Effects of Relativistic Maxwellian Distribution on the Dust Grain Electrical Potential

The effects of relativistic on the dust charging process and the dust electrical potential are investigated by taking into account the cross section of relativistic by the OLM theory (Orbit Limited Motion) theory, a kinetic model and the relativistic Maxwellian distribution function for currents carried by ions and electrons. The calculations are applied by the numerical analyses to finding the electrical potential of dust grain in the charging process. It is shown that the electrical potential of dust grain is increased in the relativistic regime, and the slope of the transition region to zero is much more severe than the non-relativistic state and also, the possible values for dust density are shifted to the larger amounts. The comparison of the results of the relativistic and nonrelativistic Maxwellian distribution functions shows in the low dust to ion density ratio, only the relativistic Maxwell distribution function can indicate the dust charging process. As another result the increase of the dust density shows the collective behavior, because of the dust grains behavior as a component from conventional multi-ionic plasma. In addition to, it is indicated that the role of mass is more colorful than the ion temperature in the light plasma such as hydrogen versa the heavy plasma such as oxygen in relativistic regime. Moreover, it is showed that, as ions are closer to the ultra-relativistic range, the dust grain electrical potential is increased and the difference between the dust grain electrical potential in oxygen, helium and hydrogen plasmas become more and more