The effects of self-fields on the electron trajectory in a two-stream free electron laser with a helical wiggler and an axial guiding magnetic field

A theory for the two-stream free-electron laser（TSFEL） with a helical wiggler and an axial guide magnetic field is developed.In the analysis,the effects of self-fields are taken into account.An analysis of the two-stream steady-state electron trajectories is given by solving the equation of motion.Numerical calculations show that there are seven groups of orbits in the presence of self-fields instead of two groups reported in the absence of self-fields.The stability of the trajectories is studied numerically.

Effects of self-fields on gain in two-stream free electron laser with helical wiggler and an axial guiding magnetic field

The theory for the two-stream free electron laser （FEL） consisting of a relativistic electron beam transporting along the axis of a helical wiggler in the presence of an axial guiding magnetic field is proposed and investigated. In the analysis, the effects of self-fields are taken into account. The electron trajectories and the small signal gain are derived. The characteristics of the linear-gain and the normalized maximum gain are studied numerically. The results show that there are seven stable groups of orbits in the presence of self-fields instead of two groups reported in the absence of the self-fields. It is also shown that the normalized gains of three groups decrease while the rest increase with the increasing of normalized cyclotron frequency g20. Furthermore, it is found that the two-stream instability and the self-field lead to a decrease in the maximum gain except for group 3. The results show that the normalized maximum gain is enhanced in comparison with that of the single stream.

Gain enhancement in two-stream free electron laser with a planar wiggler and an axial guide magnetic field

The theory for a two-stream free electron laser （FEL） consisting of a relativistic electron beam transported alongthe axis of a planar wiggler in the presence of an axial guiding magnetic field is proposed and investigated. The electron trajectories and the small signal gain are derived. The characteristic of the linear gain and the normalized maximum gain are studied numerically. The result shows that the normalized maximum gain is considerably enhanced in comparison with that of the single stream. The effect of the difference between the energies of the two beams in this configuration of FEL is also considered, and we find that the gain is affected by the energy differences between groups 1 and 2.

Effects of self-fields on dispersion relation and growth rate in two-stream electromagnetically pumped free electron laser with axial guide magnetic field

A theory for a two-stream free-electron laser （FEL） with an electromagnetic wiggler （EMW） and axial guide magnetic field is developed. In the analysis, the effects of self-fields are taken into account. The growth rate is derived. The characteristics of the growth rate are studied numerically. The dependence of the normalized wave number, which corresponds to the maximum growth rate, on the cyclotron frequency is presented. The comparisons between the normalized maximum growth rate and its corresponding wave number normalized by employing the axial magnetic field, for the cases with and without self-fields in the two-stream FEL are studied numerically.

The effects of self-fields on the electron trajectory and gain in a two-stream electromagnetically pumped free-electron laser with axial guiding field

A theory of a two-stream flee-electron laser in a combined electromagnetic wiggler （EMW） is developed, in which we use an axial-guide magnetic field and take into account the effects of the self-fields. The electron trajectories and the small signal gain are derived. The stability of the trajectories, the characteristics of the linear-gain, and the normalised maximum gain are studied numerically. The results show that there are nine stable groups of orbits in the presence of self-fields instead of seven groups reported in the absence of the self-field. It is also shown that the normalised gains of four groups of the orbits are decreasing and those for the rest of them are increasing with growing J20. Furthermore, it is found that the two-stream laser with seff-field enhances the maximum gain in comparison with the single stream case.

Effects of self-fields on electron trajectory and gain in two-stream electromagnetically pumped free-electron laser with ion channel guiding

A theory for the two-stream free-electron laser with an electromagnetic wiggler （EMW） and an ion channel guiding is developed. In the analysis, the effects of self-fields have been taken into account. The electron trajectories and the small signal gain are derived. The stability of the trajectories, the characteristics of the linear gain and the normalized maximum gain are studied numerically. The dependence of the normalized frequency ω corresponding to the maximum gain on the ion-channel frequency is presented. The results show that there are seven groups of orbits in the presence of the self-fields, which are similar to those reported in the absence of the self-fields. It is also shown that the normalized gains of 2 groups decrease while the rest increase with the increasing normalized ion-channel frequency. Furthermore, it is found that the two-stream instability and the self-field lead to a decrease in the maximum gain except for group 4.

Effects of self-fields on electron trajectory and gain in planar wiggler free-electron lasers with two-stream and ion-channel guiding

The effects of self-fields on electron trajectories and gain in planar wiggler free-electron lasers with two-stream and ion-channel guiding are investigated. An analysis of the two-stream quasi-steady-state electron trajectories is given by solving the equation of motion in the presence of ion-channel guiding and the planar wiggler. The electron trajectories and the gain are derived. The stability of the trajectories, the characteristics of the linear gain, and the normalized maximum gain are studied numerically. The numerical calculations show that there are eight group trajectories rather than the two groups reported in the absence of the self-fields. It is also shown that the normalized gain group seven （G7） decreases while the rest increases with the increase in normalized ion-channel frequency. The two-stream instability and the self-field lead to a decrease in the maximum gain, except for G7.

