Beam Asymmetry, Divergence and Energy Spread Effects on the Radiation from Planar Undulators

Abstract

The theoretical study of the effect of electron beam parameters, in particular, the emittance and its asymmetry on the radiation from relativistic electrons in undulators is conducted both analytically and numerically. The reasons for the odd and even harmonic generation and radiation are explored. The difference in the underlying physical reasons for the spontaneous and stimulated radiation of harmonics in free electron lasers (FELs) is elucidated. The generalized forms of the special functions of the Bessel and Airy type are employed to account analytically for the off-axis and angular effects together with the effect of the beam energy spread. A comparative analysis of the radiation spectra for undulators with different beams is performed. The examples of the radiation at SPARC and LEUTL are given. The effect of the asymmetry of the beam on the radiation properties is analyzed. The alternative theoretical approaches of other authors are also employed for the analytical calculation of the harmonic powers in FELs. The results are compared with existing experimental data.

Correction of the Mathematical Method for Studying a Cathode Lens with Two Planes of Symmetry

“…Currently, charged particle beams are widely used in many high-tech analytical devices and scientific and technological systems [13][14][15][16]; therefore, solving theoretical problems that have not yet been considered for the study of properties and design of various modified cathode lens circuits with improved focusing characteristics is an important task.…”