Electrostatic potential in cylindrical dielectric media using the image charge method

We derive a simple analytical expression for the electric potential produced by a point charge in a cylindrical pore with relative permittivity different from that of the surrounding medium. The interface between the pore and the surrounding media may contain electric charge or be electrically neutral. The expression reduces to the known solutions when the surrounding dielectric medium is identical to the pore or an electric conductor. We discuss the convergence of the series expansion and numerically evaluate the electrostatic potential inside the cylindrical pore. The calculated potential shows the effect of the dielectric permittivity difference of the media. The results demonstrate that the expression can be implemented in a numerical dynamic simulation of charged systems in cylindrical geometry. We also give an expression for the case when the source charge is in the medium outside the cylinder.     

Electrostatic potential in a gravitational field

The electrostatic potential in a gravitational field is estimated up to the order ofe ² G ² in the framework of the conventional quantum field theory. It is shown that the electrostatic potential is different from the classical one. We find that this discrepancy is attributable to the process in which a particle emits three massless ones which are absorbed by three other particles.     

均匀带电线与接地导体薄圆筒内的等势线与电场线方程

利用电象法和解析函数的规律,得出均匀带电线与接地薄导体圆筒内的电势和电场强度表达式,并给出了等势线与电场线方程.     

Electrostatic potential of a point charge lattice having lamina geometry

The Coulomb potential energy of a lattice of point charges having infinite extension in two dimensions only is evaluated using an Ewald-like transformation. An exponential rather than a Gaüssian charge spreading function is used. The derived expansion is rapidly convergent.     

轴对称荷电圆盘的静电势

讨论了电荷分布呈轴对称时圆盘的静电势问题。用方程法和延拓法求解了电荷分布为幂函数时的静电势,在原有的延拓法则之外,总结出新的补充法则。     

Conformal field theories near a boundary in general dimensions

The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions d. Calculations of the universal function of a conformal invariant ξ which appears in the two-point function of scalar operators in conformally invariant theories with a plane boundary are undertaken to first order in the ge = 4 − d expansion for the operator φ² in φ⁴ theory. The form for the associated functions of ξ for the two-point functions for the basic field φ^α and the auxiliary field λ in the N → ∞ limit of the O(N) nonlinear sigma model for any d in the range 2 < d < 4 are also rederived. These results are obtained by integrating the two-point functions over planes parallel to the boundary, defining a restricted two-point function which may be obtained more simply. Assuming conformal invariance this transformation can be inverted to recover the full two-point function. Consistency of the results is checked by considering the limit d → 4 and also by analysis of the operator product expansions for φ^αφ^β and λλ. Using this method the form of the two-point function for the energy-momentum tensor in the conformal O(N) model with a plane boundary is also found. General results for the sum of the contributions of all derivative operators appearing in the operator product expansion, and also in a corresponding boundary operator expansion, to the two-point functions are also derived making essential use of conformal invariance.     

Acoustic streaming in a sound field near a free boundary

Stationary acoustic streaming that occurs near the free boundary of a compressible viscous liquid in the field of a standing sound wave excited along this boundary is theoretically investigated.     

Electrostatic field and charge distribution in small charged dielectric droplets

The charge distribution in small dielectric droplets is calculated on the basis of continuum medium approximation. There are considered charged liquid spherical droplets of methanol in the range of nanometer sizes. The problem is solved by the following way. We find the free energy of some ion in dielectric droplet, which is a function of distribution of other ions in the droplet. The probability of location of the ion in some element of volume in the droplet is a function of its free energy in this element of volume. The same approach can be applied to other ions in the droplet. The obtained charge distribution differs considerably from the surface distribution. The curve of the charge distribution in the droplet as a function of radius has maximum near the surface. Relative concentration of charges in the vicinity of the center of the droplet does not equal to zero, and it is the higher, the less is the total charge of the droplet. According to the estimates the model is applicable if the droplet radius is larger than 10 nm.     

均匀带电线与接地导体薄圆筒内的电势

利用保角变换和电象法,分别得出均匀带电线与接地薄导体圆筒内的电势.     

Resonant field amplification near the RWM stability boundary in a tokamak

Evolution of a resistive wall mode (RWM)—a magnetic field perturbation produced by a plasma and partially stabilized by a conducting wall—is considered. It is assumed that there is a small resonant harmonic in the spectrum of the static error field. It is shown that the effect of this harmonic on the dynamics of stable RWMs increases as the plasma approaches the RWM stability boundary. The error field is “amplified” during the transition through this boundary. The smaller the rotation velocity of the perturbation and the longer the time during which the plasma stays near the stability boundary, the stronger this amplification is.     

The field of a point source near planar and cylindrical boundaries of a metamaterial

The properties of the two-dimensional electromagnetic fields excited by a filamentary source located near planar and cylindrical boundaries of bodies made of metamaterials with their permittivity and permeability close to minus one are considered. The subwavelength field localization effects, the phenomena associated with the resonances of surface waves, and the nonresonant field enhancement effects are investigated.     

The analysis of the charge on a cylindrical dielectric particle in unipolar corona field

In this study, a nonlinear integro-differential equation is derived to express the charging kinetics of stationary and rotational cylindrical dielectric particle in unipolar corona field. An algorithm is developed to solve the derived equation numerically by using Euler method. The variation of charge on the dielectric cylindrical particle is presented and evaluated by considering the variable parameters of the particle, medium and field. Assessments of the numerical results demonstrate that the limit charge value on stationary cylindrical dielectric particle during the charging process in unipolar corona field is less in comparison with the rotational cylindrical particle in identical conditions. Also this is an important factor for electron–ion technology in the aspect of charging kinetic problems.     

Numerical investigation of space charge electric field for a sheet electron beam between two conducting planes

Analytical and numerical study of the stability of sheet electron beam in periodically cusped magnetic field (PCM) is made. The beam has been considered as having diffused density profile. The conditions for beam focusing are discussed.     

Electrostatic energy and screened charge interaction near the surface of metals with different Fermi surface shape

Using the Poisson equation Green function for a self-consistent field in a spatially inhomogeneous system, expressions for the electrostatic energy and screened charge interaction near the surface of a semi-infinite metal and a thin quantizing film are derived. It is shown that the decrease law and Friedel oscillation amplitude of adsorbed atom indirect interaction are determined by the electron spectrum character and the Fermi surface shape. The results obtained enable us to explain, in particular, the submonolayer adsorbed film structure on the W and Mo surfaces.     

Spatial rectification of the electric field of space charge waves

A new phenomenon associated with a nonlinear interaction of optically excited space charge waves has been discovered in photorefractive crystals of the sillenite family. This interaction provides a spatial rectification of the electric field of the space charge waves and leads to a temporally oscillating, but spatially homogeneous electric field of the order of 50-60 V/cm which is detected by a probe beam via the electro-optic effect. Taking into account that the displacement current plays an important role, we demonstrate a very good agreement between the experimental data and the suggested theoretical model.     

Numerical computation of potential profiles and energy spectrum in the space charge region of semiconductors at high electric field

Numerical computations of the potential profiles are performed for the space charge region of semiconductors with a spherical nonparabolic conduction band at a high electric field externally applied to the surface. For the obtained potential profiles, the energy spectrum in the surface region was calculated for an electron moving perpendicularly to the surface (field emitted electron). To perform this calculation, a special iterative procedure was developed to compute the complex eigenvalues of the Hamiltonian with an arbitrary potential.