Chaotic electron trajectories in a circular free electron laser

The motion of a relativistic electron is analyzed in the field configuration consisting of a circular wiggler magnetic field, an axial magnetic field, and the equilibrium self-electric and self-magnetic fields produced by the non-neutral electron ring. By generating Poincare surface-of-section maps, it is shown that when the equilibrium self-fields is strong enough, the electron motions become chaotic. Although the realistic circular wiggler magnetic field destroys the integrability of the electron motion as the equilibrium self-fields do, the role the latter plays to make the motions become chaotic is stronger than the former. In addition, the axial magnetic field can restrain the occurrence of the chaoticity.     

在环型自由电子激光器中电子运动的混沌特性

本文分析了相对论性电子在环型摆动器磁场,轴向磁场和由非中性电子束产生的平衡自电场和自磁场中的运动。通过数值计算画出Poincare截面映射图,表明当自场足够强时,这种运动变成混沌的。虽然现实的环型摆动器场和自场一样使电子运动方程成为不可积的,但自场使运动产生混沌的作用要比摆动器场强。轴向磁场有抑制混沌发生的作用。     

The influence of equilibrium self-fields on the spontaneous emission and stimulated emission of fel with a linearly polarized wiggler

The orbits of an electron in a linear wiggler and axial field under the influence of self-fields are calculated. Then the spontaneous emission coefficient and the growth rate of the stimulated scattering are obtained. The numerical results show under some condition the self-fields can enhance the radiation.     

CHARACTERISTIC STUDY OF A FREE ELECTRON LASER WITH LINEARLY POLARIZED WIGGLER AND RECTANGULAR WAVEGUIDE

The characteristics of coherent radiation produced by a cylindrical electron beam passing through a rectangular waveguide and linearly polarized wiggler are studied. The instability analysis is based on the linearized Vlasov-Maxwell equations for the perturbations about a self-consistent beam equilibrium. The dispersion equation of TMmn mode is deduced and by making use of numerical calculation the radiation frequency and growth rate as a function of electron beam energy and radius, axial magnetic field, wiggler field and wave length are presented and discussed.     

等离子体波摆动器中电子运动的混沌特性

本文用Ｐｏｉｎｃａｒｅ截面及Ｌｙａｐｕｎｏｖ指数两种方法，研究了新型的等离子体波摆动器中电子运动的混沌特性，结果表明，当摆动器强度增大时电子从规则运动向混沌状态发展，这是提高自由电子激光输出功率时必须解决的一个重大课题。     

Phase velocity of a transverse electric wave propagating in a magnetized electron beam

In this paper three-dimentional simulations are carried out to the phase velocity of a transverse electric wave which propagates in a relativistic electron beam magnetized by a wiggler field and an axial guide magnetic field. Results show that the phase velocities are quite different from each other as the axial guide magnetic field changes its direction.     

平衡自场对有线性摆动器的自由电子激光器的自发辐射和受激辐射的影响

本文计算了在平衡自场、线性摆动器场和轴向磁场作用下的电子轨道,并由此求得有线性摆动器的自由电子激光器的自发辐射和受激辐射。结果表明自场有增强辐射的作用。     

纵向摇摆器磁场中的电子轨道

本文求解纵向摇摆器磁场加直流磁场中的电子运动方程,在直角坐标系中求得电子速度的严格解析解,并导出直角坐标和圆柱坐标中电子位置坐标的近似析解。同时用电子运动模拟计算进行了校验,指出近似解析解有较好的准确性。     

THE TRANSVERSAL GEOMETRIC EFFECTS IN A FREE ELECTRON LASER

The effects of a beam thickness and a conducting wall in a free electron laser with a linearlypolarized wiggler magnetic field and an axial magnetic field are investigated within the framework of fluid-Maxwell equations.The growth rate of free electron laser instability is obtained,in which the nonlinear bulkand surface current density are simultaneously considered.The numerical calculations indicate that the bulkcoupling is dominant.There is an optimum beam thickness and separation between the conducting walls forwhich the growth rate is maximum.     

加反向导引场自由电子激光动力学理论

本文对加反向导引场自由电子激光加以描述，假定摇摆场是理想化的，分析电子的运动轨道，解得运动常数，求解符拉索夫方程得到扰动分布函数，从波方程可得色散关系，进而得增益公式，该公式近似适用于有导引场和无导引起的情况。     

Chaotic characteristics of electron motion in the static magnetic fields and self-fields of the electron beam

In this paper We study the properties of electron motion when a nonneutral electron beam goes through a static magnetic field. The self-electronic and magnetic fields also affects on the test electron. The Hamiltonian equations of electron motion are deduced and the Poincare surface of section and the Lyapunov exponent are used to prove that the electron motion becomes chaotic when the fields are strong enough.     

