Some uniqueness results for stationary solutions to the Maxwell-Born-Infeld field equations and their physical consequences

Uniqueness is established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell-Born-Infeld equations in boundary-free space under the condition that either the charge or current density vanishes. In addition, it is also shown that the simpler Maxwell-Born equations admit at most one stationary finite-energy electromagnetic field solution, without the above condition. In these theories of electromagnetism the following physical consequences emerge: source-free field solitons moving at speeds less than the vacuum speed of light c do not exist; any electrostatic (resp. magnetostatic) field is the unique stationary electromagnetic field for the same current-density-free (resp. charge-density-free) sources. These results put to rest some interesting speculations in the physics literature.     

Aharonov-bohm effect as the basis of electromagnetic energy inherent in the vacuum

The Aharonov-Bohm effect shows that the vacuum is structured, and that there can exist a finite vector potentialA in the vacuum when the electric field strengthE and magnetic flux densityB are zero. It is shown on this basis that gauge theory produces energy inherent in the vacuum. The latter is considered as the internal space of the gauge theory, containing a field made up of components ofA, to which a local gauge transformation is applied to produce the electromagnetic field tensor, a vacuum charge/current density, and a topological charge g. Local gauge transformation is the result of special relativity and introduces spacetime curvature, which gives rise to an electromagnetic field whose source is a vacuum charge current density made up ofA and g. The field carries energy to a device which can in principle extract energy from the vacuum. The development is given forU(1) andO(3) invariant gauge theory applied to electrodynamics. Former Edward Davies Chemical Laboratories, University College of Wales, Aberystwyth SY32 1NE, Wales, United Kingdom.     

Space charge limiting current of an electron beam transported in a coaxial drift chamber

An expression for the space charge limiting current of an electron beam in a vacuum coaxial drift chamber is obtained in the strong field approximation. The expression is an analogue of the Bogdankevich-Rukhadze interpolation formula for a cylindrical drift chamber. The space charge limiting currents in the coaxial and cylindrical chambers are compared. The space charge limiting current in the vacuum coaxial chamber is numerically calculated and compared to analytical predictions.     

关于真空中的位移电流、Maxwell方程组、电磁场的源及Jefimenko公式的几点注记

通过分析指出：电磁场是一个不可分割的整体，Maxwell方程组是电磁场的运动方程，电磁场的源是电荷与电流的分布，Jefimenko公式是真空中Maxwell方程组的解。     

Magnetic response to applied electrostatic field in external magnetic field

We show, within QED and other possible nonlinear theories, that a static charge localized in a finite domain of space becomes a magnetic dipole, if it is placed in an external (constant and homogeneous) magnetic field in the vacuum. The magnetic moment is quadratic in the charge, depends on its size and is parallel to the external field, provided the charge distribution is at least cylindrically symmetric. This magneto-electric effect is a nonlinear response of the magnetized vacuum to an applied electrostatic field. Referring to the simple example of a spherically symmetric applied field, the nonlinearly induced current and its magnetic field are found explicitly throughout the space; the pattern of the lines of force is depicted, both inside and outside the charge, which resembles that of a standard solenoid of classical magnetostatics.     

Five-dimensional relativity theory

The five-dimensional relativity theory proposed by Kaluza is formulated covariantly for a Riemannian space containing a Killing geodesic vector field. From this five-dimensional space a four-dimensional physical space is extracted. The field equations in empty 5-space are essentially uniquely determined and correspond to the Einstein-Maxwell equations in 4-space. In the presence of a field in 5-space the field equations involve a tensor which is associated with energy, momentum, charge and current densities in 4-space. For a 5-space containing dust the field equations lead to particle motion described by the geodesic equations. The latter correspond in 4-space to the Lorentz equations of motion for particles with arbitrary ratios of charge to mass and also for certain entities (tachyons and luminons) unobserved hitherto.     

Self-duality,helicity and coherent states in non-Abelian gauge theories

Solutions of the non-linear classical Yang-Mills field equations obtained by iteration from self-dual solutions of the linearized equations are shown to be themselves self-dual. In Minkowski space, such solutions are necessarily complex. We give a quantum theory interpretation of these solutions which relates them to the matrix element of the field operators between the vacuum state and a coherent state of spin-one quanta of definite helicity.     

Operator Derivation of the Gauge-Invariant Proca and Lehnert Equations; Elimination of the Lorenz Condition

Using covariant derivatives and the operator definitions of quantum mechanics, gauge invariant Proca and Lehnert equations are derived and the Lorenz condition is eliminated in U(1) invariant electrodynamics. It is shown that the structure of the gauge invariant Lehnert equation is the same in an O(3) invariant theory of electrodynamics.     

