Harmonic Generation In Free-electron Lasers Research Articles

Comparative Theoretical Analysis of Harmonic Generation in Free-Electron Lasers with Different Electron Beam Parameters

Comparative Theoretical Analysis of Harmonic Generation in Free-Electron Lasers with Different Electron Beam Parameters

Numerical study of the second harmonic generation in FELs

A numerical study of the effect of betatron oscillations on the second harmonic generation in free-electron lasers (FELs) is presented. Analytical expressions for the effective coupling strength factors are derived that clearly distinguish all contributions in subharmonics and each polarization of the radiation. A three-dimensional time-dependent numerical FEL code that takes into account the main FEL effects and the individual contribution of each electron to the second harmonic generation is presented. Also, the X- and Y-polarizations of the second harmonic are analyzed. The second harmonic was detected in experiments at the Advanced Photon Source (APS) Low Energy Undulator Test Line (LEUTL) and Linac Coherent Light Source (LCLS) in the soft X-ray regime. The approach presented in the article can be useful for a comprehensive study and diagnostics of XFELs. In the paper, the LCLS and Pohang Accelerator Laboratory X-ray Free-Electron Laser (PAL-XFEL) experiments are modeled. The simulation results are in a good agreement with the experimental data.

Soft x-ray femtosecond coherent undulator radiation in a storage ring

We propose to produce femtosecond pulses of soft x-ray coherent undulator radiation in a storage ring for user pump–probe experiments using two energy exchanges between a picosecond relativistic electron bunch and two external ultra-short laser pulses. The coherent emission is generated thanks to the two laser–electron interactions that modulate the longitudinal charge distribution of the electron bunch at a harmonic of the laser wavelength, such as in the echo-enabled harmonic generation in free-electron lasers. Application to the SOLEIL storage ring in the soft x-ray range leads to coherent radiation and improvement of the flux of the photons by several orders in magnitude compared to the conventional slicing scheme. This is also accompanied by a significant enhancement of the signal-to-noise ratio.

Effect of undulator harmonics field on free-electron laser harmonic generation

The harmonics field effect of a planar undulator on free-electron laser (FEL) harmonic generation has been analyzed. For both the linear case and the nonlinear case, the harmonic fraction of the radiation can be characterized by the coupling coefficients. The modification of the coupling coefficients is given when the third harmonics magnetic field component exists, thus the enhancement of the harmonic radiation can be predicted. The numerical results show that with the third harmonics magnetic field component that has the opposite sign to the fundamental, the intensity of third-harmonic radiation can be increased distinctly for both the small signal gain and the nonlinear harmonic generation. The increase is larger for the smaller undulator deflecting parameter.

Free-electron laser harmonic generation in an electromagnetic-wave wiggler and ion channel guiding

A theoretical study of electron trajectories, harmonic generation, and gain in a free-electron laser (FEL) with a linearly polarized electromagnetic-wave wiggler is presented for axial injection of electron beam. The relativistic equation of motion for a single electron has been derived and solved numerically. It is found that the trajectories consist of two regimes. The stability of these regimes has been investigated. The results show that the trajectories are stable except for some parts of the regime one. The effects of interaction on the transverse velocity of the electron are a superposition of two oscillation terms, one at the wiggler frequency and the other at the betatron ion-channel frequency. A detailed analysis of the gain equation in the low-gain-per-pass limit has been employed to investigate FEL operation in higher harmonics generation. The possibility of wave amplification at both wiggler frequency and betatron ion-channel frequency for their odd harmonics has been illustrated.

