Geoscience Reference
In-Depth Information
E
=−∇
φ
(2.27d)
∇·
J
=
0
=∇·
B
(2.27e)
∇×
B
=
μ
0
J
(2.27f)
Note that from (2.26) we have the important result that the number of electrons
per unit volume must be almost equal to the number of positive ions of all types
n
e
=
ions
n
j
This means we can define a plasma density
n
, which is equal to both
n
e
n
e
and
j
n
j
.
2.2 Steady-State Ionospheric Plasma Motions Due to
Applied Forces
In this section we start with (2.27a) and derive the equations that determine the
electrodynamic response of a partially ionized plasma to applied steady forces.
For the present we specify the distribution of plasma density and the wind field.
Considering (2.27a), with the plasma pressure distribution specified, we can
argue that the response of the plasma constituents to changing forces occurs
very quickly (i.e.,
d
V
j
/
0). This can be seen by comparing the terms in
(2.27a) that include the velocity. The acceleration terms on the left-hand side are
of order
V
j
/τ
dt
≈
and,
V
j
/
is the response time to a new set of forces and
L
is a distance scale for velocity change. The Lorentz term (the third term on the
right-hand side) is of order
V
j
j
, where
L
, where
τ
, and
the frictional term is of order
V
j
v
j
where
v
j
is the collision frequency. As long as
τ
−
1
j
is the gyrofrequency (
q
j
B
/
M
j
)
j
or
v
−
j
, the acceleration term can be neglected. Collision frequencies
and gyrofrequencies are sufficiently high that, in most problems of interest to
macroscopic dynamics, the acceleration term can be ignored. Also, since fluid
velocities are usually subsonic, if
L
is greater than the gyro radius and the mean
free path, the advective term is small. The plasma constituents are thus assumed
to be in velocity equilibrium with the existing force fields.
The equilibrium fluid velocity of each species may now be found from (2.27a)
by setting the total time derivative equal to zero and specifying the force fields
and pressure distributions
=−∇
n
j
k
B
T
j
+
q
j
n
j
E
B
0
n
j
M
j
g
+
+
V
j
×
n
j
M
j
v
jk
V
j
−
V
k
−
k
k
(2.28)
=
j
Search WWH ::
Custom Search