A criterion for the stability of a charged sphere in general relativity

A criterion for stability of a charged sphere is obtained by use of two different methods. The result is applied to a charged dust in order to investigate its stability.     

Charged dust spheres in general relativity

The balanced field equations [1] of general relativity have been used for presenting a model for a sphere of charged dust having different densities of matter and charge. The Schwarzschild's and Penney's solutions are the particular case of the solution arrived at herein. Further equations are solved to get a model in which gravitational attraction and electrical repulsion balance each other.     

Space-time structure and bound-charge fields

Together with a “postulate of equivalent situations,” the exact solution for the field of a charge in a uniformly accelerated noninertial frame of reference (NFR) makes it possible to find the space-time structure and fields of charged conductors of arbitrary shape without using the Einstein equations. The energy of the electric field outside of a charged plane, which is equal to the rest energy of the masses of the charges creating the field, is determined. The space-time metric outside of the charged plane is established; it could also have been found from the exact solution of the Einstein-Maxwell equations. This solution describes the equilibrium of charged dust in parallel electric and gravitational fields. The field and metric are found outside of a charged conducting sphere. While it eliminates the self-energy divergence, the proposed method renders the classical electrodynamics internally consistent on transition to any short distance. All-Russian Scientific Research Institute of Opticophysical Measurements. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 63–74, October, 1997.     

The influence of dust particle geometry on its charge and plasma potential

In this paper, a self‐consistent numerical model describing the behaviour of plasma around isolated highly charged dust particles with different shapes of rotation figures is presented. Dust particles in the form of a sphere, oblate ellipsoids (disk‐like particles), and elongated ellipsoids (rod‐like particles) are considered in the presence of an external electric field. Using the developed model, self‐consistent distributions of a space charge and plasma potential are obtained around non‐spherical dust particles. These distributions are carefully analysed by decomposing them in a series of Legendre polynomials. Decompositions of these distributions are compared with particles of different geometry. In addition, for different geometries of dust particles, the dependencies of the charge of a dust particle on geometry in the absence of an external field are investigated.     

The diffusion of macroparticles and criteria of phase transitions for dust structures in weakly ionized plasma

The dynamics of charged particles is investigated under conditions close to those of experiments in a weakly ionized laboratory gas-discharge dust plasma. The existing phenomenological criteria of phase transitions for dust structures in such a plasma are treated, and new criteria are suggested. The parameters responsible for the order and scaling of dynamic processes in Yukawa dissipative systems are determined. The relation for the diffusion coefficient D of macroparticles in strongly correlated liquid structures is derived.     

Interactions of charged dust particles in clouds of charges

Two charged dust particles inside a cloud of charges are considered as Debye atoms forming a Debye molecule. Cassini coordinates are used for the numerical solution of the Poisson-Boltzmann equation for the charged cloud. The electric force acting on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the average distance between dust particles should be approximately equal to two Debye radii. Second, attraction takes place when similar charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of total charge of the same polarity, repulsion between the particles takes place at all distances. We apply our results to the experiments with thermoemission plasma and to the experiments with nuclear-pumped plasma.     

Accretion of exotic matter onto a Reissner-Nordström black hole

The physical processes that arise when exotic matter accretes onto a charged Reissner-Nordström black hole are considered. Exotic matter is chosen in the form of dust with a negative mass. The various types of horizons and throats that arise in the accretion process are considered. The Einstein equations are integrated analytically by taking into account the contributions from various types of matter (dust and magnetic field). The derived expressions are reduced to a form convenient for their analytical study. Particular solutions of the system are found for a certain class of initial conditions and constraints related to the possibility of dust-layer intersection are investigated. A fundamental change in solution characteristics related to the possibility of black-hole disappearance is found.     

