Numerical Study of Small-Scale Instability Parameters at the Upper Fronts of Equatorial Plasma Bubbles

Results of numerical simulations on the dynamics of small-scale instabilities arising in the regions of developed equatorial plasma bubbles in the Earth’s ionosphere are presented. The equations for perturbations in the electric field potential and electron density are solved. Background values were derived from a numerical solution of the authors' two-dimensional model of Rayleigh–Taylor instability development in the equatorial ionosphere, obtained under evening conditions. The perturbation model for electric potential and electron density are used to perform a series of numerical experiments for the region corresponding to the upper part of plasma bubbles. These simulations have been used to model the growth rate of small-scale gradient-type instabilities. The calculations assumed strong elongation of equatorial plasma bubbles along the geomagnetic field lines. Unlike the authors' previous works, this model accounts for background electron density gradients, modifies the algorithm for solving the difference equations of the potential by combining the method of even–odd reduction and iterations on the right-hand side of this equation, and changes the technique for estimating the instability growth rate; specifically, the method of initializing the original perturbation on the basis of pseudorandom deviations from the background has been used. This paper aims to analyze the features of instabilities for the upper part of developed equatorial plasma bubbles rising to the upper ionosphere of the Earth. The use of a scenario of a pseudorandom number generator allows us to calculate the value of the near-maximum nonlocal growth rate. The numerical experiments revealed high growth rates comparable to those of the Kelvin–Helmholtz instability in the outer ionosphere. This makes it possible to assess the potential for the development of small-scale inhomogeneities at evening and nighttime, with parameters typical of equatorial F-region scattering conditions.