Calculation and analysis of the magnetic field of a linearly tapered undulator

There is an empirical formula describing the relationship between the peak magnetic field and the undulator structure parameters for a uniform-parameter hybrid undulator.In this paper, we investigate the relationship for a linearly tapered undulator through numerical calculation by using the code RADIA, and check it with the empirical formula.The results imply that this empirical formula is also effective for linearly tapered undulators at a big enough scope for the requirements of normal FEL experiments.Therefore, for a linearly tapered undulator,we can use the empirical formula to design the variation of the undulator gap.For the tapering rate demanded by normal FEL experiments, the gap of a linearly tapered undulator increases almost linearly, and the tapering rate will keep constant while adjusting the undulator gap with the same variation for each undulator period.     

Studies of classical radiation emission from plasma wave undulators

The authors examine the characteristics of the classical radiation emitted by a relativistic electron beam that propagates perpendicularly through a large amplitude relativistic plasma wave. Such a study is useful for evaluating the feasibility of using relativistic plasma waves as extremely short wavelength undulators for generating short wavelength radiation. The electron trajectories in a plasma wave undulator are obtained using perturbation techniques and are then compared to numerical simulation results. The frequency spectrum and angular distribution of the spontaneous radiation emitted by a single electron and the stimulated radiation gain are obtained analytically, and are then compared to 3-D numerical simulations. The characteristics of the plasma wave undulator are compared to the AC free-electron laser (FEL) undulator and the conventional FEL     

Generation of Coherent Radiation in the Near X-Ray Band by a Cascade FEL with a Two-Frequency Undulator

Generation of X-ray radiation in a cascade self-amplified spontaneous emission free-electron laser (SASE FEL) using the harmonics of a two-frequency undulator is studied. The advanced phenomenological model of a one-pass FEL that accounts for the main losses in real FELs is presented: the electron energy spread in the beam, the beam divergence, diffraction, and the fact that emission losses are greater at higher harmonics than in the main frequency range. The FEL mathematical model was performed using the Mathematica software and calibrated within the experiment carried out at the operating SPARC facility via complex three-dimensional numerical simulations. The phenomenological model is used to analyze FEL dynamics for generation of a high-energy X-ray emission at a relatively short length. It is proposed to use a two-frequency undulator for the initial electron grouping and subsequent frequency multiplication in a cascade FEL with higher harmonic amplification (HGHG). The advantages of the two-frequency undulator are presented for electron grouping at higher harmonics of the undulator radiation (UR). The operation of several types of FEL is simulated with amplification of the seed laser wave frequency in two and three cascades to generate the soft X-ray radiation. A seed laser with a wavelength of 11.43 nm corresponding to the peak reflectivity of mirror coatings with MoRu/Be is proposed for generating the intensive X-ray laser radiation with λ ~ 1.27–3.37 nm. Here, the intensive radiation power reaches 50 MW at a length of only 35 meters; the radiation shows good temporal coherence corresponding to the performance of a low-power seed laser with a lower frequency.     

Self-amplified spontaneous emission free-electron laser with an energy-chirped electron beam and undulator tapering

We report the first experimental implementation of a method based on simultaneous use of an energy chirp in the electron beam and a tapered undulator, for the generation of ultrashort pulses in a self-amplified spontaneous emission mode free-electron laser (SASE FEL). The experiment, performed at the SPARC FEL test facility, demonstrates the possibility of compensating the nominally detrimental effect of the chirp by a proper taper of the undulator gaps. An increase of more than 1 order of magnitude in the pulse energy is observed in comparison to the untapered case, accompanied by FEL spectra where the typical SASE spiking is suppressed.     

用于THz源的混合型波荡器数值模拟

波荡器是基于自由电子激光的小型THz源关键器件, 其可调节的周期性磁场结构与两端的光腔配合, 使得穿越的电子束产生带增益的相干辐射, 最终达到THz源所需要的功率. 同纯永磁结构相比, 混合型波荡器通过软铁材料调节由永磁块磁化方向性差异导致的磁场分布误差, 同时可提供更高的场强. 本文针对小型THz源需求, 对混合型波荡器进行了相关物理设计. 在解析方法分析的基础上, 采用OPERA3D/TOSCA有限元分析软件, 对波荡器进行了三维磁场数值模拟和积分场优化. 通过对波荡器端部结构的调整, 优化后模型的一次场积分(导向误差)小于0.01Gs﹒m, 电子轨迹偏移小于0.02mm.     

