A comparative study of the full dispersion relation, Compton dispersion relation, and Raman dispersion relation of a free-electron laser in helical wiggler and guiding magnetic fields

The full dispersion relation obtained for a free-electron laser in the presence of circularly polarized, periodic, static wiggler and guiding magnetic fields by the kinetic approach incorporating the particle trajectories is reduced to Compton and Raman regime approximations in the case of a tenuous electron beam. The temporal growth rate has been compared between the full dispersion relation and the Compton dispersion relation, as well as between the full dispersion relation and the Raman dispersion relation in the microwave region. The results show the maxima of growths in the full dispersion relation and the Compton dispersion relation, as well as the full dispersion relation and the Raman dispersion relation, are at the same locations, but the growth rates in both regimes are enhanced with respect to the full dispersion relation for the same plasma frequency and cavity parameters.     

A hierarchy of rational Timoshenko dispersion relations

This paper shows that the conventional Timoshenko dispersion relation for bending waves is the (0,1) member of a two-parameter family (m,n) of approximations to the exact dispersion relation obtained from linear elasticity. Higher members of the family are shown to converge rapidly to the exact dispersion relation; in particular, any number of branches can be captured accurately over their entire length, i.e. up to arbitrarily high frequencies and wavenumbers. The theory admits a rigorous accuracy analysis, and demonstrates that the conventional Timoshenko dispersion relation is a completely rational approximation, thus answering some previous doubts about this matter. Lower members of the two-parameter family include the Euler-Bernoulli dispersion relation and a Rayleigh-type inertia correction. Especially useful is the Timoshenko (1,2) dispersion relation, which extends the conventional Timoshenko (0,1) dispersion relation by capturing the first four branches of the exact dispersion relation rather than merely the first two, and is accurate over a wide range. An inertia-corrected Timoshenko dispersion relation is also derived, and is shown to include many previous approximations as special cases.     

Dispersion of laser generated surface waves in an epoxy-bonded layered medium

In this paper, the dispersion of laser generated surface wave in an epoxy bonded copper-aluminum layered specimen is studied. A laser ultrasonic experiment based on the point-source/point-receiver (PS/PR) technique was conducted to measure the surface wave signals in the layered specimen. The received wave signals were then processed in the frequency domain to obtain the dispersion relation of the fundamental surface wave mode. Theoretical calculations of the dispersion relations of the fundamental surface wave modes in two-layered and three-layered specimens were conducted to explore the influence of the bonding layer thickness on the dispersion relation. The experimental dispersion relation for the epoxy bonded copper-aluminum layered specimen is in good agreement with the calculated dispersion relation. The influence of the bonding layer thickness on the dispersion relation is studied and the potential application of the present results to the NDE of bonded layered media based on laser ultrasonics is also addressed.     

虚阴极的单电荷层模型

 通过引入虚阴极振荡的单电荷层模型，得到了虚阴极振荡产生微波的线性色散关系。同时，分析了入射、反射、透射束流中振荡成份与虚阴极振荡的两本征模式相互作用，得到非线性色散关系，并给出了虚阴极振荡产生微波的机制。     

相对论q分布正负电子对等离子体横振荡

研究了无磁化、无碰撞、各向同性相对论q分布正负电子对等离子体横振荡色散关系,通过理论推导得到与非广延参数q有关的色散方程。从该色散方程出发,得到极端相对论情况下长波支和短波支下等离子体横振荡色散关系解析解,为了得到完整的色散曲线,对色散方程进行数值计算,在极端相对论情况下数值结果与解析结果在长波支和短波支下完全吻合。研究发现相对论q分布下色散关系与非广延参数q和温度有关,当q1时,则渐进结果与经典统计下的一致。     

