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.     

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.     

Undulator with permanent ferrimagnetic magnets

Undulator for terahertz FEL is created of ferrite materials. The length of the undulator period is 9 cm and the number of periods is 27. By means of selection and redistribution of magnetic elements it was succeeded to reduce the spread in amplitudes of the magnetic field down to 7%. Additional windings in magnetic elements were used to compensate for the residual spread. The needed focusing gradient of the magnetic field is obtained by means of relative displacement, along the x-axis, of alternating poles with opposite signs of the magnetic field. The undulator parameters, including the properties of focusing in the horizontal plane, are studied.     

An analysis of undulator optimization in self-seeding free electron lasers

A simple analysis is given for the optimum length of undulator in a self-seeding free electron laser(FEL).The obtained relations show the correlation between the undulator length and the system parameters.The power required for the seeding in the second part of the undulator and the overall efficiency of monochromatizating the seeding determine the length of the first part of the undulator;the magnitude of seeding power dominates the length of the second part of the undulator;the whole length of the undulator in a self-seeding FEL is determined by the overall efficiency for getting coherent seed,and is about half as long again as that of SASE,not including the dispersion section.The requirement of the dispersion section strength is also analyzed.     

北京大学SASE FEL的参数优化研究

SASEFEL是获得短波长X射线激光的最佳途径,SASEFEL的理论和实验研究是当前FEL研究的热点.本文利用北京大学超导加速器装置提供的电子束,通过解析理论和3D模型的数值模拟方法得到了实现SASEFEL的扭摆器的优化参数,并讨论了电子束的束流品质参数对SASEFEL的饱和长度和功率的影响,对加速器的设计和调试有重要的参考意义.     

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.     

Experimental study of magnet undulators with pulsed-wire method

Experimental study of magnetic characteristics of planar magnet undulator for terahertz FEL has been carried out with use of pulsed-wire method. Special attention was given to the procedure of measurement of the second integral of undulator magnetic field, which shows variation of the beam position at passing the undulator magnetic system.     

FEL undulator with permanent ferromagnetic magnets

A terahertz FEL ferromagnetic undulator has been created. The length of the undulator period is 9 cm with the number of the periods at 27. By means of the selection and redistribution of magnetic elements, the spread of the amplitudes of the magnetic field was reduced to 7%. Additional windings of the magnetic elements were used to compensate for residual spread. The required focusing gradient of the magnetic field was obtained as a result of the relative displacement of alternating poles with an opposite charge of the magnetic field along the x axis. Parameters of undulator, including the focusing properties in the horizontal plane, were investigated.     

磁压缩对高频稳定性的要求

 曲柄式磁压缩系统是北京大学SASE自由电子激光装置中非常重要的部分，通过其对电子束团的压缩为扭摆器提供高流强、短脉冲的电子束，使电子束在扭摆器内较短的距离实现饱和出光。曲柄式磁压缩需要利用偏离高频峰位的加速相位使得电子束产生能量-位置关联，主要讨论高频相位抖动与能量-位置关联的相互关系，高频相位抖动使得束团的能量-位置关联不同，即束团内电子能量随位置分布不同。进而研究其对磁压缩性能的影响，即能量-位置关联不一样会导致磁压缩得到的束团长度出现涨落。     

一种用于波荡器磁中心高精度标定的磁靶标

波荡器磁中心轴的标定是保证自由电子激光装置波荡器安装准直精度的重要前提。介绍了一种利用磁靶标实现波荡器磁中心高精度标定的方法。设计制造了由若干块永磁块组合构成的磁靶标,其能产生一正一斜两个高梯度四极场。测出了两四极场垂直分量的零点位置分布并依此给出了磁靶标的具体使用方法。结果表明:标定后的波荡器磁中心在磁靶标坐标系中水平方向测量精度好于±20 μm,垂直方向测量精度好于±2 μm。     

变参数波振器小信号增益的三维效应

本文对前文导出的变参数波振器小信号增益积分表达式,利用非均匀天线阵列概念与Madey定理作出了物理解释,并将该式推广为三维。我们考虑了电子束发射度,不同聚焦方式,光束的强度与相位横向分布以及FEL系统中磁场轴、电子束中心、光轴三轴不准直……对增益的影响,进行了数值计算。作为具体实例,我们对波音公司的实验装置进行了数值计算,与他们的数值摸拟结果作了比较。     

Optimization of the lattice function in the planar undulator applied for terahertz FEL oscillators

Since the beta function of the electron beam within the undulator has a great influence on the power gain of the free electron laser (FEL), optimization of the undulator lattice becomes important. In this paper, the transfer matrix of the planar undulator is obtained from differential equations of the electron motion. Based on this, the lattice function of the planar undulator in a terahertz FEL oscillator proposed by Huazhong University of Science and Technology (HUST-FEL) is optimized and the expressions of the average beta function are derived. The accuracy of the optimization result was confirmed well by the numerical method. The application range of this analytical method is given as well. At last, the emittance growth in the horizontal direction due to the attenuation of the magnetic field is discussed.     

