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the “polar wind.” The velocity of the light ions can, in fact, be supersonic at
times. The existence of the polar wind and the depressed light ion concentra-
tions at high latitudes indicates that in this region the light ion population of
the ionosphere is usually not in diffusive equilibrium along the magnetic field
lines.
9.1.2 Hydrodynamic Theory of the Polar Wind
In Chapters 2 and 5 we discussed the forces that contribute to motion of the
ionospheric plasma along the magnetic field. In these discussions we included the
generation of an electric field with a component along the magnetic field lines
that was created internally by the plasma. This “ambipolar” field does not drive
a current parallel to the magnetic field but merely serves to equalize the forces on
the ions and electrons so they move together. In the inner magnetosphere the field
lines are closed and relatively short in length. This allows the flux tubes to fill to a
condition of equilibrium on a time scale of a day or so. Under normal conditions,
then, the plasma is produced during the daytime and tends to flow slowly up into
the inner magnetosphere. At night the flow is reversed and plasma tends to flow
back into the ionosphere from above, replacing the ionospheric plasma against
recombination losses. Charge exchange converts O + to H + and vice versa at the
top of the ionosphere. The crucial difference between the high- and low-latitude
cases is that, in the former, the flux tubes are either open or so long that no
semblance of diffusive equilibrium exists. In effect, whatever plasma is produced
by sunlight or particle influx merely expands into a near vacuum.
Below about 2000 km, we learned that collision frequencies and gyrofrequen-
cies are sufficiently high that, for most problems, the acceleration term may be
neglected in the equations of motion. In this region the plasma is said to be colli-
sion dominated, meaning that the ions undergo several collisions while moving
through one scale height. A plasma is collision dominated if
(
V i /
H i ) ν i
where V i is the field-aligned ion velocity and H i and
ν i are the ion scale height and
appropriate collision frequency, respectively. However, since the upper boundary
condition is crucial at high latitudes, we cannot make this approximation or
restrict ourselves to altitudes below 2000 km. Note that it is not our intent here
to provide all the mathematical details involved in the theoretical formation of
parallel ion flow in such a situation; we only outline the initial steps and give
some physical insight into the phenomenon based on experiments and simple
model calculations.
In a collision-dominated plasma with multiple ion species, where one ion may
move relative to another at a high speed that varies with altitude, the advective
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