A nonlinear theory for large aspect angle echoes in the auroral E region

Abstract

It has been argued by a number of authors that existing conventional theories of small‐scale E region irregularities such as the linear and quasi‐linear theories cannot account for a number of physical features of E region irregularities revealed by the observations as well as the simulations. We present a fully nonlinear theory based on a two‐fluid model for the ions and electrons. We discuss two limits, that of the plasma within the electrojet where the ion collision frequency is larger than the ion gyrofrequency νi ≫ Ωi, and the case above the electrojet where νi ≪ Ωi. In both cases a set of coupled nonlinear equations governing the evolution of the density and electrostatic potential is derived. An argument regarding the nonlinear saturation of the turbulence is developed, and its consequences on the threshold drift velocity as well as the maximum aspect angle are discussed. By introducing both the effects of turbulence through frequency broadening and anomalous electron collision frequencies perpendicular and parallel to the magnetic field, we are able to predict the large aspect angles revealed by some of the radar observations. We then discuss two possible closure schemes, namely the “direct interaction approximation” and the “eddy damped quasi‐normal markovian” approximations, that allow us to evaluate self‐consistently the frequency broadening and the saturated spectra for both the density and the potential fluctuations.