Theory of a double-undulator free-electron laser

In this paper, we present a general theory of the double-undulator free-electron laser, in which an additional undulator with period close to the beam electron betatron oscillation period in the main undulator is introduced. A set of self-consistent equations is developed to describe the evolution of the optical wave in this device. The basic nonlinear equations are analyzed in the low-gain regime, the high-gain regime, and the saturation regime, respectively. By properly selecting parameters of the additional undulator, we may enhance the gain or efficiency of the free-electron laser.