Study on combined immersion electrostatic-magnetic focusing lenses without crossovers

Wide electron beam focusing properties of combined immersion electrostatic-magnetic focusing system are studied; their curvilinear axis aberration coefficients are derived. Based upon ray tracing method and curvilinear axis theory of wide electron beam systems, a program was written and as an example, a practical structure of the lens is numerically simulated. The computed results show that demagnified images with high resolution of tens of nanometers can be obtained for an object field size in millimeter range.     

阴极透镜象差的变分理论

本文运用变分原理研究了电磁复合聚焦阴极透镜的象差理论,导出了在任意象平面中象差系数的普遍公式。它们可以用Glaser导出的象差系数的线性组合来表示。这就表明了宽束与细束电子光学系统的象差都可以用统一的变分方法处理,并建立了两者之间的联系,本文采用矢量形式描写阴极透镜的近轴轨迹,并采用矩阵形式描写象差。本文所得的象差系数较之文献上已有结果形式更为简洁且适用于计算机计算。本文考虑了阴极面上磁场和横向电场不为零的情况,因而所得结果较为普遍。 关键词：     

A simple quadrupole-octupole electromagnetic lens

Charged particle beam trajectories in a simple electromagnetic quadrupole-octupole lens are numerically calculated based on analytical expressions for the +potential distribution. Locations of the lens foci in the image space are determined over a wide range of initial conditions. Relationships between the electrostatic and magnetic lens components that provide correction for chromatic aberrations of off-axis beams, which are different from classical beams, are obtained. Phase contours at the lens exit are calculated for beams occupying the major part of the aperture, and conditions for transforming the phase contour with minimal distortions are found.     

Electron mirror as a corrector of electron microscope objective aberrations

We describe a new optoelectronic system for correcting aberrations of the objective lens with the help of an electron mirror. The system is based on the implementation of a special focusing regime (so-called regime of superimposed images) in which two images of the object are formed in the plane passing through the center of the curvature of the mirror. One of these images is formed by the beams (with aberrations) emerging from the objective lens, and the other is formed by the beams (with cancelled aberrations) reflected from the mirror. The separation of the two superimposed images and visualization of the image with cancelled aberrations are performed by deflection of the electron beam in the axisymmetric magnetic field whose symmetry axis passes through the center of curvature of the electron mirror. The magnetic field distribution ensuring aberration-free deflection of the electron beam is calculated.     

两电极静电同心球系统的近轴电子光学及其空间-时间像差

将从近轴解出发研究两电极静电同心球系统的空-时轨迹及其像差.由近轴轨迹方程和近轴运动方程出发,先求解两电极静电同心球系统中自光阴极逸出的运动电子的近轴空间-时间轨迹,然后讨论此系统的静动态电子光学及其空间-时间像差,揭示近轴光学系统成像的一般规律.文中定义和推导了各级近轴空间像差和近轴时间像差,得到了与关于近轴空间-时间像差同样的结论,表明完全可以直接由近轴轨迹方程和近轴运动方程出发来研究理想成像及其空间-时间像差.     

A different algebraic method for the fifth-order combined geometric-chromatic aberrations of practical magnetic electron lenses

In this paper, differential algebraic (DA) method is applied to fifth-order combined geometric-chromatic aberrations of practical magnetic electron lenses. The magnetic fields of magnetic electron lenses, which are computed by FEM or FDM method, are in the form of discrete arrays. Thus the developed new DA method is applicable to engineering design and programs were written for computing the fifth-order combined geometric-chromatic aberrations of practical magnetic electron lenses. An example is given. The combined geometric-chromatic aberrations up to fifth order are calculated. It is proved that the numerical results for the magnetic fields in the form of discrete arrays have good accuracy compared with the results computed by using the magnetic fields expressed in analytical form. The accuracy is limited only by the accuracy of the numerical computation of the fields and the arithmetic errors. Finally, a practical magnetic electron lens is analyzed and discussed as an example.     

高电流密度圆柱状电子光学系统设计

设计了高电流密度圆柱状电子枪,并分析了枪体参数对电子注品质的影响;运用径向力平衡理论计算了聚焦磁场.三维模拟软件CSTPARTICLESTUDIO模拟显示,在枪体电极和空间电荷形成的静电场,以及聚焦磁场作用下,电子呈角向先变速后匀速螺旋状运动,其旋转半径始终与出射阴极面时的半径相同,从而在枪区和互作用通道内维持了注包络水平.模拟结果与设计理论相符.注平均电流密度达到24·4A/cm2,层流性良好,填充因子76·7%,流通率100%.     