Phonon dispersion relations of crystalline solids based on LAMMPS package

The phonon dispersion relations of crystalline solids play an important role in determining the mechanical and thermal properties of materials. The phonon dispersion relation, as well as the vibrational density of states, is also often used as an indicator of variation of lattice thermal conductivity with the external stress, defects, etc. In this study, a simple and fast tool is proposed to acquire the phonon dispersion relation of crystalline solids based on the LAMMPS package. The theoretical details for the calculation of the phonon dispersion relation are derived mathematically and the computational flow chart is present. The tool is first used to calculate the phonon dispersion relation of graphene with two atoms in the unit cell. Then, the phonon dispersions corresponding to several potentials or force fields, which are commonly used in the LAMMPS package to modeling the graphene, are obtained to compare with that from the DFT calculation. They are further extended to evaluate the accuracy of the used potentials before the molecular dynamics simulation. The tool is also used to calculate the phonon dispersion relation of superlattice structures that contains more than one hundred of atoms in the unit cell, which predicts the phonon band gaps along the cross-plane direction. Since the phonon dispersion relation plays an important role in the physical properties of condensed matter, the proposed tool for the calculation of the phonon dispersion relation is of great significance for predicting and explaining the mechanical and thermal properties of crystalline solids.     

Analytical relation between effective mode field area and waveguide dispersion in microstructure fibers

For optical fibers exhibiting a radially symmetric refractive index profile, there exists an analytical relation that connects waveguide dispersion and the Petermann-II mode field radius. We extend the usefulness of this relation to the nonradially symmetric case of microstructure fibers in the anomalous dispersion regime, yielding a simple relation between dispersion and effective mode field area. Assuming a Gaussian mode distribution, we derive a fundamental upper limit for the effective mode field area that is required to obtain a certain amount of anomalous waveguide dispersion. This relation is demonstrated to show excellent agreement for fiber designs suited for supercontinuum generation and soliton lasers in the near infrared.     

Excitations in a Dipolar Bose–Einstein Condensate

We study excitations in a dipolar Bose–Einstein condensate with Green’s function. In Bogoliubov approximation, we obtain the dispersion relation. The excitation energy is dependent on the angle between the momentum and the magnetic moment. In the long-wave limit, the dispersion relation reduces to an anisotropic phonon-like dispersion relation.     

Lieb mode in a quasi-one-dimensional bose-einstein condensate of atoms

We calculate the dispersion relation associated with a solitary wave in a quasi-one-dimensional Bose-Einstein condensate of atoms confined in a harmonic, cylindrical trap in the limit of weak and strong interactions. In both cases, the dispersion relation is linear for long-wavelength excitations and terminates at the point where the group velocity vanishes. We also calculate the dispersion relation of sound waves in both limits of weak and strong coupling.     

Specific features of magnetoabsorption resulting from exactly taking into account the electronic band spectrum

Effects related to the periodicity of the carrier dispersion relation in the reciprocal space are investigated. It is shown that, under certain conditions, magnetoabsorption in crystals exhibiting such dispersion significantly differs from the magnetoabsorption in crystals characterized by a parabolic dispersion relation for charge carriers.     

微环耦合谐振光波导中的色散控制模型与数值仿真

本文利用传输矩阵法得到了微环耦合谐振光波导的色散关系,讨论了耦合损耗、传输损耗及耦合系数对微环耦合谐振光波导色散的影响,改变耦合损耗、传输损耗及耦合系数可控制其色散曲线的形状、位置、以及带宽,色散曲线的变化及控制对微环耦合谐振光波导在滤波、光信号延迟及缓存等方面的应用有重要意义. 关键词： 光波导 微环光波导 传输矩阵法     

Cubic dispersion relation for a relativistic backward-waveoscillator

The cubic approximation to the dispersion relation for a relativistic backward-wave oscillator is obtained, and the utility and limits of the approximation are presented. The approximation is obtained by Taylor series expansion of the wave admittance in the dispersion relation for the transverse-magnetic and free-streaming modes of a relativistic, thin, hollow, cylindrical electron beam moving along the axis of a disc-loaded waveguide in a strong axial magnetic field. The resulting cubic dispersion relation yields instability growth rates and frequencies which fall off beyond their maximum more sharply with increasing wavenumber than for the complete dispersion relation. The approximation is found to be quite good near the operating points of contemporary high-power relativistic backward-wave oscillators, namely, for relatively long wavelength and small ratio of Budker's parameter to the relativistic gamma factor of the beam     

