Design of a mirror aberration corrector and a beam separator for LEEM

A SPLEEM (spin polarized low energy electron microscope) has been designed with a numerical simulation of electrostatic and magnetic field distributions and electron ray trajectories. Highly (more than 90%) spin polarized electron source has been used. A Wien type spin manipulator and a magnetic lens type spin rotator are used to align spin direction. A magnetic field free objective lens is designed to observe magnetic domain structure of magnetic materials. High or low magnification mode can be selected by using a combined electrostatic and magnetic objective lens for a high spatial resolution and a wide imaging area observation. An electrostatic mirror aberration corrector is installed after the image forming objective lens. A double deflection 45° beam separator is used to bend the direction of electrons from the source to the objective lens and from the objective lens to the mirror aberration corrector.     

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.     

Differential algebraic method for time of flight property of electrostatic electron lenses

Differential algebraic method is a powerful technique in computer numerical analysis. It presents a straightforward method for computing arbitrary order derivatives of functions with extreme high accuracy limited only by the truncation error of the computer. When applied to nonlinear dynamical systems, the arbitrary high-order transfer properties of the systems can be computed directly with high precision. In this article, the time of flight (TOF) property of electrostatic electron lens systems is studied by differential algebraic method and their arbitrary order TOF transfer properties can be numerically calculated. As an example, Schiske's model electrostatic lens has been studied by the efficient differential algebraic TOF method.     

La/B4C small period multilayer interferential mirror for the analysis of boron

An La/B₄C multilayer interferential mirror with small period d (4.8 nm) was produced by diode sputtering for the detection of the boron K emission by wavelength‐dispersive x‐ray spectrometry at a large Bragg angle (close to 45°). The structure of the mirror was characterized by grazing incidence x‐ray reflectometry and its performance at the energy of the boron K emission (183 eV) was evaluated by means of polarized synchrotron radiation. Spectrometric measurements showed that the La/B₄C mirror improved the detection limit of boron using by a factor of 2 with respect to similar Mo/B₄C mirrors and by a factor of 4 with respect to a lead stearate crystal. Copyright © 2005 John Wiley & Sons, Ltd.     

Twisted electrostatic waves in a self‐gravitating dusty plasma

A generalized response (dielectric) function for twisted electrostatic waves is derived for an un‐magnetized self‐gravitating thermal dusty plasma, whose constituents are the Boltzmann‐distributed electrons and positive ions in the presence of negatively charged micrometre‐sized massive dust particulates. For this purpose, a set of Vlasov–Poisson coupled equations is solved along with the perturbed Laguerre–Gauss distribution function, as well as the electrostatic and gravitational potentials in the limit of paraxial approximation. For plane wave solution, the wavefronts of the dust‐acoustic (DA ) wave are assumed to have a constant phase with electric and gravitational field lines propagating straight along the propagation axis. On the other hand, non‐planar wave solutions show helical (twisted) wavefronts, in which field lines spiral around the propagation axis owing to the azimuthal velocity component to account for the finite orbital angular momentum (OAM ) states. The dispersion relation and damping rate for twisted DA waves are studied both analytically and numerically. It is shown that finite OAM states, the dust to electron temperature ratio, and dust self‐gravitation effects significantly affect the linear dispersion and Landau damping frequencies. In particular, the phase speed of twisted DA waves is reduced with the variation of the twist parameter η (= k /lq_ϕ ), dust concentration δ (= n_{d 0}/n_{i 0}), and dust self‐gravitation α (= ω_Jd /ω_pd ). The relevance of our findings to interstellar dust clouds is also discussed for micrometre‐sized massive dust grains.     

A video camera system for coaxial observation of a sample with an incident soft X‐ray beam

A video camera system for observing a sample from the direction of an incident soft X‐ray beam has been developed. The sample is seen via two reflecting mirrors. The first mirror, which has a hole to allow the soft X‐ray beam to pass through, is set on the beam axis in a vacuum. The second mirror is used to cancel out the mirror inversion of the image. This camera system is used for efficient positioning of samples in a soft X‐ray beam.     