电子束曝光机偏转系统及可动物镜分析

电子束大扫描场偏转系统设计中 ,像差的确定是一个必须解决的实际问题。以SDS 3电子束曝光机的磁复合偏转系统为基础 ,以双通道扫描原理进行扫描 ,分析了像差与电子束主轨迹的关系。给出了可动物镜的条件 ,并利用这一条件分析电子束最佳轨迹的结构和方法。并使用计算机辅助设计研究电子束曝光机聚焦偏转系统的结构。由该电子束曝光机试验结果表明 ,复合系统结构简单紧凑 ,像差小而可以不用动态校正。采用矢量描写电子轨迹 ,以积分式表示像差。以 0 .0 0 5rad半张角 ,5× 10 -5的高压纹波 ,5 0mm的像距 ,10mm× 10mm扫描场的边脚处 ,使动态校正前的总像差为 0 .0 3μm。     

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.     

宽束和细束电磁复合聚焦球面阴极透镜的象差理论

本文研究了对宽束和细束阴极透镜普遍适用的电磁复合聚焦球面阴极透镜的象差理论。在考虑物场和象场弯曲以及阴极面上磁场和横向电场不为零的情况下,导出了任意理想象面上的一级近轴横向象差和包括色象差在内的全部三级横向象差矩阵公式。所得的结果较为完整、普遍。本文详细讨论了宽束和细束阴极透镜的关系,并用轨迹法和变分法严格证明了:当考虑阴极面逸出电子具有一定的初能量和初角度分布,并采用准规范化电位表示的近轴轨迹方程来讨论系统的理想成象时,宽束和细束两类阴极透镜从象差理论以至导出的三级横向象差、象差系数表示式都可以统一起来。本文采用矢量描写轨迹,运用矩阵表示象差,形式简洁,象差系数积分收敛,适合于计算机计算。 关键词：     

Static and dynamic imaging electron optics and spatial-temporal aberrations in a bi-electrode spherical concentric system with electrostatic focusing

In imaging electron optics, for a concentric spherical system composed of two spherical electrodes with electrostatic focusing, the electrostatic potential distribution and the spatial-temporal trajectory of electron motion can be expressed by analytical forms. It is naturally to take such system as an ideal model to investigate the imaging properties, as well as the spatial-temporal aberrations, to analyze its particularity and to find the clue of universalities and regularities. Research on this problem has important significance, which can afford theoretical foundation not only in studying static electron optics for the night vision devices, but also in studying dynamic electron optics for high-speed image converter tubes.In the present paper, based on the practical electron ray equation and electron motion equation for a bi-electrode concentric spherical system with electrostatic focusing, the spatial-temporal trajectories of moving electrons emitted from the photocathode have been solved, the exact and approximate formulae for image position and flight time of electrons, have been deduced. Start from solutions of spatial-temporal trajectories, the electron optical spatial-temporal properties of this system are then discussed. According to the definitions of spatial-temporal aberrations, the paraxial and geometrical lateral aberrations, as well as the paraxial and geometrical temporal aberrations, have been deduced, that are classified by the order of and .     

Far-field vector-diffraction of off-axis parabolic mirror under oblique incidence

Based on a full vector-diffraction theory, a detailed theoretical study is carried out, aiming at providing a clear insight into the effects of different focusing and off-axis parabola parameters on far-field vector-diffraction properties of an offaxis parabolic mirror in the presence of misalignments of the incoming beam. The physical origin of these effects is also explored. The results show that the far-field intensity profile is altered by the distortion-, coma-, and astigmatism-like aberrations, which are caused by oblique incidence rather than inherent aberrations for the off-axis configuration. The radius of 90% encircled energy also increases but does not change monotonically with incident beam size increasing, or rather,it first decreases and then increases. The focal shift strongly depends on the effective focal length and oblique incidence angle, but it is almost independent of the beam size, which affects the focusing spot patterns. The intensity distribution produces a higher astigmatic image with off-axis angle increasing. Coma-like aberration starts to become dominant with beam size increasing and results in larger curved propagation trajectory. The incident polarization also affects the intensity distribution. The variation in the Strehl ratio with oblique incidence angle strongly depends on the misalignment direction and beam size as well. In addition, we find that the difference in locus between the catacaustic and the diffraction focus in the meridian is small. But the locus of the sagittal foci is obviously different from the locus of the meridian foci and the catacaustic focus. Moreover, the peak intensity of the sagittal focus is maximum, and the ratio of the peak intensity to that in the meridian plane is approximately 1.5. Understanding these effects is valuable for assessing a practical focused intensity and describing the motion of charged particles under a strong electric field in ultraintense laser–matter interaction.     