Generation of double pulses at the Shanghai soft X-ray free electron laser facility

In this article, we present the promise of a new method generating double electron pulses in picosecondscale pulse length and tunable interpulse spacing at several picoseconds. This has witnessed an impressive potential of application in pump–probe techniques, two-color X-ray free electron laser, high-gradient witness bunch acceleration in a plasma, etc. Three-dimensional simulations are carried out to analyze the dynamic of the electron beam in a linear accelerator. Comparisons are made between the new method and existing ways.

Smith-Purcell free electron laser based on the semi-elliptical resonator

A novel Smith-Purcell （S-P） free electron laser composed of an electron gun, a semi-elliptical resonator, a metallic reflecting grating and a collector, is presented for the first time. This paper studies the characteristics of this device by theoretical analysis and particle-in-cell simulation method. Results indicate that tunable coherent S-P radiation with a high output peak power at millimeter wavelengths can be generated by adjusting the length of the grating period, or adjusting the voltage of the electron beam. The present scheme has the following advantages： the semi-elliptical resonator can reflect all radiation with the emission angle {？ and random azimuthal angles, back onto the electron beam with same-phase and causes the electrons to be modulated, so the output power and efficiency are improved.

First commissioning results of the coherent scattering and imaging endstation at the Shanghai soft X-ray free-electron laser facility

The Shanghai soft X-ray free-electron laser(SXFEL)user facility project started in 2016 and is expected to be open to users by 2022.It aims to deliver ultra-intense coherent femtosecond X-ray pulses to five endstations covering a range of 100–620 eV for ultrafast X-ray science.Two undulator lines are designed and constructed,based on different lasing modes:self-amplified spontaneous emission and echo-enabled harmonic generation.The coherent scattering and imaging(CSI)endstation is the first of five endstations to be commissioned online.It focuses on high-resolution single-shot imaging and the study of ultrafast dynamic processes using coherent forward scattering techniques.Both the single-shot holograms and coherent diffraction patterns were recorded and reconstructed for nanoscale imaging,indicating the excellent coherence and high peak power of the SXFEL and the possibility of‘‘diffraction before destruction’’experiments at the CSI endstation.In this study,we report the first commissioning results of the CSI endstation.

Review of fully coherent free-electron lasers

Generation of intense, fully coherent radiation with wide spectral coverage has been a long-standing challenge for laser technologies. Several techniques have been developed in recent years to extend the spectral coverage in optical physics, but none of them hold the potential to produce X-ray laser pulses with very high-peak power. Urgent demands for intense X-ray light sources have prompted the development of free-electron lasers(FELs), which have been proved to be very useful tools in many scientific areas. In this paper, we give an overview of the basic principle of FELs, techniques for realizing fully coherent FELs, and the development of fully coherent FEL facilities in China.

Application of Laser Dispersion Method in Apparatus Combining H Atom Rydberg Tagging Time-of-Flight Technique with Vacuum Ultraviolet Free Electron Laser

Photodissociation of H2S in the VUV region plays an important role in the atmospheric chemistry and interstellar chemistry.To date,however,few studies have been focused on this topic.In this article,we have described a laser dispersion method applied in the apparatus combining the high-n H atom Rydberg tagging time-of-flight technique with the vacuum ultraviolet free electron laser(VUV FEL).The Lyman-αlaser beam(121.6 nm)used in the H-atom detection was generated by the difference frequency four-wave mixing schemes in a Kr/Ar gas cell.After passing through an off-axis biconvex LiF lens,the 121.6 nm beam was dispersed from the 212.6 nm and 845 nm beams due to the different deflection angles experienced by these laser beams at the surfaces of the biconvex lens.This method can eliminate the background signal from the 212.6 nm photolysis.Combined with the VUV FEL,photodissociation of H2S at 122.95 nm was studied successfully.The TOF spectrum was measured and the derived total kinetic energy release spectrum was displayed.The results suggest that the experimental setup is a powerful tool for investigating photodissociation dynamics of molecules in the VUV region which involves the H-atom elimination processes.