C 78 IPR fullerenes: Computed B3LYP/6-31G*//HF/3-21G temperature-dependent relative concentrations

The five isolated-pentagon-rule (IPR) satisfying isomers of C₇₈, labeled 1-5, or according to symmetry as D₃, C_2v, C' _2v , D_3h, and D' _3h , are computed. The cage geometries are optimized at the ab initio HF level with the standard 3-21G basis set (HF/3-21G). The separation energetics is then computed using the B3LYP density-functional treatment in the standard 6-31G* basis set (B3LYP/6-31G*//HF/3-21G). Harmonic vibrational frequencies are calculated by the SAM1 semiempirical method. The computed energies, structural and vibrational data are employed in the construction of isomeric partition functions and evaluation of the relative Gibbs free energies. The results are converted into relative concentrations for a wide temperature interval. The C' _2v structure is the most populated throughout while the D_3h species is negligible at all temperatures. The agreement between theory and experiment is reasonable, though some aspects are still to be clarified. Received 28 November 2000     

中低速C3+与He，Ne，Ar原子相互作用过程中单电子转移绝对截面的测量

实验测量了1.7v₀—4.2v₀(v₀为玻尔速度,v₀=2.19×10⁸cm/s)的C³⁺与He,Ne,Ar原子碰撞过程中单电子转移绝对截面.将实验结果与多体经典轨道蒙特卡罗模拟计算结果做了比较,发现测量结果与多体经典轨道蒙特卡罗模拟计算结果在趋势上相符.当入射离子速度在1.7v₀—2 关键词： 离子-原子碰撞 单电子转移 绝对截面     

自聚焦透镜准直应用的长度计算与实验

根据近轴子午光线方程,研究了自聚焦透镜准直应用。在未知n_o和A值情况下,本文提出解决准直应用自聚焦透镜长度计算问题。     

On the theory of temporal aberrations for cathode lenses

A new approach to the theory of temporal aberration for cathode lenses is given in the present paper. A definition of temporal aberration is given in which a certain initial energy of electron emission along the axial direction ε_z1 (0ε_z1ε_0max) is considered. A new method to calculate the temporal aberration coefficients of cathode lenses named “direct integral method” is also presented. The “direct integral method” gives new expressions of the temporal aberration coefficients which are expressed in integral forms. The difference between “direct integral method” and “τ-variation method” is that the “τ-variation method” needs to solve the differential equations for the three of temporal geometrical aberration coefficients of second order, while the “direct integral method” only needs to carry out the integral calculation for all of these temporal aberration coefficients of second order.All of the formulae of the temporal aberration coefficients deduced from “direct integral method” and “τ-variation method” have been verified by an electrostatic concentric spherical system model, and contrasted with the analytical solutions. Results show that these two methods have got identical solutions and the solutions of temporal aberration coefficients of the first and second order are the same as with the analytical solutions. Although some forms of the results seem different, but they can be transformed into the same form. Thus, it can be concluded these two methods given by us are equivalent and correct, but the “direct integral method” is related to solve integral equations, which is more convenient for computation and could be suggested for use in practical design.     

双变形镜自适应光学系统像差解耦研究

对由大行程变形镜和高空间频率变形镜组成的双变形镜自适应光学系统中的像差解耦原理和限定像差校正算法做了理论分析。认为在高空间频率变形镜的斜率响应矩阵中加入限定像差向量,根据直接斜率法分别计算出两个变形镜的控制电压,可以实现两个变形镜分别对低阶像差和高阶像差的闭环校正。仿真研究了19单元变形镜和61单元变形镜组成的双变形镜自适应光学系统对低阶像差和高阶像差分别校正的情况,结果说明双变形镜自适应光学系统的校正效果与理想行程的单变形镜自适应光学系统的校正效果相当,避免了制作同时具有大行程和高空间频率两个特征的变形镜。     

Relationship between torsional frequency and potential barrier height forAB n type molecular system

A relationship between the torsional frequency (v ₁₀) and the potential barrier (V _n) has been determined forAB _n type molecular system havingn-fold symmetry axis. It is found thatv ₁₀ varies prominently asV _n ^1/2 ,V _n andV _n ² in certain ranges. TheV _n value computed fromv ₁₀ andI* _r has been compared with that obtained from other experimental data for someAB _n units in different molecular-crystalline systems. Although there is in general a good agreement, in some cases the values differ significantly, perhaps due to the erroneous assignment of torsional mode and/or the large errors in theV _n value obtained from other experimental data.     

