The Effect of Wiggler Imperfections on Nonlinear Harmonic Generation in Free-Electron Lasers

The generation of harmonics through a nonlinear mechanism driven by bunching at the fundamental has sparked interest in using this process as a path toward an X-ray free-electron laser (FEL). An important issue in this regard is the sensitivity of the nonlinear harmonic generation to wiggler imperfections. Typically, linear instabilities in FELs are characterized by increasing sensitivity to both electron beam and wiggler quality with increasing harmonic number. However, since the nonlinear harmonic generation mechanism is driven by the growth of the fundamental, the sensitivity of the nonlinear harmonic mechanism is not severely greater than that of the fundamental. In this paper, we study the effects of wiggler imperfections on the nonlinear harmonics in a 1.5-Å FEL, and show that the decline in the third harmonic emission with increasing levels of wiggler imperfections roughly tracks that of the fundamental.