Application of transition radiation in a small dihedral angle to detection of relativistic particles

The features of transition radiation excited by a relativistic particle in a dihedral angle with an opening comparable to the angular divergence of transition radiation are considered. It is shown that the radiation distribution in the dihedral angle is more sensitive to the direction of emitting particle motion and to the position of the surface intersection by the particle, than the radiation excited when a plane surface is intersected. It is indicated that the spectral radiation density in the small dihedral angle is higher than the density of radiation excited when a plane surface is intersected. These features offer additional opportunities to use transition radiation in systems for measuring particle parameters.     

Transient radiation of particles in dihedral and trihedral angles

The image method is used for determining the field of transient radiation emitted by a charged particle intersecting a dihedral angle formed by ideally conducting charged planes. The spectral-angular distributions of radiation intensity in a dihedral angle with different corner angles are calculated. The effect of the direction of motion of the particle and of the position of the point at which the particle intersects the plane on radiation parameters is considered. Transient radiation distributions in a trihedral angle are also obtained.     

Peculiarities of the spectral-angular distribution of transition radiation from a relativistic particle in a dihedral angle

The spatial distributions of transition radiation from relativistic particles entering and exiting the edge of a dihedral angle formed by perfectly conducting flat surfaces have been investigated. The angular distributions of the radiation intensity in dihedral angles with various opening angles have been calculated. The angular distributions of forward radiation (when the particle exits the dihedral angle) and backward radiation (when the particle enters the dihedral angle) are shown to differ significantly.     

Experimental study of coherent transition radiation from relativistic electron bunches entering a dihedral angle

The angular distributions of the intensity of transition radiation from a bunch of relativistic electrons entering a dihedral angle between two conducting planes have been measured in a millimeter wavelength range. A microtron with a particle energy of 7.4 MeV is used as a source of electrons. The effect of the particle injection direction and the magnitude of the dihedral angle on the angular distribution of the radiation intensity has been analyzed. The measurements show that the character of the distribution of radiation from a charge entering the dihedral angle significantly differs from that for a charge escaping the angle. A comparatively small change in the magnitude of the dihedral angle can lead to qualitative changes in the angular distribution of radiation from a charge entering the dihedral angle.     

Experimental study of coherent transition radiation from relativistic electrons in a dihedral angle

Angular intensity distributions for transition radiation excited by a beam of relativistic electrons in the emitter in the form of a dihedral angle are measured in the millimeter range. The angle is formed by the intersection of two conducting planes. The source of radiation is a microtron with an electron energy of 7.4 MeV. We analyze the effect of the magnitude of the dihedral angle of the emitter, the position of the electron transition point on the surface of the angle, and the direction of motion of electrons on the angular distribution of radiation intensity. It is shown that the spectral and angular distributions of radiation intensity in the dihedral angle substantially differ from analogous distributions for a particle intersecting a planar conducting surface. The possibility of using radiation to measure the energy, spatial position, and direction of motion of charges is considered.     

Transition radiation detectors with a dihedral angle or a cone as a radiator

The spectral and angular distributions of the transition radiation produced by a charge crossing an interface shaped like a dihedral angle or a cone are considered. The effects of the variation in the dihedral angle and cone angle, the location of the crossing point on the interface, and the direction of the charge motion on the spatial distribution of the radiation are discussed. The radiation characteristics of the particles that are incident on the interface and those leaving it are given. The features of transition-radiation detectors with dihedral-angle or cone radiators and detectors with plane-surface radiators are compared.     

Spatial distribution of transition radiation of relativistic particles in the dihedral angle formed by perfectly conductive planes

Spatial distributions of transition radiation intensity of particles entering the dihedral angle and escaping from it are calculated. It was shown that radiation of escaping charge at any opening of the dihedral angle ?? is concentrated near the motion direction. If the particle enters the angle, the radiation distribution is defined by the opening angle. At opening angles ?? = ??/n, radiation is concentrated near the direction of actual charge motion when n is an even number and near the direction of image charge motion when n is an odd number. At other opening angles, the spatial distribution of entering particle radiation has two maxima whose positions are defined by the injection angle.     

