The Sun ionizes a small fraction of Earth's atmosphere above roughly 60 km, producing the plasma that constitutes the ionosphere. Radio signals passing through the ionosphere scatter off of plasma density structures created by the Farley-Buneman instability (FBI). While numerous studies have characterized the FBI's intrinsic nature, its evolution within the broader context of the surrounding plasma remains enigmatic. This dissertation answers two fundamental questions about the FBI: How does it interact with density gradients? How does its non-linear evolution depend on the background plasma? The fourth chapter examines the combined development of the FBI and the gradient drift instability (GDI) using a 2-D simulation of the equatorial ionosphere. A half-kilometer wave perturbs a plasma layer perpendicular to the ambient magnetic field, causing the perturbed layer to develop GDI waves along the gradient aligned with the ambient electric field, as well as FBI waves in a region where the total electric field exceeds a certain threshold. Early radar observations suggested that these two instabilities were distinct phenomena; the reported results illustrate their coupled nature. The fifth chapter presents 2-D simulations in which a one-kilometer plasma wave develops an electric field large enough to trigger meter-scale waves. Such large-scale waves arise via the GDI within the daytime ionospheric gradient around 100-110 km. Typical ionospheric radars only observe meter-scale irregularities but observations show meter-scale waves tracing out larger structures. Simulated meter-scale FBI in the troughs and crests of kilometer-scale GDI matches radar observations of the daytime equatorial ionosphere, answers a question about electric-field saturation raised by rocket observations in the 1980s, and predicts an anomalous cross-field conductivity important to magnetosphere-ionosphere (M-I) coupling. The sixth chapter of this dissertation presents 3-D simulations of the FBI at a range of altitudes and driving electric fields appropriate to the auroral ionosphere, where it plays a role in M-I coupling. Research has thoroughly established the linear theory of FBI but rigorous analysis of radar measurements requires an understanding of the turbulent stage. These simulations explain the change in instability flow direction with altitude, with regard to the direction of background plasma flow.

Research over the years has established that the Gradient Drift Instability process causes small-scale irregularities, mostly along the edges of the high-latitude polar cap patches. Studying these irregularities will help in the development of a global Scale Ionospheric model, which is a central part of a global space weather forecast system. Much theoretical work has been done with varying degrees of complexity to study this instability in the high latitude patches. In this work we have used the Utah State University Time Dependent Ionospheric Model to model the high-latitude patches, calculate the growth rate of the instability, and perform a macro-scale study of the phenomenon. This is the first time that real ionospheric values have been used to calculate the growth rate and to provide two-dimensional maps identifying Gradient Drift Instability-caused irregularity regions in the polar cap. Our research shows that regions of intense instability occur along the edges of the tongue of ionization and its throat regions with strong rates along the borders of the cusp region.