Electrodynamics of Hyperbolically Accelerated Charges: IV. Energy-Momentum Conservation of Radiating Charged Particles

The relativistic equation of motion of a radiating charge is discussed with special emphasis upon a clarification of the significance of the Schott energy for the energy-momentum conservation of the charge and the field it produces. In particular hyperbolic motion is studied. The case that a charge with constant velocity enters and leaves a region with hyperbolic motion is analysed. We find that the Schott energy is increased as the particle enters the region and that the energy it radiates while the charge moves hyperbolically comes from the Schott energy. A result of our analysis is that this energy is localized in the field close to the charge.     

介质存在时利用镜像法求解电势的讨论

镜像法是解析求解静电定解问题时一种比较简单的方法,即在所求解的空间之外引入镜像电荷,并使得由镜像电荷与源电荷激发的场的叠加形成的总场满足边界条件及边值关系即可.当将这种方法应用于介质存在的情形时,本文发现可以选择两种不同的镜像电荷,最终求得空间中同样的电势解.这也符合静电问题的唯一性定理,因为无论哪种镜像电荷,均没有改...     

Electrostatic Charge Measurement and Charge Neutralization of Fine Aerosol Particles during the Generation Process

An aerosol charge analyzer has been constructed to measure the charge distribution of NaCl particles generated in the laboratory. A radioactive electrostatic charge neutralizer utilizing Po‐210 was used to neutralize the electrostatic charge of the particles. The atomization technique was used to generate NaCl particles with diameters of 0.2 to 0.8 μm, while the evaporation and condensation method was adopted to generate particles of 0.01 to 0.2 μm in diameter. The experimental data demonstrates that the absolute average particle charge depends on the particle diameter, and is higher than that calculated by the Boltzmann charge equilibrium for particles within the range of 0.2 to 0.8 μm. The charge increases with decreasing NaCl concentration. When these particles are neutralized using the Po‐210 neutralizer, it is found that the electrostatic charge reaches the Boltzmann charge equilibrium. For 0.01 to 0.2 μm NaCl particles generated using the evaporation and condensation method, test results show that the absolute average particle charge is higher than that calculated by the Boltzmann charge equilibrium for particles larger than 0.03 to 0.05 μm in diameter, while it is lower than that predicted by the Fuchs theory [1], for particles smaller than 0.03 to 0.05 μm. However, after charge neutralization, particles with diameter above 0.05 μm reach the Boltzmann charge equilibrium condition, and the charges for particles with diameters of 0.010 to 0.05 μm, agree well with Fuchs' theory.     

Electrodynamics of hyperbolically accelerated charges V. The field of a charge in the Rindler space and the Milne space

We describe the electromagnetic field of a uniformly accelerated charge in its co-moving Rindler frame. It is shown that the electrical field lines coincide with the trajectories of photons. The self force of a charged particle at rest in Rindler space, and the increase of its weight due to its charge, is calculated. The general case of an accelerated charge in Rindler space is also considered. It is shown that the electrical field inside a uniformly charged spherical shell can be used as a measure of it 4-acceleration. A result that has earlier been deduced in a different way by Fugmann and Kretzschmar is confirmed, namely that the intensity of radiation from a point charge instantaneously at rest in an accelerated frame is proportional to the square of the relative acceleration of the charge and the observer. In particular it is shown that a freely falling charge in Rindler space radiates in accordance with Larmor’s formula. In this case the radiation energy is taken from the Schott energy. The energy of the electromagnetic field is analysed from the point of view of the Hirayama-separation, which generalizes the Teitelboim-separation to non-inertial frames, of the field in a bound part and an unbound part. A detailed account, with reference to the Rindler frame, of the field energy and particle energy is given for the case of a charge entering and leaving a region with hyperbolic motion. We also consider the electromagnetic field of a uniformly accelerated charge with reference to the Milne frame, which covers a different part of spacetime than the Rindler frame. The radiating part of the electromagnetic field is found in the Milne sector of spacetime.     

