Conducting axisymmetric body in a coaxial varying magnetic field

We calculate the vector potential and magnetic field strength in an axisymmetric conductor introduced into a preset coaxial external magnetic field varying harmonically with time. The proposed method involves the representation of the vector potential as the sum of a converging series each term of which is a solution to the Helmholtz equation with constant coefficient at infinity. The next terms of each series are determined from the preceding terms using the known Green function. The adequacy of the numerical results is confirmed by their comparison with the exact values for a sphere in a uniform magnetic field and by comparison of the numerical results obtained using two different series for an ellipsoid in a nonuniform magnetic field.     

Nonlocal ion transport in a weakly ionized nonequilibrium plasma

Nonlocal ion transport in a weakly ionized plasma with a strong electric field is analyzed. It is assumed that charge-exchange interactions are the main mechanism of ion scattering. Ion density and drift velocity are determined for nonuniform time varying electric field by using both the direct solution of the kinetic equation and the Chapman-Enskog-type approach. The ion mean velocity is given by an integro-differential operator applied to the electric field. Ion density and drift velocity exhibit resonant behaviour when ω≃kW0, which corresponds to the resonance between ions moving with average velocity W₀ and wave traveling with the phase velocity ω/k     

Self-consistent mechanism for sustaining ionization waves in a low-pressure discharge

The possibility of constructing a self-consistent model for the sustaining of ionization waves is demonstrated for a low-pressure discharge in an inert gas. The model is based on the combined solution of the kinetic equation of the electrons and the equation of motion of the ions in a spatially periodic field. The distribution function is constructed in an experimentally measured field and then used to calculate the spatial distributions of the plasma density and the ionization rate. The solution of the equation of motion of the ions makes it possible to reconstruct a field similar to the original one. One specific feature of the mechanism considered is the pronounced nonlocal character of the formation of the electron distribution function by the entire nonuniform potential profile of the ionization wave. Zh. Tekh. Fiz. 67, 24–30 (February 1997)     

Radial Distributions of Dusty Plasma Parameters in a DC Glow Discharge

A non‐stationary non‐local kinetic model for radial distributions of dusty plasma parameters based on the solution of Boltzmann equation for electron energy distribution function is presented. Electrons and ions production in ionizing collisions and their recombination on dust particle surface were taken into account. The drift‐diffusion approximation for ions was used. To obtain the self‐consistent radial distribution of electric potential the Poisson equation was used. It is shown that at high dust particle density the recombination of electrons and ions can exceed their production in ionization collisions in the region of dusty cloud. In this case the non‐monotonous radial distribution of the electric field is formed, the radial electric field becomes reversed and the radial electron and ion fluxes change their direction toward the center of the tube (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical analysis of ion motion in a gas subjected to an alternating-sign periodic asymmetric-waveform electric field

The motion of ions in a gas subjected to an alternating-sign periodic asymmetric-waveform electric field is mathematically analyzed based on solving the continuity equation. Solutions to the transfer equation are found that describe the ion distribution in the gas in planar and cylindrical cavities. The effect of ion focusing arising in the spatially nonuniform field is evaluated. The analytical results may be helpful in designing ion mobility increment spectrometers—instruments that detect microadditives of explosives, drugs, and other hazardous materials.     

Acoustic analysis of a rectangular cavity with general impedance boundary conditions

A Fourier series method is proposed for the acoustic analysis of a rectangular cavity with impedance boundary conditions arbitrarily specified on any of the walls. The sound pressure is expressed as the combination of a three-dimensional Fourier cosine series and six supplementary two-dimensional expansions introduced to ensure (accelerate) the uniform and absolute convergence (rate) of the series representation in the cavity including the boundary surfaces. The expansion coefficients are determined using the Rayleigh-Ritz method. Since the pressure field is constructed adequately smooth throughout the entire solution domain, the Rayleigh-Ritz solution is mathematically equivalent to what is obtained from a strong formulation based on directly solving the governing equations and the boundary conditions. To unify the treatments of arbitrary nonuniform impedance boundary conditions, the impedance distribution function on each specified surface is invariantly expressed as a double Fourier series expansion so that all the relevant integrals can be calculated analytically. The modal parameters for the acoustic cavity can be simultaneously obtained from solving a standard matrix eigenvalue problem instead of iteratively solving a nonlinear transcendental equation as in the existing methods. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current method for various impedance boundary conditions, including nonuniform impedance distributions.     

