schunk and Nagy (2000). The momentum equation
we shall primarily use for each ionized species is then
n
j
q
j
E
B
−
k
j
k
ρ
j
v
jk
V
j
−
V
k
d
V
j
dt
=−∇
ρ
j
p
j
+
ρ
j
g
+
+
V
j
×
=
Viscosity and momentum transfer by waves are ignored in this equation and will
be discussed only briefly in the text where appropriate.
2.1.5 The Complete Equation Sets
The equations we have thus far obtained for the fluids making up the ionosphere
may be summarized as follows. The neutral atmospheric equations of continuity,
momentum, and state are
∂ρ/∂
t
=−∇·
(ρ
U
)
(2.21a)
2
U
ρ
d
U
/
dt
=−∇
p
+
ρ
g
+
η
∇
−∇·
π
w
−
2
ρ
×
U
+
J
×
B
(2.21b)
(2.21c)
p
=
ρ
k
B
T
n
/
m
n
=
n
n
k
B
T
n
where the subscript “
n
” stands for neutrals.
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