The effect of surface temperature on H2/D2(v = 0, j = 0)–Ni(100) scattering processes

We carry out both four-dimensional (4D×2D) and six-dimensional (6D) quantum dynamics on a parametrically time- and temperature-dependent effective Hamiltonian for H₂/D₂(v = 0,j = 0)–Ni(100) collision process. Such an effective potential was derived within a theoretical framework of mean-field approximation by considering weakly correlated interaction between molecular degrees of freedom, phonon modes and electron– hole pair (elhp) coupling through a Hartree-product-type wave function, where the initial state distribution of the surface modes and elhp coupling were introduced through Bose– Einstein and Fermi– Dirac probability factor, respectively. The temperature-dependent dissociation and state-to-state transition probabilities for H₂/D₂(v = 0,j = 0)–Ni(100) system are depicted as a function of initial kinetic energ of the incoming diatom. Though such effect appears negligibly small for H₂(v = 0,j = 0)–Ni(100) system, it is prominent in the case of D₂(v = 0,j = 0)–Ni(100) collision. It appears that the change of dissociation and transition probabilities of D₂ with the increase of surface temperature is exclusively dictated by the phonon modes directed along Z-axis, but the effect of elhp coupling particularly for transition probabilities is insignificant.     

Das Neutralgasprofil und die Elektronentemperatur in der Freifallsäule bei hohem Ionisationsgrad

The neutral gas flux from the wall into the column - connected with the ion flux to the wall - and the anisotropy of the velocity distribution of the neutral gas are included into the theory of the steady-state positive column. d/l_n and v_n0/v₀ occur as characteristic parameters. d denotes the radius of the column, l_n the mean free path of the neutral atoms for ionization, v_n0 the mean velocity of the neutral atoms re-emitted from the wall, v₀ = (2kT_e/M)^1/2, M the ion mass, T_e the electron temperature. On the axis the neutral gas density N_n is decreasing, if d/l_n is rising. At the wall N_n is increasing for v_n0 ? v₀, but it is almost constant or decreasing for v_n0 ? v₀ at the same time. In the plasma the total number of the atoms and the ions is taken as constant. In the case of small v_n0 the degree of ionization is high only for d ? l_n. However, it is already high for d ≈ l_n in the case of high v_n0. Therefore, the radial profiles of the neutral gas densities of different gases in a column can differ from each other. Almost full ionization can be reached near the axis. These results hold, too, if the initial velocity of the ions and a magnetic field are taken into account. d/l_n, the degree of ionization, and the electron temperature are given as functions of the electric power input and of the total number of the neutrals and the ions. The velocities of the re-emitted atoms depend on the accomodation coefficient of the ions recombining at the wall. With rising d/l_n an increasing number of the neutral atoms is re-emitted with superthermal velocities and the total number of the neutrals and the ions can be decreased. The anisotropy of the velocity distribution of the neutral atoms and the ions must be taken into account for the interpretations of spectroscopical measurements.     