Kinetic Description of Particle Interaction with a Gravitational Wave

The interaction of charged particles, moving in a uniform magnetic field, with a plane polarized gravitational wave is considered using the Fokker-Planck-Kolmogorov (FPK) approach. By using a stochasticity criterion, we determine the exact locations in phase space, where resonance overlapping occurs. We investigate the diffusion of orbits around each primary resonance of order m by deriving general analytical expressions for an effective diffusion coefficient. A solution of the corresponding diffusion equation (Fokker-Planck equation) for the static case is found. Numerical integration of the full equations of motion and subsequent calculation of the diffusion coefficient verifies the analytical results.     

Dust Sheared Flow Driven Instability of Dust Drift Waves in a Nonuniform Magnetoplasma

We investigate instability of dust drift waves in a nonuniform dusty magnetoplasma containing transverse sheared plasma flow that is produced by a nonuniform electric field. By using Boltzmann distributed electrons and ions, Poisson’s equation, as well as the dust continuity equation with perpendicular guiding center dust drift speed, we derive an eigenvalue equation, which strongly depends on the profiles of dust sheared flow and dust density gradient. The eigenvalue equation is analytically solved to obtain expressions for the growth rate and threshold of a convective instability arising from resonant interactions between the dust drift waves and sheared flows. The result may be relevant to the understanding of short wavelength (in comparison with the ion gyroradius) electrostatic fluctuations in magnetized plasmas of Saturn rings and in cometary tails. PACS numbers: 52.27.Lw; 52.35.Fp     

Analytical regularization based analysis of a spherical reflector symmetrically illuminated by an acoustic beam

A mathematically accurate and numerically efficient method of analysis of a spherical reflector, fed by a scalar beam produced by a complex source-point feed, is presented. Two cases, soft and hard reflector surface, are considered. In each case the solution of the full-wave integral equation is reduced to dual series equations and then further to a regularized infinite-matrix equation. The latter procedure is based on the analytical inversion of the static part of the problem. Sample numerical results for 50-lambda reflectors demonstrate features that escape a high-frequency asymptotic analysis.     

Lie symmetry analysis,conservation laws and analytical solutions for a generalized time-fractional modified KdV equation

In this paper, a generalized time fractional modified KdV equation is investigated, which is used for representing physical models in various physical phenomena. By Lie group analysis method, the invariance properties and the vector fields of the equation are presented. Then the symmetry reductions are provided. Moreover, we construct the explicit solutions of the equation by using sub-equation method. Based on the power series theory, the approximate analytical solution for the equation are also constructed. Finally, the new conservation theorem is applied to constructed conservation laws for the equation.     

Electrostatic potential and field near the boundary between space charge and no charge regions within a cylindrical pipe

In electronic industries, a corona ionizer is widely used for the elimination of electrostatic charge on the material. Although the high frequency AC ionizer proved the effectiveness of its performance, the corona ions must be sent through a metal pipe to reach targeting area. In order to analyze the behavior of ions in elimination process, the potential and electric field within a pipe must be known. Since the potential and field distribution near the boundary between space charge and no charge regions are extremely important, the analytical solution for this problem was sought by using Bessel functions. Analytical solution showed that even in no charge region, there exists potential distribution within a pipe. Numerical calculation of electric field on the inner pipe surface indicated useful information to estimate the charge density in the pipe. Furthermore, some mathematical formulae were obtained by using Bessel functions.     

Conditions for runaway electrons in a gas diode with a strongly nonuniform electric field

The dynamics of runaway electrons in a gas diode in a sharply nonuniform electric field determined by the geometry of electrodes is considered. The analytical solution of the equation of motion of electrons for an edge cathode shows that their runaway at the periphery in the region of weak field is possible only if the applied potential difference exceeds a certain threshold determined by the interelectrode distance and the parameters of the gas. This condition supplements a classical runaway condition that the field strength at the emission edge of the cathode should be higher than a threshold value depending only on the parameters of the gas. According to our estimates, this new condition imposes higher requirements than the classical condition on the field strength in the limit of the strongly sharp edge of the cathode.     

Radial focusing of ion beams in a mass analyzer with an electrostatic lens and a sector-shaped inclined-wall magnetic prism

The ionic and optical properties of an inclined-wall magnetic mass analyzer with electrostatic direction focusing of ions in a nonuniform (r ^?1) magnetic field were studied. A condition for ion focusing in the radial plane was derived, and the basic parameters of the mass analyzer were determined.     

基于Fourier-Bessel级数的Bessel型超声场二次谐波近场特性研究

将Fourier-Bessel级数引入KZK方程的求解，用于计算黏滞媒质中零阶Bessel型超声场的二次谐波声场，得到其级数形式的解析解，并由此得出二次谐波声场在近场分布的一个新结论.设声源表面声压分布为J₀(α₀r)，则二次谐波声压在近场的径向分布服从J²₀(α₀r)函数规律.这一结论合理解释了相关的实验结果，表明二次谐波声场在近场和远场有不同的径向分布，从而解决了非线性Bessel型超声场二次谐波的近场分布问题.研究还发现二次谐波声场具有类似基波声场的有限衍射特性.给出了一个数值计算和仿真实例.     