Effect of normalized plasma frequency on electron phase-space orbits in a free-electron laser

Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that the irregularity of the electron phase-space orbits could be caused in several ways, such as varying the wiggler amplitude and inducing sidebands. Based on a Hamiltonian model with a set of self-consistent differential equations, it is shown in this paper that the electron- beam normalized plasma frequency functions not only couple the electron motion with the FEL wave, which results in the evolution of the FEL wave field and a possible power saturation at a large beam current, but also cause the irregularity of the electron phase-space orbits when the normalized plasma frequency has a sufficiently large value, even if the initial energy of the electron is equal to the synchronous energy or the FEL wave does not reach power saturation.

FREE ELECTRON LASER PROJECT AT SINR

The Shanghai FEL (SFEL) project at SINR is based on a RF linac in collaboration with the SIOFM. The prime goal of the project is to provide laser beams from the ultraviolet,visible to mid-IR with a few tens of MW in peak power and of Watts in average power. In the future, the wavelength region will be extend to the far-IR and vacuum ultraviolet. The SFEL will be a user facility for interdisciplinary studies.

THE TRANSVERSAL GEOMETRIC EFFECTS IN A FREE ELECTRON LASER

The effects of a beam thickness and a conducting wall in a free electron laser with a linearlypolarized wiggler magnetic field and an axial magnetic field are investigated within the framework of fluid-Maxwell equations.The growth rate of free electron laser instability is obtained,in which the nonlinear bulkand surface current density are simultaneously considered.The numerical calculations indicate that the bulkcoupling is dominant.There is an optimum beam thickness and separation between the conducting walls forwhich the growth rate is maximum.

THE LONG PULSE EFFECT IN FREE ELECTRON LASERS

The spontaneous radiation from a single pulse electron beam in Free Electron Lasers is dealt withby solving one-dimensional wave equations.The obtained results show that there is the long pulse effect aswell as the well-known short pulse effect.

CHAOTIC ELECTRON TRAJECTORIES IN A CIRCULAR FREE ELECTRON LASER

The motion of a relativistic electron is analyzed in the field configuration consisting of a circular wiggler magnetic field, an axial magnetic field, and the equilibrium self-electric and self-magnetic fields produced by the non-neutral electron ring. By generating Poincare surface-of-section maps, it is shown that when the equilibrium self-fields is strong enough, the electron motions become chaotic. Although the realistic circular wiggler magnetic field destroys the inte-grability of the electron motion as the equilibrium self-fields do, the role the latter plays to make the motions become chaotic is stronger than the former does. In addition, the axial magnetic field can restrain the occurrence of the chaoticity.

Gain calculation of a free-electron laser operating with a non-uniform ion-channel guide

Amplification of an electromagnetic wave by a free electron laser （FEL） with a helical wiggler and an ion channel with a periodically varying ion density is examined. The relativistic equation of motion for a single electron in the combined wiggler and the periodic ionbchannel fields is solved and the classes of possible trajectories in this configuration are discussed. The gain equation for the FEL in the low-gain-per-pass lirnit is obtained by adding the effect of the periodic ion channel. Numerical calculation is employed to analyse the gain induced by the effects of the non-uniform ion density. The variation of gain with ion-channel density is demonstrated. It is shown that there is a gain enhancement for group I orbits in the presence of a non-uniform ion-channel but not in a uniform one. It is also shown that periodic ion-channel guiding is used to reach the maximum peak gain in a low ion-channel frequency （low ion density）.

CHARACTERISTIC STUDY OF A FREE ELECTRON LASER WITH LINEARLY POLARIZED WIGGLER AND RECTANGULAR WAVEGUIDE

The characteristics of coherent radiation produced by a cylindrical electron beam passing through a rectangular waveguide and linearly polarized wiggler are studied. The instability analysis is based on the linearized Vlasov-Maxwell equations for the perturbations about a self-consistent beam equilibrium. The dispersion equation of TMmn mode is deduced and by making use of numerical calculation the radiation frequency and growth rate as a function of electron beam energy and radius, axial magnetic field, wiggler field and wave length are presented and discussed.

Axial magnetic field effect in numerical analysis of high power Cherenkov free electron laser

Cherenkov free electron laser(CFEL) is simulated numerically by using the single particle method to optimize the electron beam. The electron beam is assumed to be moving near the surface of a flat dielectric slab along a growing radiation. The set of coupled nonlinear differential equations of motion is solved to study the electron dynamics. For three sets of parameters, in high power CFEL, it is found that an axial magnetic field is always necessary to keep the electron beam in the interaction region and its optimal strength is reported for each case. At the injection point, the electron beam’s distance above the dielectric surface is kept at a minimum value so that the electrons neither hit the dielectric nor move away from it to the weaker radiation fields and out of the interaction region. The optimal electron beam radius and current are thereby calculated. This analysis is in agreement with two previous numerical studies for a cylindrical waveguide but is at odds with analytical treatments of a flat dielectric that does not use an axial magnetic field. This is backed by an interesting physical reasoning.