Coupling of the Perkins instability and the sporadic E layer instability derived from physical arguments -: art. no. A06301

Tsunoda and Cosgrove [ 2001] recently pointed out that the F layer and sporadic E (Es) 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 Es 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 (EsL) 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 x 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 EsL instability growth rates. We compare the result with the exact computation of Cosgrove and Tsunoda [ 2004].