X-ray harmonic radiation in free electron lasers with variable deflection parameter of the undulators
Department of Theoretical Physics, Faculty of Physics, M.V.Lomonosov Moscow State University, 119991, Moscow, Russia
Accepted: 18 June 2021
Published online: 4 July 2021
We study theoretically the radiation from free electron lasers (FEL) with harmonics in the X-ray band. The analysis is based on the exact calculations of the Bessel coefficients for each harmonic with account for the off-axis effects in the finite sized electron beams. The radiation power evolution along the undulators of high-gain FELs is modeled with the help of analytical expressions. They allow individual study of the contributions of all each loss-factor to the radiated power of a given FEL harmonic with account for higher sensitivity to losses of the electron–photon interaction on high harmonic wavelengths. The FEL experiments with harmonic lasing self-seed (HLSS) in the undulators with variable deflection parameter k are studied, modeled, analyzed and compared with the direct SASE in the same installations. The spectrum lines of the radiation are analytically computed and compared with the measured spectral characteristics. The examples of the FEL facilities of FLASH, European XFEL, SACLA and SwissFEL are considered. The effects of the undulator period length and of the range of variation of the deflection parameter k are explored. The roles of the beam energy spread and emittance are analyzed with regard to the possibility to use HLSS and to its efficiency for the harmonic amplification. The obtained theoretical results are compared with the experiments at the considered installations. The possibilities of the harmonic use at SACLA and SwissFEL facilities are explored. The harmonic multiplication at SACLA appears problematic due to high initial spread of the electron beam; on the contrary, excellent beam properties of the SwissFEL allow the second harmonic at λ = 0.7 nm amplification from the buncher with k = 1.8. Moreover, very high quality of the beam and the installation itself and very low losses yield the saturation length under 30 m with the lowest of all X-RAY FELs current, I0 = 2.7 kA in the HLSS and at 40 m in standard SASE FEL. The advantages of HLSS vs. SASE in the FELs with variable undulator parameter k are shown for the considered installations and compared with available experimental data.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021