Abstract
In the framework of irreversible thermodynamics, we study nonlinear ion-acoustic waves (IAWs) in viscous and collisional plasmas. Electrons, which form the background, are assumed to be nonthermal. On account of ion viscosity and ion-electron collisions, we investigate using ion fluid equations. We study the effects of the nonthermally distributed electrons beta and the temperature ratio sigma (= T(i)/T(c)) on the stability, where the stability for Burger's equation is analyzed by two methods: the phase portrait method and irreversible thermodynamics relations at different values of sigma and beta We usa a reductive perturbation technique, where the nonlinear evolution of an JAW is governed by the driven Burger equation. This equation is solved exactly by using two methods: the tanh-function method and the Cole-Hopf transformation. Both methods produce shock wave solutions, their results compared, and good agreement exists in most predictions. The analytical calculations show that an IAW propagates as a shock wave with subsonic speed. The flow velocity, pressure, number density, electrostatic potential, and thermodynamic characteristics are estimated and illustrated as functions of time t and the distance x. It is found via the tanh-function method that the amplitudes of the sought-for functions of the system are suppressed and move towards an equilibrium state at the highest value of beta. The tanh-function method reveals an advantage over the Cole-Hopf method in the viscous and collisional cases of IAWs, where it satisfies the stability conditions at the highest value of beta with the chosen sigma values when applied to evaluate the Onsager relation.