Dynamics and Electrodynamics of the Equatorial Zone - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 95

along with the horizontal current and the electron drift (Pfaff et al., 1997). As
discussed in detail in the next chapter, these fields create electron drifts that are
unstable to the generation of plasma waves. Peak vertical electric fields in the
range 10-20mV/m have been predicted theoretically and would create electron
drift speeds of 350-700m/s. This exceeds the acoustic speed C s , which is about
360m/s, and leads to the generation of intense plasma waves via the two-stream
instability. Indeed, as we shall see, very large Doppler shifts occur when radar
signals are scattered from the electrojet waves. These observations show that the
vertical electric field reaches values at least as large as that given by E z =

9mV/m at the very threshold of the two-stream instability, and it is very likely
that the field reaches values half again as large. This is the largest electric field
found in the ionosphere below subauroral zone latitudes. Remarkably, the data
in Fig. 3.17a are the only vertical electric field measurements ever made.
The measurements in panels (a-c) have been combined in the right-hand panel
to show the differential (net current) velocity as well as the E

C s B

B drift speed. At
high altitudes the agreement is quite good, but below 104 km there is a systematic
difference. As discussed in Chapter 2, neutral winds in the E region carry the ions
with them but barely affect the electrons at all. The systematic difference between
the two curves in panel d suggests that a high, westward neutral wind may have
been present, a result in agreement with TMAmeasurements made in the evening
two days later (Larsen and Odom, 1997).
Notice that the measured current density in Fig. 3.17a field peaks almost 5 km
above the theoretical curve. This has been a mystery ever since Gagnepain et
al. (1977). A fix can be made by arbitrarily quadrupling the electron-ion col-
lision frequency. This approach works for horizontal magnetic field measure-
ments as well (P. Alken, personal communication, 2008). However, Ilma and
Kelley (2009) have shown that merely by evaluating the field line-integrated
conductivity and using it to calibrate the current, the problem goes away. As in
the F region, this is due to the increasing length of the line integral as a func-
tion of altitude. This effect is classical but for zonal electric fields larger than
1mV/m, plasma waves “anomalously” decrease the conductivity (Kelley et al.,
2009b).
An electrojet theory suitable for comparison with such detailed data must
include realistic altitude and latitude variations of

×

σ
is often expressed in geographic rather than geomagnetic coordinates, and the
resulting conductivity tensor is not as simple as (3.6). If R is the rotation matrix
relating geographic and geomagnetic coordinates, we have

σ . Away from the equator,

E ) R · J = R · ( σ ·

where E = R − 1 E + U × B . Inserting the identity matrix I = · R , we have

R − 1 E

· = ( · σ · ) · ·

R J R R