Temporal Evolution of a Three-Wave Parametric Instability

Abstract

We solve exactly the temporal evolution and spatial dependence of a three-wave parametric instability in an inhomogeneous plasma. An initial fluctuation develops into a pulse and grows initially with the same growth rate as it would in a homogeneous plasma. Growth continues until convection saturation occurs. The pulse broadens as it grows and eventually assumes the form of a totally amplified region flanked by two shock fronts. Effects of damping are also discussed.