On the Existence of Hypersonic Electrostatic Solitons (Estimation of Limiting Mach Numbers of Ion-Sound Solitons in a Warm Plasma)

We develop a nonlinear theory of ion-sound waves in a collisionless warm electron–ion plasma. The theory is based on analysis of the Sagdeev pseudopotential. We consider two (isothermal and adiabatic) models of ion-sound waves. We calculate the dependences of the maximal Mach number for solitons on reduced temperature (nonequilibrium parameter) of the plasma in both models. It is shown that the maximal value of the Mach number cannot exceed the fundamental limit (2.54). We have answered the question concerning the existence of hypersonic ion-sound solitons: hypersonic solitons do not exist.