Equatorial Plasma Instabilities and Mesospheric Turbulence - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 196

E z 0 is left the same, the perturbation electric fields will cause high-density plasma
to drift into higher-density regions, which is stabilizing. Thus, for instability the
zero-order vertical electric field must have a component parallel to the zero-
order density gradient. At the equator during normal daytime conditions (see
Chapter 3), the unstable gradient direction is upward since E z 0 is upward, while
at night the unstable gradient is downward.
There is no threshold drift requirement for the gradient drift instability in
the physics thus far. However, if recombination is considered, a term in the
continuity equations of the form

n 2 must be included which, when linearized,

− α

− α

n 0 δ

becomes of the form n and a finite threshold thus exists for the gradient

drift process. Fejer et al. (1975) found that the electron drift threshold velocity
for instability to occur is given by

2

L 2

k 2 C s ν e /ν i e

V D > α n 0 ( 1 + 0 )( i /ν i ) + ( 1 + 0 )

Finally, following Fejer et al. (1975), the complete linear theory must include a
finite zero-order ion drift velocity V Di and the possibility of an arbitrary k vector
(but still perpendicular to B ), yielding the following set of expressions for the
linear theory of both the gradient drift and two-stream modes:

ω r = k · ( V D + V Di )/( 1 + ) (4.48a)

+ ) − 1

ω r −

k 2 C s V Di 2 γ = ( 1 (/ν i ) k · −

1

Lk 2 ! ω r − V Di ( ν i / i ) k x " − + / k · 2 α n 0 (4.48b)

with

= 0 k 2 k 2

e k x /

k 2

2
e

2

⊥ /

+ /ν (4.49)

and under the assumption that γ ω r .

If the latter assumption is relaxed, Kudeki et al. (1982) have shown that waves
with

λ L propagate more slowly; that is, amore exact result for the linear theory

with k · B = V Di = 0 is given by

k

1

k 2 V D 1 k 0 / ω r + i γ = k · + ik 0 / ( 1 + 0 ) + (4.50)

where k 0 . This is the linear theory for large scale waves.

Finally, we note that recombination is muchmore important during daytime con-
ditions than nighttime, since the zero-order density is large and 2

= (ν i / L i )/( 1 + 0 )

n 0 is sizable.
The linear theory outlined here has been applied to data from three rocket
flights and the results are reproduced in Fig. 4.33 (Pfaff et al., 1985). Panel
(a) shows the current density and electron density profiles. Panel (b) shows the

α