Metal oxidation—I. Ionic transport equation

An equation for the transport of a single ionic species through a crystalline solid film is developed which relates the local flux density to the local electrostatic field and mobile ion concentration, and their spatial derivatives, and allows for the inclusion of space charge effects. The equation consists of an infinite series which may be reduced to closed form to various levels of approximation under different conditions. The ranges of validity of these approximate equations are established. An ‘exact’ closed form equation is obtained for the homogeneous field case and is shown to be a good approximation for both high and low field strengths provided that the space charge concentration does not exceed 5×10¹⁹ e cm^?3. Integrated expressions for the closed form equations are obtained which include the effect of space charge due to the transporting ions, and the question of their applicability to the problem of metal tarnishing is considered.     

On the mechanism of liquid metal electron and ion sources

The mechanisms of electron and ion generation from Taylor cones of liquid metals are discussed. In the case of electron emission the vacuum arcing mechanism of Swanson and Schwind, which accounts for the observed high current repetitive pulsing is briefly reviewed. For ion emission mechanisms from onset to the high current regime are proposed. It is concluded that at onset ions are generated exclusively by field desorption. A theory to account for the observed emitter heating is advanced, and it is concluded that high currents result from field ionization of thermally evaporated atoms. It is shown that space charge becomes important even at very low ion currents and'is instrumental in providing stabilization in all regimes of ion emission.     

Nonequilibrium mechanisms of weak electrolyte electrification under the action of constant voltage

The formation of space charge in weak electrolytes, specifically in liquid dielectrics, has been considered. An analytical solution is given to a simplified set of Nernst–Planck equations that describe the formation of nonequilibrium recombination layers in weak electrolytes. This approximate analytical solution is compared with computer simulation data for a complete set of Poisson–Nernst–Planck equations. It has been shown that the current passage in weak electrolytes can be described by a single dimensionless parameter that equals the length of a near-electrode recombination layer divided by the width of the interelectrode gap. The formation mechanism and the structure of charged nonequilibrium near-electrode layers in the nonstationary regime have been analyzed for different injection-to-conduction current ratios. It has been found that almost all charge structures encountered in weak dielectrics can be accounted for by the nonequilibrium dissociation–recombination mechanism of space charge formation.     

同轴结构中压力波法测量空间电荷分布的物理模型研究

从压力波法测量平板样本中空间电荷分布的理论分析出发,提出了对于同轴结构的固体电介质中空间电荷分布的压力波法测量的物理模型,并得出了测量电流的解析的数学表达式.依据泊松方程,考虑样品内的电场强度、介电常数和空间电荷密度随外界声波扰动而发生变化,将圆柱试样受到的压力波的影响分解成样品形变和质点位移两部分,进而得到了以同轴结构中空间电荷分布的压力波法测量的电压与电流表达式.测量电流的数学表达式表明,对于同轴结构,压力波法的测量电流信号不像平板结构中那样基本正比于空间电荷分布,而是应该做进一步的修正处理.     

Space charge solution of Rittner photoconductor equation for a HgCdTe detector

The steady-state charge continuity equations are linearized to derive a space charge field that accompanies the ambipolar diffusion and drift described by the Rittner equation. The space charge field is evaluated for a typical 14.2 μm cutoff wavelength HgCdTe detector operating at 85 K. It is found that the space charge density is ∼10⁻⁵ times the hole and electron population density generated by photon flux. This corroborates that Rittner's equation gives an accurate solution for the hole and electron densities. But, at relatively high photon flux levels that are found in some Geostationary Operational Environment Satellite instrument channels, the small average space charge field can have a noticable effect on the linearity of detector response. Divergence of electric field terms in the continuity equations, which are absent from the Rittner equation, can also contribute a non-linearity to detector response.     

轴对称真空二极管空间电荷限制流

基于ArcPIC代码采用PIC-MCC方法,模拟研究了轴对称真空二极管放电时电子密度和阴极表面场强分布情况,同时给出了二维空间电荷限制流的一阶和二阶拟合公式。研究发现,真空二极管放电时阴极表面电场会随阴极注入电流密度的增加而增加,而后出现振荡并趋于一个稳定状态;二维空间电荷限制流密度值随阴极发射半径的增大而减小,且阴极发射半径越大越接近一维空间电荷限制流值。     

