Electron Motion in the Three-Dimensional Field of Undulator

In this paper we consider the motion of relativistic electrons in an ideal three-dimensional magnetic field of an undulator. The ideality of the magnetic field means that, on the undulator axis, the field is directed strictly vertically upward and has a strictly sinusoidal shape. In the overwhelming majority of cases, only this leading component of the field is taken into account in calculating the electron trajectory. In this paper, in the equations of motion of an electron in the magnetic field of an undulator, all three components of the field are taken into account, so that the undulator field under consideration satisfies the stationary Maxwell equations. In this case, the differential equations of motion of the electron are solved analytically with the help of perturbation theory, and not by the method of averaging over fast oscillations of the electron, as was done in a number of previous papers. These analytic expressions for trajectories describe the behavior of particles in the focusing magnetic field of an undulator much more completely. An analysis of these expressions shows that the behavior of electrons in such a three-dimensional field of the undulator is much more complicated than what follows from the equations obtained by the averaging method. In particular, there is a cross effect when changes in the initial vertical parameters of the electron trajectory cause changes in the horizontal component of its trajectory and vice versa. A comparison of the solutions obtained analytically with the results of numerical calculations of electron trajectories using the Runge–Kutta method demonstrates their high accuracy.     

De Haas-van Alphen Effect of Free Electron Gas Revisited

The free electron gas in a uniform magnetic field at low temperature is restudied. The grand partition function previously obtained by Landau＇s quantitative calculation contains three parts, which are all approximate. An improved calculation is presented, in which two of the three parts are obtained in exact forms. A simple remedy for Landau and Lifshitz＇s qualitative calculation in the textbook is also given, which turns the qualitative result into the same one as obtained by the improved quantitative calculation. The chemical potential is solved approximately and the thermodynamic quantities are caiculated explicitly in both a weak field and a strong field. The thermodynamic quantities in a strong field obtained here contain both non-oscillating and oscillating corrections to the corresponding results derived from Landau＇s grand partition function. In particular, Landau＇s grand partition function is not sufficiently accurate to yield our nonzero results for the specific heat and the entropy. An error in the Laplace-transform method for the problem is corrected. The results previously obtained by this method are also improved.     

Transverse Thermomagnetic Effect in the Two-Dimensional Electron Gas of Surface Semiconductor Superlattice

Journal of Experimental and Theoretical Physics - The surface current density of charge carriers in two-dimensional doubly periodic n-type semiconductor superlattices in an external magnetic field...     

Ferromagnetism of Electron Gas

We here investigate the density and temperature dependence of polarization using the relativistic formalism for the electron–electron interaction within the Fermi liquid model. The variational method has been used: the free energy has been minimized with respect to the effective mass and the polarization parameter. Then we obtained the equation of state and magnetic susceptibility of the system. The exact results for polarization and magnetic susceptibility have been obtained at zero temperature. It has been shown that for a given temperature (density) there is a critical density (temperature) at which the ferromagnetic phase can appear in an electron gas. The results are in agreement with previous work. Our results show that at nonzero temperatures and in very low and very high densities the ferromagnetism phase cannot exist.     

To the Theory of Inhomogeneous Electron Gas

Nonrigorous character of the density-functional theory for inhomogeneous electron gas based on the hypothesis assuming the existence of a universal density functional is demonstrated. A single-particle density matrix must be determined to calculate the ground-state energy of a finite system with a finite number of electrons. A single-particle Green function can be used to unambiguously determine the ground-state energy of an inhomogeneous electron system that satisfies the thermodynamic limit.     

Neutron Irradiation Effect in Two-Dimensional Electron Gas of AlGaN/GaN Heterostructures

AlGaN/GaN heterostructures have been irradiated by neutrons with different fluences and characterized by means of temperature-dependent Hall measurements and Micro-Raman scattering techniques. It is found that the carrier mobility of two-dimensional electron gas （2DEG） is very sensitive to neutrons. At a low fluence of 6.13 × 10^15 cm^-2, the carrier mobility drops sharply, while the sheet carrier density remains the same as that of an unirradiated sample. Moreover, even for a fluence of up to 3.66 × 10^16 cm^-2, the sheet carrier density shows only a slight drop. We attribute the degradation of the figure-of-merit （product of ns×μ ） of 2DEG to the defects induced by neutron irradiation. Raman measurements show that neutron irradiation does not yield obvious change to the strain state of AlGaN/GaN heterostructures, which proves that degradation of sheet carrier density has no relation to strain relaxation in the present study. The increase of the product of ns × μ of 2DEG during rapid thermal annealing processes at relatively high temperature has been attributed to the activation of GeGa transmuted from Ga and the recovery of displaced defects.     

