A Retarded Time Superposi Ion Principle and the Relativistic Collision Opera

A retarded time superposition principle is formulated and proved for two-particle correlation function in a multispecies relativistic, and fully electromagnetic plasma. This principle is used to obtain the relativistic collision operator. Starting from the relativistic Klimontovich equation, the statistical (Liouville) average of the Klimontovich equation yields an expression for the collision operator in terms of the two-time two-point correlation function for two particles, G12 (1, ti; 2, t2). It is proved that G12(1, ti; 2, t2) can be written in a retarded time superposition form in terms of the self correlation W 1 (1, ti; 2, t2) and the discreteness response function P(1, t1 ; 2, t2). The equation for the pair correlation finction G12 (1, ti; t, t2) excluding triplet or higher order correlations, is thus replaced by the simpler equation for P(1, t1 ; 2, t 2). This is the test particle problem, which relates P(1, tj; 2, t2) to the discreteness source term Wu(1, tj; 2, t2 ). The equations for P(1, tj; 2, t2 ) and W 1 (1, tj; 2, t2) are solved for stationary, homogeneous plasmas without external fields. With these solutions, the collision operator is expressed in terms of the relativistic dielectric properties of the plasma.