Stability and bifurcation analysis of low‐frequency electrostatic waves in warm negative ion plasmas

Abstract

In this paper, we perform stability and bifurcation analysis of ion-acoustic waves in a plasma consisting of warm adiabatic positive and negative ions, evolving against a uniform background of isothermal electrons. The model consists of two nonlinear ordinary differential equations incorporating ion temperature, negative ion concentration and negative-to-positive ion mass. We derive the normal form of bifurcation which allows the determination of travelling wave solutions for various regions in the parameter space of warm negative ion plasmas. It is shown that negative/positive ion temperature broadens the region prior to the saddle-node bifurcation, thereby allowing the propagation of solitary and supernonlinear periodic waves. For a range of ion mass ratio and ion temperature, we find different existence domains of stability region, and examine the occurrence of transcritical bifurcation as a function of various plasma parameters.Further, we perform a numerical phase portrait analysis of the complex system including homoclinic orbits, nonlinear periodic and super nonlinear periodic orbits. The effects of ion mass ratio and ion temperature on the characteristic of these nonlinear structures are discussed in detail. Our results are relevant to wave solutions in laboratory and space plasmas, where simultaneous presence of warm negative/positive ions are observed.

Normal form for bifurcations of ion acoustic traveling waves in positive-negative ion species plasmas

“…They investigated different kinds of cyclic firing diagram from saddle-node bifurcations. Recently, we have studied the properties of nonlinear electrostatic disturbances in dusty plasmas [59] and multi-ion plasmas [60,61], through the phase portrait analysis and bifurcation analysis. We showed that the concentration of plasma particles and ions temperature play a crucial role in the propagation of different kinds of nonlinear waves and transition between different modes.…”