Analytical Description of Electron Motion in a Three-Dimensional Undulator Field

The motion of relativistic electrons in an ideal three-dimensional magnetic undulator field satisfying the stationary Maxwell equation is considered. The system of nonlinear differential equations of the electron motion is solved analytically using perturbation theory rather than the method for averaging fast oscillations of the electron trajectory (the focusing approximation), as was done in a series of previous studies. The obtained analytical expressions for the trajectories describe the behavior of particles in a three-dimensional magnetic undulator field much more accurately than the formulas obtained within the framework of the focusing approximation. The analysis of these expressions shows that the behavior of electrons in a three-dimensional undulator field is much more complicated than that described by equations obtained using the averaging method. In particular, it turns out that the electron trajectories in the undulator have a cross dependence; in this case, variations in the initial trajectory parameters in the vertical plane cause changes in the horizontal trajectory components, and vice versa. The results of calculations of the trajectories carried out using analytical expressions are close to those of numerical calculations using the Runge-Kutta method.     

A High-Order Numerical Method to Study Three-Dimensional Hydrodynamics in a Natural River

A high-order numerical method for three-dimensional hydrodynamics is presented. The present method applies high-order compact schemes in space and a Runge-Kutta scheme in time to solve the Reynolds-averaged Navier-Stokes equations with the $k-ϵ$turbulence model in an orthogonal curvilinear coordinate system. In addition, a two-dimensional equation is derived from the depth-averaged momentum equations to predict the water level. The proposed method is first validated by its application to simulate flow in a $180^◦$ curved laboratory flume. It is found that the simulated results agree with measurements and are better than those from SIMPLEC algorithm. Then the method is applied to study three-dimensional hydrodynamics in a natural river, and the simulated results are in accordance with measurements.     

相关光谱法在光纤气体传感中的应用

本文提出了一种新的基于相关光谱法的光纤气体检测方案，在对传统相关光谱检测理论进行详细分析的基础上，提出了一种新的实现方案。这种方法继承了传统相关光谱法在信号检测的时候所具有的高选择性的优点，在调制方法上有创新，使得利用宽带光源（LED）在检测甲烷和乙炔等在近红外具有梳状吸收峰的气体时变得简单易行。本文对该系统进行了详尽的理论分析，在合理选择器材的基础上实际构建和调试了一个基于光谱检测的光纤甲烷气体检测系统。文中给出了存在干扰气体情况下检测结果。实践中干扰气体引起的信号变化相当于甲烷信号变化的7．4％，已经达到国际上相关光谱检测现有的最佳值。     

A Curved Noninteracting 2D Electron Gas with Anisotropic Mass

In da Costa's thin‐layer approach, a quantum particle moving in a 3D sample is confined to a curved thin interface. At the end, the interface effects are ignored and the quantum particle is localized on a curved surface. A geometric potential arises and, since it is due to this confinement procedure, it depends on the transverse to the surface mass component. The effects due to an anisotropic effective mass on a noninteracting two‐dimensional electron gas confined to a curved surface are reported. By tailoring the mass, many investigations carried out in the literature can be improved, which in turn can be useful to better designing electronic systems without modifying the geometry of the given system. Some examples are examined, such as a particle on a helicoidal surface, on a cylinder, on a catenoid and on a cone, with some possible applications briefly discussed.     

Spatial Position Detection of Three-Dimensional Objects by Effective Three-Dimensional Correlation Based on Fourier Transform Profilometry

Spatial position detection of a three-dimensional (3D) object by a correlator based on Fourier transform profilometry is discussed. The presence of the 3D object and its precise spatial position can be recognized by the correlator using the position and phase of the correlation peak. The spatial position is obtained by the relative displacement from the position where the reference object is originally placed. The characteristic of the correlator with respect to the moving direction of a 3D object is experimentally verified. Effects of the baseline factor on 3D object recognition are also investigated.     

