Waves and Instabilities at Midlatitudes - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 329

corresponding electric field at the equilibrium layer altitude on the right. In this
example, the layer evolution becomes quickly nonlinear, and there is an 8mV/m
electric field pulse associated with the instability growth phase.

6.7.7 Coupling of E s Layers and the F Layer
As far back as 1960 (Bowman, 1960), researchers have noted the apparent rela-
tionship between structures in the F layer and in E s layers. Farley (1959) demon-
strated that electric fields of sufficient spatial scale should map between the E and
F regions due to the extremely high conductivity in the magnetic field-aligned
direction, thus giving the beginning of a theoretical foundation for the observa-
tions. Tsunoda and Cosgrove (2001) accounted for the Haldoupis et al. (1996)
polarization mechanism and described a scenario for positive feedback between
an E s layer and the F layer as a way to account for the relationship between E s -
layer and F-layer structure. In companion papers, Haldoupis et al. (2003) and
Kelley et al. (2003a) invoked the Haldoupis et al. (1996) polarization mechanism
to explain new observations of E s -F-layer coupled behavior. Kelley et al. (2003a)
noted that an eastward E-region perturbation electric field of sufficiently large
scale would cause the F region to rise, reducing its conductivity and thus its load
on the E region. All of this led up to a unified treatment of the F and E s layers
and of the Perkins and E s -layer instabilities as a single coupled system (Cosgrove
and Tsunoda, 2004a,b).
Using the assumption that electric fields of sufficient spatial scale map unat-
tenuated along B between the E and F regions, Cosgrove and Tsunoda (2004a)
solved the equations of motion associated with the Perkins instability (see equa-
tion 6.21b) together with the equations of motion associated with the E s LI to
obtain the growth rate for the coupled E s -F-layer system. In general, they found
two unstable modes. Under conditions in which a significant relative drift existed
between the E s and F layers, one mode corresponded to the Perkins instability
and the other corresponded to the E s -layer instability. However, when the rela-
tive drift between the E s and F layers was small, there was only a single unstable
mode, indicating a true coupling of the two instabilities. In this case they found
that the overall system growth rate was normally more than doubled by the cou-
pled electrodynamic effect. Of course, the implication is that the E-region neutral
wind and the F-region E

B drift are equal, which would be rare.
To treat the coupled condition when the wavelength is not long enough to
assume 100% efficiency of the electric field mapping between the E and F regions
and to obtain an approximate analytic expression for the coupled system growth
rate, Cosgrove and Tsunoda (2004b) employ a circuit model approach similar to
that given for the barium cloud in Fig. 6.19. Figure 6.41 shows the development
of this circuit model, which is generally useful for the two-layer coupled
problem, under the Farley (1960) mapping criteria. The resistors R 0 ,

×

R F , and

R Es are defined in terms of the field-aligned conductivity ( σ 0 ), the FLI Pedersen