Calculation of a triode field-emission system with a modulator

The electrostatic potential of a triode field-emission system with a modulator that represents a circular diaphragm is calculated. A tip field-emission cathode serves as an emitter. The inner part of the system under study is filled with two insulators. In the calculation of the potential distribution, a real field-emission cathode is changed by a virtual cathode whose surface coincides with an equipotential surface, so that the effect of the cathode on the distribution of the electrostatic potential is simulated as the effect of a finite charged wire that is located at the axis of the system. The separation of variables is used to solve the problem. The potential is represented as an expansion in terms of eigenfunctions, and the expansion coefficients are found from the solution to a system of linear algebraic equations.     

Calculation of the electrostatic potential of the diode system based on a sharp-edged field cathode

A mathematical model of a diode system based on a sharp-edged field cathode is presented. The surface of the sharp-edged cathode is simulated by two infinitely thin spherical segments, while the anode is modeled by a single infinitely thin spherical segment. The region occupied by the cathode is a lens (lune-shaped region). The problem of the electrostatic potential distribution in the entire domain occupied by the system is solved.     

Obtaining of preset electrostatic fields in a quasi-electrode system

A method for obtaining electrostatic fields of a preset form in a quasi-electrode cylindrical system is considered. “Distributed” electrodes (filamentary conductors) make it possible to solve the inverse boundary-value problem, viz., to preset an azimuthal electric potential distribution over the cylinder surface for obtaining the required field in the cylinder, thus ensuring a larger working region as compared to an obviously electrode system.     

Mathematical Simulation of a 2D Diode System with a Blade-Shaped Field Emitter

Technical Physics - The electrostatic potential distribution in a 2D diode system with a blade-shaped field emitter on a flat substrate has been calculated. The anode of the system represents a...     

用圆 坐标示形冰筒的表电问题

用圆环坐标分析带电球形法拉第冰筒的静电问题,得出其空间电势分布函数,证明内外同电荷的差为常量,计算其电容量,并给出静电应用的近似法。     

Electrostatic charging of an electrically insulated metal body as a result of thermionic emission from its surface

The electrostatic charging of an electrically insulated metal body (emitter) as a result of thermionic emission current from the body to the ambient is investigated. The cases when the body is in vacuum and in plasma are considered. It is assumed that electrons in the surface layer of the metal body have its temperature or are heated to the temperature of “hot” electrons. The electric currents determining the charging/discharging processes in the body are determined. The values of the electric charge, field strength, and potential of the metal body are estimated.     

Interaction of a dielectric macroparticle with a point charge in plasma

The electrostatic interaction of a charged spherical dielectric macroparticle with a point charge in a plasma in the presence of an external uniform electric field is considered. The electrostatic force and the torque acting on the macroparticle have been determined, and the form of the interaction potential has been established for a nonuniform distribution of free charge on the macroparticle surface. A simple (for calculations) expression for the interaction potential that describes well the exact potential at all interparticle distances is proposed. The angular velocity of the spinning of dust particles caused by a nonuniform distribution of free charge over their surface has been estimated.     

Electrostatic field of a thin, unclosed spherical shell and a torus

The electrostatic problem for a thin, unclosed spherical shell and a torus is reduced to paired summation equations in the Legendre polynomials by means of formulas relating the spherical and toroidal harmonic functions. The paired equations are transformed to a Fredholm integral equation of the second kind. Formulas are obtained for computing the charges of the conductors in the form of a series in a small parameter. The capacitance is computed for certain geometrical parameters of the conductors. Zh. Tekh. Fiz. 68, 1–6 (July 1998)     

Toward the theory of a loop antenna in an anisotropic plasma

We consider the problem of determining the current distribution along a loop antenna consisting of an infinitely thin perfectly conducting strip coiled into a ring. The antenna is immersed in an anisotropic plasma medium perpendicular to the external magnetic field and is excited by a given EMF. Primary attention is focused on the frequency band in which the excitation of electrostatic waves is possible. The problem is reduced to solving a system of integral equations with logarithmic and singular kernels. Using the solution of these equations, we found expressions for the antenna current distribution and input impedance. The analysis of these expressions is presented. Radiophysical Research Institute, Lobachevsky State University, Nizhny Novgorod, Russia. Translated from izvestiya Vysshikh Uchbnykh Zavedenii, Radiofizika, Vol. 41, No. 3, pp. 358–373, March, 1998.     

