The refined theory of transversely isotropic piezoelectric rectangular beams

The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the general solution of transversely isotropic piezoelasticity and Lur’e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory. As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply supported piezoelectric beam is examined.     

The electromagnetic field of a guided Gaussian beam

An electromagnetic wave traveling along a dielectric slab between two parallel, plane conductors is analyzed for a special case that is particularly relevant to guided laser beams employed in integrated optics. The beam is assumed to have an approximate gaussian field dependence along the y-direction, defined to be transverse to the direction of propagation and to the normal to the conductor planes. Approximate expressions for the field in a well collimated beam are derived. Asymptotic approximations, valid far away from the focus of a beam that is not necessarily well collimated, are also derived. It is found that the TE and TM guided gaussian beams are not linearly polarized. This is unlike the case for the usual waveguide modes whose fields are constant along the y direction. It is also found that the guided gaussian beam must have a focus and that the divergence from focus is more rapid than for a similar gaussian beam in free space.     

自由电子激光的单粒子理论及其应用

本文建立了圆极化摇摆场自由电子激光的单粒子理论,导出了电子未扰轨道及其稳定性判据和自由电子激光单程增益的表达式。单程增益由三项构成,其中第一项即自由电子激光不稳定性的增益与动力学理论得到的指数增益相符。第二项和和三项表明存在一对新的不稳定性——正不稳定性和负不稳定性。该理论没有对电子未扰轨道纵向速度作任何假设,不仅可以更合理地用于常规自由电子激光的研究,而且可以用于短周期摇摆器弱相对论自由电子激光研究。后者由于电子未扰轨道纵向速度比较低,已有的单粒子理论中所作的电子纵向速度约等于光速的假设不再成立。借助数值分析,我们发现:(1)稳定轨道Ⅱ的弱导引场区域也出现了动力学理论描述过的与自由电子激光互作用机理相悖的现象。(2)正不稳定性和负不稳定性在稳定轨道Ⅰ的导引磁场临界值附近可能严重影响自由电子激光的工作。(3)可以使用较弱的短周期摇摆场和较强的导引场产生高频率高增益相干受激辐射。     

Simulation of a Radio-Frequency Photogun for the Generation of Ultrashort Beams

A radio-frequency photogun for the generation of ultrashort electron beams to be used in fast electron diffractoscopy, wakefield acceleration experiments, and the design of accelerating structures of the millimeter range is modeled. The beam parameters at the photogun output needed for each type of experiment are determined. The general outline of the photogun is given, its electrodynamic parameters are calculated, and the accelerating field distribution is obtained. The particle dynamics is analyzed in the context of the required output beam parameters. The optimal initial beam characteristics and field amplitudes are chosen. A conclusion is made regarding the obtained beam parameters.     

Excitation of an upper hybrid wave by two intense laser beams and particle acceleration

This Letter presents an investigation of the excitation of an upper hybrid wave (UHW) by cross focusing of two intense laser beams in a collisionless hot magnetoplasma, when relativistic and ponderomotive nonlinearities are operative. The electric vectors of the two beams are polarized along uniform static magnetic field and the beams propagate perpendicular to the static magnetic field. Analytical expressions for the beam width of the laser beams, electric vector and power of the excited UHW and energy gain have been obtained. The UHW generation at the difference frequency and particle acceleration has also been studied. The nonlinear coupling between intense laser beams and UHW is so strong that UHW gets excited and a large fraction of the laser beam energy gets transferred to UHW and this UHW accelerates electrons. It has been shown that the presence of a magnetic field affects significantly the power of the UHW and energy gain by the electron in the presence of the UHW.     

Characteristics of electron beams formed in a diode with magnetic insulation

The problems of the formation of relativistic electron beams in a cylindrical diode with an annular cathode are discussed in the approximation of an infinitely strong guiding magnetic field. The beams are treated as infinitely thin. The following cases are investigated: 1) The formation of an electron beam moving off the cathode with an initial velocity. The case in which the field on the cathode is not equal to zero is investigated. It is shown that the potential of the electron beam can be determined in a nonunique fashion in the drift region. 2) The formation of a two-velocity electron beam. The possibility of controlling the flow of kinetic energy of the beam by varying the fraction of fast electrons in it is shown. 3) The formation of an electron beam in a diode with the help of two opposed cathodes at different potentials. A strong dependence of the current in the diode on the potential difference between the cathodes is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 36–39, December, 1981.     

