Asymptotic screened hydrogenic radial integrals

The screened hydrogenic radial dipole integral for discrete-discrete transitions from initial state n'l' to final state nl is asymptotically expanded to the lowest order such that the final quantum number n --> infinity. The analytical expression obtained is in terms of confluent hypergeometric functions, and explicit expressions for a few of the specific transitions are derived from them as examples.     

Observation of long-distance radial correlation in toroidal plasma turbulence

This Letter presents the discovery of macroscale electron temperature fluctuations with a long radial correlation length comparable to the plasma minor radius in a toroidal plasma. Their spatiotemporal structure is characterized by a low frequency of ～1-3 kHz, ballistic radial propagation, a poloidal or toroidal mode number of m/n=1/1 (or 2/1), and an amplitude of ～2% at maximum. Nonlinear coupling between the long-range fluctuations and the microscopic fluctuations is identified. A change of the amplitude of the long-range fluctuation is transmitted across the plasma radius at the velocity which is of the order of the drift velocity.     

狭缝式环形超声聚能器的径向振动特性

对一种狭缝式环形超声聚能器的径向振动特性进行了研究。基于机电类比原理,通过引入面积比系数,推出了聚能器的径向振动机电等效电路及频率方程;得出了其径向位移振幅放大系数表达式。通过数值计算,探讨了聚能器第1、2阶径向共振频率及振幅放大系数与其半径比的关系;分析了狭缝长度、角度及数目对聚能器振幅放大系数及共振频率的影响,并进行了有限元仿真。研究表明,聚能器的振幅放大系数随其半径比的变化存在极大值,并随狭缝数量、长度及宽度增加而增大;而其径向共振频率则随三者的增加而减小,理论与有限元仿真及实验结果符合较好。     

径向线内电子束的空间极限电流

为了对径向线内电子束的空间极限电流及相关物理参量进行分析, 在径向方向无穷长与束流密度轴向均匀的假设条件下, 对电势满足的线性泊松方程进行了解析求解, 得到了空间极限电流的解析表达式, 接下来对束流密度轴向非均匀分析条件下电势满足的非线性方程进行了数值求解, 并与解析结果进行了对比。研究表明径向电子束具有较高的空间极限电流且当束流接近于极限电流传输时, 束密度的非均匀性明显增加, 相关结论可以为径向高功率微波器件的设计提供指导。     

Virtual source for a Laguerre-Gauss beam

A virtual source that generates a cylindrically symmetric Laguerre-Gauss wave of radial mode number n is introduced. An expression is derived for this Laguerre-Gauss wave that in the appropriate limit yields the corresponding Laguerre-Gauss beam. From the spectral representation of the Laguerre-Gauss wave, the first three orders of nonparaxial corrections for the paraxial Laguerre-Gauss beam are determined. On the beam axis, the number of orders of nonvanishing nonparaxial corrections is found to be equal to n .     

径向线内电子束的空间极限电流

为了对径向线内电子束的空间极限电流及相关物理参量进行分析, 在径向方向无穷长与束流密度轴向均匀的假设条件下, 对电势满足的线性泊松方程进行了解析求解, 得到了空间极限电流的解析表达式, 接下来对束流密度轴向非均匀分析条件下电势满足的非线性方程进行了数值求解, 并与解析结果进行了对比。研究表明径向电子束具有较高的空间极限电流且当束流接近于极限电流传输时, 束密度的非均匀性明显增加, 相关结论可以为径向高功率微波器件的设计提供指导。     

弱光场下电子与库仑势散射的微扰解

外光场下电子与库仑势散射的Schr?dinger方程可用Floquet分波法分离变量,径向波动方程是一组无限耦合的二次线性微分方程组,当弱外光场可视为微扰,方程组将近似为二次常微分方程并且可积,由此可得径向波函数、S矩阵、截面。无论何种极化或是否作偶极近似,共振谱线是普遍存在的,并给出共振能量和强度的计算公式。     