A free electron laser experiment on "angular steering"

A paper by Jerby (1990) has discussed a number of mechanisms whereby FEL radiation may be directed electronically into different radiation patterns. We have devised an experiment (1992) to test this concept using the Columbia microwave FEL, which amplifies radiation at 24 GHz to a level <1 MW. A 4 mm dia, electron beam (580 kV) is propagated in a guiding field of 0.8 T inside an overmoded 24 mm dia. cylindrical waveguide. A TE11 mode is grown in a 33 cm long first undulator section (period 3.36 cm), and upon entering the following undulator section (period 2.26 cm, length 40 cm), the electron bunches convert to TM11 radiation which is further amplified. The far-field pattern of the TM11 emitted power is distinct from the TE11 pattern. Numerical and experimental studies are described in this paper showing the resulting radiation pattern.<>     

变参数波振器中小信号增益公式

利用微扰展开技术推导出变参数波振器的小信号增益两个近似求积表达式并将其计算结果与数值模拟结果进行了比较,二者吻合很好。利用近似解析式对小信号增益进行了初步探讨,得到了电子入射能量可低于初始谐振能,能散度允许范围受波振器设计影响以及降低锥度改变率可提高小信号增益等新结论。     

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.     

渐变摇摆场拉曼自由电子激光实验

采用渐变摇摆场技术进行了拉曼型自由电子激光实验,获得了最大辐射功率31MW、波长8～10.4mm的微波辐射输出,电子能量转换效率达9.68％。实验表明,对强流低能(0.45MeV)电子束拉曼自由电子激光器,渐变摇摆场比恒定摇摆场的自由电子激光器能量转换效率高2.6倍。     

`Spiking' radiation in the Columbia free electron laser

A report is presented on the observation of spikes of high-intensity radiation emitted from a 2-mm wavelength Raman free electron laser oscillator. The spikes are correlated with a well-developed sideband spectrum, including several sideband harmonics, together with the carrier. A pulse width ~150 ps is obtained from analysis of data obtained with a two-slit Young's experiment. An even shorter pulse width results from a numerical model. Using an elementary model of the spike, it is estimated that the peak spike pulse power is ~100 MW     

自由电子激光同步振荡边带超辐射的数值模拟研究

给出了描述自由电子激光同步振荡边带超辐射的方程组和它的解法,用编制的数值计算程序,对系统进行数值模拟研究,给出边带超辐射的频率和功率的定量结果,并证明在边带辐射中诱导辐射仍是主要的。     

自由电子激光放大啁啾脉冲的数值模拟

 利用1维非定态程序对单程自由电子激光(FEL)放大器放大线性啁啾脉冲的过程进行了数值模拟,得到了不同啁啾参数的脉冲通过FEL放大器的增益曲线,计算了不同啁啾参数的脉冲被单程FEL放大器放大后的腔外压缩情况。通过对数值模拟结果的定性分析得出：影响输出脉冲宽度和峰值功率的主要因素是FEL放大器的增益线宽和啁啾参数,并以此说明,通过先使用FEL放大器放大啁啾脉冲、然后再将其在腔外压缩的方法产生超短脉冲FEL是可行的。     

Undulator beamline optimization with integrated chicanes for X‐ray free‐electron‐laser facilities

An optimization of the undulator layout of X‐ray free‐electron‐laser (FEL) facilities based on placing small chicanes between the undulator modules is presented. The installation of magnetic chicanes offers the following benefits with respect to state‐of‐the‐art FEL facilities: reduction of the required undulator length to achieve FEL saturation, improvement of the longitudinal coherence of the FEL pulses, and the ability to produce shorter FEL pulses with higher power levels. Numerical simulations performed for the soft X‐ray beamline of the SwissFEL facility show that optimizing the advantages of the layout requires shorter undulator modules than the standard ones. This proposal allows a very compact undulator beamline that produces fully coherent FEL pulses and it makes possible new kinds of experiments that require very short and high‐power FEL pulses.     

