Gain of harmonic generation in high gain free electron laser

In a planar undulator employed free electron laser (FEL), each harmonic radiation starts from linear amplification and ends with nonlinear harmonic interactions of the lower nonlinear harmonics and the fundamental radiation. In this paper, we investigate the harmonic generation based on the dispersion relation driven from the coupled Maxwell-Vlasov equations, taking into account the effects due to energy spread, emittance, betatron oscillation of electron beam as well as diffraction guiding of the radiation field. A 3D universal scaling function for gain of the linear harmonic generation and a 1D universal scaling function for gain of the nonlinear harmonic generation are presented, which promise rapid computation in FEL design and optimization. The analytical approaches have been validated by 3D simulation results in large range.     

上海深紫外自由电子激光的非线性谐波辐射研究

 自由电子激光中的非线性谐波辐射能达到较高的谐波功率,可以用来得到短波长辐射或者降低第4代先进光源对电子束团品质的严厉要求。基于3维自由电子激光软件,深入详细地研究了上海深紫外自由电子激光装置的非线性谐波辐射,并且提出了谐波辐射实验和测量建议。研究表明上海深紫外自由电子激光装置3次非线性谐波辐射的功率可以达到基波功率的2%水平。     

Harmonic operation of high gain harmonic generation free electron laser

In high gain harmonic generation (HGHG) free electron laser (FEL), with the right choice of parameters of the modulator undulator, the dispersive section and the seed laser, one may make the spatial bunching of the electron beam density distribution correspond to one of the harmonic frequencies of the radiator radiation, instead of the fundamental frequency of the radiator radiation in conventional HGHG, thus the radiator undulator is in harmonic operation (HO) mode. In this paper, we investigate HO of HGHG FEL.Theoretical analyses with universal method are derived and numerical simulations in ultraviolet and deep ultraviolet spectral regions are given. It shows that the power of the 3rd harmonic radiation in the HO of HGHG may be as high as 18.5% of the fundamental power level. Thus HO of HGHG FEL may obtain short wavelength by using lower beam energy.     

Harmonic operation of high gain harmonic generation free electron laser

In high gain harmonic generation (HGHG) free electron laser (FEL), with the right choice of parameters of the modulator undulator, the dispersive section and the seed laser, one may make the spatial bunching of the electron beam density distribution correspond to one of the harmonic frequencies of the radiator radiation, instead of the fundamental frequency of the radiator radiation in conventional HGHG, thus the radiator undulator is in harmonic operation (HO) mode. In this paper, we investigate HO of HGHG FEL. Theoretical analyses with universal method are derived and numerical simulations in ultraviolet and deep ultraviolet spectral regions are given. It shows that the power of the 3rd harmonic radiation in the HO of HGHG may be as high as 18.5% of the fundamental power level. Thus HO of HGHG FEL may obtain short wavelength by using lower beam energy.     

Design of cascading two stages of high gain harmonic generation scheme based on Shanghai deep ultraviolet free electron laser

Cascading stages of high gain harmonic generation free electron laser (FEL) seem to be a feasible way to generate short wavelength radiation. With help of the analytical estimates, we design a two-stage cascading scheme to achieve 131 nm DUV radiation on the basis of the Shanghai deep ultraviolet free electron laser test facility. Detailed studies on the FEL performance, the stability and the sensitivity of the output power to parameter variation have been achieved by GENESIS1.3, and design of the lattice structure is presented.     

相干谐波储存环自由电子激光

相干谐波自由电子激光不用光学谐振腔及反射镜,可望工作在紫外和真空紫外光波段,是第四代同步辐射光源的可能途径之一。由于对束流品质要求很高,相干谐波自由电子激光首先是以储存环作为驱动器而发展起来的。由于光阴极微波电子枪的发展和直线加速器技术的进步,目前,已开始有直线加速器驱动的高增益相干谐波自由电子激光的建议。文章介绍了相干谐波储存环自由电子激光的原理、现状及展望。     

Experimental characterization of nonlinear harmonic radiation from a visible self-amplified spontaneous emission free-electron laser at saturation

Nonlinear harmonic radiation was observed using the VISA self-amplified, spontaneous emission (SASE) free-electron laser (FEL) at saturation. The gain lengths, spectra, and energies of the three lowest SASE FEL modes were experimentally characterized. The measured nonlinear harmonic gain lengths and center spectral wavelengths decrease with harmonic number, n, which is consistent with nonlinear harmonic theory. Both the second and third nonlinear harmonics energies are about 1% of the fundamental energy. These experimental results demonstrate for the first time the feasibility of using nonlinear harmonic SASE FEL radiation to produce coherent, femtosecond x rays.     

