The sensitivity of nonlinear harmonic generation to electron beam quality in free electron lasers

The generation of harmonics through a nonlinear mechanism driven by bunching at the fundamental has sparked interest as a path toward enhancing and extending the usefulness of an X-ray free-electron laser (FEL) facility. The sensitivity of the nonlinear harmonic generation to undulator imperfections, electron beam energy spread, peak current, and emittance is important in an evaluation of the process. Typically, linear instabilities in FELs are characterized by increased sensitivity to both electron beam and undulator 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 expected to be significantly greater than that of the fundamental. In this paper, we study the effects of electron beam quality, more specifically, emittance, energy spread, and peak current, on the nonlinear harmonics in a 1.5 Å FEL, and show that the decline in the harmonic emission roughly follows that of the fundamental.