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

Abstract

The normal form for saddle-node and transcritical bifurcation of nonlinear ion-acoustic waves is derived in complex negative-positive plasmas. The physical parameters of four different kinds of multi-ion plasmas which mainly comprise of positive ions (i.e. Xe+ and Ar+) with a minority constituent of negative ions (i.e. and F −), inspired from the experimental studies, are examined on the types of bifurcations and nonlinear wave profiles. We find that such multi-ion plasmas admit transcritical bifurcation preceding the onset of saddle-node bifurcation. The fractional concentration of negative ions controls the dynamics of ion acoustic traveling waves and causes the appearance of solitary structures and supernonlinear periodic waves. When two nonlinear waves disappear via a saddle-node bifurcation on increasing the negative ion concentration, a nonlinear periodic wave is formed. Further, we reveal critical values of ion density marking the transition between nonlinear modes. Such critical points that can be detected analytically give rise to the propagation of new solitary structures. The results obtained here not only limited to laboratory plasmas, but can also be applied to explain wave excitations in space plasma environments.