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.     

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.     

Investigation of parameters of undulators with permanent magnets

Investigations of a hybrid type undulator for the terahertz FEL with ferrite magnets were carried out. The study began with an undulator simulation in FEMLAB environment and measurements on the created model. The work presents the results of study of the dependence of magnetic field on the height of the magnetic elements and study of the magnetic induction depending on the ratio of the width of magnetic elements to the distance between them. It is shown that the hybrid undulator scheme allows selecting the optimum parameters of the undulator. The obtained results can be used for choosing the optimum parameters of undulators of the terahertz-range FEL.     

波荡器谐波场增强效应对电子自发辐射谱的影响

 有效利用电子束在波荡器中运动时产生的谐波辐射,是获得更短波长辐射最直接的方法之一。提高波荡器磁场的谐波分量可以提高电子束的谐波辐射光场强度。分析了一种改进Halbach型波荡器结构,计算了其磁场的构成,分析表明这种结构可以使磁场的三次谐波分量提高至基波分量的25%左右。以合肥光源的电子束参数为例,计算了波荡器磁场谐波分量增强后对电子束自发辐射谱的影响。计算结果表明,波荡器磁场谐波分量增强至25%时,可以使电子束自发辐射的三次谐波辐射增强至基波辐射光子通量的67%左右。     

On the radiation of a planar undulator with constant magnetic field on its axis taken into account

The intensity of undulator radiation, distortion of the spectrum, and the broadening of spectral lines of a planar undulator with a constant component of the magnetic field on its axis are studied using the technique of generalized special functions. Based on the obtained mathematical solutions, it is shown how the choice of certain values of the undulator parameters makes it possible to decrease the distortions of its radiation spectrum. The dependence of distortion of the spectral lines on the number of periods, the magnetic field, and other undulator parameters is determined analytically. The broadenings of the spectral lines caused by homogeneous and inhomogeneous effects produced by the constant-field components in undulators are compared. The possibility of the influence of the Earth’s magnetic field on the radiation of an undulator with a large number of periods is analyzed.     

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。     

Influence of a constant magnetic field on the radiation of a planar undulator

The influence of a constant magnetic field on the radiation of a planar undulator is studied analytically with the use of generalized Bessel functions. The behavior of on-axis radiation intensity in the undulator and the influence of a magnetic field on off-axis radiation are investigated. The critical magnitude of the constant component of the magnetic field, which has a significant effect on the motion of electrons in the undulator, is calculated analytically. The examples of several planar undulators are discussed, and the influence of the Earth’s magnetic field on their spectrum is evaluated.     

In situ characterization of undulator magnetic fields

A new in situ method is proposed to characterize the peak magnetic fields of undulator sources. The X‐ray beam emitted by the HU52 Apple‐2 undulator of the DEIMOS beamline of the SOLEIL synchrotron is analyzed using the Bragg diffraction of a Si(111) crystal. Measurements over the undulator gap range in linear horizontal polarization are compared with simulations in order to rebuild the Halbach function linking the undulator gaps to their peak magnetic fields. The method presented also allows information about the electron beam to be obtained.     

上海深紫外自由电子激光波荡器的端部磁结构设计

 针对固定间隙的上海深紫外自由电子激光（SDUV-FEL）混合型波荡器的端部,用Radia程序进行了模拟计算。在端部不加任何电磁线圈补偿的情况下,通过减小端部磁铁、磁极的体积和变动端部磁极位置的方法对波荡器磁场进行了优化,优化以后波荡器横向磁场的边缘场强度降到5×10^-4 T（距离端部磁块边缘10 mm处）,边缘场波形没有了明显突起,优化后的横向磁场的一次积分曲线和二次积分曲线都有很大改善,端口处的一次积分值、二次积分值接近于零。     

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.     

W波段同轴静磁波荡器自由电子激光优化设计

基于同轴静磁波荡器的自由电子激光主要利用环形电子束与同轴TE模式的相互作用产生电磁辐射,是一种重要的毫米波辐射源。分析了同轴结构作用区内外半径、工作模式、电子束电压、波荡器周期等参数对辐射频率的影响规律,研究了电子束平均半径的选取原则和束波互作用腔的设计方法,设计了辐射频率在W波段的基于同轴静磁波荡器的自由电子激光,并进行了粒子模拟,在电子束电压为720 kV,电子束流为1 kA的情况下,获得了频率107 GHz、辐射功率35 MW的TE01模,束波转换效率为4.9%,束波作用腔总长度小于200 mm,同轴静磁波荡器的磁场幅度0.34 T。     

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.     

Theoretical and numerical analysis of electron motion in a three-dimensional undulator field

The results of numerical calculations of electron trajectories in the three-dimensional ideal magnetic field of an undulator are given. These trajectories can be regarded as exact results in our case. It is shown that, in a series of cases, results of the calculation of trajectories using approximate analytical formulas significantly differ from those obtained using numerical methods. The obtained numerical results show that the influence of the undulator on the dynamics of the electron beam is very complicated and cannot be reduced only to the focusing properties of the undulator magnetic field or wiggler.     

太赫兹自由电子激光波荡器的设计、测量与优化

波荡器电子轨迹中心偏移和磁场误差对CTFEL装置性能影响很大,通过前期设计和后期测量与优化将其限制在指标要求范围内。在前期设计中尽量避免引入全局性的系统误差:磁结构具有平面反对称结构,保证电子轨迹中心和波荡器磁轴重合;磁结构端部的特殊设计减弱了间隙对出口磁场二次积分的影响;机械系统的大梁和立柱具有良好的刚性,闭环控制系统保证了高的波荡器间隙控制精度,这些措施降低了间隙不一致引入的磁场误差。在后期测量与优化中削弱了磁场的残存全局系统误差和局部随机误差:利用磁场点测台测量了波荡器磁场的纵向和横向分布,通过调节标准单元组件位置对磁场进行了垫补和优化,优化后电子轨迹中心偏移、峰峰值误差、相位误差、好场区及其误差均满足指标要求。     

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。     

纯永磁波荡器基波与谐波磁场的三维计算与测试

 对标淮的纯永磁波荡器进行了三维磁场的有限元计算,给出了纯永磁波荡器的基波与谐波磁场的幅值与相位,并与测试结果进行对比,结果表明,标准的纯永磁波荡器谐波磁场幅值比基波幅值低两个数量级。     

The prototype of new variable period undulator for Novosibirsk free electron laser

To improve the parameters of the second stage Novosibirsk free electron laser we plan to replace the existing electromagnetic undulator by permanent-magnet variable-period undulator (VPU). The VPUs have several advantages compared to conventional undulators, which include wider radiation wavelength tuning range and an option to increase the number of poles. Both these advantages will be realized in the new undulator under development in Budker INP. There are some technical problems, which have to be solved before this idea can be implemented in practice. To check the solution of these problems we designed and manufactured a small undulator prototype, which has just several periods. In this paper, the results of mechanical and magnetic measurements of this undulator prototype are presented and compared with simulations.     

Effect of the correction of the motion of relativistic electrons in a magnetic undulator on the properties of undulator radiation

The properties of undulator radiation of electrons in a planar undulator with an arbitrary number of periods of the magnetic field and with correcting sections along the ends of the undulator are investigated. It is shown that in setups with relatively large number of periods of the field, the emission of particles in the correcting sections has a large effect on the general characteristics of undulator radiation of electrons in the setup. The experiment confirmed the basic assumptions of the theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 52–58 November, 1981.     

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.     

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.