Instabilities and Structure in the High-Latitude Ionosphere - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 527

northward electric field, while a downward gradient is unstable for a southward
field. The gradient scale length perpendicular to B is L ) − 1 , where

⊥ =

L N ( cos I

I is the dip angle. For the same value of L N , is much larger at high latitudes

than in the midlatitude or equatorial case. Even when classical sporadic E layers
form at high latitudes, the cos I term reduces their importance. Steep horizontal
gradients may arise due to very intense localized auroral arcs. However, such
arcs have a high electron density, which drastically increases the recombinational
damping. Thus, the gradient drift process is less important at high latitudes than
elsewhere in the ionosphere.
That said, we now proceed to show that the gradients still cannot be totally
ignored. In Fig. 10.33 the electron density profile and intermediate to short-
wavelength wave data are plotted side by side for two rocket flights through the
auroral electrojet. In the upper case, E had a northward component, while in
the lower case E was southward. In each case the solid trace on the left shows
the true electron density variation with altitude. In the upper plot the wave activ-
ity shows a local minimum exactly where the density gradient changes sign. In
the lower example the wave activity increases when the vertical density gradi-
ent changes sign. The implication is that the electron density gradient controls
or at least affects the intensity of electrojet turbulence but that the two-stream
process is the dominant source of wave activity. In both of these events the elec-
tron drift speed was well over 1000m/s, much higher than the typical sound
speed.
One example which clearly seems to show an auroral event in which a domi-
nant role is played by the gradient drift instability was shown earlier in Fig. 10.28.
Here large-wavelength electric field fluctuations were observed on the bottom-
side. The waves are quite intense (

L ⊥

δ E ≈ 25mV/m) and are polarized in the direc-

tion of the E B drift (Pfaff, 1985). Of course, this low-apogee flight was one

of the few rocket experiments capable of detecting large-scale waves on the bot-
tomside and thus they may well exist much of the time when the electric field is
northward and when the electron density, n 0 , is not so high that recombination
dominates.
This example is potentially quite interesting because it illustrates the altitude
dependence of the wave amplitude. A detailed study of the linear theory for the
event has been carried out and the results were plotted in panel c of Fig. 10.28.
Indeed, the long-wavelength waves are observed at the same altitude as those
where the growth rate in panel c shows positive values at long wavelengths. The
observed longest-wavelength waves (panel e) seem to cut off just above 100 km
altitude, although the intermediate to short-wavelength waves (panel d) remain
strong between 100 and 110 km.
We now consider the extent to which these long-wavelength waves map to
higher altitudes along the magnetic field lines. The theory of the mapping of elec-
trostatic fields (which can include the fields associated with the long-wavelength
waves) along magnetic field lines was reviewed in Chapter 2. Although the
magnetic field lines may sometimes be considered equipotentials, in practice

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