Abstract
A theoretical study of the synchrotron radiation (SR) from electrons in periodic magnetic fields with non-periodic magnetic components is presented. It is applied to several free electron lasers (FELs) accounting for the real characteristics of their electron beams: finite sizes, energy spread, divergence etc. All the losses and off-axis effects are accounted analytically. Exact expressions for the harmonic radiation in multiperiodic magnetic fields with non-periodic components and off-axis effects are given in terms of the generalized Bessel and Airy-type functions. Their analytical forms clearly distinguish all contributions in each polarization of the undulator radiation (UR). The application to FELs is demonstrated with the help of the analytical model for FEL harmonic power evolution, which accounts for all major losses and has been verified with the results of well documented FEL experiments. The analysis of the off-axis effects for the odd and even harmonics is performed for SPRING8 Angstrom Compact free-electron LAser (SACLA) and Pohang Accelerator Laboratory (PAL-XFEL). The modelling describes theoretically the power levels of odd and even harmonics and the spectral line width and shape. The obtained theoretical results agree well with the available data for FEL experiments; where no data exist, we predict and explain the FEL radiation properties. The proposed theoretical approach is applicable to practically any FEL.
Highlights
The first theoretical results for the radiation of a charge on a circular orbit were obtained by Lienard in the end of the 19th century
We have presented analytical formulation of the harmonic generation in free electron lasers (FELs) with multiperiodic magnetic the harmonic and constant components and off-axis effectswith in
We fields have accounting presented for analytical formulation of thefield harmonic generation in FELs undulators
Summary
The first theoretical results for the radiation of a charge on a circular orbit were obtained by Lienard in the end of the 19th century. Interest in theoretical studies of the synchrotron radiation in the 21st century is determined in great part by applications to FELs. Modeling of a FEL is usually done by numerical algorithms, which solve complex system of equations for electrons and radiation and describe the evolution of the electron beam and photon pulse. Coupled with the phenomenological FEL model, whose latest version is given in the Appendix A, we get the analytical description of the harmonic power evolution in FELs. Applications to a number of FEL experiments at SPRING8 Angstrom Compact free-electron LAser (SACLA) and Pohang Accelerator Laboratory X-ray Free electron Laser (PAL-XFEL) are provided and discussed in the context of other facilities, such as at Linac Coherent Light Source (LCLS) etc
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