Dispersion relation of excitation mode in spin-polarized Fermi gas

We study the dispersion relation of the excitation mode in a spin-polarized Fermi gas.In the frame of the imaginarytime finite temperature field theory,the polarization tensor is calculated by taking the random phase approximation.The population imbalance effects on the dispersion relation of the excitation mode and the spin-spin correlation susceptibility are investigated.The numerical results in terms of the imbalance ratio indicate the polarization effects on the dispersion relation and susceptibility χ.     

VLASOV EQUATION,GENERALIZED POISSON EQUATION AND DISPERSION RELATION

A quantum mechanical analog of the Vlasov equation is derived. If the residual nuclear field is taken as generalized Poisson equation, the dispersion relation is consistent with the classical dispersion relation in Ref.[1].     

Dispersion relation of excitation mode in spin-polarized Fermi gas

We study the dispersion relation of the excitation mode in a spin-polarized Fermi gas. In the frame of the imaginary-time finite temperature field theory, the polarization tensor is calculated by taking the random phase approximation. The population imbalance effects on the dispersion relation of the excitation mode and the spin-spin correlation susceptibility are investigated. The numerical results in terms of the imbalance ratio indicate the polarization effects on the dispersion relation and susceptibility χ.     

Measurements of the shear Alfvén wave dispersion for finite perpendicular wave number

Measurements of the dispersion relation for shear Alfvén waves as a function of the perpendicular wave number are reported for the regime in which V(A) approximately V(Te). By measuring the parallel phase velocity of the waves, the measurements can be compared directly to theoretical predictions of the dispersion relation for a parameter regime in which particle kinetic effects become important. The comparison shows that the best agreement between theory and experiment is achieved when a fully complex, warm plasma dispersion relation is used.     

Dispersion gap and localized spiral waves in a model for intracellular Ca2+ dynamics

The dispersion relation is the dependence of the velocity of periodic planar wave trains on their wavelength. We study the occurrence of a velocity gap in the dispersion relation in a bistable three component reaction-diffusion system modeling intracellular Ca2+ dynamics. In two spatial dimensions, localized pinned spirals are observed, if their wavelength falls into the dispersion gap. Destruction of free spirals occurs already for conditions where the asymptotic planar wave train exists and the dispersion gap is absent.     

电子束电流对介质切伦科夫脉塞色散关系的影响

采用等离子体流体理论,从线性扰动方程出发,研究了电子束电流大小对介质切伦科夫脉塞中束波相互作用色散关系的影响,得到了当等离子体返回电流能有效中和与不能有效中和电子束电流两种情形下色散关系和波的增长率,并讨论了电子束电流对束波相互作用色散关系和波增长率的影响。研究表明,等离子体返回电流能有效中和与不能有效中和电子束电流两种情况下有着不同的色散关系和波的增长率。在波导参数和背景等离子体参数固定的情况下,电子束电流并不是越大越好,电子束电流过大不利于提高器件效率,它们之间存在最佳匹配关系。     

Note on the Constraint on Modified Energy-Momentum Relation

Quantum gravity can modify the usual energy-momentum dispersion relation. We provide evidence for the argument that the modified dispersion relation is constrained by the black hole thermodynamics, for consistency of quantum gravity.     

Surface plasmons on corrugated metal films

The dispersion relation for a surface plasmon, propagating across a corrugated metal film on a dielectric substrate, is obtained by the method of reduced Rayleigh equations. It is found that the surface plasmon dispersion curve has an infinite number of branches. Numerical solutions of the dispersion relation are obtained for a film, characterized by a free-electron metal dielectric function and a sinusoidal profile function.