Fluctuations of fractional charge in soliton anti-soliton systems

The total charge in a soliton-anti-soliton system has integer eigenvalues. However, when soliton-induced charge fractionization occurs, it is possible to make a Bogoliubov transformation on the eigenstates of the total charge, so that in the limit of infinite soliton anti-soliton separation., the transformed states become eigenstates of a charge operator suitably localized at the soliton. In the limit, the localized charge operator has fractional eigenvalues, without fluctuations.     

Maxwell Equations without a Polarization Field,Using a Paradigm from Biophysics

When forces are applied to matter, the distribution of mass changes. Similarly, when an electric field is applied to matter with charge, the distribution of charge changes. The change in the distribution of charge (when a local electric field is applied) might in general be called the induced charge. When the change in charge is simply related to the applied local electric field, the polarization field P is widely used to describe the induced charge. This approach does not allow electrical measurements (in themselves) to determine the structure of the polarization fields. Many polarization fields will produce the same electrical forces because only the divergence of polarization enters Maxwell’s first equation, relating charge and electric forces and field. The curl of any function can be added to a polarization field P without changing the electric field at all. The divergence of the curl is always zero. Additional information is needed to specify the curl and thus the structure of the P field. When the structure of charge changes substantially with the local electric field, the induced charge is a nonlinear and time dependent function of the field and P is not a useful framework to describe either the electrical or structural basis-induced charge. In the nonlinear, time dependent case, models must describe the charge distribution and how it varies as the field changes. One class of models has been used widely in biophysics to describe field dependent charge, i.e., the phenomenon of nonlinear time dependent induced charge, called ‘gating current’ in the biophysical literature. The operational definition of gating current has worked well in biophysics for fifty years, where it has been found to makes neurons respond sensitively to voltage. Theoretical estimates of polarization computed with this definition fit experimental data. I propose that the operational definition of gating current be used to define voltage and time dependent induced charge, although other definitions may be needed as well, for example if the induced charge is fundamentally current dependent. Gating currents involve substantial changes in structure and so need to be computed from a combination of electrodynamics and mechanics because everything charged interacts with everything charged as well as most things mechanical. It may be useful to separate the classical polarization field as a component of the total induced charge, as it is in biophysics. When nothing is known about polarization, it is necessary to use an approximate representation of polarization with a dielectric constant that is a single real positive number. This approximation allows important results in some cases, e.g., design of integrated circuits in silicon semiconductors, but can be seriously misleading in other cases, e.g., ionic solutions.     

Does magnetic charge imply a massive photon?

In Abelian monopole theories the magnetic coupling is required to be enormous. Using the electric-magnetic duality of electromagnetism, it is argued that the existence of such a large, nonperturbative magnetic coupling should lead to a phase transition where magnetic charge is permanently confined and the photon becomes massive. The apparent masslessness of the photon could then be used as an argument against the existence of such a large, nonperturbative magnetic charge. Finally it is shown that even in the presence of this conjectured dynamical mass generation the Cabbibo-Ferrari (1962) formulation of magnetic charge gives a consistent theory.     

Nonlinear instability of charged liquid jets: Effect of interfacial charge relaxation

A linear and nonlinear study has been made of cylindrical interface, carrying a uniform surface charge in the presence of a finite rate of charge relaxation, is investigated by using multiple scales method. The linear stability flow is analyzed by deriving a dispersion relation for the growth waves, and solving it analytically and numerically to find marginal stability curves. We investigate the electric charge relaxation effects on the stability of the flow by considering various limiting cases. We also examine the effects of finite charge relaxation times in axisymmetric and nonaxisymmetric modes. In the nonlinear approach, it is shown that the evolution of the amplitude is governed by a Ginzburg–Landau equation. There is also obtained a nonlinear modified Schrödinger equation describing the evolution of wave packets for small charge relaxation time. Further, the classic Schrödinger equation is obtained when the influence of relaxation time charge is neglected. On the other hand, the complex amplitude of quasi-monochromatic standing waves near the cutoff wavenumber is governed by a similarly type of nonlinear Schrödinger equation in which the roles of time and space are interchanged. This equation makes it possible to estimate the nonlinear effect on the cutoff wavenumber. The nonlinear theory, when used to investigate the stability of charged liquid jet, appears accurately to predict a new unstable regions. The effects of the surface charge and charge relaxation on the stability are identified. The various stability criteria are discussed both analytically and numerically and the stability diagrams are obtained.     

