Coupling of the Perkins instability and the sporadic E layer instability derived from physical arguments

Tsunoda and Cosgrove [2001] recently pointed out that the F layer and sporadic E ( E s ) layers in the nighttime midlatitude ionosphere must be considered electrodynamically as a coupled system in light of the presence of a Hall polarization process in E s layers [ Haldoupis et al. , 1996 ; Tsunoda , 1998 ; Cosgrove and Tsunoda , 2001 , 2002a ] and the fact that kilometer‐scale electric fields map efficiently between the E and F regions. They further noted the apparent presence of positive feedback between processes in those regions. Cosgrove and Tsunoda [2002b , 2003] have since shown that E s layers are unstable with properties not unlike those of the Perkins instability in the F region [ Perkins , 1973 ], motivating the idea that the two instabilities may couple. Finally, Cosgrove and Tsunoda [2004] derived the linear growth rate for the coupled system of a E s layer and the F layer, thus realizing a unified formalism for the Perkins and E s layer ( E s L) instabilities. They found that the growth rate was significantly enhanced by the coupling. However, the growth rate computed in Cosgrove and Tsunoda [2004] was expressed only as the largest eigenvalue of a very complex 3 × 3 matrix. In this paper we present a physical interpretation of the E ‐ F coupled‐layer (EFCL) instability, and derive the condition for maximal coupling. We obtain a circuit model for the coupled‐layer system that provides a physical interpretation for the wavelength dependence of electric field mapping between layers, and allows quantitative predictions. Using the circuit model we derive a “rule of thumb” for computing the two growth rates of the coupled system from the isolated Perkins and E s L instability growth rates. We compare the result with the exact computation of Cosgrove and Tsunoda [2004] .