MODULATIONAL INSTABILITY OF THREE DIMENSIONAL WAVES IN A PLASMA WITH VORTEX ELECTRON DISTRIBUTION

In the present work, employing the three dimensional equations of a plasma composed of a cold electron fluid, hot electrons obeying a trapped /vortex-like distribution, and stationary ions, we study the amplitude modulation of an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations with fractional power type of nonlinearity, we obtained the three dimensional form of the modified nonlinear Schr¨odinger equation as the evolution equation of the same order of nonlinearity. The modulational instability of the homogeneous harmonic solution is investigated and the criteria for the instability is discussed as a function of the obliqueness angle.The numerical calculations show that the critical value of the wave number of the envelop wave increases with the wave number k of the carrier wave and the obliqueness angle γ.