We investigate effects of the bunch density gradient in self-amplified spon
taneous emission, including the role of coherent spontaneous emission (CSE)
in the evolution of the free-electron laser process. In the exponential ga
in regime, we solve the coupled Maxwell-Vlasov equations and extend the lin
ear theory to a bunched beam with energy spread. A time-dependent, nonlinea
r simulation algorithm is used to study the CSE effect and the nonlinear ev
olution of the radiation pulse. Published by Elsevier Science B.V.