兰州重离子加速器冷却储存环中电子冷却性能

为了在兰州重离子加速器冷却储存环(HIRFL-CSR)上开展一维离子束序化的研究,在CSR主环上,对6.39 MeV/u的58Ni19+离子束进行了冷却累积实验。测量了离子束与电子束之间不同的水平、垂直夹角以及不同电子束剖面的情况下,束流累积及束流寿命变化情况;重点研究了离子束衰减过程中动量分散随离子数的变化规律,拟合计算得到了动量分散随离子数按照幂函数衰减的指数;在给定离子数的情况下,动量分散随夹角、电子束剖面的依赖关系,为下一步在CSR上获得纵向一维有序化离子束的研究做准备。在实验中观测到在较大的夹角情况下,离子束出现纵向振荡和中心频率移动。     

Coherent interaction of ion and electron beams in systems with electron cooling

A hydrodynamic approximation is used to study the behavior of dipole modes of the transverse oscillations of an ion beam in a storage ring with an electron cooling section. It is shown that in addition to the finite interaction time of the beams, instability may be caused by a specific interaction effect between the ion and electron beams in the magnetic field which leads to redistribution of energy between the various modes of the ion beam oscillations. In this case, the condition that the determinant of the transfer matrix for the cooling section does not exceed unity no longer guarantees the stability of the transverse coherent oscillations of the ion beam and all the eigenvalues of the complete matrix of the ion motion including the storage ring must be analyzed. Calculations of the stability of ion beam dipole oscillations are presented for the parameters of CELSIUS.     

Stimulated Cherenkov radiation of a relativistic electron beam moving over a periodically corrugated surface (quasi-optical theory)

The propagation of waves over periodically corrugated surfaces and their excitation by relativistic electron beams are investigated within the framework of a quasi-optical approach. The dispersion equation is derived for normal waves under the assumption of a small (in the scale of the period and wavelength) corrugation depth, based on which two limiting cases are identified. In the first limiting case, the wave frequency is far from the Bragg resonance, and the propagation of waves can be described in terms of the impedance approximation, in which the fundamental spatial harmonic slows down. In the second limiting case realized at frequencies close to the Bragg resonance, the field is represented as two counterpropagating quasi-optical wave beams coupled on a corrugated surface and forming a normal surface wave. When interacting with an electron beam, convective instability, which can be used to realize amplifier regimes, corresponds to the first case, and absolute one, which is applied in surface-wave oscillators, corresponds to the second case. The developed theory is used to determine basic characteristics of amplifier and oscillator schemes: the growth rates, the energy exchange efficiency, and the formation of a self-consistent spatial structure of the radiated field. The practical realization of relativistic submillimeter amplifiers and surface-wave oscillators is shown to hold promise.     

Efficiency enhancement of a two-beam free-electron laser using a nonlinearly tapered wiggler

A nonlinear and non-averaged model of a two-beam free-electron laser (FEL) wiggler that is tapered nonlinearly in the absence of slippage is presented. The two beams are assumed to have different energies, and the fundamental resonance of the higher energy beam is at the third harmonic of the lower energy beam. By using Maxwell's equations and the full Lorentz force equation of motion for the electron beams, coupled differential equations are derived and solved numerically by the fourth-order Runge-Kutta method. The amplitude of the wiggler field is assumed to decrease nonlinearly when the saturation of the third harmonic occurs. By simulation, the optimum starting point of the tapering and the slopes for reducing the wiggler amplitude are found. This technique can be applied to substantially improve the efficiency of the two-beam FEL in the XUV and X-ray regions. The effect of tapering on the dynamical stability of the fast electron beam is also studied.     

Electron beam generation in a magnetron diode with metal secondary-emission cathode

The effects of electric and magnetic field intensities, the triggering-pulse droop rate, and the electrode diameter on the processes of electron beam formation and generation were studied experimentally. The results of mathematical simulation of the secondary-emission multiplication of the electron flow are presented. Tubular electron beams with a wall thickness of 1.5–2 mm, a current density of 1–70 A/cm², and a particle energy of 5–100 keV were obtained. It was shown that several electron bunches could be obtained during a single voltage pulse.     