On the electrostatic potential distribution in a screened Corbino disk carrying a transport current under conditions of the quantum Hall effect

It is shown that the characteristic features of the chemical potential for 2D electrons in a magnetic field, which lead to sharp dips in the magnetic field dependence of the capacitance of a 2D system, also affect the electrostatic potential distribution in the direction of the transport current flowing through a 2D Corbino disk under conditions of integral magnetic filling factor. The associated details of the temperature dependence of the electrostatic potential distribution, the distances to the screening electron, and the transport potential difference at the Corbino edges are investigated. The possibilities of experimentally observing these features of the electrostatic potential distribution along a Corbino disk with a transport current under conditions of the quantum Hall effect are discussed. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 8, 545–550 (25 October 1997)     

Irregular dielectric or permeable bodies in an external field

An integral equation is derived for the electrostatic potential ψ that arises when a uniform dielectric body of arbitrary shape is placed in an applied electrostatic field. By expansion of ψ in a certain basic set, the integral equation becomes a set of linear equations for the expansion coefficients, and it is often practical to solve the set by truncation. As a test, the equations are applied to the problem of a spheroid in a uniform field, and they easily yield the standard results that are usually derived by introducing spheroidal harmonics. Either the integral equation or the equivalent linear equations can be solved in an iterative approximation (the analog of the Born approximation) when the dielectric constant of the body is not too far from unity. For bodies that differ from spherical or cylindrical ones by a small parameter λ, perturbation formulae are derived that solve the equations in powers of λ. The problem of a homogeneous permeable body of arbitrary shape in an external magnetostatic field is reducible to the dielectric problem, but in addition an alternate integral equation for the magnetic problem is discussed.     

Calculating coefficients for a system of moment equations used to describe the magnetization kinetics of a superparamagnetic particle in a fluctuating field

A system of equations is derived for moments [averages of spherical harmonics 〈Y _l,m 〉(t)] that determine the dynamics of the magnetization M of a superparamagnetic particle in a fluctuating field. The system is derived by representing the Gilbert equation in a fluctuating field, and the corresponding Fokker-Planck equation for the distribution function of M, in terms of angular momentum operators, which in turn makes it possible to express the coefficients of the system of moment equations in terms of Clebsch-Gordan coefficients. Fiz. Tverd. Tela (St. Petersburg) 41, 2020–2027 (November 1999)     

Effect of the size of macroparticles on their electrostatic interaction in a plasma

The electrostatic interaction of two spherical macroparticles in a plasma has been considered. Primary attention has been focused on investigating the electrostatic interaction at short distances where polarization effects of the surface charge of finite-size macroparticles begin to play a dominant role. The first part of this study is devoted to the interaction of a point charge with a charged conducting sphere in an equilibrium plasma. It has been shown that the presence of a plasma in the system leads to a decrease in the potential barrier when two like-charged macroparticles approach each other and that this decrease proves to be the most significant in the case where the macroparticle radius is comparable to the Debye screening length. The second part of this study is concerned with the interaction of two conducting spheres in the bispherical system of the coordinates under the assumption that the charges of the conducting spheres are constant and under the assumption that the surface potentials of the spheres are constant. The latter case is closer to the physics of electrostatic interaction of two macroparticles in a plasma medium where the electrostatic potential of their surface is determined by the floating potential of the plasma. It has been demonstrated that the interaction potentials in these two cases are substantially different from each other and that, at constant macroparticle charges, the energy of the electrostatic field is an interaction potential, but, in the case of macroparticles with constant surface potentials, which are independent of the interparticle distance, the energy of the electrostatic field is not an interaction potential. In the latter case, account must be taken of the work done by external sources on the macroparticle potentials to maintain them constant. The form of the interaction potential has been established in this case from the analysis of the interaction force in terms of the Maxwell tension tensor. In the third part of this study, the interaction of two macroparticles has been considered in the spherical system of coordinates and analytical expressions for the interaction potentials have been derived for both the case of constant macroparticle charges and the case of constant surface potentials of the macroparticles.     

