| This thesis focuses on numerical simulations of the mid-latitude ionospheric F region plasma instabilities by solving Perkins' [1973] partial differential equation set that models the F region electrodynamics. High-accuracy pseudo-spectral method codes were developed and implemented in different conditions. In the TEC (total electron content) homogeneous (two-equation) cases, the linear growth stage was simulated with results that are very consistent with the analytical approximations. A saturation case in which the instability ceases growth was simulated and displays steady state turbulence behavior. A Gaussian initial condition case was carried out showing that resultant structures move at the usual E x B drift velocity. In the TEC inhomogeneous (three-equation) cases, a linear analytical approximation was developed showing that the growth rates of the conductivity and potential are usually different and can be much larger than those in the two-equation cases. Single mode simulations in the three-equation cases show that when the wave vectors are directed northwest, saturation is a very common phenomenon. Further simulations show that in the three-equation cases, the growth rates of both the conductivity and potential can be much larger than those in the two-equation cases in both linear and nonlinear stages. A simulation of a turbulence case on a much larger space scale (256 x 256 km 2) is given, yielding structures similar to the 630 nm airglow images from all-sky cameras. A revised physical explanation of the Perkins instability is provided and mathematical derivations show that it explains the wave growth very well. Derivation and linearization of the Perkins instability equations with neutral wind included are shown in the appendices. |