热扩散效应在热声分离中的作用机理

在充满二元混合气体的声波谐振管中,振荡的气体会在径向上建立振荡的温度梯度,径向的温度梯度会引起两种组分的分子沿着不同方向进行扩散,在这种热扩散效应和热声效应的共同作用下,声波能够把混合气体中的两种组分分别带向谐振腔的速度节点和压力节点,使得混合气体在声波传播方向上逐渐分离。为了研究热声分离过程的机理,本文对一个半波长的声波谐振管进行了二维的建模,并基于可压缩的SIMPLE算法,通过求解He-Ar混合气体的速度场、温度场和一种组分的浓度场,对谐振腔内的传热传质过程进行了详细的数值模拟研究。数值模拟结果与文献的理论计算值进行了比较,结果符合良好。随后,通过研究一个周期内径向上的温度、速度和Ar的摩尔分数分布,揭示了径向上的热扩散过程,以及中间气体与边界层内气体之间的热质交换过程,完整地解释了热声分离过程的发生机理。     

激光波带片衍射性质的数值模拟

根据亥姆霍兹-基尔霍夫积分,对菲涅尔波带片的高斯激光场在轴向、径向强度分布进行了理论分析,研究了高斯激光束照射下波带片的衍射场规律.数值计算表明：沿轴向光场呈系列焦点,各焦点附近光强分布有振荡现象,随焦点级次的增大光强迅速增大;有焦移现象,焦移量随焦点级次的增大而增大;焦深随焦点级次的升高按平方反比律减小,随波带数减小或焦距增大而增大.在焦平面上,光斑大小与最外环宽度成正比,与焦点级次成反比.     

Radiation pattern of cylindrically symmetric scalar Laguerre-Gauss beams

The exact full-wave generalization of the cylindrically symmetric scalar real-argument Laguerre-Gauss beam is determined. The radiation intensity of the resulting Laguerre-Gauss wave is deduced, and the main characteristics of the radiation intensity pattern are described. The total power P(n) is evaluated, where n is the radial mode number. By the use of 1/P(n) as the quality parameter, the characteristics of the quality of the paraxial beam approximation to the full Laguerre-Gauss wave are discussed.     

Temperature dependence of the electric field gradient in GaN measured with the PAC-probe 181Hf

A radial inhomogeneous magnetic field produced by counter-propagating currents in anti-Helmholtz configuration coils has been superimposed to a Penning trap. The confinement properties of electrons in such a trap have been studied experimentally. Without the radial B-field we find a number of operating conditions where instabilities occur, arising from higher order contributions to the quadrupolar trapping field. When we apply the radial field the trap properties remain essentially unchanged until the strength of this field at the boundary of the electron cloud is of the same order as the homogeneous Penning field. Then a sudden breakdown in the confinement appears. The experiments have been performed in low magnetic fields. The equations of motions of the trapped particles can be cast in a dimensionless form and our results can be considered as independent of the field strength. Contribution was presented at the TCP06, Vancouver Island, 2006.     

Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation,then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function.     

幂函数型环形聚能器径向振动的等效电路

基于机电类比原理和变厚度薄圆环的平面应力方程,推导了幂函数型环形聚能器径向振动的等效电路、共振频率方程和位移放大系数。讨论了第一、二阶径向共振频率及相应的位移放大系数随圆环半径比的变化关系。结果表明,幂函数型环形聚能器径向振动的等效电路是一种非互易二端口等效网络;一阶和二阶共振频率随圆环内外半径比的增大而增大;一阶径向共振模式下位移放大系数随圆环半径比的增大先降低后升高,二阶径向共振模式下位移放大系数随圆环半径比的增大而降低,但二阶时的位移放大系数整体大于一阶,因此二阶径向共振模式具有更好的径向振动性能。用COMSOL有限元软件对解析理论分析结果进行了验证,仿真模拟结果与解析理论符合良好。根据幂函数型环形聚能器的等效电路模型,进一步设计了一种压电环形换能器,计算了第一、二阶径向共振频率、反共振频率及有效机电耦合系数,通过与COMSOL有限元软件模拟结果对比,符合良好。本文研究结果为幂函数型环形聚能器及压电环形换能器的工程应用提供了简明设计理论,文中研究结论可作为一种径向超声切割刀在超声工程中获得重要应用。     

Second-harmonic generation of the nth-order Bessel beam

We investigate the second-harmonic generation of the nth-order Bessel beam in the nonlinear medium. The analysis is based on the Khokhlov-Zabolotskaya-Kuznetsov wave equation under the second-order approximation in nonlinear acoustics. The theory indicates that for an nth-order Bessel beam, the second-harmonic beam is nearly diffraction-free in the radial direction and behaves as a Bessel beam of the order 2n, and that the axial pressure amplitude is proportional to the square root of propagation distance. A variety of applications in many fields of nonlinear acoustics and nonlinear optics is expected.     

