# Equatorial Plasma Bubbles: A Review
## 3 Development of EPBs and Associated Irregularities: Theoretical Aspects
### Electrostatic Rayleigh-Taylor Instability
\(U_{L}^{P}\) is the Pedersen conductivity-weighted neutral wind perpendicular to the geomagnetic field in the magnetic meridian plane, which is a vertical plane that contains the geomagnetic field line, considered to be dipolar in this derivation; \(g_{e}\) is the altitude-corrected acceleration due to gravity (considered to be negative) and \(v_{eff}^{F}\) is the effective ion-neutral collision frequency weighted by electron density. \(K^{F}\) is the inverse of flux tube electron content vertical gradient scale length, and \(R_{T}\) is the electron density-weighted flux tube recombination rate. Linear growth rates of GRT instability for different ambient conditions have formed the basis of several investigations into probable causes for the day-to-day variability in the occurrence of EPBs at equatorial and low-latitude locations. Some of these have used ground-based measurements of a few ionospheric parameters, while others have estimated the parameters using coupled ionosphere-thermosphere models. Going beyond the linearized equations, [PERSON] et al. [60] considered a three-mode system to study the nonlinear evolution of electrostatic R-T instability, including ion inertia as well as ion-neutral collisions. They found that the nonlinear equations that determined the evolution of this system had the same form as the Lorenz equations, which were originally used to approximately describe the evolution of Rayleigh-Benard instability [61]. For electrostatic R-T instability, it was found that the fixed states of the three-mode system became unstable when \(v_{in}~{}<~{}\sqrt{g/~{}2L}\), leading to the conclusion that R-T instability could result in the chaotic behavior of equatorial F region plasma at altitudes above about 500 km, where this condition would be satisfied. Two-dimensional simulations of the non-linear development of EPBs have yielded other important insights besides showing that the EPBs can rise to the linearly stable top side of the equatorial ionosphere. Two-dimensional simulations have demonstrated how neutral winds and background Pedersen conductivity influence the non-linear development of EPBs [55] and the critical role played by conditions on the top side of the equatorial F region in the evolution of EPBs [62]. The effects of vertical shear and zonal electric field patterns on the nonlinear evolution of EPBs have also been evaluated using 2-D simulations [63]. It was mentioned earlier that the EPB phenomenon, also sometimes referred to as 'convective equatorial ionospheric storm', spans a large range of scale sizes. The initial seed perturbation on the bottom side of the equatorial F region may have a wavelength of a few hundred km. Generalized R-T instability gives rise to structures with scale sizes in the range of 100 m to 20 km [54], which are involved in causing scintillations on VHF and L-band signals. The first results on the development of multiple bifurcated structures, secondary instabilities, and supersonic flows in EPBs were also obtained from 2-D simulations with a spatial resolution of 1.3 km in the east-west direction [64]. A unique feature of the low-latitude ambient ionosphere is the equatorial ionization anomaly (EIA). An eastward electric field \(\mathbf{E}\) in the equatorial ionosphere causes the F region plasma to drift upward with velocity \(\mathbf{E}~{}\times~{}\mathbf{B}/B^{2}\) to higher altitudes. After that, under the influence of pressure gradients and gravity, the plasma moves down the geomagnetic field lines to off-equatorial locations, creating regions of anomalously high density which are referred to as EIA regions. Thus, plasma density at the crest of the EIA region may be an order of magnitude higher than that at the dip equatorial F peak, even at nighttime. Ground-based observations of airglow and scintillations from different low-latitude locations demonstrated the necessity of 3-D simulations in understanding the 3-D evolution of EPBs. In the first 3-D simulation of the nonlinear evolution of EPBs, [PERSON] et al.