Accepted articles

Instruments and methods of investigation

Undulator and FEL radiation with analytical account for the field harmonics and off-axis effects

Lomonosov Moscow State University, Department of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation

Analytical description of the generation of the undulator radiation (UR) harmonics in a generalized elliptic undulator is given with account for the magnetic field harmonics. We obtained exact expressions for the spectrum density and radiation intensity in terms of the generalized Bessel and Airy functions. They describe the elliptic undulator with different orthogonal field harmonics and reduce to the known cases of planar and helical undulator with field harmonics. The beam size, emittance, position, energy spread, external magnetic components are accounted for analytically. The obtained expressions distinguish the contributions of field components, beam and undulator parameters on the radiated UR harmonics. Using the analytical description of free electron laser (FEL) power evolution, we model and analyze the harmonic radiation in the LCLS, LEUTL and SACLA FEL experiments. The presence of the strong second FEL harmonic is explained: it is shown that it can be caused by the detected beam deviation off the undulator axis in ~15 μm on one gain length 1.5 m in the LCLS FEL; in the LEUTL FEL the second harmonic arises due to the wide beams, whose size is ~200 μm. The modelling results agree with the experiments; this confirms the validity of the presented theory for the FEL power evolution and spectral density.

Keywords: undulator, magnetic field, free electron laser, harmonic generation
PACS: 41.60.m, 41.60.Ap, 41.60.Cr (all)
DOI: 10.3367/UFNe.2020.06.038803
Citation: Zhukovsky K V "Undulator and FEL radiation with analytical account for the field harmonics and off-axis effects" Phys. Usp., accepted

Received: 26th, December 2019, revised: 2nd, April 2020, 29th, June 2020

Оригинал: Жуковский К В «Излучение ондуляторов и ЛСЭ с аналитическим учетом гармоник поля и внеосевых эффектов» УФН, принята к публикации; DOI: 10.3367/UFNr.2020.06.038803

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