Algebra of Observables and Charge Superselection Sectors for QED on the Lattice

Quantum Electrodynamics on a finite lattice is investigated within the hamiltonian approach. First, the structure of the algebra of lattice observables is analyzed and it is shown that the charge superselection rule holds. Next, for every eigenvalue of the total charge operator a canonical irreducible representation is constructed and it is proved that all irreducible representations corresponding to a fixed value of the total charge are unique up to unitary equivalence. The physical Hilbert space is by definition the direct sum of these superselection sectors. Finally, lattice quantum dynamics in the Heisenberg picture is formulated and the relation of our approach to gauge fixing procedures is discussed. Received: 21 October 1996 / Accepted: 10 February 1997     

Binding properties between ferroic oxides and metals

Using first principles calculations the binding characteristics of a metallic film covering a piezo-electric oxide is studied. The band structures and the charge densities of interfaces and single compounds are calculated. Comparing the overlaps of the densities of states and the differences in the charge densities, it is found that the interface stabilitydepends on the thickness of the metallic film. The bonding is shown to be a result of charge transfer.     

Instability of a spherical drop in a nonuniform electric field

Analytical calculation in the first order of smallness shows that the equilibrium shape of a drop in the field of a point charge is axisymmetric about the plane passing through the center of mass of the drop normally to the axis connecting the center of mass with the point charge. Whether the equilibrium shape of the drop is stable or not depends on the value of the field parameter, which, in turn, depends on the point charge and the distance to it. There is an asymptotic value of the critical parameter above which all modes become unstable. In the field of the point charge, the mode coupling grows; that is, a mode excited at the zero time generates oscillations of the six nearest modes with amplitudes proportional to that of the initially excited mode. If the initially excited mode loses stability, all the modes coupled with it also become unstable. The surface instability of the drop also develops when the initially excited mode is stable but at least one of the modes coupled with it is unstable.     

Ion charge state distributions of pulsed vacuum arcs-interpretationof their temporal development

Ion charge states of vacuum arcs are enhanced at the beginning of each arc pulse. The ion charge states drop with time and become steady-state after about 100 μs, with some dependence on the cathode material. A reduction of ion charge states has been observed at the end of each are pulse. In this note it is shown that the charge-state-dependent ion drift velocity in the plasma expansion zone contributes to the effect measured by the time-of-flight method, although it is not solely responsible for it. A quantitative evaluation as well as literature data of other measuring methods prove the physical significance of the effects observed     

电流型探测器单粒子灵敏度标定的原理及应用

 采用电荷模数转换记录单个脉冲电荷的方法,标定了单能射线在电流型闪烁探测器中产生的平均电流,从而得到其灵敏度。标定结果与传统的电流法在±8%的范围内一致。该标定方法准确度高,扣除本底容易,对标定源的强度要求也大大降低。加上飞行时间法,还可对粒子进行甄别,能在中子-γ射线混合场中将中子和γ射线的电荷贡献分开,得到探测器对每种射线单独的灵敏度。该方法适用于在单个脉冲电荷信噪比较高的场合下标定脉冲电流型探测器。     

AC space-charge effects in gyroklystron amplifiers

The effects of AC space charge on multicavity gyroklystron amplifiers are studied. It is found that when AC space charge is included in the analysis of weakly relativistic multicavity gyroklystron amplifiers, the optimized nonlinear efficiency becomes a function of beam current. For a cold beam (no velocity spread), the efficiency is maximum at zero current and decreases monotonically as the current increases. The zero current limit of the optimized efficiency when AC space-charge effects are included is not the same as the optimized efficiency with no space charge; it is significantly higher. This behavior is regularized when velocity spread is taken into account; in that case, the nonlinear efficiency increases with beam current until it reaches a maximum, then falls off slowly. The increase in efficiency is attributed to enhanced bunching associated with the saturation of the space-charge instability in the drift region; the reduction in efficiency at high current occurs because space charge induces an additional velocity spread in the beam     

