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.     

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.     

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.     

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.     

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.     

Momentum spread in a relativistic electron beam in an undulator

The motion of the relativistic electron beam in the spatially periodic magnetic field of an undulator has been considered taking into account the effect of the incoherent field of the spontaneous undulator radiation on the motion of the electrons. An expression for the rms momentum of the electrons has been obtained. It has been shown that the momentum spread in the ultrarelativistic electron beam increases in the spontaneous incoherent emission mode. Conditions for the self-amplification of the spontaneous undulator radiation in ultrashort-wavelength free-electron lasers have been discussed.     

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.     

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.     

横向聚焦波荡器磁场的计算与分析

横向聚焦波荡器可用于电子束能量较低、函数较小的情况。在现有横向聚焦波荡器设计方案的基础上,通过倾斜磁块端面和磁极面提出了几种不同结构的横向聚焦波荡器方案。利用三维磁场模拟程序Radia,对这些波荡器的聚焦场特性进行了模拟计算,对其聚焦特性与主要参数的关系进行了研究,并与现有其他横向聚焦波荡器的聚焦特性进行了对比。对弱聚焦和强聚焦两种情况,分别给出较好的结构方案。对于弱聚焦,平均聚焦梯度随中心场强的增大而略有增大,变化不明显;对于强聚焦,平均聚焦梯度随中心场强的增大而明显增大,呈高次曲线关系。     

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.     

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。     

强聚焦混合型扭摆器的优化设计

扭摆器是自由电子激光装置的一个核心部件.强聚焦混合型扭摆器具有结构紧凑等一系列优点,但其结构复杂,技术难度很高,在国内还没有成功研制的先例.本文描述该类型扭摆器研制的一个基础而关键性的工作:一台10周期的强聚焦混合型扭摆器的优化设计     

Effects of energy spread on brightness and coherence of undulator sources

The (spectral) brightness for partially transverse coherent sources such as synchrotron radiation and free‐electron laser sources can be defined as the maximum of the Wigner distribution. Then, the brightness includes information on both coherence and wavefront characteristics of the radiation field. For undulator sources, it is customary to approximate the single‐electron electric field at resonance with a Gaussian beam, leading to great simplifications. Attempts to account for the modified spatial and angular profile of the undulator radiation in the presence of detuning due to energy spread, currently build on the simplified brightness expression derived under the assumption of Gaussian beams. The influence of energy spread on undulator radiation properties is becoming important in view of diffraction‐limited rings with ultralow emittance coming on‐line. Here the effects of energy spread on the brightness of undulator radiation at resonance are discussed, as well as relevant relations with coherence properties.     

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.     

Diamagnetic and Paramagnetic Effects in Free-Electron Lasers

The effect of high-current relativistic electron beams (REB's) on the undulator field amplitude in free-electron lasers (FEL's) is investigated. Two mechanisms of excitation of periodic magnetostatic self-fields by REB are considered: 1) a static mechanism that is realized at stationary motion of REB in the undulator field; and 2) a dynamic mechanism that is realized at signal wave amplification. The static mechanism in the absence of an axial magnetic field leads to a decrease of the total undulator field amplitude (a diamagnetic effect). The dynamic mechanism for low-density beams leads to an increase of the total undulator field amplitude (a paramagnetic effect), with a subsequent increase of electron efficiency. For high-density beams, the effect of the phase shift of the total undulator field is most essential, due to which the growth of the signal wave amplitude is limited by nonlinear mismatch of synchronism.     

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。     

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.     

Acceleration and focusing of intense ion beams in rf undulator structures

Bunching, acceleration, and transverse focusing of intense ion beams in an undulator linac are considered. Such an accelerator features the absence of an rf field harmonic synchronous with the beam. A 3D equation of motion in the Hamiltonian form is derived in the smooth approximation, and the general conditions for ion beam acceleration and transverse focusing in the undulator linac are formulated. Basic analytical results are compared with the results of numerical simulation of the beam dynamics in the polyharmonic field of an accelerating cavity.     

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。