Optimizing X‐ray mirror thermal performance using matched profile cooling

To cover a large photon energy range, the length of an X‐ray mirror is often longer than the beam footprint length for much of the applicable energy range. To limit thermal deformation of such a water‐cooled X‐ray mirror, a technique using side cooling with a cooled length shorter than the beam footprint length is proposed. This cooling length can be optimized by using finite‐element analysis. For the Kirkpatrick–Baez (KB) mirrors at LCLS‐II, the thermal deformation can be reduced by a factor of up to 30, compared with full‐length cooling. Furthermore, a second, alternative technique, based on a similar principle is presented: using a long, single‐length cooling block on each side of the mirror and adding electric heaters between the cooling blocks and the mirror substrate. The electric heaters consist of a number of cells, located along the mirror length. The total effective length of the electric heater can then be adjusted by choosing which cells to energize, using electric power supplies. The residual height error can be minimized to 0.02 nm RMS by using optimal heater parameters (length and power density). Compared with a case without heaters, this residual height error is reduced by a factor of up to 45. The residual height error in the LCLS‐II KB mirrors, due to free‐electron laser beam heat load, can be reduced by a factor of ～11 below the requirement. The proposed techniques are also effective in reducing thermal slope errors and are, therefore, applicable to white beam mirrors in synchrotron radiation beamlines.     

Non-adiabatic potentials for H2 +

In principle exact non-adiabatic pseudo-potentials for H₂ ⁺ and D₂ ⁺ are formulated in terms of the theory of conditional probability amplitudes in wave mechanics. Numerical results for the v = 0 and v = 1 (J = 0) states of H₂ ⁺ are derived from previously computed accurate non-adiabatic wave-functions. These results indicate that the non-adiabatic pseudo-potentials only differ from the adiabatic potential by small energies of the same magnitude as the non-adiabatic corrections to the adiabatic energy levels.     

激光靶心冲击波观测镜折反式光学系统设计

设计了一种激光靶心冲击波观测镜的光学系统.用反射式光学系统代替折射式光学系统,解决了普通玻璃在200 nm端透过率较低的问题.反射镜不引入色差,有利于系统在200~800 nm谱段消色差.为消系统轴外像差,反射系统选型为对称式.反射镜全部采用球面镜,为消反射镜以及平板玻璃窗带入的球差,引入校正镜(材料JGS1),在满足要求的条件下,控制折射镜的厚度,使系统色差满足瑞利判据的色差允差,得到了良好的成像质量.     

Ronchi线条法检验大非球面镜的理论计算

由光线追迹和三级像差理论计算大抛物面的Ｒｏｎｃｈｉ弯线条。分析这两种理论计算方法的结果和偏差，其偏差值随镜子的口径增大而增加，用所计算的结果制作的Ｒｏｎｃｈｉ弯线条检验可移动式平行光管的φ７００ｍｍ口径的抛物面主镜。给出检验结果。     

非均匀激光辐照下硅镜热变形对光束传输特性的影响

 使用有限元法计算了硅镜在DF化学激光器非稳腔输出的中空非均匀激光辐照下镜面温升和反射面面形随时间变化的特性,使用65阶Zernike多项式对镜面面形进行了曲面拟合,使用光线追迹的方法计算了平行光束经不同数量硅镜反射后的光束波前分布PV值、Strehl比和Zernike像差系数随时间变化的特性。计算结果表明：在典型的DF激光器输出的中空方形光束辐照下,硅反射镜的热变形将使反射光束产生波前畸变,波前畸变中,y方向像散项占据主要地位,其次是离焦项;随着激光系统中反射镜面数量的增加,高阶像差系数将逐渐增大,且波前PV值与反射次数成线性关系。     

Structural and electronic properties of silver-doped gold clusters Au n Ag v (2 ≤ n ≤ 10; v = 0, ±1): comparison with pure gold clusters

The structural and electronic properties of silver-doped gold clusters Au _n Ag ^v (2?≤?n?≤?10; v?=?0,?±1) have been systematically investigated using density functional theory. The results show that the ground state optimal structures of the cationic and neutral clusters are found to be planar up to n?=?3 and 9, respectively. However, for the anionic clusters, no three-dimensional lowest-energy structures are obtained according to DFT calculations. The calculated binding energy and dissociation energy as a function of cluster size exhibit odd–even alternations. The natural population analysis indicates that in Au _n Ag ^v clusters charges transfer from the Ag atom to the Au frames. The trends for the vertical detachment energies, adiabatic electron affinities, adiabatic ionization potentials, and chemical hardness of Au _n Ag ^v clusters, as the cluster size increases, are studied in detail and compared with the available experimental data.