Different algebraic method for computing the high-order aberrations of practical combined focusing-deflection systems

Differential algebraic (DA) method is an effective technique in computer numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. Some complicated nonlinear dynamics problem including high-order aberrations of electron optical systems can be solved effectively by mapping properties of DA quantities. However, the existing study applying DA method to the practical system is limited to simple electron lenses. In this paper, the application of DA method is extended to practical combined focusing-deflection systems, and the aberrations up to fifth order are calculated. The electric and magnetic fields of the electron lenses and deflectors, which are computed by finite element method (FEM) or finite difference method (FDM), are in the form of discrete arrays. Local analytical expressions for electric and magnetic field quantities are constructed from these arrays for arbitrary place where electron is traced in DA computation. Thus the developed DA method is applicable for engineering design and computing problem. Based on the study of the expressions and the structure of the aberration coefficients for the fifth-order aberrations of the combined focusing-deflection system and the local analytic expression of the practical electromagnetic field, correlative computer software was developed, whose interface is convenient to calculate the high-order aberrations of the practical systems. The new DA method and software are tested with a uniform magnetic field deflection having an analytic solution. And the results show that the accuracy is sufficiently high, only limited by machine precision. Finally, as an example, a practical combined magnetic focusing and magnetic deflection system is analyzed and discussed.     

电磁复合聚焦—偏转球面阴极透镜的相对论象差理论

本文应用变分原理研究了电磁复合聚焦-偏转球面阴极透镜的相对论象差理论。在考虑阴极面逸出电子具有一定的初能量和初角度分布,物场和象场弯曲以及阴极面上磁场和横向电场不为零的情况下,导出了任意理想象面上的一级近轴横向象差和包括色球差在内的全部三级几何横向象差,以及各种特殊类型象差系数的明显表达式。本文导出的象差公式不仅普遍适用于宽束和细束阴极透镜,而且普遍适用于相对论或非相对论,阴极和屏为球面或平面时的各种情况。本文以复数描写轨迹,用矩阵表示象差,形式简洁,适合于计算机计算。 关键词：     

静电透镜与磁偏转器的复合系统的电子光学性质和象差理论

本文将文献[1]的方法和结果加以推广,研究了旋转对称静电透镜和磁偏转器的复合系统。给出了场和轨迹的普遍表达式,讨论了高斯光学性质,得出了这种系统普遍的三级象差和象差系数的公式。这两篇文章有助于较全面地研究各种电子束管和电子光学仪器的偏转象差。 关键词：     

Differential algebraic method for computing the high order aberrations of practical electron lenses

Differential algebraic method is of an effective technique in computer numerical analysis. It implements exactly differentiation up to arbitrary high order based on the nonstandard analysis. Some complicated nonlinear dynamics problems including high order aberrations of electron optics systems can be solved by mapping properties of differential algebraic quantities. However, the existing electron optical differential algebraic method can only be applied to those problems where the electric and/or magnetic fields are expressed in analytic forms. In this paper, the principle of differential algebraic method is applied to practical electron lenses whose electric/magnetic fields are in the forms of discrete arrays, for example, the files computed by FEM or FDM method. Thus the developed new differential algebraic method is applicable to engineering design. The programs were written for computing the high order aberrations of practical electron lenses. An example is given to show that the numerical results have good accuracy compared with the results computed by using the electric fields expressed in analytical form; the accuracy is limited only by the accuracy of the numerical computation of the fields and the arithmetic errors, and it is enough for engineering design.     

Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2)

We describe a method to measure the aberrations of a high numerical aperture off-axis paraboloid and correct for the aberrations using adaptive optics. It is then shown that the characterized aberrations can be used to accurately calculate the electromagnetic field at the focus using the Stratton–Chu vector diffraction theory. Using this methodology, an intensity of 7×10²¹ W/cm² was demonstrated by focusing a 45-TW laser beam with an f/0.6, 90^∘ off-axis paraboloid after correcting the aberrations of the paraboloid and the low-energy reference beam. The intensity can be further increased to 1×10²² W/cm² by including in the correction algorithm the wavefront difference between the reference beam and the high-energy beam. This revised version was published online in May 2005. The authors addresses were completed PACS numbers were added Equation (31) was corrected Textual corrections were made in Sects. 3, 4.1, and 5 Reference no. 12 was completed. An erratum to this article can be found at .     

两电极静电同心球系统的成像电子光学及其空间-时间像差

基于实际轨迹方程和电子运动方程对两电极静电同心球系统求解由光阴极逸出的运动电子的空间和时间轨迹,推导成像位置和电子飞行时间的精确和近似表达式,并由空间和时间轨迹的解析解出发讨论系统的空间-时间特性.对空间像差和时间像差给出统一的定义,即横向像差可视为近轴横向像差和几何横向像差的合成,时间像差可视为近轴时间像差和几何时间像差的合成,并导出了所有相应的像差表示式.     

Differential algebraic method for arbitrary-order chromatic aberration analysis of electrostatic lenses

In this paper, differential algebra is applied to calculate arbitrary high-order chromatic aberrations of electrostatic electron lenses. Expressions of differential algebraic form of high-order combined chromatic aberration coefficients are obtained and arbitrary-order chromatic aberrations can be calculated numerically. As an example, a typical Schiske's electrostatic lens has been studied. All the first- to third-order chromatic aberration coefficients of the lens have been calculated, and the pattern of the first-order chromatic aberration has been given as well.