Modelling of ions for seeding technique to electrify the atmosphere

There are number of ways in which weak electrification can affect the microphysics of clouds, with consequences for cloud lifetime, radiative properties, and precipitation efficiency. Kauffman [2011] suggested ions produced by direct current generators will add to and enhance the catalysing effects that cosmic ray ions are now known to produce in among other things, lowering nucleation barriers, stimulating charged particle growth and stability and increasing the scavenging rate in clouds. Thus to electrify the atmosphere ions can be generated artificially in abundance along with large electric field.Ions can be generated by the corona effect using Atmospheric electrifiers (a device used to generate negative ions) which makes use of corona discharge phenomenon to charge the air particles. Exact assessment of electric field and charge density distributions and the flow dynamics inside the electrifiers is essential to understand the particle behaviour inside the electrifiers.In this paper, a novel model of governing equations to evaluate the space charge density, electric field intensity and velocity of ionized airflow is suggested as a function of applied voltage. The Poisson and charge conservation equations are derived and hence can be used to estimate the electric field and charge density distributions. Navier stokes equation can be used to get the velocity of ionized airflow because of electric force on the air. Simulation is carried out to validate the proposed model and verify that velocity is function of input voltage and is proportional to it.     

螺旋线行波管注波互作用时域理论

研究了螺旋线行波管中电子注与高频场互作用的时域理论.电子对场的作用由高频场方程和空间电荷场方程模拟,场对电子注的作用由运动方程模拟.在螺旋导电面模型下利用安培环路定理和法拉第电磁感应定律得到了时域高频场方程.利用空间电荷波模型处理空间电荷场,得到了空间电荷场方程.将高频场和空间电荷场代入洛伦兹力方程,得到了运动方程.利用耦合阻抗处理高频场方程的激励源,使得高频场方程的求解能够借助诸如HFSS或HFCS等高频模拟软件来实现,增强了时域理论的灵活性.基于上述理论,编写软件数值模拟某螺旋线行波管,验证了时域理论的可行性.     

基于库仑定律的二极管空间电荷限制效应研究

真空二极管是电子束源装置中的一个关键部件, 其阴极发射的电子束进入二极管阴阳极间隙区会产生很强的空间电荷限制效应. 本文针对平板真空二极管中的空间电荷限制效应物理模型, 从库仑定律的积分形式出发, 选取了不同参数的阴极半径与阴阳极间隙距离之比, 计算得到了真空二极管阴阳极间隙区的电场分布情况, 从而避免了采用Poisson方程求解时需要处理复杂的非线性偏微分方程这一问题. 结果表明, 基于库仑定律的计算结果与从Child-Langmuir定律分析得到的结果仅相差一个与二 极管极板边界条件有关的修正量. 当二极管阴极半径与阴阳极间隙距离之比 R/D>10时,一维空间电荷限制定律将是一个较好的近似结果,当 R/D较小时, 用该定律计算误差较大,在实际物理问题中需要谨慎使用.     

Electrodynamics of spin currents in superconductors

In recent work we formulated a new set of electrodynamic equations for superconductors as an alternative to the conventional London equations, compatible with the prediction of the theory of hole superconductivity that superconductors expel negative charge from the interior towards the surface. Charge expulsion results in a macroscopically inhomogeneous charge distribution and an electric field in the interior, and because of this a spin current is expected to exist. Furthermore, we have recently shown that a dynamical explanation of the Meissner effect in superconductors leads to the prediction that a spontaneous spin current exists near the surface of superconductors (spin Meissner effect). In this paper we extend the electrodynamic equations proposed earlier for the charge density and charge current to describe also the space and time dependence of the spin density and spin current. This allows us to determine the magnitude of the expelled negative charge and interior electric field as well as of the spin current in terms of other measurable properties of superconductors. We also provide a `geometric' interpretation of the difference between type I and type II superconductors, discuss how superconductors manage to conserve angular momentum, discuss the relationship between our model and Slater's seminal work on superconductivity, and discuss the magnitude of the expected novel effects for elemental and other superconductors.     

A three-dimensional time-dependent theory for helix traveling wave tubes in beam-wave interaction

This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beamwave interaction.The radio frequency electromagnetic fields are represented as the superposition of azimuthally symmetric waves in a vacuum sheath helix.Coupling impedance is introduced to the electromagnetic field equations’ stimulating sources,which makes the theory easier and more flexible to realize.The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations.The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included.The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields,focusing fields and space-charge fields.The numerically simulated results of a tube are presented.     

Geometrical mass of charged particle in Brans-Dicke theory

We develop a special class of solutions of the Brans-Dicke equations from vacuum solutions of Einstein's equations by applying a method due to Teixeira, Wolk, and Som. It is shown that the electric charge contributes positively to the geometric mass while the Brans-Dicke scalar field diminishes the geometric mass effectively.