Plasma instability under the combined influence of the gravity and an eastward electric field, commonly referred to as the generalized Rayleigh-Taylor instability, is considered for a time-dependent equilibrium situation. In the nighttime equatorial ionosphere the time-dependent equilibrium situation arises because of the vertically upward E-0 x B-0 drift of the plasma in conjunction with the altitude-dependent recombination process and the collisional diffusion process. After determining the time-dependent equilibrium density and, in particular, the inverse density gradient scale length L-1, which determines the growth rate of the instability, the stability of small-amplitude perturbations is analyzed. The general solution of the problem, where the effects of all of the above-mentioned processes are included simultaneously, requires numerical analysis. In this paper the effects are studied in limiting situations for which useful analytic solutions can be obtained. The effect of diffusion on L-1 is studied by neglecting both the upward plasma drift and the altitude variation of the recombination frequency upsilon(R), and it is verified that the effect is negligible for typical values of the ionospheric parameters. The effects of the other two processes on L-1 are studied by neglecting diffusion. The effect of the altitude variation of upsilon(R) on the linear growth of the perturbations is studied by adopting the so-called local approximation. It is found that the value of L-1 and hence the value of the growth rate are enhanced by the altitude variation of upsilon(R). The enhancements rapidly increase with time to large values at lower altitudes and to significant values at higher altitudes when compared with the values for the spatially uniform upsilon(R) case. Consequently, the time evolution of the instability and, more importantly, the level of fluctuations at saturation will be significantly affected by the enhancements. The nonlocal aspect of the instability in the upward drifting plasma is studied by neglecting, for the sake of obtaining a closed form analytic solution, both the altitude dependence of upsilon(R) and the thermal effects. It is shown that to a very good approximation, the unstable modes are localized in the vertical direction with localization distance proportional to lambda(1/2), where lambda is the wavelength of the mode, and that the localized mode, while it grows in time, drifts vertically upward with the same speed as the upward drifting plasma. In view of the result that the altitude variation of upsilon(R) significantly enhances the local growth of the perturbations, it should be retained in the nonlocal analysis; in which case, the appropriate differential equations have to be solved numerically.
