A non-ideal dusty plasma is considered, consisting of a mixture of three gases: inertia less electrons and ions, and a gas of negatively charged granules. Electrons and ions in the plasma are assumed to obey the Boltzmann distribution, while the granular gas follows the equation of state of a non-ideal gas proposed by C. Dieterici. For the first time, stationary granular-acoustic waves (GAWs) in such a plasma are investigated within the framework of a gasdynamic approach. A linear theory of GAWs is developed, from which the dispersion relation is derived and an exact expression for the linear speed of granular sound is obtained. Furthermore, a nonlinear theory of large-amplitude GAWs in a non-ideal granular plasma is developed for the first time, based on the Bernoulli pseudopotential method. Analysis of the pseudopotential shows that stationary GAWs in the considered plasma can take the form either of nonlinear periodic waves or of granular-acoustic (GA)-solitons. The corresponding ranges of wave velocities for both forms are determined. The dependences of the maximum soliton velocity and the maximum Mach number on the relative electron concentration in the plasma are calculated. It is found that, with increasing relative electron concentration, the maximum velocity of the GA-soliton increases slightly and almost linearly. The developed theory can be applied to describe GAWs arising in dense non-ideal granular plasmas occurring in volcanic ejecta of planets or in soil ejection during meteorite impacts on planetary surfaces and their satellites.
Дубинов et al. (Thu,) studied this question.