Series Solution for Localization and Entanglement of an Exciton in a Quantum Dot Molecule by an ac Electric Field

The Schrödinger equation involving the phenomenon of the localization and entanglement for an exciton in a quantum dot molecule by an ac electric field is analytically investigated. New exact series solutions for the Schrödinger equation have been obtained for the first time. The analytical expressions can further describe the dynamical behaviors of an interacting electron-hole pair in a double coupled quantum dot molecule under an ac electric field accurately.     

The use of quantum green functions for the calculation of the frequency spectrum of the lattice vibrations of isotopic binary substitutional alloys. I

The paper derives a new method for the calculation of the frequency spectrum of isotopic binary substitutional alloys. The distribution of the admixture in the alloys is described by means of an operator field. Thus an equation for the quantum Green function in the form of functional derivatives can be formulated. In a purely analytical way two methods of successive approximations for the solution of this equation and the expansion in the form of a series in powers of the mass defect are deduced. In the second part of the paper an expansion of the solution in the form of a series of concentrations of the admixture is deduced and a more detailed discussion of the character of the frequency spectrum is performed.     

Interaction of electromagnetic waves with a magnetized nonuniform plasma slab

The absorption, reflection, and transmission of electromagnetic waves by a nonuniform plasma slab immersed in an ambient uniform magnetic field of various strengths are studied in this paper. The effects of the plasma parameters and magnetic field strength on the absorbed, reflected, and transmitted power are discussed. The magnetized nonuniform plasma slab is modeled by a series of magnetized uniform plasma subslabs. The calculation results show that the effects of the magnetic field strength and density gradient on the absorbed power, as well as the frequency band of resonant absorption, are significant. A complete analysis utilizing the scattering matrix method is also used to compare the above calculation results which neglect multiple reflections between subslab interfaces. Broadband absorption of electromagnetic waves can be achieved by changing the magnetic field strength and plasma density. More than 90% of the electromagnetic wave power can be absorbed in a magnetized nonuniform plasma slab with width of 12 cm and the absorption bandwidth can range from 1 to 20 GHz with different plasma parameters and external magnetic field strengths.     

基于二阶矢量位的矩形截面回折线圈阻抗和脉冲磁场的解析建模与计算

本文基于二阶矢量位建立了回折线圈的阻抗和磁场计算的解析模型,并提出了计算磁场脉冲响应的方法.根据回折线圈用于涡流检测和电磁超声检测时的通用模型,将回折线圈的阻抗和磁场计算问题转化为多个单匝矩形线圈阻抗和磁场的叠加问题.基于二阶矢量位和时谐电磁场方程,推导了回折线圈的频域标势表达式;利用标势与矢量磁位和磁通密度间的关系,推导了计算区域的磁通密度和式样表面涡流的频域解析计算公式;通过计算线圈的感应电势和阻抗变化表达式,得到了线圈阻抗的频域解析表达式;采用FFT-IFFT方法计算了脉冲磁场的时域响应.以一双层双 关键词： 无损检测 回折线圈 二阶矢量位 解析建模     

The perpendicular permittivity of magnetized toroidal plasmas with elliptic magnetic surfaces

The Vlasov equation for charged particles is analyzed in an axially symmetric toroidal plasma configuration with an elliptic cross section of magnetic surfaces. The asymptotic solution of the Vlasov equation is found. The analytical expressions for the perpendicular component of the dielectric permittivity tensor are obtained. These expressions are used for theoretical analyses of the trapped and untrapped ion influence on the collisionless cyclotron wave dissipation. The evaluated dielectric tensor components can be used for computer calculations of the radio frequency field structure and the collisionless dissipated power related to trapped and untrapped ions in tokamak plasmas. It is shown that ion cyclotron resonance dissipation in tokamaks depends on toroidicity and ellipticity parameters and does not depend on plasma temperature. This work was supported by the State University of Rio de Janeiro (UERJ), Rio de Janeiro Research Foundation (FAPERJ) and Brazilian National Council of Research (CNPq).     

Forced diffusion in magnetic fluids under the influence of a strong magnetic field gradient

We have investigated the forced diffusion of magnetic nanoparticles suspended in a carrier liquid under the influence of a magnetic field gradient. A cylindrical layer of the suspension was exposed to an azimuthal magnetic field with radial gradient. The radial distribution of the concentration of magnetic particles was determined for different times. The obtained experimental data are compared with a numerical solution of the diffusion equation and good agreement has been observed.