静电摇摆器自由电子激光的自发辐射

基于静电摇摆器中电势场的一种典型二维模型 ,在小振幅振动情况下讨论了相对论电子束在其中的运动规律 ,计算得到了该类型自由电子激光的自发辐射谱。上述结果与平面磁摇摆器有类似的形式     

Small signal gain of free electron lasers with nonuniform wigglers

The small-signal gain of free electron lasers is calculated by solving the single-electron equations of motion to second order in the laser field. Analytic results for free electron lasers with linearly varying wiggler resonant frequency show that the small signal gain of such lasers behaves differently from that of lasers with uniform wiggler resonant frequency and is significantly smaller.     

Three-dimensional theory of free electron lasers with an axial guide field

The collective interaction in a free electron laser with a combined helical wiggler and uniform axial guide field is presented in the low-gain regime. The wiggler model we employ is fully self-consistent and includes all transverse inhomogeneities. The analysis is performed for a free electron laser (FEL) amplifier in which the radial dependence of the radiation is treated using both the TE and TM waveguide modes. Substantial discrepancies are found to exist between the results for the realizable and ideal wigglers, and a selection rule relating the TElnand TMlnmodes with resonant amplification at thelth harmonic of the FEL Doppler upshift.     

Analog computer solutions for correction of ripple in magnetically-collimated electron beams

Analysis of the dynamics of an electron beam in a magnetic collimating field leads to formulas which can be processed conveniently in an analog computer to obtain individual solutions. This technique is applied to the problem of correcting the ripple which is generally imposed upon the envelope of the beam after passage through a spatial variation or reversal of the collimating field. However, a relatively general viewpoint is retained in developing methods and formulas for studying the motion of an outermost electron of a relatively uniform, round, straight electron beam. Fer this reason the results can be applied to beams from shielded or unshielded cathodes, passing through uniform, periodic, or nonperiodic reversing magnetic collimating fields. A simplified development of the mathematical theory of magnetically confined electron beams is presented, including the effects of spatial variations and reversals in the collimating magnetic fields. Formulas are developed for the equilibrium electron beam radius, and for the ripple frequency, axial wavelength, amplitude, and phase of the outermost electrons, in terms of the field parameters and the initial beam conditions. Analog computer solutions for an electron beam with various collimating magnetic fields serve to illustrate and confirm the developed formulas. From these computer solutions, suggestions are derived for guidance in shaping collimating magnetic fields so that electron beam ripple will be prevented or reduced.     

渐变Wiggler技术在低能电子束喇曼型自由电子激光器中的应用

本文利用有质动力势导出了自由电子激光器效率提取表达式,分析了渐变Wlggler技术对提高激光器效率的作用,并利用这一技术进行了渐变Wiggler场强自由电子激光器实验。结果表明其效率是相应恒定Wiggler自由电子激光器的2.6倍。     

Equilibrium solutions for partially immersed relativistic electron beams

The equations relating the beam radius and axial electron velocity to easily measurable external beam parameters are developed for solid, relativistic beams. The beam parameters are tunnel voltage, beam current, axial magnetic field, cathode magnetic field, tunnel radius, and cathode radius. The equations are sufficiently complex to warrant the use of a digital computer if many cases are to be evaluated. Error indicators are formulated to prevent use of the relations beyond their range of validity. The equilibrium solutions for relativistic electron beams from unshielded cathodes show that the required magnetic focusing field is lower than that computed from nonrelativistic formulas. The angular magnetic field produced by the beam itself aids in focusing the electrons. The potential depression due to space charge is analyzed. Correction curves are given which allow the use of nonrelativistic equations in predicting equilibrium behavior. The maximum possible microperveance of relativistic beams is shown to be lower than the classical value of 25.4.     

电子在多层膜摇摆器中的辐射

提出了利用多层膜作自由电子激光器的摇摆器,利用虚光子和康普顿散射讨论了运动电子在多层膜摇摆器中的自发辐射。(Fe/Cr)N等铁磁-非磁层状材料的铁磁层之间存在反铁磁耦合,因此可以利用磁性多层膜制作自由电子激光器的摇摆器。考虑到静磁场的空间周期只有7.8nm,要精确计算电子在多层膜摇摆器中运动的自发辐射的波长和辐射功率就必须考虑电子的反冲。给出了运动电子在多层膜摇摆器中的自发辐射波长和辐射功率的精确计算表达式。结果发现,自发辐射波长和辐射功率表达式中都含有康普顿波长。     

自由电子激光器中相对论电子与wiggler同轴性的要求

讨论了自由电子激光器中,相对论电子束与wiggler的轴线有小夹角时激光增益的变化,并给出了最大容许偏角。     

喇曼自由电子激光器辐射谱的测量

本文报道了利用微波栅摄谱仪测量在超辐射工作条件下的喇曼自由电子激光器辐射谱的初步结果。观察到了毫米波自由电子激光器的调谐特性。实验结果表明,辐射谱的中心频率随波荡场强度的增加而减小,这与考虑波导模影响的集体制式自由电子激光的有关理论预言相符。