Scattering of a Plane Electromagnetic Wave by an Infinite Dihedral Wedge with a Slotted Cylinder at the Apex

The problem of scattering of a plane electromagnetic wave by a perfectly conducting dihedral wedge with a slotted cylinder at the apex in rigorous formulation is reduced to solving a system of linear algebraic equations for unknown coefficients of the Fourier expansion of the scattered field. The results of calculation of the far-zone field with a given accuracy are presented in the case of an E-polarized incident wave. It is shown that for a slot with a large opening angle, the radiation patterns of the field in the long-wavelength far zone has a shape similar to a cardioid and does not depend on the incident-wave direction and the dielectric permittivity of the cylinder. In the case of a narrow slot, the radiation-pattern shape depends significantly on the incidence angle of the wave.     

Transition radiation generated by a particle passing through the apex of a conducting cone

The spatial field distribution is determined for the transition radiation generated by a particle passing through the apex of a cone along its axis. Expressions for the angular distribution of the radiation intensity are obtained for apex angles between 0 and π. Characteristics of transition radiation emitted into a “funnel” and a dihedral angle are compared.     

Equilibrium configurations of the conducting liquid surface in a nonuniform electric field

Possible equilibrium configurations of the free surface of a conducting liquid deformed by a nonuniform external electric field are investigated. The liquid rests on an electrode that has the shape of a dihedral angle formed by two intersecting equipotential half-planes (conducting wedge). It is assumed that the problem has plane symmetry: the surface is invariant under shift along the edge of the dihedral angle. A one-parametric family of exact solutions for the shape of the surface is found in which the opening angle of the region above the wedge serves as a parameter. The solutions are valid when the pressure difference between the inside and outside of the liquid is zero. For an arbitrary pressure difference, approximate solutions to the problem are constructed and it is demonstrated the approximation error is small. It is found that, when the potential difference exceeds a certain threshold value, equilibrium solutions are absent. In this case, the region occupied by the liquid disintegrates, the disintegration scenario depending on the opening angle.     

角锥棱镜谐振腔激光模式模拟研究

为了探究角锥棱镜谐振腔激光模式,以角锥-平面镜腔为例,将角锥棱镜等效为衍射光栅,考虑角锥镜棱宽在谐振腔中的衍射效应以及二面角误差引起的附加相位分布对谐振腔激光模式的影响,在光学谐振腔理论的基础上,建立了求解本征模式的理论分析模型.采用快速傅里叶法数值模拟不同腔长、角锥镜棱宽和二面角误差情况下该无源谐振腔激光输出模式分布情况.结果表明,在腔长30 cm、角锥镜棱宽小于75μm、二面角误差在-10′~5′之间时,可实现光斑完整的圆形分布输出模式,且有较好的光束质量;棱宽不小于0.4 mm,二面角误差在-40′~10′之间时,光斑为TEM 03阶横模,光场呈六瓣分布;当角锥镜棱宽为0.4 mm、二面角误差为3′,腔长从30~90 cm范围内增加时,该谐振腔输出的激光模式从TEM 03转换成TEM 10.     

O (3P) + H2 → OH+H反应的立体动力学研究

用BMS1势能面[Brandão 等, J.Chem.Phys. 121, 8861 (2004)],选取碰撞能为34.6kcal/mol,用准经典轨线方法研究了O ( ) + 反应的立体动力学性质。计算并讨论了k与j'的夹角的分布关系P ( )以及描述k-k'- j'三者关系的二面角分布。（k为反应物速度方向,k'为产物的速度方向,j'为产物的角动量方向） 的峰值在90°附近并且关于90°呈对称性分布,这表明产物角动量的方向与初速度的方向垂直。二面角分布P( )关于散射平面呈反对称性分布,这一结果表明产物的角动量具有强烈的极化效应。另外,我们还研究了振动激发对产物角动量的影响,结果表明产物的矢量性质对反应物的初始振动态非常敏感。     

O(3P)+H2→OH+H反应的立体动力学研究

利用BMS1势能面[Brandao等,J.Chem.Phys.121,8861(2004)],选取碰撞能为34.6 kcal/mol,用准经典轨线方法研究了O(3P)+H2反应的立体动力学性质.计算并讨论了k与j'的夹角的分布关系P(θr)以及描述k-k'-j'三者关系的二面角分布P((ρ)r).(k)为反应物速度方向,k'为产物的速度方向,j'为产物的角动量方向)P(θr)的峰值在90°附近并且关于90°呈对称性分布,这表明产物角动量的方向与初速度的方向垂直.二面角分布P((ρ)r)关于散射平面呈反对称性分布,这一结果表明产物的角动量具有强烈的极化效应.另外,我们还研究了振动激发对产物角动量的影响,结果表明产物的矢量性质对反应物的初始振动态非常敏感.     