3.3MeV直线感应加速器的电子束传输研究

采用SLAC-226程序,模拟了电子束在3.3MeV加速器中的加速与传输过程,并与从电子束传输的层流近似出发所推导的边包络方程解进行了比较。程序和包络方程都考虑了束流的自生电磁场及外加电磁场。     

Energy exchange between a test charge and an unstable electron beam

An investigation is made of the interaction between a test charge and an electron beam which is convectively unstable against plasma oscillations. An analysis is made of the negative-mass instability of the longitudinal motion. Expressions are derived for the reaction force exerted by the electron plasma polarized by the moving charge and for the diffusion tensor arising from electric field fluctuations. The approximation of uniform rectilinear motion of a test particle is used to estimate the systematic and diffusion components of the rates of change in its energy. It is shown that in this case, interaction with an unstable electron beam leads to acceleration of the particle in respect to the longitudinal degree of freedom (antifriction) and under certain conditions enhances the friction effect (cooling) in respect to the transverse degrees of freedom. An assessment is made of the possibility of obtaining an overall positive friction effect by using a special “sweeping” procedure whereby the longitudinal velocity of the electron beam is changed in a specific manner consistent with the cooling process. Zh. Tekh. Fiz. 67, 58–61 (November 1997)     

等离子体填充波纹波导中低频模式特性分析

采用等离子体流体模型和线性场理论，导出了在强引导磁场下，一无限薄环形等离子体加载 波纹波导中电磁波传播的色散关系.数值计算并分析了在不同的等离子体填充密度下，低频 等离子体模式的色散特性和行波管的小信号增益.研究发现，低频等离子体模式可与相对论 电子束发生同步互作用使高频信号放大.同时，在无限薄环形等离子体填充条件下，波纹波 导中的低频等离子体模式严格满足Floquet定理所要求的周期性，其上截止频率不再受到等 离子体频率的限制，当密度较大时，等离子体模式还可与TM模式发生耦合. 关键词： 等离子体 波纹波导 色散关系 增益     

电子在激光驻波场中运动产生的太赫兹及X射线辐射研究

采用单电子模型和经典辐射理论分别对低能和高能电子在线偏振激光驻波场中的运动和辐射过程进行了研究. 结果表明: 垂直于激光电场方向入射的低速电子在激光驻波场中随着光强的增大, 逐渐从一维近周期运动演变为二维折叠运动, 并产生强的微米量级波长的太赫兹辐射; 高能电子垂直或者平行于激光电场方向入射到激光驻波场中, 都会产生波长在几个纳米的高频辐射; 低能电子与激光驻波场作用中, 激光强度影响着电子的运动形式、辐射频率以及辐射强度; 高能电子入射时, 激光强度影响了电子高频辐射的强度, 电子初始能量影响着辐射的频率; 电子能量越高, 产生的辐射频率越大. 研究表明可以由激光加速电子的方式得到不同能量的电子束, 并利用电子束在激光驻波场的辐射使之成为太赫兹和X射线波段的小型辐射源. 研究结果可以为实验研究和利用激光驻波场中的电子辐射提供依据.     

ELECTROSTATIC WAVE EXCITATION BY LITHIUM ION BEAM IN UPSTREAM RECION OF AMPTE LITHIUM RELEASES

It is shown that the electron cyclotron harmonic waves and the ion acoustic broad band obsefved in the transition region and the upstream region of the two AMPTE lithium releases can be explained ,by the interaction of the lithium ion beams and the solar wind plasmas.The cycloidal motion of the freshly produced lithium ion in the solaz wind magnetic and electric fields is essential for these wave excitations.Two simplified models in ion velocity distribution are used in the dispersion relation analysis,one is an orientating ion beam, the other is an ion beam ring (the hollow beam).It is shown that the electron cyclotron. harmonics can be effectively excited by both of these beams if they are very cold. Satisfactory consistence of the theory with the observed results is obtained for the harmonic excitations.The strong Iow frequency (much less than the electron cyclotron frequency) noices might be multioriginal.It is also proposed that the interaction of the lithium ion beam and the solar wind protons provides a suitable mechanism for exciting these broad bands.     

