Hot Quantum Electron-Ion-nonmagnetized Dusty Plasma: ion sound waves and dispersion relation.

Abstract: The dispersion equation for isothermal ionic sound waves is derived and analyzed for collisionless nonmagnetized dusty plasma consisting of quantum gases of electrons, ions, and dust at hot temperatures. and an exact expression is obtained for the linear velocity of ionic sound. Analysis has been carried out by the method of the Bernoulli pseudopotential. The quantum effects include, Fermi degenerate pressure, and exchange correlation potential. The ranges of phase velocities of periodic ionic sound waves and soliton velocities are determined. It is shown that in the plasma under investigation, the soliton velocity cannot be lower than the linear velocity of ionic sound. A graph should plotted between the frequency and wave number, three region should obtained, solutions in the form of periodic ionic sound waves should be sought precisely in the range of velocities The profiles of physical quantities in a periodic wave and in a soliton are constructed, as well as the dependences of the velocity of sound and the critical velocity on the ionic concentration in the plasma. It is shown that these velocities increase with the ion concentration and the term of dusty plasma as well as term of hot quantum electron and ion may effect on the dispersion relation. The application of this work has been pointed out for laboratory as well as for space dusty plasmas.