Starting from a combination of Maxwell's laws for the electromagnetic field and the conservation. equations for a fully ionized plasma, the appropriate equations describing electrodynamic laser propagation and plasma dynamic particle motion are developed and solved. Calculations for multiply ionized transient conditions are carried out to yield electric field amplitudes, radial electron number density distributions and the progress of formation of a self-focused beam filament as a function of the target plasma density distribution and the laser pulse power-time history, among other parameters. Separate solutions emphasizing field-induced plasma motion on the one hand and significant beam contraction on the other are illustrated.