The quantum yield of a metallic nanoantenna

The local-field factor and quantum yield of a metallic nanoantenna are studied to identify its enhancement of an emitter’s emission within the feed gap. For simplicity, a two-dimensional model, an Au nanoantenna with an emitter at the center, is studied. The electromagnetic field is solved by a set of surface integral equations. An incident plane wave irradiating the nanoantenna is modeled to simulate the excitation of the emitter by illuminating light, and the local-field factor is used to evaluate the amplification of the electric field in the feed gap of the metallic nanoantenna. Once the emitter becomes excited, a model of an electric dipole interacting with the nanoantenna is used for calculating the radiative and nonradiative powers to obtain the quantum yield of the excited emitter in the presence of the nanoantenna. The numerical results of quantum yield indicate that an Au nanoantenna acts as a low-pass filter for the emission of the emitter. Moreover, the smaller the feed gap, the larger the local-field factor but the less the quantum yield. PACS 78.67.-n; 33.80.-b; 33.50.-j; 42.30.-d; 42.50.Hz; 81.07.Pr     

Semi-analytical method of calculating the electrostatic interaction of colloidal solutions

We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis functions such as spherical harmonic function and cylinder function. The expansion coefficients can be obtained by solving the equations of the boundary conditions, combining an analytical translation transform of the coordinates and a numerical multipoint collection method. The precise electrostatic potential and the interaction energy are then obtained automatically. The method is available not only for the uniformly charged colloids but also for nonuniformly charged ones. We have successfully applied it to unconfined diluted colloid system and some confined systems such as the long cylinder wall confinement, the air–water interfacial confinement and porous membrane confinement. The consistence checks of our calculations with some known analytical cases have been made for all our applications. In theory, the method is applicable to any dilute colloid solutions with an arbitrary distribution of the surface charge on the colloidal particle under a regular solid confinement, such as spherical cavity confinement and lamellar confinement.     

Asymptotic analysis of nonlinear nonaxisymmetric waves on the surface of a neutral dielectric jet in a longitudinal electrostatic field

The problem of calculation of finite-amplitude waves on the cylindrical surface of an ideal incompressible dielectric liquid jet in a uniform electrostatic field collinear to the unperturbed jet axis is solved using a second-order asymptotic analytic procedure in ratio of the wave amplitude to the jet radius. Nonlinear corrections to the jet profile, velocity field potential, and electrostatic potentials inside and outside the jet are of resonant nature. The degenerate resonant interaction between the wave determining the initial strain and the waves excited due to nonlinearity of the hydrodynamic equations can take place for waves with different symmetries (different azimuth numbers).     

Calculation of the electrostatic field of a system of spherical segments

The electrostatic potential distribution is determined for a system of axisymmetric electrodes in the form of nonconcentric spherical segments.     

On the transverse distribution of a resonance field excited by a Gaussian electromagnetic beam on the critical surface of a radially nonuniform plasma sphere

The transverse distribution of the resonance field excited by a Gaussian electromagnetic field on the critical surface of a radially nonuniform plasma sphere is studied. Analytical expressions are obtained for this distribution. It is shown that when a laser beam is focused in front of or behind a spherical target, identical values of the integrated resonance coefficient can correspond to substantially different (in width) distributions of the resonance field over the spherical critical surface. Zh. Tekh. Fiz. 67, 125–128 (October 1997)     

Screened electrostatics of charged particles on a water droplet

We study the electrostatic properties of charged particles trapped at an interface in a water-in-oil microemulsion. The electrostatic potential and the counterion distribution in the water droplet are given in terms of the ratio of the Debye screening length κ^-1 and the droplet radius R. In the limit R→∞ we recover the well-known results for a flat interface. Finite-size corrections are obtained in terms of the small parameter 1/κR. Part of the counterions spread along the interface and form a charged layer of one Debye length thickness. In particular, there is a uniform surface charge contribution. We derive explicit expressions for the electric field, the mobile charge density, and the charge-induced pressure on the interface.     

Capacitance of a tube

The electrostatic problem of a hollow, conducting tube of finite length held at a fixed potential is solved using two methods. A two-term Galerkin solution is constructed for the surface distribution of induced charge. The sum of a uniform component and a simple edge-condition term provides a variational solution to the dual integral equations that are the equations-of-motion for the mixed boundary value problem. Comparisons are made with the numerical results of an independent boundary element or moment method. The numerical solution uses collocation or point matching and a piecewise constant basis for the charge density.