上海深紫外自由电子激光装置波荡器磁场调整

 在对上海深紫外项目的波荡器建造过程中，应用亥姆霍兹线圈系统测量了全部单磁块，并使用模拟退火法对磁块进行组合排序优化，使反映磁场的成本函数下降了3个数量级。对一段波荡器进行了多次测量、调整，使积分场、峰峰值误差、位相误差等各项指标达到设计要求。     

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0PERA3/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0.0lGs.m,电子轨迹偏移小于0.02mm.     

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.     

混合型波荡器的研制

介绍一台１．５ｍ的混合型波荡器（ＵＮＤＵＬＡＴＯＲ）的研制，包括设计、磁块的优化组合、磁场测量系统和磁场调整技术。这台波荡器主要用于中红外自由电子激光的研究，其磁场峰值均方根误差０．５％，磁场导向误差１ｍＴ·ｃｍ，电子轨迹偏离０．０３ｍｍ。     

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。     

高能同步辐射光源低温波荡器的结构优化设计

高能同步辐射光源验证装置(HEPS-TF)插入件系统目前正研制一台低温波荡器(CPMU)样机。为了保证辐射强度,必须严格控制磁场误差。低温波荡器由于其结构的特殊性,承载磁铁的真空内大梁工作在真空、低温环境。低温收缩引起的变形量会引起相位误差,从而降低同步辐射光的相干性。因此,控制和优化真空内大梁的变形是低温波荡器机械设计的重点。采用数值模拟计算的方法,对真空内大梁的变形量进行了分析和优化,最终通过结构优化和补偿机构的设计有效降低了其变形量,使之满足设计指标。     

用模拟退火法进行纯永磁波荡器磁块组合优化

 纯永磁波荡器由多个磁块组成，磁块的剩磁离散性会引起波荡器磁场误差，从而影响储存环工作状态和自发辐射谱质量。在波荡器磁块安装之前，使用模拟退火法对磁块进行组合排序优化，可以使峰值场强误差降低到10 ^-4量级以下，磁场一次积分降低到10^-6 T·m量级，二次积分降低到10 ^-6 T·m ²量级，优化结果不依赖于初始状态的选择。给出优化的详细过程，提出了根据磁块剩磁快速计算波荡器峰值场强误差和积分场的方法。     

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。     

翻转线圈系统在波荡器积分场测量中的应用

 为了更有效地测量用于上海同步辐射光源波荡器的积分场误差,在已有的伸展线磁测系统的基础上研制了一套翻转线圈磁测系统,该系统的运动控制、数据采集和数据分析处理均可自动完成。在利用这套磁测系统测量3.4×10^-6 T·m磁场积分时获得高于1×10^-6 T·m的测量精度,初步的实验结果表明这套波荡器积分磁场测量系统具有测量精度好、速度快的特点,与已有的伸展线磁测系统、平移线圈磁测系统和霍尔点测系统相比,它更适合于测量波荡器的一、二次场积分和多极场分量。     

波荡器位相误差及垫补计算

 给出了波荡器位相误差的函数式, 可由磁场峰值分布直接计算波荡器位相均方根误差。给出了波荡器垫补修正场的简单解析计算式, 可根据垫片的位置、大小、厚度、磁极间隙等参数直接计算出对磁场及位相的修正 。     

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).     

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.     

Analytical Description of Electron Motion in a Three-Dimensional Undulator Field

The motion of relativistic electrons in an ideal three-dimensional magnetic undulator field satisfying the stationary Maxwell equation is considered. The system of nonlinear differential equations of the electron motion is solved analytically using perturbation theory rather than the method for averaging fast oscillations of the electron trajectory (the focusing approximation), as was done in a series of previous studies. The obtained analytical expressions for the trajectories describe the behavior of particles in a three-dimensional magnetic undulator field much more accurately than the formulas obtained within the framework of the focusing approximation. The analysis of these expressions shows that the behavior of electrons in a three-dimensional undulator field is much more complicated than that described by equations obtained using the averaging method. In particular, it turns out that the electron trajectories in the undulator have a cross dependence; in this case, variations in the initial trajectory parameters in the vertical plane cause changes in the horizontal trajectory components, and vice versa. The results of calculations of the trajectories carried out using analytical expressions are close to those of numerical calculations using the Runge-Kutta method.     

Electron Motion in the Three-Dimensional Field of Undulator

In this paper we consider the motion of relativistic electrons in an ideal three-dimensional magnetic field of an undulator. The ideality of the magnetic field means that, on the undulator axis, the field is directed strictly vertically upward and has a strictly sinusoidal shape. In the overwhelming majority of cases, only this leading component of the field is taken into account in calculating the electron trajectory. In this paper, in the equations of motion of an electron in the magnetic field of an undulator, all three components of the field are taken into account, so that the undulator field under consideration satisfies the stationary Maxwell equations. In this case, the differential equations of motion of the electron are solved analytically with the help of perturbation theory, and not by the method of averaging over fast oscillations of the electron, as was done in a number of previous papers. These analytic expressions for trajectories describe the behavior of particles in the focusing magnetic field of an undulator much more completely. An analysis of these expressions shows that the behavior of electrons in such a three-dimensional field of the undulator is much more complicated than what follows from the equations obtained by the averaging method. In particular, there is a cross effect when changes in the initial vertical parameters of the electron trajectory cause changes in the horizontal component of its trajectory and vice versa. A comparison of the solutions obtained analytically with the results of numerical calculations of electron trajectories using the Runge–Kutta method demonstrates their high accuracy.     

On Undulator Radiation in Infrared and Millimeter Wave Ranges: Part 1—Classical Description

In this paper the results of theoretical and experimental research of the motion and radiation of low-voltage electron beams in Motz undulator are given. Constant magnetic field of undulator ordinary magnet under some conditions can be substituted for field of magnet dipole. Such substitution allows us to accurately integrate the electron trajectory. We can with the high accuracy consider this field as chaotic and this fact allow us to use well-known Ginsburg theory for estimation of power of braking radiation. There are longitudinal and transversal components of magnetic fields of described structure. The longitudinal component can be gained by covering of external longitudinal constant magnetic field. In this connection certain resonance effects are observed.     

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。     

特大非球面度离轴非球面补偿器结构设计与装调

针对快焦比特大非球面度离轴非球面反射镜,设计了3片式Offner补偿器。为应对3片式补偿器对中心偏差及镜间隔严格的公差要求,设计了相应的补偿器镜筒结构。该结构使透镜中心倾斜及平移调整相分离,实现补偿器的高精度装调。根据中心偏差测量仪的测量结果,2片补偿镜之间倾斜误差4.4″,平移误差3.5 μm, 镜间隔误差3.8 μm;补偿镜组与场镜之间倾斜误差5.3″,平移误差4.2 μm, 镜间隔误差7.2 μm,满足检测使用要求。利用该补偿器及4D动态干涉仪对精抛光阶段的离轴非球面进行检测,面形结果PVq值达到0.135λ,RMS值达到0.019 5λ,优于设计要求。     

Magnetic design and modelling of a 14 mm‐period prototype superconducting undulator

The magnetic design of a ten‐period (each period 14 mm) prototype superconducting undulator is reported using RADIA. The results of modelling the magnetic flux density are presented in an analytical formula. The dependence of the field integrals and phase error on the current density and undulator gap has been calculated, and temperature curves are determined for the models and are compared with earlier reported Moser–Rossmanith fits.