Unified Analysis for Calculating the Incoherent Spontaneous Emission of Cooperative Radiations

A unified analysis is presented to calculate the incoherent spontaneous power of cooperative radiations based on self-amplified spontaneous emission. Using quantum mechanical tools, we derive analytical expressions for the incoherent spontaneous power of undulator and Cherenkov free-electron lasers(FELs). The undulator and Cherenkov FELs are considered as two different examples for the radiation that accumulate cooperatively. In the case of the undulator FEL, we show an excellent agreement between an expression for the incoherent radiation power derived in the present work and that obtained using a completely different approach [Phys. Rev. E65(2002) 026501] For the Cherenkov radiation,we demonstrate a satisfactory agreement between the incoierent power predicted in our analysis and previous experimental results.     

自由电子激光放大啁啾脉冲的数值模拟

利用1维非定态程序对单程自由电子激光(FEL)放大器放大线性啁啾脉冲的过程进行了数值模拟,得到了不同啁啾参数的脉冲通过FEL放大器的增益曲线,计算了不同啁啾参数的脉冲被单程FEL放大器放大后的腔外压缩情况。通过对数值模拟结果的定性分析得出：影响输出脉冲宽度和峰值功率的主要因素是FEL放大器的增益线宽和啁啾参数,并以此说明,通过先使用FEL放大器放大啁啾脉冲、然后再将其在腔外压缩的方法产生超短脉冲FEL是可行的。     

Possible application of X-ray optical elements for reducing the spectral bandwidth of an X-ray SASE FEL

A new design for a single pass X-ray Self-Amplified Spontaneous Emission (SASE) FEL is proposed. The scheme consists of two undulators and an X-ray monochromator located between them. The first stage of the FEL amplifier operates in the SASE linear regime. After the exit of the first undulator the electron bunch is guided through a non-isochronous bypass and the X-ray beam enters the monochromator. The main function of the bypass is to suppress the modulation of the electron beam induced in the first undulator. This is possible because of the finite value of the natural energy spread in the beam. At the entrance to the second undulator the radiation power from the monochromator dominates significantly over the shot noise and the residual electron bunching. As a result the second stage of the FEL amplifier operates in the steady-state regime when the input signal bandwidth is small with respect to that of the FEL amplifier. Integral losses of the radiation power in the monochromator are relatively small because grazing incidence optics can be used. The proposed scheme is illustrated for the example of the 6 nm option SASE FEL at the TESLA Test Facility under construction at DESY. As shown in this paper the spectral bandwidth of such a two-stage SASE FEL (Δλ/λ 5 × 10⁻⁵) is close to the limit defined by the finite duration of the radiation pulse. The average brilliance is equal to 7 × 10²⁴ photons/(s × mrad² × mm² × 0.1% bandw.) which is by two orders of magnitude higher than the value which could be reached by the conventional SASE FEL. The monochromatization of the radiation is performed at a low level of radiation power (about 500 times less than the saturation level) which allows one to use conventional X-ray optical elements (grazing incidence grating and mirrors) for the monochromator design.     

Design of an Efficiency-Enhanced Raman FEL Oscillator

The paper reports numerical calculations appropriate for the design of an "efficiency-enhanced" Raman free electron laser (FEL) oscillator. A helical undulator is used which consists of a constant period section followed by a section where the period is decreased roughly 10 percent. Simulation of the FEL is done by following the radiation dynamics in both the small- and large-signal regimes, using the "generalized pendulum equation" with self-consistent radiation field. It is found that the efficiency of the oscillator may be enhanced from ? 8 (no taper) to ? 15 percent (with taper). The configuration of an experimental oscillator is described; this device should produce ? 25 MW at a wavelength ? 1.8 mm using an 800-kV electron beam.     

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.     

无引导磁场Raman自由电子激光实验的理论分析

本文分析Raman自由电子激光中常用的双绕螺旋线摇摆器的自聚焦过程和自聚焦能力,得出束流稳定传输的条件,并与无引导磁场Raman自由电子激光实验中测得的传输束流进行分析比较。文中还对在电子脉冲线加速器EPA-74上完成的无引导磁场自由电子激光实验的辐射输出进行分析。理论分析与实验结果相符合。 关键词：