Theory of nonlinear harmonic generation in free-electron lasers with helical wigglers

Coherent Harmonic Generation (CHG), and in particular Nonlinear Harmonic Generation (NHG), is of importance for both short wavelength Free-Electron Lasers (FELs), in relation with the achievement of shorter wavelengths with a fixed electron-beam energy, and high-average-power FEL resonators, in relation with destructive effects of higher harmonics radiation on mirrors. In this paper we present a treatment of NHG from helical wigglers with particular emphasis on the second harmonic. Our study is based on an analytical solution of Maxwell's equations, derived with the help of a Green's function method. In particular, we demonstrate that nonlinear harmonic generation (NHG) from helical wigglers vanishes on axis. Our conclusion is in open contrast with results in literature, which include a kinematical mistake in the description of the electron motion.

Nonlinear Harmonic Generation in Free-Electron Lasers with Helical Wigglers

It is widely believed that harmonics are suppressed in helical wigglers. However, linear harmonic generation (LHG) occurs by an azimuthal resonance that excites circularly polarized, off-axis waves, where the hth harmonic varies as exp((ihtheta). Nonlinear harmonic generation (NHG) is driven by bunching at the fundamental and has different properites from LHG. While NHG has been studied in planar wigglers, there has been no analysis of NHG in helical wigglers. The 3D simulation code medusa has been modified for this purpose, and it is shown that NHG is substantial in helical wigglers and that the even and odd harmonics have comparable intensities.

The effect of wiggler imperfections on nonlinear harmonic generation in free-electron lasers

The generation of harmonics through a nonlinear mechanism driven by bunching at the fundamental has sparked interest in using this process as a path toward an X-ray free-electron laser (FEL). An important issue in this regard is the sensitivity of the nonlinear harmonic generation to wiggler imperfections. Typically, linear instabilities in FELs are characterized by increasing sensitivity to both electron beam and wiggler quality with increasing harmonic number. However, since the nonlinear harmonic generation mechanism is driven by the growth of the fundamental, the sensitivity of the nonlinear harmonic mechanism is not severely greater than that of the fundamental. In this paper, we study the effects of wiggler imperfections on the nonlinear harmonics in a 1.5-/spl Aring/ FEL, and show that the decline in the third harmonic emission with increasing levels of wiggler imperfections roughly tracks that of the fundamental.

Nonlinear harmonic generation in free-electron lasers

A three-dimensional nonlinear simulation code to treat multiple frequencies simultaneously is described and used to study nonlinear harmonic generation in free-electron lasers (FELs). Strong nonlinear harmonic gain is found where the gain length varies inversely with the harmonic number. Substantial power levels are found in the harmonics. The odd harmonics are favored with generally higher power levels since a planar wiggler geometry is employed; however, the second harmonic exhibits substantial power as well. The analysis is relevant to the emission expected from self-amplified spontaneous emission (SASE) free-electron laser schemes.

Harmonic generation in free-electron laser with circularly polarized wiggler and ion-channel guiding

A detailed analysis of the trajectory of an electron injected axially in a free-electron laser (FEL), having a circularly polarized wiggler and ion-channel focusing, has been carried out using single particle dynamics. We show that along with transverse oscillations at the wiggler frequency, betatron oscillations due to the ion-channel field are also setup. This leads to axial oscillations in the electron motion. It is found that spontaneous emission is possible at the upshifted ion-channel betatron frequency and its odd harmonics. Further, we evaluate the gain in radiation at these frequencies with the help of the pendulum equation, in the low-gain-per-pass limit.

Storage-ring free-electron lasers and self-consistent harmonic generation

We employ a semianalytical model to study the self-consistent higher harmonic generation in free-electron lasers operating with storage rings. The model combines the rate equations, governing standard storage-ring free-electron laser dynamics, with the equations describing the evolution of the bunching coefficients. The developed technique is amenable to a straightforward numerical implementation and provided reliable results, whose correctness is proved by means of a more complete numerical procedure.

Harmonic generation in free-electron lasers.

A nonlinear formulation of the free-electron-laser amplifier with a linearly polarized wiggler magnetic field is used to study harmonic generation. Substantial emission is found to occur at the harmonics for a cold beam; however, the harmonics are far more sensitive to beam thermal effects than is the fundamental.