Instabilities and Structure in the High-Latitude Ionosphere - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 502

Finally, since the species gyroradius is given by the expression
r gj = k B T j / M j 1 / 2

− 1
j

(10.14b)

the perpendicular diffusion coefficient of some species j may be written

r gj ν j D j ⊥ = (10.14c)

where r gj is the gyroradius and ν j is the collision frequency. Intuitively this makes

sense, since a particle will randomly walk one gyroradius between each collision.
Since r gj is much larger for ions than for electrons, the ions tend to diffuse more
rapidly down a density gradient which exists perpendicular to the magnetic field
than do the electrons. However, when this occurs an electric field builds up
parallel to

∇

n , so the ion motion across the field lines is retarded and the electron
motion is enhanced. The result (derived following) is that an isolated plasma
structure diffuses across a magnetic field with a diffusion coefficient equal to the
low electron diffusion coefficient.
The preceding discussion assumes that the F-region plasma is the only plasma
in the system. However, if an E region exists due to production of plasma by
sunlight or production by auroral particle precipitation, the ambipolar electric
field discussed previouslywill be shorted out and the ions may then diffuse rapidly
across the magnetic field. The electrons still cannot move across B , but they can
move along the magnetic field to complete the circuit through the E region and
therefore neutralize the ambipolar electric field. The entire process is illustrated
schematically in Fig. 10.17a. The converging arrows in the E region represent
the ambipolar electric field, which maps down to the E region due to the high
conductivity parallel to B . Those arrows also show the direction of the E region
ion current that completes the circuit. The inner and outer sets of arrows show
the electron flow direction. The line through the F-region structure represents
the vertical magnetic field line.
A quantitative description of this diffusion process must allow for altitude vari-
ations in all the relevant quantities. Vickrey and Kelley (1982) have performed
such calculations for a model ionosphere and computed the typical effective dif-
fusion coefficient plotted in Fig. 10.17b as a function of the ratio of E region to
F-region conductivities. The effective (field-line-integrated) diffusion coefficient
increases from roughly 1m 2 /s to more than 10m 2 /s as the E-region conductivity
increases. Also plotted is the e -folding time,

⊥ ) − 1 , for a horizontal
structure with a characteristic perpendicular wavelength of 1 km. Even for high
E-region conductivity the diffusion time scale is several hours for such a struc-
ture, and it could survive considerable transport around the high-latitude zone. In
this particular calculation, the F layer had a Chapman distribution characterized
by the parameters listed in the plot. Kelley et al. (1982b) used this semiquan-
titative approach to calculate the relative amplitude of kilometer-scale struc-
tures produced at various places in the auroral oval which were then allowed to

k 2
⊥

τ ⊥ = (

D