Numerical solution of the FEL correlation function equation

The equation for two-particle correlation function in FEL was derived recently to provide a new way of noise calculations in SASE FELs [O.A. Shevchenko, N.A. Vinokurov, Nucl. Instr. and Meth. A 507 (2003) 84]. In this paper, this equation is solved numerically for the simplest case of narrow electron beam. Time-independent solution with saturation is obtained. It is compared with the results of quasilinear theory and results of previous SASE linewidth estimates.