Splitting between quadrupole modes of dilute quantum gas in a two-dimensional anisotropic trap

We consider quadrupole excitations of quasi-two-dimensional interacting quantum gas in an anisotropic harmonic oscillator potential at zero temperature. Using the time-dependent variational approach, we calculate a few low-lying collective excitation frequencies of a two-dimensional anisotropic Bose gas. Within the energy weighted sum-rule approach, we derive a general dispersion relation of two quadrupole excitations of a two-dimensional deformed trapped quantum gas. This dispersion relation is valid for both statistics. We show that the quadrupole excitation frequencies obtained from both methods are exactly the same. Using this general dispersion relation, we also calculate the quadrupole frequencies of a two-dimensional unpolarized Fermi gas in an anisotropic trap. For both cases, we obtain analytic expressions for the quadrupole frequencies and the splitting between them for arbitrary value of trap deformation. This splitting decreases with increasing interaction strength for both statistics. For a two-dimensional anisotropic Fermi gas, the two quadrupole frequencies and the splitting between them become independent of the particle number within the Thomas-Fermi approach. Received 21 September 2001 and Received in final form 9 December 2001     

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.     

Self-consistent theory of cyclotron autoresonance maser in a uniform planar waveguide

A general dispersion relation for the cyclotron autoresonance maser (CARM) that takes into account self-consistent couplings between TE, TM and ac space charge perturbations in a uniform planar waveguide is derived. The dispersion relation predicts enhanced growth rate due to ac space charge effects. Results from computer simulations of a planar CARM amplifier are presented to support this finding.     

Dispersion relations of the intercalate modes in graphite intercalation compounds

We study the dynamics of the charged intercalate molecules. The model for the intercalate is a two dimensional plasma with the appropriate screening due to the charge carriers in the graphite layers. The dependence of the dispersion relation on stage and charge transfer is discussed and the relation of these modes to conductivity is pointed out.     

Solitons of the KP equation in dusty plasma with variable dust charge and two temperature ions: energy and stability

The propagation of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions is analyzed. By using the reductive perturbation theory, the Kadomtsev-Petviashivili (KP) equation is derived. A Sagdeev potential has been investigated. This potential is used to study the stability conditions for existence of solitonic solutions. Also, it is shown that a rarefactive soliton can exist in most of the cases. The energy of the soliton has been calculated and by using the standard normal-mode analysis a linear dispersion relation has been obtained. The effects of variable dust charge on the amplitude, width and energy of soliton and its effects on the angular frequency of linear wave are also discussed.     

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。     

Slow cyclotron instability in a high-power backward-wave oscillator

The linear dispersion relation of a backward-wave oscillator (BWO), derived earlier by the authors, is modified to include effects of RF surface current at the beam-vacuum interface. This modified dispersion relation results in an unstable interaction between the slow cyclotron mode (SCM) and the structure mode in addition to the conventional Cherenkov instability caused by the slow space charge mode. Numerical analysis is then carried out using parameters of a BWO experiment at University of Maryland. Fine structure of the SCM instability is elucidated. The analysis indicates that BWO radiation would not be suppressed near cyclotron absorption in an infinitely long system.     

Dispersion and absorption of Alfven wave in ion-implanted group-IV semiconductor

By considering that the implanted ions in a group-IV semiconductor agglomerate to form nanoclusters (NCs) and some of them acquire negative charge, we present an analytical study on excitation and propagation of Alfven wave (AW). Using multi-fluid analysis and Maxwell's equations, a linear dispersion relation for the AW in a semiconductor plasma has been derived. The presence of charged NCs is shown to split the waves into two components and significantly modifying their dispersion and absorption characteristics by creating a charge imbalance in the semiconductor plasma. The NCs, on account of their heavy masses, are assumed to be stationary in the background.     

The instability of dust acoustic waves in inhomogeneous dusty plasmas with non-adiabatic dust charge fluctuation

This paper investigates the propagation of linear dust acoustic waves in inhomogeneous dusty plasmas due to spatial gradients of dust charge, plasma densities. A linear dispersion relation is obtained with the non-adiabatic dust charge iguctuation and the non-thermally distributed ions. The numerical results show that the inhomogeneity, nonthermal ions and non-adlabatic dust charge iguctuatlon have strong iniguence on the frequency and the damping rate of waves.     

