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In this paper, we consider a clockwise rotating magnetic field around the $z$-axis and charge carriers which impinge normally to the $x-y$ plane. We obtained analytically the spectrum of the momentum operator $p_z$ and found the existence of a band structure from which the movement of these charge carries is filtered according to the spatial period of the magnetic field or its intensity. Also we exhibit the existence of three band gaps (one total or primary and two partials) whose width depends on the system parameters.

Synchrotron radiation produced either in storage rings or SASE-FELs is longitudinally incoherent. In this paper a way to produce short longitudinally coherent X-ray pulses is discussed. In addition it is investigated if these sources can be modified to use them as light sources for vacuum electron accelerators.

The physics of synchrotron radiation, undulator radiation, and free electron lasers is reviewed with an emphasis on the underlying physical principles and the experimental observables, such as the radiation spectrum, angular distribution, and radiation polarization.

This article reviews some fundamental concepts and presents several recent techniques used for calculation of radiation in various environments. They include properties of longitudinal and transverse formation lengths of radiation, usage of the parabolic equation and the Kirchhoff diffraction integral in radiation, coherent radiation and fluctuations in the beam, and the radiative reaction force resulting from coherent radiation.

The physics of synchrotron radiation, undulator radiation, and free electron lasers is reviewed with an emphasis on the underlying physical principles and the experimental observables, such as the radiation spectrum, angular distribution, and radiation polarization.

Japan constructed the first ‘compact’ X-ray free-electron laser (XFEL), and started user operation in 2012. This chapter describes the historical development of the compact XFEL concept, the underlying physical principles of XFEL, the details of the accelerator system, the details of the photon beam line, and the scientific applications, followed by a brief comment on the future trend of the XFEL facilities.

The CUP experiment is a first important step of a more ambitious project that investigates the possibility to create new powerful sources of high-frequency monochromatic electromagnetic radiation: crystal undulator and γ-laser based on channeling of positrons in crystals. Moreover, within the CUP project we are going to design a new experimental facility based on positron source. In this work the main goal of the CUP experiment and the first measurements at the DAΦNE BTF facility will be presented.

This article reviews some fundamental concepts and presents several recent techniques used for calculation of radiation in various environments. They include properties of longitudinal and transverse formation lengths of radiation, usage of the parabolic equation and the Kirchhoff diffraction integral in radiation, coherent radiation and fluctuations in the beam, and the radiative reaction force resulting from coherent radiation.