Time-dependent phase conjugation and four-wave mixing in plasmas

Summary form only given. Time-dependent four-wave mixing and phase-conjugation in plasmas with counterpropagating electromagnetic pump waves are treated, taking into account resonant longitudinal plasma modes which show up in a grating Green´s function. When ponderomotive force is the dominant nonlinearity, the Green´s function is simply expressed in terms of linear quasi-longitudinal susceptibilities. The main concern has been with unmagnetized inhomogeneous plasmas, although the results are formally relevant to other nonlinearities and to magnetized plasmas in simple geometries, Response times, decay times, and thresholds for resonant absolute instabilities are found analytically, and interpreted for ion-acoustic and Langmuir wave gratings. It is found that plasma nonuniformity can speed up the response of the conjugate wave when the phase-mixing time is shorter than the damping time of a resonant grating. This could be important for applications of plasma phase conjugation to tracking fast-moving targets