Abstract:
Problem of evaluating the equlibrium distribution functions $\mathscr G_{\alpha,\dots ,\gamma}$ of systems of charged particles (plasma, soluted and melted electrolytes etc) is formulated in the most general form. Substitution of the energy values obtained from the electrostatics
into the transformed Bogoliubov equations (s. the previous article by the author) leads
to the exact closed system of equations for the unary $\mathscr G_{\alpha}$ and $\mathscr G_{\alpha\beta}$ distribution
functions. Besides the physical solutions, the system also possesses the solutions decreasing
too slowly at the infinity. In order to remove such solutions, the general and
local neutrality conditions are necessary, and after imposing these conditions, all the
divergent terms are removed. The system obtained splits out into the electrostatics
equations, by means of which charge densities are determined from $\mathscr G_{\alpha}$ and $\mathscr G_{\alpha\beta}$
statistics equations expressing the conditions that the electro-chemical potentials of the
groups of one and two particles are constant, $\mu_{(p)}$=const, $p=1, 2$. The solution of the
equations obtained should be constructed in such a way that all the neutrality conditions
were satisfied exactly in every approximation order. The methods of constructing the
solutions by means of the expansion over the small parameter powers and by means of
the successive approximations are formulated. In both cases divergences do not arise
in the evaluations of leading terms.