Congruent reduction in parametrically unstable space- and time-varying plasmas

A recently developed congruent reduction technique is applied to the parametric amplification problem in space- and time-varying plasmas. The systematic reduction procedure yields a second-order system of partial differential equations describing mode coupling in the presence of a strong pump wave. This system is similar in form to that characterizing the general multidimensional mode conversion problem so that the solution in both cases proceeds similarly. The method allows a consistent derivation of the expression for the parametric amplification coefficient in general geometry. An unmagnetized plasma case is considered as an example.