求正交曲线坐标系中速度和加速度的解析方法

引入“广义速度”和“广义加速度”的概念，把正交曲线坐标系或的速度加速度简化为广义坐标及其微商的偏导。     

带电粒子束传输中横向发散的类ABCD定律

 傍轴近似下带电粒子束传输可完全类比于近轴光线椭圆高斯光束的传输。基于这种类比，建立了带电粒子束传输中横向发散的复曲率半径的类ABCD定律，引入了带电粒子在横向的复曲率半径的概念，并以复曲率半径的实部表征带电粒子束的敛散特性，虚部表征带电粒子束的束斑大小。由此提出：带电粒子束整体可被看作类椭圆高斯光束，其发射度与光束波长的作用相同。通过这种类比可知，在适宜的加速器环境下，理论上可能产生相干带电粒子束。     

Gaussian wave formalism model for propagation of charged-particle beam through a first-order optical systems

An elliptical Gaussian wave formalism model of a charged-particle beam is proposed by analogy with an elliptical Gaussian light beam. In the paraxial approximation, the charged-particle beam can be described as a whole by a complex radius of curvature in the real space domains. Therefore, the propagation and transform of charged-particle beam passing through a first-order optical system is represented by the \textit{ABCD}-like law.As an example of the application of this model, the relation between the beam waist and the minimum beam spot at a fixed target is discussed. The result, well matches that from conventional phase space model, and proves that the Gaussian wave formalism model is highly effective and reasonable.     

ABCD—Type Law for Charged—Particle Beam Transport in Paraxial Approximation

Based on the similarity between charged-particle beam transversal transport and transmission of ellipse Gaussian light beam in Daraxial approximation, it is shown that charged-particle beam transversal transport in real space is governed by the ABCD-type law for a complex curvature radius of the charged-particle beam in which the beam transverse emittance plays the role of wavelength, from this, a novel technique for characterizing charged-particle beam is proposed. Finally, this analogy provides an insight observation that it is hopeful to attain possible coherent charged-particle beam in favourable accelerator environment.     

光束分数傅里叶变换几何特性的相空间束矩阵分析方法

提出一种分析傍轴光束分数傅里叶变换几何特性的相空间束矩阵变换的简单方法. 以分析椭圆高斯光束分数傅里叶变换几何特性为例，研究表明，利用本方法讨论傍轴束分数傅里叶变换的几何特性简单可靠、从几何图像理解傍轴束分数傅里叶变换清晰直观. 为研究光束传输变换的特性提供了一种简单方便的新途径. 关键词： 相空间束矩阵 分数傅里叶变换 椭圆高斯光束     

Transformation of general astigmatic Gaussian beams in a four-dimensional phase space

A phase space model of two-dimensional (2D) Gaussian beam propagation is generalized for three-dimensional (3D) general astigmatic Gaussian beam passing through first-order optical system. The general astigmatic Gaussian beam is represented by a four-dimensional (4D) phase super-ellipsoid that defined by an associated 4×4 real matrix, then the transformation formula of the phase super-ellipsoid of the beam through first-order optical system is derived. In particular, in the phase space framework, the beam propagation factor M2 value is proved to be a ratio of phase area of real beam to ideal beam, and a novel approach for a qualitative examination of the properties of fractional Fourier transform (FRT) for the beam is also provided.     

二氧化钛纳米管阵列薄膜的超声辐射阳极氧化制备

通过使用铂片作为对电极在含有氢氟酸的二甲基亚砜溶液中, 将金属钛片进行阳极氧化的方法制备得到二氧化钛纳米管阵列薄膜. 在施加40 V偏压超声辐射作用下阳极氧化24 h条件下得到的二氧化钛纳米管长达到680 nm, 管内直径25 nm, 管壁厚度约3～5 nm. 采用了XRD和TEM等分析手段表征了二氧化钛纳米管阵列薄膜的微观结构和表面形貌, 分别测试了薄膜的光吸收性能、循环伏安特性和光化学转换效率, 并和碱性溶胶-凝胶方法制备的纳米晶二氧化钛薄膜作了对比研究. 实验制备的二氧化钛纳米管阵列薄膜电极的光吸收率比纳米晶二氧化钛薄膜提高了40%, 光电化学转换效率前者是后者的6倍, 实验结果表明二氧化钛纳米管阵列薄膜结构有利于加快电子的传输, 并能减少电荷复合, 采用这种二氧化钛纳米管阵列薄膜结构的染料敏化太阳能电池光电极有望进一步提高太阳能电池的效率. 本文还探讨了在超声波辐射作用下二氧化钛纳米管阵列薄膜的形成机理.