σ-电子受体试剂与硫酸阿托品的电荷转移反应及应用研究

本文研究了硫酸阿托品与I2 在氯仿溶液中的荷移反应并探讨其反应机理 ,指出I2 为电子受体 ,硫酸阿托品为电子给体 ,经试验知形成 1∶1的复合物。其λmax=2 80nm ,表观摩尔系数为 2 6 6× 10 4L·mol- 1 ·cm- 1 ,确定了用此原理测定硫酸阿托品的方法及最佳条件 ,比尔定律线性范围 0～ 35 μg·mL- 1 ,本法测定简便、快捷、选择性强     

Charge to radius dependency for conductive particles charged by induction

Particle charge is a critical parameter that needs to be determined in order to accurately predict behavior of a charged particle exposed to electrical forces. The effectiveness of various electrostatic applications depends directly on this charge or, more specifically, the charge to mass ratio. Previous studies report conflicting data for the size dependency of charge. In this paper, the relation between the value of charge on a conductive particle and the particle radius in the process of induction charging is investigated. The results of numerical simulations of a liquid atomization process are presented and a novel approach to the analytical solution of the problem is introduced. It is found that the exponent in the particle charge to radius dependency is equal to two when the particle is in the direct contact with the bulk material. The radius exponent decreases rapidly as the atomizing ligament length is increased. For ligament lengths many times greater than the particle radius, the radius exponent approaches one. Agreement between numerical and analytical results is found to be very good. The results of this study clarify some of the conflicting data in the previously published literature and suggest that the particle charge is practically linearly dependent on radius for atomized liquid particles and proportional to particle surface area for solid particles. In addition it is shown that the charge to mass ratio for liquid particles can be maximized by ensuring the ligament length during atomization is maximum.     

电解质浓度对胶体粒子表面有效电荷的影响

胶体粒子的表面有效电荷是决定胶体性质的重要物理量,但溶液环境(如电解质溶液浓度)是否影响其数值至今尚无统一认识,近年来的一些研究工作给出了存在争议的不同结果和假设.在直接实验测量方面,由于电解质离子和胶体表面吸附离子的置换,粒子表面基团的不完全电离和胶体粒子对离子吸附的共同作用,使得对这类粒子在不同溶液环境下的表面有效电荷的测量和变化机理的认识极为困难.针对该问题,本文测定了羧基和磺酸基修饰的聚苯乙烯胶体颗粒在不同粒子浓度和HCl浓度下的电导率,由于两种粒子与HCl电离产生的阳离子相同(均为H+),可根据电导率-数密度法(迁移法)得到胶体颗粒表面有效电荷数.通过实验结果分析,明确了HCl浓度以及粒子数密度对胶体粒子表面电荷的影响规律以及表面电荷随HCl浓度增大的原因.除此之外,羧基修饰颗粒比磺酸基修饰颗粒的表面电荷随HCl浓度变化更快;对于同一HCl浓度,磺酸基修饰胶体表面电荷不受粒子数密度影响,而羧基修饰胶体颗粒却与之相关.基于粒子表面电荷的理论模型,对这些问题都给出了相应的解释.     

Calculation of core-level-shifts from an alternative ionicity scale

Shevchik et al.^1,2 proposed an electrostatic model relating charge transfer between ions and chemical shifts in ionic compounds. The charge transfer can be calculated from the ionicity. If one uses Phillips ionicities one obtains the wrong sign for the calculated core-level-shifts of copper halides as it is pointed out by Shevchik et al.^1,2. We show that the shifts can be computed fairly successfully if one uses an alternative definition of ionicity recently proposed⁴. Using this definition it is further shown that the charge transfer is identical with the longitudinal (Callen) charge of a crystal.     

Measurement of avalanche size and position resolution of RPCs with different surface resistivities of the high voltage provider

The effects of surface resistivity of the high voltage provider on the space dispersion of the induced charge of a prototype Resistive Plate Chamber (RPC) have been studied experimentally and theoretically. The results of both experiment and theory agree and confirm that a two-Gaussian function can be used to fit the dispersion of the induced charge of the RPC. It is shown that the Gaussian function with the narrower width is mainly due to the expansion of the avalanche charge in the gas gap of the RPC, and the Gaussian function with the larger width is due to the charge dispersion when it passes through the resistive carbon film. This will be useful in the RPC design when one wants to make an RPC with high position resolution.