Radar studies of ionospheric dusty plasma phenomena

We discuss the influence of charged dust on radar observations in the Earth ionosphere. This region in the upper Earth atmosphere can be described as a partially ionized, low‐temperature plasma. Plasma parameters vary by orders of magnitude spatially and in time. Dust particles influence the charge balance, in some cases dusty plasma condition is met. The polar mesospheric echoes are an example of dust plasma interactions observed with radar. The mesosphere is a region where atmospheric temperature decreases with altitude and can reach frost point temperature. The formation of the polar mesospheric radar echoes involves neutral atmosphere dynamics, which is latitude dependent and it involves charged dust particles, especially icy dust that forms in the polar summer mesosphere. Charged dust can also influence incoherent scatter that results from electromagnetic waves scattering off electrons, where the electrons are coupled to other charged components. Observers rarely report charged dust signatures in the incoherent scatter spectra; we show that there is a good chance for doing so with improved observations. The incoherent scatter can possibly also be used to estimate the amount of charged dust in the direct vicinity of a meteor, as we show based on the order of magnitude considerations. This prospect of new observational results makes theoretical investigations of radio‐wave scattering in the presence of charged dust with size distributions worthwhile.     

UV-induced Coulomb crystallization of dust grains in high-pressuregas

A scheme for forming a Coulomb lattice of positively charged dust grains in a high-pressure (P>torr) gas is discussed theoretically. The grains are charged positively by photoemission in the presence of a flux of ultraviolet (UV) photons with energy larger than the work function of the grains, but lower than the ionization potential of the background gas. Methods for levitating and containing the dust using photophoretic forces (both UV and non-UV), gas drag, and electrostatic forces are considered     

Levitation and dynamics of a collection of dust particles in afully ionized plasma sheath

Examines the dynamics of a collection of charged dust particles in the plasma sheath above a large body in a fully ionized space plasma when the radius of the large body is much larger than the sheath thickness. The dust particles are charged by the plasma, and the forces on the dust particles are assumed to be from the electric field in the sheath and from gravitation only. These forces will often act in opposite directions and may balance, making dust suspension and collection possible. The dust particles are supplied by injection or by electrostatic levitation. The ability of the sheath to collect dust particles, will be optimal for a certain combination of gravitation and plasma and dust particle parameters. In a dense dust sheath, the charges on the dust particles contribute significantly to the total space charge, and collective effects become important. These effects will reduce the magnitude of the sheath electric field strength and the charge on the dust particles. As dust particles are collected, the dust sheath is stretched and the largest dust particles may drop out, because the sheath is no longer able to suspend them. In a tenuous dust sheath, the inner layer, from the surface and about one Debye length thick, will be unstable for dust particle motion, and dust will not collect there. In a dense dust sheath, collective effects will decrease the thickness of this inner dust-free layer, making dust collection closer to the surface possible. By linearization of the force and current equations, the necessary and sufficient conditions for a stable dust sheath are found. The authors consider conditions which resemble those of planetary system bodies, but the results may also be of relevance to some laboratory plasmas     

Comment on “Potential profile near the virtual cathode in presence of charged dust”

The characteristics of the virtual cathode and its potential profile in the presence of negatively charged dust particles have been reported by Rathod et al. They have studied the role of charged dust particles in the formation of virtual cathode near the emitting surface. Two conditions of the dust charge number, Z_d = 1 and Z_d = 1,000 are used to study the role of dust density (n_d) for the formation of virtual cathode. This work is original and will be more interesting in case of using the correct model equations and realistic dusty plasma conditions.     

Study of charge distribution in a dust beam using a Faraday cup

After getting charged in plasma, dust grains in a dust beam are scanned by a Faraday cup and electrometer. At different operating conditions, including a dc field, and analysis of the dust current profile, dust charge distribution is studied and information on the nature of the nonuniform distribution obtained.     

Off-centre charge model of the planar electric double layer for asymmetric 2:1/1:2 valencies

ABSTRACT

Grand canonical Monte Carlo simulation results are reported for the structure and capacitance of a planar electric double layer containing off-centre charged rigid sphere cations and centrally charged rigid sphere anions. The ion species are assigned asymmetric valencies, +2:?1 and +1:?2, respectively, and set in a continuum dielectric medium (solvent) characterised by a single relative permittivity. An off-centre charged ion is obtained by displacing the ionic charge from the centre of the sphere towards its surface, and the physical double layer model is completed by placing the ionic system next to a uniformly charged, non-penetrable, non-polarizable planar electrode. Structural results such as electrode-ion singlet distribution functions, ionic charge density and orientation profiles are complemented by differential capacitance results at electrolyte concentrations of 0.2?mol/dm³ and 1?mol/dm³, respectively, and for various displacements of the cationic charge centre. The effect of asymmetry due to off-centre cations and valency asymmetry on the double layer properties is maximum for divalent counterions and when the cation charge is closest to the hard sphere surface.     

