The startup from noise problem in SASE FELs is usually treated in linear approximation. In this case amplification of initial density fluctuations may be calculated, and averaging over initial conditions may be fulfilled explicitly. In general nonlinear case the direct averaging is not applicable. During last years we developed the approach based on the BBGKY hierarchy for the n-particle distribution functions. The interaction of particles in FEL is retarded. Nevertheless, using special time-coordinate transformation, it is possible to eliminate the interaction lag and then to write down the BBGKY equations. Similar to plasma physics, the equations may be truncated after the second one (for the two-particle correlation function). Using this approach we consider several particular cases which illustrate some peculiar features of the SASE FEL operation
Multiplicity Dependence of Two-particle Correlation in $pp$ and $p$Pb at the LHCb