Density distribution for a weakly non-ideal non-uniform plasma

An attempt is made to develop an equilibrium kinetic equation for a weakly non-ideal non-uniform plasma utilizing the Bogoliubov-Born-Green-Kirkwood Yvon hierarchy of equations. The time-independent pair correlation function is shown to be a product of two single-particle non-uniform distribution functions and the binary interaction potential that is taken to be Coulombian. In order to obtain a closed form of kinetic equation, it is necessary to express the first-order corrections to the Vlasov equation arising out of correlations in terms of average plasma potential. The singular nature of the Coulomb potential gives rise to certain divergences that can be removed by the choice of Landau and Debye lengths as the lower and upper limits of the impact parameter. This procedure enables a representation of pairwise interaction potential in terms of average macroscopic potential. The first-order kinetic equation is utilized to obtain a modified Boltzmann distribution that includes the effects of correlations.