Choice of the parameters of a magnetic undulator

The total output power of undulator radiation is investigated as a function of the constructional parameters of the undulator and its supply current. Calculations are presented of the magnetic field in the undulator, and the optimum undulator dimensions for maximum magnetic field intensity per unit length of the system are calculated. It is shown that the total radiated power of the charged particles depends on the undulator periodicity.     

Three-dimensional numerical investigations of the laser-beam interactions in an undulator

Laser-beam interaction in an undulator is commonly suggested in the development of free electron laser(FEL)schemes. In this paper, a three-dimensional algorithm is developed to assist in laser-beam interaction simulation in an undulator, which is built on the basis of the fundamentals of electrodynamics, i.e.the electron's behavior is determined by the magnetic field and the laser electric field in the time domain. On the basis of the algorithm, the detuning effect in a laser heater, the carrier envelope phase effect of a few-cycle laser in attosecond X-ray FEL schemes and output wavelength tuning in a high gain harmonic generation FEL are numerically discussed.     

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。     

混合型波荡器的3维优化

 以波荡器辐射波和共振电子能及混合型波荡器的解析计算为基础，通过3维磁场的有限元计算，在欧洲光源横向优化基础上，给出了同步辐射和自由电子激光用混合型波荡器纵向优化参数，进而给出了用于DUV FEL混合型波荡器的设计计算参数。加侧位和顶部永磁块后，峰值磁场分别提高到0.722T和0.773T，辅助以1μm量级分辨率的磁间隙调节机械系统，磁场分辨率好于10^-4T量级。     

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。     

摆动器场误差对自由电子激光器自发辐射谱的影响

在考虑平面型摆动器（Ｗｉｇｇｌｅｒ）场误差△Ｂ（ｚ）的情况下，求解电子在磁场中运动的洛仑兹（Ｌｏｔｅｎｔｚ）方程，得到场误差对电子横向速度的改变，然后作傅里叶变换即为电子自发辐射谱的改变，并讨论了各种场误差对自由电子激光器自发辐射谱的影响，选择北京自由电子激光器（ＢＦＥＬ）参数，进行模拟，最后确定出各种场误差的可接受条件。     

Development of an Algorithm for Magnet Sorting and Field Shimming for TPS Elliptically Polarized Undulators

A spatially periodic magnetic field is essential to cause an electron beam to wiggle and to emit electromagnetic radiation in a synchrotron (SR) source of radiation, and to provide fully coherent light in free electron lasers (FEL). To create this field, permanent magnets (PM) or electromagnets are patterned in a device commonly called an insertion device for SR and a radiator or modulator for FEL. In reality, magnet blocks or iron poles are not identical, in terms of geometry and magnetic properties, even with progressive manufacture. Compensatory methods are thus desired to recover the magnetic field and also to decrease the duration of construction. Magnet sorting is a pre-process that aims to eliminate the effect of manufacturing error. Before assembly of an insertion device, data of each component, especially the magnetic properties of each magnet block and the gap variation of mechanical structure, are organized to optimize the performance of the magnetic field. After that process, there is sometimes an optimization to shim the magnetic field. An effective algorithm of both processes is significant, particularly for a long undulator and an elliptically polarized undulator (EPU).     

Efficiency and sideband observations of a Raman FEL oscillator witha tapered undulator

Power and spectral measurements are reported from the Columbia Raman free-electron laser (FEL) oscillator experiment. High-power radiation pulses (~12 MW, 100 ns) are generated at a wavelength of ~2.5 mm, using a 750-kV electron beam injected into a helical undulator. The undulator is made up of a 40-cm long constant-period (1.45 cm) section followed by an equal length of tapered undulator. The period is decreased by 7.6% in such a way that the on-axis field remains constant. It is reported that the taper allows an increase in total power efficiency from ~4 to ~12%. Most noteworthy is that the tapered undulator reduces the sideband radiation compared with a constant-period undulator FEL which is studied in the same configuration. The power was measured calorimetrically and compared with the results of a 1-D Raman code. The reduction of sideband power observed in the experiment was consistent with computational results obtained with a 2-D sideband code