Effects of bunch density gradient in high-gain free-electron lasers

We investigate effects of the bunch density gradient in self-amplified spontaneous emission, including the role of coherent spontaneous emission (CSE) in the evolution of the free-electron laser process. In the exponential gain regime, we solve the coupled Maxwell–Vlasov equations and extend the linear theory to a bunched beam with energy spread. A time-dependent, nonlinear simulation algorithm is used to study the CSE effect and the nonlinear evolution of the radiation pulse.