How the bounded geometry affects the wave instability in a plasma

Abstract

In order to understand how the bounded geometry affects the ion-acoustic wave, present paper chooses a plasma bounded in a cuboid. A modified nonlinear Schrödinger equation is obtained by using the reductive perturbation method. It is found that the amplitude, frequency, phase velocity and the initial phase of the linear ion-acoustic wave may be changed by the bounded geometry. It is also found that the bounded geometry can suppress the modulational instability. Localized nonlinear waves such as the bright envelope solitary waves and the rogue waves may exist in the bounded plasma. It is found that the amplitudes of nonlinear waves decay exponentially with the time. The smaller the width of the cuboid, or the larger the viscosity coefficient of the plasma, the stronger the decrease of the wave amplitudes in the bounded plasma. Our results may have potential applications in the inertial confinement fusion and the charged particle accelerator.