Instabilities and Structure in the High-Latitude Ionosphere - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 530

10.6.2 The Two-Stream Instability and Type 4 Radar Echoes
Of course, the two-stream instability is very easily excited in the auroral case and
it is probably responsible for most radar echoes. The possibility that such waves
heat E region electrons to temperatures far in excess of that of the neutral gas
makes their study very interesting, since such wave-induced processes are very
important in space plasma physics in general.
The type 4 observations discussed earlier give evidence for local increases in
the ion acoustic speed of up to 900 m/s. For a mean ion mass of 31 amu and
an ion temperature of about 500K, this corresponds to an electron temperature
of about 2500K for isothermal ions and electrons. The temperature would be
reduced when electrons are nonisothermal, and slightly reduced for different
specific heat ratios. Electron temperatures of this magnitude have been measured
with incoherent radars during highly active periods (see Fig. 10.29). Cosmic
noise absorption levels measured during events of this type are also consistent
with large increases in the effective electron temperature in the locally heated
region (Stauning, 1984).
Schlegel and St.-Maurice (1981) argued that the large electron temperature
enhancements in the unstable electrojet layer cannot be explained by either
particle precipitation or classical Joule heating. These enhancements maximize
at the height (about 110 km) where two-stream waves are strongest. This led
St.-Maurice et al. (1981) to suggest that these waves are responsible for the elec-
tron heating throughout the unstable region. Several theories were developed to
explain the possible heating of the electron gas by strongly driven two-stream
waves. Originally, St.-Maurice et al. (1981) considered a quasi-linear modified
two-stream instability theory with the assumption that the wave energy is con-
centrated in a narrow band of short-wavelength ( 20 cm) waves where the

linear growth rate is a maximum. However, the wave amplitudes necessary to
generate the observed electron temperatures are much larger than measured by
in situ probes in this wavelength range (e.g., Pfaff et al., 1984). St.-Maurice and
Laher (1985) then suggested that heating of the electron gas is caused by par-
allel electric fields associated with long-wavelength gradient drift waves, while
Primdahl and Bahnsen (1985) emphasized the role of an anomalous collision fre-
quency,

λ ≈

ν ∗ . Robinson (1986) also considered the heating of the electrons by the
perpendicular gradient drift wave component in the presence of anomalous elec-
tron collisions. In this formulation, the electron heating rate can also be written

ν ∗ V D − k 2

dW e / dt | waves = n 0 m C s k

|| /

ν ∗ is the anomalous electron collision frequency. Self-consistent calcula-
tions of anomalous electron collision frequencies necessary for the saturation of
the two-stream waves and of the corresponding electron temperatures were in
excellent agreement with the experimental results. (The concept of a

where

ν ∗ was first
proposed by Sudan (1983b), who used it to explain limitation of the wave phase
velocity.)