Title: Characteristics of FEL-generated THz waves using linear and helical undulators

Abstract: Emission of terahertz waves in free electron lasers (FELs) with both linear and helical undulators has been explored. The analysis employs Lienard-Wiechert fields to characterize FEL radiation within the THz region. Specifically, the study delves into the analytical examination of radiation pattern of THz waves, which provides insight into the angular distribution of radiation energy. The variations of radiation pattern for various parameters such as different harmonics, Lorentz factor, magnetic parameter, and total number of periods of linear and helical undulators were investigated. The Fourier transform of free electron laser electric field is showcased across four distinct sets of FEL parameters. The interplay between electron beam and undulators parameters sheds light on how these factors influence the directionality of THz waves. Simulation results indicate that linear undulators often produce radiation with noticeable side lobes, especially at higher harmonics, while helical undulators typically exhibit reduced side lobes, resulting in a more focused main radiation peak. However, the radiation pattern of THz waves tends to concentrate predominantly in the forward direction and the polarization of the emitted radiation is determined by the properties of the undulator and electron beam, rather than the specific undulator geometry. The study underscores that an optimal selection of undulator and beam parameters can effectively maximize the angular distribution of emitted radiation.