NON-LINEAR EVOLUTION OF A 3 DIMENSIONAL LONGITUDINAL PLASMA WAVEPACKET IN A HOT PLASMA INCLUDING THE EFFECT OF ITS INTERACTION WITH AN ION-ACOUSTIC-WAVE

Assuming amplitudes as slowly varying functions of space and time and using perturbation method three coupled nonlinear partial differential equations are obtained for the nonlinear evolution of a three dimensional longitudinal plasma wave packet in a hot plasma including the effect of its interaction with a long wavelength ion-acoustic wave. These equations are used to derive the instability conditions of a uniform longitudinal plasma wave train including the effect of its interaction, both at resonance and nonresonance, with a long wavelength ion-acoustic wave. At resonance, the threshold amplitude of the longitudinal plasma wave for the onset of instability is determined. At nonresonance, the plasma wave may become modulationally unstable if mod Vglx mod < omega L and if the difference mod omega L-V glx mod is sufficiently small, where l is the wavenumber of perturbation and omega L is the frequency of the ion-acoustic wave having a wave-vector l. This effect vanishes completely when the ion motions are disregarded. Assuming the usual particular type of dependence of amplitudes on space and time the coupled equations are transformed into three other coupled equations which reduce to a single nonlinear Schrodinger equation when three dimensionality is disregarded.