上海软X射线自由电子激光外种子运行模式的模拟研究

上海软X射线自由电子激光用户装置（SXFEL）是我国首台可以运行在水窗波段的自由电子激光装置,未来可以为5个实验线站供光,其主要运行模式为自放大自发辐射模式以及外种子模式。本文就SXFEL的外种子模式进行了从头到尾的模拟研究,主要包括EEHG-HGHG混合级联与单级EEHG两种方案。模拟结果表明,虽然EEHG-HGHG混合级联模式较为复杂,但能够产生更高功率的高次谐波辐射。除此之外,我们还研究了各种三维效应对EEHG的影响。模拟和分析结果表明,通过上述两种方案,采用紫外波段的种子激光,用户可以得到全相干、窄带宽、短脉冲的水窗波段自由电子激光。     

Phase‐merging enhanced harmonic generation free‐electron laser with a normal modulator

A phase‐merging enhanced harmonic generation free‐electron laser (FEL) was proposed to increase the harmonic conversion efficiency of seeded FELs and promote the radiation wavelength towards the X‐ray spectral region. However, this requires a specially designed transverse gradient undulator (TGU) as the modulator to couple the transverse and longitudinal phase space of the electron beam. In this paper, the generation of the phase‐merging effect is explored using the natural field gradient of a normal planar undulator. In this method, a vertical dispersion on the electron beam is introduced and then the dispersed beam travels through a normal modulator in a vertical off‐axis orbit where the vertical field gradient is selected properly in terms of the vertical dispersion strength and modulation amplitude. The phase‐merging effect will be generated after passing through the dispersive chicane. Theoretical analysis and numerical simulations for a seeded soft X‐ray FEL based on parameters of the Shanghai Soft X‐ray FEL project are presented. Compared with a TGU modulator, using the natural gradient of a normal planar modulator has the distinct advantage that the gradient can be conveniently tuned in quite a large range by adjusting the beam orbit offset.     

Fully coherent hard X-ray generation by two-stage phase-merging enhanced harmonic generation

Cascading stages of seeded free electron lasers (FELs) is a promising way to produce fully coherent X-ray radiation. We study a new approach to produce coherent hard X-rays by cascading the recently proposed phase-merging enhanced harmonic generation (PEHG) The scheme consists of one dogleg and two PEHG configurations, and may be one of the leading candidates for the extracted undulator branch in future X-ray FEL facilities. FEL physics studies show that such a scheme is feasible within the present technology and can provide high brightness X-ray radiation pulses with narrow bandwidth and full coherence The radiated peak power at 1 Å wavelength converted from an initial 200 nm seed laser is over 2 GW.     

FEL光学速调管的升级性能分析

通过三维磁场的有限元计算,给出了自由电子激光（FEL）研究用光学速调管升级后的磁参数。国家同步辐射实验室合肥光源（HLS）电子储存环能量可以日常运行在200～800 MeV间,为了与电子储存环能量匹配,并在较高束电子能量下进行实验和得到较多的相干辐射光子,光学速调管从原来的对称结构升级成非对称结构,用于HLS储存环谐波产生FEL实验。给出了升级后非对称光学速调管的几组匹配磁参数,用于在HLS储存环注入能量和可以运行的最高能量下进行谐波FEL实验。初步计算表明,HLS 储存环电子束性能优越,能散很低,FEL实验用最高能散仅为2.05×10-4,相应FEL辐射的能散修正因子在0.96以上,可以忽略不计。     

自由电子激光的计算机模拟

本文使用1(2/2)维电磁相对论粒子程序对自由电子激光进行计算机模拟。在线性段,计算机模拟与用解析理论计算的增长率符合很好。与没有轴向引导磁场的自由电子激光相比,加一弱轴向引导磁场时,Wiggler场的强度可降得较低。加一强轴向引导磁场时,波能量达到饱和水平所需时间较短。     

