GENERALIZED RAYLEIGH-TAYLOR INSTABILITY IN THE PRESENCE OF TIME-DEPENDENT EQUILIBRIUM

Plasma instability under the combined influence of the gravity and an eastward electric field, commonly referred to as the generalized Rayle igh-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 recom bination process and the collisional diffusion process. After determin ing the time-dependent equilibrium density and, in particular, the inv erse density gradient scale length L-1, which determines the growth ra te 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, req uires numerical analysis. In this paper the effects are studied in lim iting situations for which useful analytic solutions can be obtained. The effect of diffusion on L-1 is studied by neglecting both the upwar d plasma drift and the altitude variation of the recombination frequen cy upsilon(R), and it is verified that the effect is negligible for ty pical values of the ionospheric parameters. The effects of the other t wo processes on L-1 are studied by neglecting diffusion. The effect of the altitude variation of upsilon(R) on the linear growth of the pert urbations 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 enhancement s 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 evol ution of the instability and, more importantly, the level of fluctuati ons at saturation will be significantly affected by the enhancements. The nonlocal aspect of the instability in the upward drifting plasma i s studied by neglecting, for the sake of obtaining a closed form analy tic solution, both the altitude dependence of upsilon(R) and the therm al effects. It is shown that to a very good approximation, the unstabl e modes are localized in the vertical direction with localization dist ance proportional to lambda(1/2), where lambda is the wavelength of th e mode, and that the localized mode, while it grows in time, drifts ve rtically upward with the same speed as the upward drifting plasma. In view of the result that the altitude variation of upsilon(R) significa ntly enhances the local growth of the perturbations, it should be reta ined in the nonlocal analysis; in which case, the appropriate differen tial equations have to be solved numerically.