Parametric Study of Nonplanar Dust Acoustic Solitons in Two‐Dimensional Superthermal Dusty Plasmas

The nonlinear properties of two dimensional low‐frequency electrostatic excitations of charged dust particles (or defects) are studied in a collisionless, unmagnetized dusty plasma. A fully ionized three‐component model plasma consisting of kappa distributed electrons, Maxwellian ions, and negatively charged massive dust grains is considered. In this regard, the well known reductive perturbation technique is used to the hydrodynamical equations and the Poisson equation, obtaining the cylindrical Kadomtsev–Petviashvili (CKP) equation. A parametric investigation indicates that the structural characteristics of these nonlinear excitations (width, amplitude) are significantly affected by the plasma nonthermality as well as by the relevant plasma parameters, such as dust concentration and dust temperature. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dust ion-acoustic wave oscillations in single-walled carbon nanotubes

In this paper, a charged single-walled carbon nanotube that surrounded by charged nanoparticles is modeled as a cylindrical shell of electron–ion–dust plasma. By employing the fluid theory for electron–ion–dust plasma, the dispersion relation of the dust ion-acoustic wave oscillations in the composed system is studied. For negatively charged dust particles, with increasing dust charge density, the phase velocity of the dust ion-acoustic wave will increase in comparison to the pure ion-acoustic wave oscillations.     

空间尘埃等离子体对量子卫星通信性能的影响

为了研究尘埃等离子体中带电尘埃的粒子半径、粒子浓度和带电荷数对量子通信性能的影响,首先根据Mie散射理论得到单个带电尘埃粒子的光散射截面;然后通过粒子浓度求出总的消光截面,得出链路衰减的数学模型,提出了带电粒子特性与量子纠缠度的关系;针对退极化信道,当单个尘埃粒子所吸附带电粒子的个数为50时,给出了尘埃粒子半径、粒子浓度与信道容量和量子误码率的定量关系.仿真结果表明,当量子信号的传输距离为10km时,尘埃粒子浓度从1×10~(10) m~(-3)增加到10×10~(10) m~(-3),信道容量从0.6726降低到0.1075;尘埃粒子半径从0.1μm增加到10μm时,量子误码率由1.334×10~(-3)增加到5.309×10~(-3).由此可见,尘埃等离子体中带电尘埃粒子的半径和浓度对量子卫星通信性能有显著的影响.因此,为确保量子通信的可靠性,应根据所探测到的等离子体环境的状况,调整卫星通信系统的各项指标参数.     

Electrostatic charging of a conducting sphere using another conducting sphere at constant voltage

This study uses results of classical electrostatics to predict the resulting voltage of a conducting sphere that is charged by a second sphere maintained at a constant voltage. The voltage of the charged sphere is calculated as a function of the charging voltage and the size ratio of the two spheres. Theoretical predictions are verified experimentally using conducting spheres of various sizes and a Faraday ice pail apparatus. The results may seem somewhat counterintuitive. For example, a charging sphere held at 100 V will charge another sphere of equal size only to 69.3 V by contact.     

The Oppenheimer-Snyder space-time with a cosmological constant

We investigate the Oppenheimer-Snyder space-time with a positive cosmological constant A. The interior of the dust sphere is described by the closed Friedmann-Robertson-Walker space-time while the exterior is the Schwarzschild-de Sitter space-time. Due to the cosmological constant A, when the gravitational massM _o of the dust sphere is very large, there is no collapsing solution with the de Sitter-like asymptotic region which expands exponentially in the expanding universe frame. This fact suggests that the very large initial inhomogeneity does not necessarily lead to the failure of the cosmic no hair conjecture.