法拉弟磁光效应实验中介质色散特性测量方法的改进

提出利用入射角、偏向角及折射率的函数关系,以多个非近零变化率点测量及其最小二乘法的非线性拟合得到较小不确定度的系列谱线的折射率,进而获得较高精度的色散特性关系。克服以最小偏向角方法测定时临界位置主观随机影响大的局限性。从而实现基于法拉弟磁光效应的电子荷质比的高精度测量。     

Dust lattice wave dispersion relations in two-dimensional hexagonal crystals including the effect of dust charge polarization

A dusty plasma crystalline configuration with equal charge dust grains and mass is considered. Both charge and mass of each dust species are taken to be constant. Two differential equations for a two-dimensional hexagonal crystal on the basis of a Yukawa-type potential energy and a “dressed” potential energy, accounting for dust charge polarization, are derived and compared. The dispersion relation for both longitudinal and transverse wave propagation in an arbitrary direction is derived. A comparison to analytical and experimental results reported previously is carried out.     

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.     

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研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

强耦合尘埃等离子体中正电扰动下的尘埃声激波

研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

同轴慢波结构相对论高功率微波产生器理论分析

 推导了同轴波导的空间电荷限制流，其值大于圆波导的空间电荷限制流。因此在阴极电势和束流相等的情况下，同轴波导中的束流具有更高的动能，同轴器件有可能获得更高的微波转换效率。理论推导出同轴慢波结构中考虑束流空间电荷影响的色散方程，利用Matlab进行了编程求解。不考虑束流空间电荷影响时，编程计算结果与Superfish模拟结果一致。由考虑束流空间电荷影响的色散方程数值计算结果，可知文献中提出的同轴慢波结构相对论高功率微波产生器工作在准TEM模的π模，频率为7.67 GHz，峰值时间增长率较高，电子束损失的能量与其初始能量之比为34%。这些结果均与文献中的数值模拟结果一致。同时理论分析说明该种器件无论在能量转换效率，还是在产生微波脉冲的上升时间上均具有优势。     

Influence of charge carrier diffusion on the stability of a charged drop of a finite-conductivity liquid

A dispersion relation for the capillary oscillations of a spherical drop of a viscous incompressible liquid with a charge transfer finite rate is derived and analyzed with emphasis on the role of diffusion. It is shown that diffusion has the strongest influence on the stability of rapidly damped quasi-periodic motions of a low-conductivity liquid. The instability growth rate of capillary oscillations grows with the charge diffusion coefficient and decreases with rising conductivity of the liquid.     

Nonaxisymmetric oscillations of a charged jet of a finite-conductivity viscous liquid

A dispersion relation for nonaxisymmetric oscillations of a charged jet of a viscous incompressible finite-conductivity liquid is derived. In the low-viscosity limit, when the dispersion relation can be reduced to a power algebraic equation, analytical expressions for its roots are found and their dependences on the conductivity of the liquid and carrier mobility are analyzed. Taking into account a finite rate of electric charge transfer introduces an additional damping and somewhat decreases the instability growth rates.     

Surface plasmon dispersion for very small metallic spheres: A quantum mechanical formulation

We have derived a pair of matrix equations describing the surface plasmon dispersion for a very small spherical metal particle, using the quantum mechanical random-phase approximation (RPA). The surface of the sphere is represented by an infinite spherical potential well for the conduction electrons and the positive ions are assumed to be uniformly distributed into a “jellium”. The dispersion relation is obtained as the condition that a solution of the RPA integral equation for charge fluctuation would exist for the particle.     

四层异质结构的表面和界面光学声子模

用连续介电模型研究了有限厚度四层异质结构的表面和界面光学声子模。精确得到本征失量、色散关系和面电荷密度。前人关于介电平板、双层、三层以及无限四层结构等所有已得结果，都可从此文普遍关系重新推出。另外，还给出了有限阶梯量子阱等有趣而实用结构的色散关系及其数值显示。本研究可视为文献［８］的推广。 关键词：     

Kadomstev-Petviashvili (KP) equation in warm dusty plasma with variable dust charge,two-temperature ion and nonthermal electron

In this work, the propagation of nonlinear waves in warm dusty plasmas with variable dust charge, two-temperature ion and nonthermal electron is studied. By using the reductive perturbation theory, the Kadomstev-Petviashvili (KP) equation is derived. The energy of the soliton and the linear dispersion relation are obtained. The effects of variable dust charge on the energy of soliton and the angular frequency of linear wave are also discussed.