Harmonic lasing in X-ray FELs

TL;DR

Harmonic lasing in X-ray FELs offers a promising, efficient way to extend wavelength ranges with more stable, narrow-band beams, and can be implemented in existing facilities like LCLS and European XFEL to enhance performance.

Contribution

This paper provides a detailed parametrization of harmonic lasing solutions, explicit gain length expressions, and methods for suppressing the fundamental harmonic, demonstrating practical feasibility and advantages.

Findings

3rd harmonic lasing is robust and widely applicable.

Harmonic lasing can extend FEL energy range up to 100 keV.

Harmonics can grow faster than the fundamental in certain parameter ranges.

Abstract

Harmonic lasing in a free electron laser with a planar undulator (under the condition that the fundamental frequency is suppressed) might be a cheap and efficient way of extension of wavelength ranges of existing and planned X-ray FEL facilities. Contrary to nonlinear harmonic generation, harmonic lasing can provide much more intense, stable, and narrow-band FEL beam which is easier to handle due to the suppressed fundamental frequency. In this paper we perform a parametrization of the solution of the eigenvalue equation for lasing at odd harmonics, and present an explicit expression for FEL gain length, taking into account all essential effects. We propose and discuss methods for suppression of the fundamental harmonic. We also suggest a combined use of harmonic lasing and lasing at the retuned fundamental wavelength in order to reduce bandwidth and to increase brilliance of X-ray beam at saturation. Considering 3rd harmonic lasing as a practical example, we come to the conclusion that it is much more robust than usually thought, and can be widely used in the existing or planned X-ray FEL facilities. In particular, LCLS after a minor modification can lase to saturation at the 3rd harmonic up to the photon energy of 25-30 keV providing multi-gigawatt power level and narrow bandwidth. As for the European XFEL, harmonic lasing would allow to extend operating range (ultimately up to 100 keV), to reduce FEL bandwidth and to increase brilliance, to enable two-color operation for pump-probe experiments, and to provide more flexible operation at different electron energies. Finally, in this paper we discover that in a part of the parameter space, corresponding to the operating range of soft X-ray beamlines of X-ray FEL facilities (like SASE3 beamline of the European XFEL), harmonics can grow faster than the fundamental wavelength.