Correlation function equation for the SASE FEL

In this paper, we develop a new approach to the SASE FEL theory. It is based on the well-known system of Klimontovich–Maxwell equations. The special choice of the independent variable makes it possible to eliminate both electromagnetic field and retardation. That allows us to write down the BBGKY hierarchy for the s-particle distribution functions. Due to the smallness of the higher-order correlations we consider only two equations from the beginning of this hierarchy.