relativistic kappa distribution effects on dust charging in critical areas of dusty plasma

The process of dust grain charging with the help the orbit limited motion theory (olm) and a kinetic model in the relativistic regime considers in the critical areas of the dust grain density when it is very low and vice versa. a relativistic kappa distribution for currents carried by ion and electron employs and the electrical potential of dust grain by the numerical analyses calculates by using the relativistic cross-section. in the critical area when the dust grain density is high, it shows that by increasing the electron-to-ion temperature ratio, the relativistic effects increase and the electrical potential of dust grain decreases. also, it indicates that in the critical areas, the colombian force between the dust grain and the plasma particles play an important role and has a great impact on the process of charging. moreover, it indicates when the density of dust grain is high, as the relativistic effects increased, the dust charging process increases and at low dust grain density, as the relativistic effect increases, the charge of the dusts decreases. it indicates that the electrical potential of the dust grain is much greater affected by the degree of electron nonextensive relative to the nonextensive degree of ion. finally, it indicates when the dust grain density is high; the relativistic effects due of increasing temperature play a more prominent role in the dust charging process, while at low dust grain density; the relativistic effects because of changing the energy of the rest mass play a more prominent role.