CsNiCl3晶体的光谱精细结构、零场分裂参量及Jahn-Teller效应

应用不可约张量理论构造了三角对称晶场中3d²/3d⁸态离子的45阶可完全对角化的微扰哈密顿矩阵，研究了CsNiCl₃晶体的光谱精细结构、晶体结构、零场分裂参量、Jahn-Telller效应以及自旋单重态对Ni²⁺离子基态能级的影响，理论与实验相符合.在此基础上，进一步研究了以前工作中被忽略的自旋-自旋耦合作用和Trees修正对CsNiCl₃晶体的光谱精细结构和零场分裂参量的影响，发现有四种机理会影响零场分裂参量：1)自旋-轨道耦合机理，2)自旋-自旋耦合机理；3)自旋-轨道与自旋-自旋联合耦合机理；4)自旋-轨道与Trees修正联合耦合机理，其中自旋-轨道耦合机理是最主要的，其他三种机理也是不可忽略的. 关键词： 基态能级 精细结构 零场分裂 自旋-自旋耦合     

Influence of Azimuthal Structure of Surface Waves on Efficiency of their Excitation by Tubular Electron Beams

The excitation of eigen surface waves by tubular electron beams in cylindrical discharge devices is studied. The influence of the wave‐field azimuthal structure on the excitation efficiency and nonlinear stage of the plasmabeam instability is investigated both numerically and analytically. Analytical expressions for the saturation amplitude and excitation efficiency of the wave under study are derived. They are found to agree well with results obtained by numerical modelling of the plasma‐beam interaction presented in this paper. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Geometric visualization of the Brewster angle from dielectric-magnetic interface

A geometric visualization is presented for the Brewster angle for a plane wave reflecting from an interface. The surface is assumed to be isotropic but it is allowed to display both dielectric and magnetic susceptibility, and hence the Brewster (polarizing) angle can attain any value between 0 and 90^°, and can exist for both parallel and perpendicular polarizations. The geometric construction (a tetrahedron) is spanned by the basic material parameters of the surface. The Brewster angle appears in one of the faces of the tetrahedron.     

The many proofs of an identity on the norm of oblique projections

Given an oblique projector P on a Hilbert space, i.e., an operator satisfying P ²=P, which is neither null nor the identity, it holds that ||P|| = ||I –P||. This useful equality, while not widely-known, has been proven repeatedly in the literature. Many published proofs are reviewed, and simpler ones are presented.     

An efficient numerical scheme for precise time integration of a diffusion-dissolution/precipitation chemical system

A numerical scheme based on an operator splitting method and a dense output event location algorithm is proposed to integrate a diffusion-dissolution/precipitation chemical initial-boundary value problem with jumping nonlinearities. The numerical analysis of the scheme is carried out and it is proved to be of order 2 in time. This global order estimate is illustrated numerically on a test case.

     

Resistance of nondiffracting vortex beam against amplitude and phase perturbations

The revival of the nondiffracting vortex beam after its interaction with the 2D on axis obstacle is examined. We show that the phase topology and the spatial distribution of the orbital angular momentum of the beam transmitted through the obstacle regenerate to the initial form during further free propagation. We verify that the healing effect appears even if the interaction is accompanied by the exchange of the orbital angular momentum.     

电子束产生大尺度等离子体过程的数值模拟研究

建立了一个四组分一维混合模型，对电子束注入大气产生大尺度等离子体的过程进行了数值模拟.结果表明了能量为140keV、流强为50mA/cm²的注入电子束，可以产生线度为0.5m，密度为10¹²cm^-3量级的大气环境下等离子体.电子束所伴随的空间电荷效应由于等离子体的产生会很快消失，不影响后续的等离子体产生过程.电子束注入流强主要影响产生等离子体的密度，而电子束能量则同时影响其空间线度和密度. 关键词： 电子束 碰撞 电离     

非傍轴平顶高斯光束M2因子两种定义的比较研究

基于功率密度的二阶矩方法,推导出了非傍轴平顶高斯(FG)光束束宽和远场发散角的解析表达式·研究表明,当w0/λ→0时,远场发散角趋于渐近值θmax=63.435°,与阶数无关·使用非傍轴高斯光束代替傍轴高斯光束作为理想光束,研究了非傍轴FG光束的M2因子,并与传统定义的M2因子作了比较·在非傍轴范畴,非傍轴FG光束的M2因子不仅与阶数N有关,而且与w0/λ有关·按照定义,当w0/λ→0时,非傍轴FG光束的M2因子不等于0,对阶数N=1,2,3时,M2因子分别趋于0.913,0.882和0.886·当N→∞时,M2因子取最小值M2min=0.816·     

非傍轴平顶高斯光束M2因子两种定义的比较研究

基于功率密度的二阶矩方法，推导出了非傍轴平顶高斯(FG)光束束宽和远场发散角的解析表达式.研究表明，当w0/λ→0时，远场发散角趋于渐近值θmax=63.435°，与阶数无关.使用非傍轴高斯光束代替傍轴高斯光束作为理想光束，研究了非傍轴FG光束的M2因子，并与传统定义的M2因子作了比较.在非傍轴范畴，非傍轴FG光束的M2因子不仅与阶数N有关，而且与w0/λ有关.按照定义，当w0/λ→0时，非傍轴FG光束的M2因子不等于0，对阶数N=1, 2, 3时，M2因子分别趋于0.913,0.882和0.886.当N→∞时，M2因子取最小值M2min=0.816.     

全光纤反射式马赫曾德尔干涉型多波长滤波器的研究

对反射式的马赫－曾德尔干涉型多波长滤波器的性能作了较详细的研究，得出了两个耦合器的分光比和两臂的臂长差对其输出谱线的影响，结论对设计制作不同性能指标的该型多波长滤波器具有重要的参考价值。实验上用光纤熔融拉锥法制作了该种器件，实验结果与理论相符合。