This study is a theoretical investigation of the self-focusing instability driven by high power radio waves in the ionosphere. Self focusing results from localized changes in ionospheric properties produced when a high power radio wave at certain frequencies is transmitted into the ionosphere. Self focusing describes the tendency for the radio waves to be focused by the resulting spatial variations. The goal of the study is to understand the role of non-ideal effects present in the experimental configuration. These include density inhomogeneities, finite pump size, plasma flow, and the irregular speckle patter of the beam intensity. Analytical and numerical techniques will be used to study the nonlinear evolution of the self-focusing instability in the presence of coherent structures or random inhomogeneities in two and three dimensions. The computational results will be compared with available experimental data and will be used to plan future ionospheric modification experiments. The results will improve our fundamental understanding of a basic physical process that occurs when high power radiowaves propagate through collisional or collisionless plasmas.
