We reconsider the derivation of semianalytical expressions providing the most significant aspects of the high-gain free-electron laser dynamics. We obtain new expressions for the growth of the laser power, of the e-beam-induced energy spread, and of the higher-order nonlinearly generated harmonics. The procedure we employ, based on theoretical ansatz and fitting methods, allows the determination of crucial quantities like the expected harmonic output power and its dependences on the e-beam parameters.

Nonlinear harmonic generation in high-gain free-electron lasers

We consider an undulator scheme to enhance harmonic generation in high gain free electron lasers. The configuration we consider consists of an undulator providing an on axis field oscillating in both transverse directions, with relatively integer multiple spatial periods. We discuss the spectral properties of the radiation emitted by relativistic electrons crossing this undulator and derive the equations describing the free electron laser evolution. We show that a device, exploiting such an undulator configuration, is a fairly useful tool to obtain simultaneous laser power at different harmonics. The analysis of the system evolution is achieved with two different simulation codes.

Two harmonic undulators and harmonic generation in high gain free electron lasers

On a fractional generalization of the free electron laser equation

This paper investigates the focusing properties of linear magnetic undulators, i.e., devices characterized by weak defocusing properties in the horizontal (wiggling) plane and strongly focusing in the vertical plane. The problem of identifying the conditions that ensure the existence of the electron beam eigenstates in the undulator lattice for a given working point of electron beam energy Eb and resonant wavelengthr is studied. For any given undulator lattice, a bandlike structure is identified defining regions in the ðEb ;� rÞ plane where no periodic matching condition can be found, i.e., it is not possible to transport the electron beam so that optical functions are periodic at lattice boundaries. Some specific cases are discussed for the SPARC FEL undulator. I. INTRODUCTION Pure permanent magnet (PPM) undulators are imple- mented in single pass free-electron lasers (FEL) as inser- tion devices featuring a magnetostatic periodic (sinusoidal) field in the longitudinal (z) direction. The transverse magnetic field ensures coupling between the transverse wiggling motion of electrons and the transverse field of the amplified optical wave. The FEL power gain length, i.e., the exponential growth folding length, is Lg ¼ � u=ð4�� ffiffiffi p Þ, where � u is the undulator period andis the Pierce parameter (1-3), proportional to the cubic root of the current density. An FEL amplifier operating in self- amplified spontaneous emission has a saturation length Ls � 18-20Lg. We typically have Ls ranging from few meters in long wavelength (visible to near UV) devices, up to several tens of meters, in hard x-ray FEL amplifiers. The optimization process of the FEL parameters has to take into consideration the focusing properties of the undulator and the design of the electron transport lattice over the undulator length, in order to optimize the transverse beam size and maximize the current density, reducing therefore the gain length. The transport lattice of FEL amplifiers operating with high energy beams, as typical soft to hard x-ray sources (4-7), is based on a focusing-drift- defocusing-drift (FODO) scheme, alternated to a seg- mented undulator (8). The effect of a (linear) undulator is that of introducing a small perturbation to the FODO: a weak focusing in the vertical plane and a negligible effect in the horizontal plane. At lower beam energies, i.e., for FEL amplifiers operating at longer wavelengths from vis- ible to UV, the role of the undulator focusing becomes

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Focusing properties of linear undulators

Free Electron coherent sources: From microwave to X-rays

An introduction to the theory of charged particle transport generalities on synchrotron radiation generalities on free electron lasers optical systems in the geometrical and wave optics framework Wigner distribution and synchrotron radiation sources synchrotron radistion sources, insertion devices and beam current limitations constructing and measuring insertion devices free electron lasers as insertion devices synchrotron radiation beam lines - X-ray optics.

F Ciocci

Papers

Insertion Devices for Synchrotron Radiation and Free Electron Laser

Free electron lasers as insertion devices