基于吸收峰混叠的红外混合气体分析方法的研究

针对5种主次吸收峰严重交叠的红外混合气体定量分析问题,提出一种基于高阶累积量分析方法,该方法将重叠的吸收谱线映射到彼此相互分开的四阶累积量空间;在四阶累积量空间中提出一种基于正则理论和最小二乘相结合的支持向量机多维数据建模方法.在小样本下有效地提高了模型的准确度和收敛速度实验结果表明,该方法使系统的引用误差小于4%,因而能满足外场使用的要求.     

A TQFT Associated to the LMO Invariant of Three-Dimensional Manifolds

We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. This is built together with its truncations with respect to a natural grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The TQFT(s) induce(s) a (series of) representation(s) of a subgroup of the Mapping Class Group that contains the Torelli group. The N = 1 truncation is a TQFT for the Casson-Walker-Lescop invariant. The results of this article were obtained when the authors were at the Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA.     

相位测量轮廓术中三维坐标校准新方法

提出了一种新的用于相位测量轮廓术中的三维坐标校准方法。该方法用一个含有三个虚拟校准平面的标准块代替传统相位测量轮廓术校准方法中使用的标准平面，每个虚拟校准平面由多个高度相同但空间离散分布的子区域组成，相应的连续相位恢复是通过一个迭代过程实现的，同时各个子区域还被用于横向坐标的校准。由于各个虚拟校准平面间高度是垂直变化的，传统的相位展开不能得到正确的相对位置关系，基于等效波长概念，提出了一种准确的虚拟校准平面连续相位间相对位置恢复的办法。此校准方法的特点是：在校准过程中不需要标准平面的多次精确平移；仅需要一次测量就可以完成高度和横向坐标的同时校准。文中给出的实验结果说明了该校准方法的有效性和可行性。     

Study of the Effect of Electron Cooling: Overview of the Current State

Technical Physics - Investigation results of the effect of electron cooling are considered. The current state-of-the-art is analyzed. The possibilities are discussed for the experimental study of...     

Effect of In Composition on Two-Dimensional Electron Gas in Wurtzite AlGaN/InGaN Heterostructures

The effect of In composition on two-dimensional electron gas in wurtzite AlGaN/InGaN heterostructures is theoretically investigated. The sheet carrier density is shown to increase nearly linearly with In mole fraction x, due to the increase in the polarization charge at the AlGaN/InGaN interface. The electron sheet density is enhanced with the doping in the AlGaN layer. The sheet carrier density is as high as 3.7×1013 cm^-2 at the donor density of 10×1018 cm^-3 for the HEMT structure with x=0.3. The contribution of additional donor density on the electron sheet density is nearly independent of the In mole fraction.     

Photoinduced Electron Transfer From Carbazole to Halomethanes in a Gas Phase

Intermolecular photoinduced electron transfer (PET) in a gas phase was studied using carbazole vapor fluorescence quenching by halomethanes (CHCl₃, CH₂Br₂, CCl₄, CHBr₃). The fluorescence quenching rate constants k _q changing from 2.3·10⁵ sec^–1·torr^–1 in mixtures with CHCl₃ to 4.6·10⁶ sec^–1·torr^–1 in mixtures with CHBr₃ at a constant temperature of 403 K were estimated. The dependence of the carbazole fluorescence decay rates in the presence of halomethanes on the free energy change G during transfer of the electron from carbazole to halomethanes is considered. It is suggested to take into account the influence of the vibrational energy of the carbazole molecule E _vib and its temperature changes in estimation of the G values. The differences between PET in the gas and liquid phases were analyzed. It is found that for mixtures with CCl₄ and CHBr₃ the negative temperature dependence of k _q is observed, when the decay rates and efficiencies of the intermolecular PET decreased with temperature increase in the range 403–573 K, i.e. these mixtures the electron transfer is not a barrier-restricted process.     

Nonlinear Transport of Three-Dimensional Electron Gases Under the Influenceo f an Intense Terahertz Radiation

We present a detailed theoretical and numerical investigation on nonlinear transport of a model three-dimensional electron gas driven by an intense terahertz (THz) radiation at lattice temperature T = 10,77,300 K using the conventional and recently developed balanceequation approach. Ionized-impurity, acoustic-phonon and polar optical-phonon scatterings were taken into account for electrons in a single parabolic band. The heating of electrons and the suppression of the dc electron mobility by the irradiation of the intense THz field are predicted. We find that the dc average mobility of electrons peaks around a certain value of the amplitude of the ac field at low lattice temperature.