Enhanced harmonic generation in x-ray free-electron lasers

Harmonic generation becomes increasingly important as x-ray free-electron lasers push to shorter wavelengths. Recent studies have pointed to the possibility of enhancing harmonic generation by detuning the fundamental. In x-ray free-electron lasers, the wiggler line is composed of multiple wiggler segments with magnetic quadrupoles in the gaps to provide for increased focusing. In this paper, we study the effect on harmonic generation in simulation by (1) varying the gap lengths between the wiggler segments and (2) varying the electron beam β function. In studying the harmonic we find enhanced harmonic generation is periodic in the gap length and peaks are found as the wiggler separation varies by λ/3 (where λ is the fundamental wavelength), which corresponds to a phase shift of 2π/3. As a consequence, enhanced harmonic generation is found both when the fundamental emission is strong by the nonlinear harmonic generation mechanism and by linear harmonic generation when the fundamental is detuned