Abstract
After a short presentation of the general theory of irreversible processes established by Prigogine and Balescu, we discuss in some detail its application to the problem of long range forces in a plasma. Our diagram technique permits an unambiguous choice of the main contributions to the distribution function. The result is an equation describing the evolution of the distribution function of momenta, which takes rigorously into account the many-body collisions. The latter results from a summation of an infinite number of diagrams, the structure of which is very simple. The successive diagrams involve more and more particles interacting simultaneously. The equation has a formal similarity with the usual Fokker-Planck equation, but the Coulomb interaction between two particles is replaced by an effective interaction, which depends on the distribution of all the other particles of the medium. At very low temperatures this effective interaction reduces to a screened Coulomb-Debye potential. The relation of our approach to the previous theories of plasmas (Fokker-Planck equation, Vlasov equation, random phase approximation) can be discussed very clearly by means of the diagrams.
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