Instabilities and Structure in the High-Latitude Ionosphere - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 491

southward neutral wind driven by ion drag in the polar cap. At the convection
boundary E is in the meridian plane and thus plays no role in the stability of the
poleward plasma density gradient which often exists at that boundary. However,
if, as argued previously, U is in the southward direction, E ×

B is poleward, and
thus the poleward wall of the trough could be unstable to the generalized E × B

process.
Concerning details of the E B instability, there are some aspects of this process

that differ from its development at equatorial and middle latitudes. Tsunoda
(1988) has written an excellent review of these phenomena and we only hit
the high points here. One feature involves the relatively high E-region Pedersen
conductivity that exists at high latitudes. This affects both the growth rate and
the loss rate of plasma structure. For example, a simple expression (Vickrey and
Kelley, 1982) for the linear growth rate of the one-dimensional E

×

× B instability

for waves perpendicular to the gradient is of the form

M

E 0
BL

− 1

k 2 D γ = − (10.5)

⊥

M

where E 0 / B is the component of E × B 2 parallel to B / ∇ n , L the inverse gra-

dient scale length, D the height-averaged perpendicular diffusion coefficient,

=

P /

⊥

E F E F

and M

P + P . In the definition of M , P is the field-line-integrated

E

Pedersen conductivity in the F region and

P is the field-line-integrated Pedersen

E F

conductivity in the E region. If

P , which is almost always the case in the
auroral oval due to particle precipitation, the E region tends to short out the
perturbation electric field,

P >

B instability and the growth
rate becomes small. This is easy to understand because “growth” in the case
of the E

δ E , produced in an E ×

B instability is just due to advection of high-density plasma down a
gradient and low-density plasma up a gradient. The rate of change of the density
is given by

×

n = γδ

∂ /∂ =− δ ·∇

n t V n (10.6)

B 2 . If the perturbation charges that set up

where E are shorted

out by current flow to the E region, the growth rate becomes small. The diffusive
damping term also depends on the E region but in a subtle fashion that we
postpone until Section 10.2.3. Tsunoda (1988) has compared M values for the
auroral case with those for equatorial spread F and for large midlatitude barium
releases. For equatorial spread F, he quotes values in the range 10 to 10 4 , while
for low-altitude barium releases M ranges from 60 for a 1 kg release to 470 for
a 48 kg release. Auroral F-region plasma enhancements, on the other hand, have

δ V = δ E × B / δ

M values less than 1.2 for reasonable E-region densities 5mho . Even for

E

P =

≤

nighttime conditions with no E layer M 10 for F-region densities as high as

10 6 cm − 3 . On this basis alone it is clear that local plasma instabilities may be
less dominant in the auroral zone than at other latitudes.