Role of radial magnetic field on heat transfer in MHD Couette flow in an annulus with viscous and Joule dissipation

This paper presents an analytical investigation of steady, fully developed MHD Couette flow of viscous, incompressible, electrically conducting fluid in the presence of radial magnetic field. Exact solutions are derived for the governing energy and momentum equations by taking into account the effects of viscous and Joule dissipations under relevant boundary conditions. The solutions obtained are graphically represented and the effects of various controlling parameters such as Hartmann number and Brinkman number on the temperature profile and consequently the Nusselt numbers are discussed. The significant result from the study is that increase in Hartmann number leads to enhancement on the Nusselt number at outer surface of inner cylinder while the role of Hartmann number is just reverse on Nusselt number at inner surface of outer cylinder. In addition, the Brinkman number has an insignificant effect on the Nusselt numbers when both surfaces are kept at equal temperature.     

夹心式径向复合压电超声换能器

对夹心式径向复合压电换能器径向振动特性进行了研究。该换能器由弹性内芯、预应力金属管及柱面压电陶瓷晶堆径向复合而成.利用机电类比法,得到了换能器的径向振动等效电路及频率方程。探讨了换能器第1、2阶径向共振频率及有效机电耦合系数与其几何尺寸的关系。研究表明,换能器第1阶径向共振频率随其内芯内径及预应力管壁厚度增大而降低;第2阶共振频率随内芯内径增大存在极小值,但随预应力管壁厚度增大单调下降。此外,采用第2阶径向共振模式能获得较高的有效机电耦合系数,并且压电陶瓷处于位移节线时,换能器有效机电耦合系数达极大值。对换能器共振频率的测试与有限元仿真表明。理论与实验及仿真结果符合较好。     

High frequency fast magnetoacoustic modes in the plasma core

Fast magnetoacoustic modes (FMM) [known also as compressional Alfvén eigenmodes (CAE) and magnetosonic modes] with frequencies exceeding or equal the ion gyrofrequency are considered. It is shown that edge-localized FMM, which presumably are responsible for the superthermal ion cyclotron emission (ICE) observed in many experiments on tokamaks and stellarators, represent a particular case of these modes. In general, FMMs with frequencies above/about the ion gyrofrequency have different radial locations and structures. They can extend over a large part of the plasma cross section and even can have maximum amplitudes at the magnetic axis. Modes with the same frequency and the same poloidal mode number are multiple, having different radial structures. These results are obtained in the approximation of cylindrical plasma with one-ion species.     

Dual focus diffractive optical element with extended depth of focus

A dual focus property and an extended depth of focus were verified by a new type of diffractive lens displaying on liquid crystal on silicon (LCoS) devices. This type of lens is useful to read information on multilayer optical discs and tilted discs. The radial undulation of the phase groove on the diffractive lens gave the dual focus nature. The focal extension was performed by combining the dual focus lens with the axilens that was invented for expanding the depth of focus. The number of undulations did not affect the intensity along the optical axis but the central spot of the diffraction pattern.     

Higher-order complex source for elegant Laguerre-Gaussian waves

We introduce a higher-order complex source that generates elegant Laguerre-Gaussian waves with radial mode number n and angular mode number m. We derive the integral and differential representations for the elegant Laguerre-Gaussian wave that in the appropriate limit yields the corresponding elegant Laguerre-Gaussian beam. From the spectral representation of the elegant Lauguerre-Gaussian wave we determine the first three orders of nonparaxial corrections for the corresponding paraxial elegant Laguerre-Gaussian beam.