Analysis of the Influence of Nonperiodic Magnetic Fields and Off-Axis Effects on the Radiation of X-Ray FEL and Other FE
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RETICAL AND MATHEMATICAL PHYSICS
Analysis of the Influence of Nonperiodic Magnetic Fields and Off-Axis Effects on the Radiation of X-Ray FEL and Other FELs K. V. Zhukovsky* Department of Physics, Moscow State University, Moscow, 119991 Russia Received April 16, 2020; revised May 14, 2020; accepted May 16, 2020
Abstract—Undulator radiation (UR) in an undulator with field harmonics in two orthogonal planes is theoretically studied taking nonperiodic magnetic components and off-axis effects into account. New analytical expressions for the UR spectrum and UR intensity are written explicitly in terms of the generalized Bessel function and Airy function. In limiting cases, they describe the radiation of a twofrequency planar undulator, a helical undulator, and an elliptical undulator. The influence of the finite size of the electron beam, the emittance, electron beam deflection from the axis, the spread of the electron energy, and the influence of the constant components of the magnetic field are taken into account analytically. The expressions make it possible to distinguish the contributions of each field component and characteristics of the beam and undulator to the generation of UR harmonics. The phenomenological FEL model is used to study the evolution of harmonic power in the FEL experiments of LCLS and LEUTL. The influence of the beam parameters and undulator parameters on the harmonic generation is analyzed. The theoretical results of the power and radiation spectrum of the FEL are in agreement with experiments. It is shown that the second harmonic in the X-ray FEL of LCLS can be due to the beam deflection from the axis by ∼12 μm, and the second harmonic in the UV-A FEL of LEUTL is due to wide (∼0.2 mm) beams of electrons and photons. Keywords: undulator, harmonic generation, magnetic field, free-electron laser. DOI: 10.3103/S002713492004013X
INTRODUCTION The latest generation sources of synchrotron radiation are free-electron lasers (FELs), in which coherent radiation is generated by electrons grouped in microbunches at a distance of the radiation wavelength from each other. They make it possible to obtain X-ray coherent radiation for studying processes in the nanoscale. This requires a high quality of the undulators and the beams, a small energy spread and beam deflection from the axis, which lead to broadening of the undulator radiation (UR) line and deterioration of electron bunching [1–5]. The field harmonics are usually in real devices, and an ideal sinusoidal field is not obtained, since it does not satisfy Maxwell’s equations. Although only odd harmonics are radiated on the axis in an ideal planar undulator, and only the pitch is radiated in a helical undulator; even harmonics are also radiated in the spectrum of real devices. The power of the harmonics varies greatly depending on the installation (for example, see [6– 10]). FELs are usually simulated numerically (see, *
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for example, [11]). This requires computing power, software, and trained personnel. Numerical simulation usually gives
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