Self-field effects on electron dynamics in a three-dimensional helical wiggler free-electron laser with axial magnetic field

An analytic linear theory of the electron dynamics in a three-dimensional helical wiggler free electron laser (FEL) with axial magnetic field is presented. Orbits are obtained by perturbing the steady state-trajectories in order to determine the characteristic frequencies Ω_± of the FEL. The effect of the self-fields on electron dynamics is studied and modified steady-state orbits and their stabilities have been analysed considering variation of electron energy and density. Among the features encountered is that in both group-I and group-II, one of the characteristic frequencies may have either signs affecting then the stability of the motion, while in group-II operation a repulsion of the frequencies at a pseudocrossing leads to highly perturbed trajectories when the wiggler frequency is approximately half the cyclotron frequency. Self-fields effects can significantly impair the stability of the electron orbits. For group-I orbits, they are more important for higher wiggler frequencies and lower beam energies. For group-II orbits, they remain less important for higher wiggler frequencies and lower beam energies before reaching the inversion zone, then they behave as for group-I orbits. It should be remarked that self-fields shift the inversion zone towards higher cyclotron frequencies the thing that is obtained by either decreasing the wiggler frequency or increasing the beam energy. It is shown that the axial velocity-induced self-magnetic field has a diamagnetic effect for both groups orbits, while the wiggler-induced self-magnetic field has a diamagnetic effect for group-I orbits and a paramagnetic effect for group-II orbits. The paramagnetic and diamagnetic effects are more important for higher beam energies and densities.     

Scattering of a Gaussian Beam by a Sphere Using a Bromwich Formulation: Case of an arbitrary location

A complete theory of Gaussian beam scattering by a sphere is exposed. It is a generalization of the Lorenz-Mie Theory to the case of Gaussian beam illumination. The spherical, isotropic and homogeneous scatterer may be located anywhere with respect to the beam. The Bromwich Scalar Potentials are used to solve the scattering problem and expressions are obtained for the scattered field (both in the near field and far field regions), the scattered intensities and the phase angle. In the limit of special cases the expressions agree with previous works restricted to more particular problems.     

Efficiency enhancement of a two-beam free-electron laser using a nonlinearly tapered wiggler

A nonlinear and non-averaged model of a two-beam free-electron laser(FEL) wiggler that is tapered nonlinearly in the absence of slippage is presented.The two beams are assumed to have different energies,and the fundamental resonance of the higher energy beam is at the third harmonic of the lower energy beam.By using Maxwell’s equations and the full Lorentz force equation of motion for the electron beams,coupled differential equations are derived and solved numerically by the fourth-order Runge-Kutta method.The amplitude of the wiggler field is assumed to decrease nonlinearly when the saturation of the third harmonic occurs.By simulation,the optimum starting point of the tapering and the slopes for reducing the wiggler amplitude are found.This technique can be applied to substantially improve the efficiency of the two-beam FEL in the XUV and X-ray regions.The effect of tapering on the dynamical stability of the fast electron beam is also studied.     

Passage of a high-current relativistic electron beam through matter

A solution is presented for the problem of passage of a high-current relativistic electron beam through matter in the stationary case with one-dimensional geometry. The system of equations describing the passage of the beam consists of the kinetic equation for fast electrons, which considers the effect of the electric field on the magnitude and direction of particle momentum, the equations for the field produced by the space charge generated by thermalized electrons, and relations connecting the conductivity of the medium to the radiation field. Higher-order perturbation theory is used for the solution. The solutions reveal that the distribution of expended energy, thermalized electrons, and other properties of the flow are highly dependent on the density of the incident flux and the conductivity of the medium. It will be shown that linear transfer theory may be applied to calculation of the passage of high-current beams through matter over a wide range of currents and conductivities, if the barrier thickness does not exceed one-half the path length, but cannot be used for calculation of passage through large-thickness barriers, i.e., with thickness comparable to the electron free path length.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 67–74, September, 1979.The author thanks A. N. Didenko and A. M. Kol'chuzhkin for their evaluation of the study.