Instabilities and Structure in the High-Latitude Ionosphere - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 500

Further evidence for a turbulent mixing process at scales on the border between
“large” and “intermediate” has been presented by Tsunoda et al. (1985). They
studied a highly structured F region that was characterized by a stable E

B
situation. They concluded that a driven mixing process was occurring but one
that was not explained by the E

×

B instability. Similarly, referring to the data
in Fig. 10.1, the high scintillation levels that were reported in association with
plasma patches in the polar cap were found throughout the patches. That is,
kilometer-scale irregularities were located on gradients with either sign, even
though the mean patch convection is associated with a particular E

×

×

B flow
direction. Scintillation studies have also shown that regions of plasma shear are
very irregular (Basu et al., 1986). We therefore conclude that impressed turbulent
electric fields of magnetospheric origin play an important role in creating iono-
spheric structure at high latitudes.

10.2.3 Diffusion and Image Formation
As noted previously, the lifetime of a horizontal structure in the high-latitude
ionosphere depends on how quickly the plasma can diffuse across the magnetic
field. Also, whether a particular plasma instability is stable or unstable at a
given k value depends on whether some positive contribution to the growth rate
exceeds diffusive damping due to terms of the form k 2 D

. In Chapter 5 we
pointed out that parallel diffusion which operates with a time scale ( k 2 D

−

⊥

|| ) − 1 is

determined by the ion diffusion coefficient and that

2 D i
The factor of 2 comes from the fact that an ambipolar electric field builds up
when electrons attempt to diffuse away quickly parallel to B due to their small
mass. In effect, each electron has to drag a heavy ion with it along B , and the
plasma diffusion coefficient is then determined by the ions.
Perpendicular to B , an analogous process occurs. The equations of conserva-
tion of momentum (2.22b) for each species in the moving reference frame of the
neutral wind are

D

|| =

V j × nM j ν jn V j

nq E + 0 =− k B T j ∇ n + nM j g + nq j ( B ) −

where we have taken d V j /

0. Let B be in the z direction and neglect
the effect of gravity and neutral winds. Then in the directions perpendicular
to B ,

dt =

0 =− k B T j (∂ n /∂ x ) + nq j E x + nq j V jy B − nM j ν jn V jx

0 =− k B T j (∂ n /∂ y ) + nq j E y − nq j V jx B − nM j v jn V jy