FEL gain in the pulsed regime: a comparison between numerical and analytical results

In this paper we present simple and general formulae for the FEL gain in the pulsed regime including both the longitudinal mode coupling and the lethargy effect. Such relations, obtained from a numerical integration of the pulse propagation equations, are then compared to similar expressions obtained analitycally in the limiting case of the long bunch approximation and the agreement is shown to be excellent.