On the possibilities of amplification and radiation of harmonics in modern X-ray free electron lasers

Abstract

X-ray free electron lasers (FELs) produce ultra short bursts of coherent radiation at the wavelengths ∼1–100 Å. In the absence of ready seed in this range, the fundamental tone is usually radiated in self-amplified spontaneous emission (SASE) FELs. During the last decade, the quality of modern FELs has improved in all aspects, and this offers possibility to use the harmonic radiation more effectively. With the goal to achieve maximum performance in minimum size and cost of a FEL, we study the harmonic multiplication in resonating undulator cascades as viable alternative to the SASE fundamental radiation. The harmonic power evolution along FELs is analyzed for the SASE and the harmonic self-seed. The analytical results are compared with available data for soft X-rays FLASH2. The possibility of harmonic radiation is studied for FELs with variable deflection parameter k: FLASH2, European FEL, SACLA, SwissFEL and currently built LCLS-II. We demonstrate earlier growth of the harmonic power in a buncher as compared with the SASE regime at the same wavelength. The difference is explained theoretically by the bunching. We find it impossible to use harmonics at the SACLA due to high initial energy spread. Excellent characteristics of the SwissFEL allow amplification of the third FEL harmonic. We propose the harmonic self-seed for it, which would allow 10 m shorter undulator length for saturation at the same power, and up to 30% shorter radiation wavelength with the existing electron beam. The amplification of the third harmonic is possible also at the European FEL; theoretical calculations show for it ∼10 m shorter saturation length, while the saturated power does not change. At the LCLS-II, good bunching at the third harmonic wavelength can be achieved in a dedicated buncher with minimal gap of the undulators. However, further amplification and radiation of the third harmonic in the undulators with small parameter k appear less efficient than its direct amplification in the FEL, where the bunching of the fundamental is disrupted between the undulator cascades.