Effect of energetic electrons on transcritical bifurcation of low-frequency electrostatic waves in plasma

This paper studies the bifurcation types and phase portrait properties of ion-acoustic traveling waves in a plasma comprising warm adiabatic ions and energetic electrons with a nonthermal distribution function. A dynamical system is first derived for the evolution of the low-frequency wave, and then the bifurcation response is determined on the fixed points-energetic electron concentration plane. Our numerical results show that the motion dynamics of traveling waves undergo a transcritical bifurcation for a given value of energetic electrons. Both solitary and nonlinear periodic waves coalesce and switch their stability at the critical electron density value. Moreover, for higher values of the fast electrons density, a saddle-node bifurcation occurs, which leads to the propagation of periodic waves in plasma. The existence domain of bifurcation and transition between nonlinear modes are also determined for different values of ion temperature and energetic electrons density.