自由电子激光振荡器中电子束能量跳跃对增益的影响

 微脉冲中电子束能量、电流的跳跃会影响电子束的质量, 从而也影响激光的增益。在CAEP FIR FEL 理论设计模型参数的基础上,利用一维定态程序对电子束能量跳跃对增益的影响进行了数值研究,并与非定态程序计算结果进行比较,给出可容许的能量跳跃范围。     

Experimental verification of the mechanisms for nonlinear harmonic growth and suppression by harmonic injection in a traveling wave tube

Understanding the generation and growth of nonlinear harmonic (and intermodulation) distortion in microwave amplifiers such as traveling wave tubes (TWTs), free electron lasers (FELs), and klystrons is of current research interest. Similar to FELs, the nonlinear harmonic growth rate scales with the harmonic number in TWTs. In klystrons, the wave number scaling applies to the nonlinear harmonic bunching and associated nonlinear space-charge waves. Using a custom-modified TWT that has sensors along the helix, we provide the first experimental confirmation of the scaling of nonlinear harmonic growth rate and wave number in TWTs. These scalings of a nonlinearly generated harmonic mode versus an injected linear harmonic mode imply that suppression by harmonic injection occurs at a single axial position that can be located as desired by changing the injected amplitude and phase.     

Storage ring free electron laser dynamics in presence of an auxiliary harmonic radio frequency cavity

In a Storage Ring Free Electron Laser (SRFEL) there is a strong interdependence between the laser beam and the electron beam from which the laser is generated. The Super ACO storage ring has a second Radio Frequency (RF) cavity at the 5th harmonic of the main RF cavity. It is used to shorten the bunch length, thereby enhancing the laser gain. Employing this RF harmonic cavity instabilities are observed with a strong effect on both the laser radiation properties and the electron beam behaviour. In this paper, we first present beam characteristics of Super-ACO as influenced by the harmonic cavity, and the instabilities of the beam due to this RF cavity. Then we discuss the FEL properties in presence of the harmonic RF cavity. In general the harmonic cavity functions as intended, and it is observed that the laser suppresses the instabilities caused by the harmonic cavity in the absence of the FEL.     

非定态FEL在线性区性态的数值模拟

利用于敏教授建立的一堆非定态ＦＥＬ方程进行数值模拟，研究了ＦＥＬ在线性区的脉冲传播、增益发展和滑移区超辐射等性态。数值结果表明，滑移对增益的影响跟电子束纵向分布和滑移长度与脉冲长度之比有关；对同样的滑移参数，滑移对增益相对于定态区增益的强弱由束电流决定。     

SASE自由电子激光起振问题及统计特性的数值模拟

 介绍一种自放大自发辐射自由电子激光（SASE FEL）的自发辐射和电子束噪声的数学描述，运用修正的一维非定态程序，对SASE FEL 起振问题及光场统计特性进行了数值模拟，分析了自发辐射谱的发展过程及一定频带宽度内光场随机特性的统计规律，数值模拟结果与理论结果符合较好。     

Echo-enabled谐波放大自由电子激光参数

通过数值模拟,结合解析计算分析,研究了Echo-enabled谐波放大自由电子激光对装置参数和主要束流参数变化的独立敏感性,给出了谐波聚束因子和饱和功率随参数变化的数值模拟结果;对色散段由相干同步辐射效应引起的能散和发射度增长进行了估算和数值模拟。结果表明:相干同步辐射效应引起的切片能散和切片发射度增长在5%以内,对最后辐射影响不大。     

光速调管FEL的小信号增益理论

 利用自由电子激光（FEL）纵模统一理论，系统地分析了光速调管FEL的小信号增益理论，并对色散参数Nd、束流能散度和发射度的影响进行了讨论。     

Physical design of a wavelength tunable fully coherent VUV source using a self-seeding free electron laser

In order to meet the requirements of the synchrotron radiation users, a fully coherent VUV free electron laser (FEL) has been preliminarily designed. One important goal of this design is that the radiation wavelength can be easily tuned in a broad range (70—170 nm). In the light of the users' demand and our actual conditions, the self-seeding scheme is adopted for this proposal. Firstly, we attempted to fix the electron energy and only changed the undulator gap to vary the radiation wavelength; however, our analysis implies that this is difficult because of the great difference of the power gain length and FEL efficiency at different wavelengths. Therefore, we have considered dividing the wavelength range into three subareas. In each subarea, a constant electron energy is used and the wavelength tuning is realized only by adjusting the undulator gap. The simulation results show that this scheme has an acceptable performance.