角锥棱镜激光谐振腔的基本特性

 分析了角锥棱镜对光束的相位变换作用，带二面角误差的角锥棱镜可等效于6块光楔的组合，其楔角的大小和方向由二面角误差决定。对在腔内往返传输的光线在镜面上的位置进行了分析，结果表明：3个二面角误差相同且不为零的角锥棱镜构成的谐振腔为约束非稳腔。用Fox-Li迭代法数值模拟得到了不同棱镜二面角误差情况下的谐振模式。模拟结果表明：圆形镜腔情况下基本振荡模式接近于TEM₀₃模的拉盖尔高斯光束；当3个二面角误差不相同时，模式中各个区域的强度分布不对称。采用3个二面角误差基本接近且绝对值较小的棱镜可以提高光束质量。     

Free vibrations and buckling of graphene sheets

The molecular mechanics method is used to determine both eigenfrequencies and modes of vibrations and the critical compressing loads and buckling modes of graphene sheets. To simulate interatomic interactions in graphene, the DREIDING field of potential forces is used. This field includes four types of potential energies of covalent atomic interactions such as central forces, the variations in the angle between the neighboring bonds, the dihedral angle that is responsible for the torsion of the covalent bond, and the inversion angle (the angle corresponding to the retiring of the atom from the plane relative to three neighboring atoms).     

Solution of a one-dimensional torsion Schrödinger equation with a general periodic potential

Relations are found for the calculation of eigenvalues and eigenfunctions of the Hamiltonian of internal rotational motion in molecules in the basis of plane waves. The dependences of kinematic coefficient F(φ) and potential V(φ) on dihedral angle φ are represented by Fourier series for both symmetric and asymmetric functions, as well as for general periodic functions. If a molecule has symmetry elements, the found solution transforms to that previously known.     

双轴晶体LiB3O5和频与倍频转换特性的研究

本文在光学主轴坐标系下,对双轴晶体LiB3O5共线和频与倍频特性进行了计算与分析.给出了xy面应用tyyeⅠ相位匹配及yz面应用typeⅡ相位匹配情况下,基波波长与相位匹配角、有效非线性系数、离散角、容承角及基波频谱带宽的关系曲线,对LiB3O5晶体的实验与应用提供了有指导意义的理论结果.     

Torsional barriers and nonlinear optical properties of 2-, 3-, 4-phenylpyridine molecules

The torsional barriers and nonlinear optical properties for all phenylpyridine molecules were calculated by using Hartree-Fock (HF) theory and Becke three-parameter functional (B3LYP) hybrid approaches within the density functional theory framework with the 6-31++G(d, p) basis set, and via the GAUSSIAN 98W. The torsional barrier computations show that dihedral angle between the two rings increases with the number of H-H vicinal interactions and torsional barriers with dihedral angles for 3-, 4-phenylpyridines are too similar for both HF and B3LYP level calculations. Also, HOMO-LUMO energy gaps, polarizabilities, anisotropy of polarizabilities, and static hyperpolarizabilities are calculated as a function of dihedral angle between benzene and pyridine rings. The study reveals that the phenylpyridines show very low nonlinear optical properties. The calculated torsional barrier, equilibrium dihedral angle and molecular dipole moment results for these molecules were compared with available experimental and other results determining from different computational methods.     

Dynamics and mechanism of the Crystal II → smecticG phase transition in TB7A by a temperature‐dependent micro‐Raman study and DFT calculations

The solid to smecticG (SmG) phase transition in a Schiff base liquid crystalline compound, terepthal‐bis‐heptylaniline (TB7A), is monitored in situ by temperature‐dependent Raman microspectroscopy, using the band of a C H in‐plane bending mode as a marker. Contrary to the earlier report of a sudden wavenumber shift, the in situ measurement shows very clearly that a new Raman band at ∼1160 cm⁻¹ appears at the Crystal II → SmG transition. The dynamics of this phase transition is discussed in terms of a triple well potential below 210 K and a double well potential above 210 K. The phase transition essentially takes place as a result of intra‐molecular rotation about the long molecular axis. The optimization energy at various fixed dihedral angles, ( C C CN ) are calculated using density functional theory (DFT) at the B3LYP/6‐31G* level of theory. The relative energy at each dihedral angle is calculated relative to optimization energy obtained without any constraints and plotted as a function of dihedral angle (Φ) between the adjacent phenyl ring planes, which also shows a double well potential at room temperature. Copyright © 2009 John Wiley & Sons, Ltd.