Effect of Fluctuation of Dust Grain Charge on Electrostatic Sheath Formation in Dusty Plasma with Tsallis Electron Distribution

The effect of dust particle charge fluctuation on the electrical potential in the plasma sheath is determined by solvation of Poisson’ equation with the help OLM theory and a Tsallis distribution for current carried by electrons, a cold ion fluid and negatively charged immobile dust grains. It is indicated that the nature of electrical potential in plasma sheath dependent to the Sagdeev potential and the properties of electrostatic sheath strongly affected by fluctuations of dust grain charge that modified the Bohm criterion condition. For the first time, by solving the Sagdeev potential, a function is obtained which shows that when this function becomes negative, the ions accelerate into the region of the sheath and form an electrostatic sheath. This nonlinear function is heavily dependent on nonextensive degree of electron, the ion density ratio to electron and kind of plasma gases. It is showed that the farther we go from the Maxwell equilibrium distribution function, the ions need a higher initial velocity to be able to separate from the main body of the plasma and move towards the plasma sheath and the wall. Finally, the results are indicated that considering the dust particle charge fluctuations and the electron nonextensivity degree play an important role on electrostatic sheath formation and modify Bohm criterion.