On the possibility of corona initiation at the surface of a liquid layer nonlinearly oscillating on the surface of a charged hailstone placed in a uniform electrostatic field

An expression for the electric field strength near a watered hailstone is derived in an approximation quadratic in the amplitude of capillary oscillations of a charged conducting liquid layer covering the hailstone. As the number of the mode governing the initial deformation of the equilibrium spherical free surface of the liquid layer increases and its thickness decreases, the electric field strength in the neighborhood of the capillary wave crests rises. Even in the case of small charges and low electric fields, the electric field near the hailstone is high enough to initiate a corona.     

On the initiation of a corona discharge near the surface of a nonlinearly oscillating liquid layer on the surface of a charged hailstone

An expression is derived for the electric field strength near a wet hailstone in an approximation quadratic in the oscillation amplitude of a charged liquid layer on its surface. It is found that the electric field strength in a small neighborhood of the capillary wave crests grows with the number of a mode governing the initial deformation of the equilibrium (spherical) shape of the liquid layer. Even if the charge is small (when the Rayleigh parameter of the hailstone equals one-hundredth of the value critical for stability against the self-charge), the electric field near the hailstone is high enough for initiating a corona discharge in its vicinity.     

Nonlinear oscillations of a charged layer of a conducting liquid on the surface of a solid spherical core

Nonlinear oscillations of a layer of an ideal incompressible perfectly conducting liquid on the surface of a charged melting hailstone (solid core) are studied using analytical asymptotic calculations of the second order of smallness in initial deformation amplitude. Specifically, it is shown that, when the thickness of the layer is much less than the characteristic linear size (radius) of the solid core, the size of the core considerably influences the amplitudes of capillary oscillation modes arising on the surface of the charged layer via nonlinear interaction. It is found that, as the liquid layer on the surface of the solid core gets thinner, the energy in the spectrum of nonlinearly excited modes is redistributed with its maximum shifting toward higher (larger number) modes.     

On nonlinear periodic capillary-fluctuation wave flow in a thin liquid film on a solid substrate

Analytical calculation of a nonlinear periodic wave flow on the free surface of a charged layer of an ideal incompressible conducting liquid resting on a solid substrate is carried out for the case when fluctuation-induced forces (the dispersion component of the wedging pressure) have a decisive effect on the system. It is shown that wave flows emerge in the liquid in calculations of the second order of smallness in the wave amplitude, which is assumed to be small compared with the thickness of the liquid layer. These flows result from nonlinear interaction as nonlinear corrections to the waves set at the zero time. The field of fluctuation-induced forces displaces these flows toward the periphery of the area of influence of these forces. This effect takes place both in the presence of an external electric field near the free surface and in its absence. The sign and value of the nonlinear corrections depend on whether an electric field is present near the free surface of the liquid. In the presence of an electric field, the curvature of the crest of the nonlinear waves increases; in its absence, the curvature decreases.     

Nonlinear oscillations of a charged jet of a conducting liquid under multimode initial deformation of its surface

The subject of consideration is a uniformly charged jet of an ideal incompressible conducting liquid moving with a constant velocity along the symmetry axis of an undisturbed cylindrical surface. An evolutionary expression for the jet shape is derived accurate to the second order of smallness in oscillation amplitude for the case when the initial deformation of the equilibrium surface is a superposition of a finite number of both axisymmetric and nonaxisymmetric modes. The flow velocity field in the jet and the electric field distribution near it are determined. The positions of internal nonlinear secondary combined three-mode resonances are found, which are typical of nonlinear corrections to the analytical expressions for the jet shape, flow velocity field potentials, and electrostatic field in the vicinity of the jet.     

Nonlinear resonance interaction between the oscillation modes of a spherical liquid layer on the surface of a melting hailstone

Evolutionary equations are derived and solved that describe the time dependence of the oscillation mode amplitudes on the surface of a charged conducting liquid layer resting on a solid core. It is assumed that the layer experiences a multimode initial deformation. The equations are solved asymptotically in the second order of smallness in the small dimensionless amplitude of capillary oscillations on the surface of the layer. Mechanisms behind internal nonlinear resonance interaction between the modes of the liquid layer oscillations and behind energy transfer between the modes both in degenerate and in secondary combination resonances are investigated. It is found that in the degenerate resonance interaction between oscillation modes, the energy may be transferred not only from lower to higher modes but also vice versa if the higher mode is excited at the zero time. This conclusion is valid not only for a liquid layer on the surface of a solid core but also for a drop.     

Nonlinear capillary vibration of a charged bubble in an ideal dielectric liquid

The problem of nonlinear radial pulsations and surface vibrations of a charged bubble placed in an ideal incompressible dielectric liquid is asymptotically solved up to the second order of smallness by the method of many scales. It is shown that, in the case of nonlinear vibrations, resonance energy exchange may take place not only between surface modes but also between the radial mode and a surface mode. A new type of instability (other than Rayleigh instability against the self-charge), instability against the excess vapor pressure in the bubble, is discovered. The new type of instability shows up as energy transfer from the centrosymmetric pulsation mode to all initially excited surface vibration modes simultaneously.     

Nonlinear degenerate resonance interaction of waves on a charged liquid surface

The physics of nonlinear degenerate resonance energy exchange between waves on the flat free charged surface of a conducting liquid is analytically (asymptotically) studied up to the second order of smallness. A set of differential equations for the evolution of the amplitudes of nonlinearly resonantly interacting waves is derived. It turns out that nonlinear computations (taking into account the dependence of the wave frequency on the finite amplitude) yield an infinite number of degenerate resonances, although computations based on frequencies found in the linear theory give a finite number of resonances. In nonlinear computations, the positions of the degenerate resonances depend on the surface charge density (or on the external electric field normal to the free surface of the liquid) in contrast to the results of linear computations (based on frequencies found in the linear theory). It is found that as the wavenumber of an exact degenerate resonance is approached (that is, in the vicinity of this number), the direction of energy transfer changes sign: now the energy is transferred from a shorter wave to a longer one and not the reverse.     

On internal nonlinear resonant interaction of capillary-gravitational waves on the flat surface of a viscous liquid

Mechanisms behind internal nonlinear resonant interaction of periodic capillary-gravitational waves on the uniformly charged flat surface of an infinitely deep viscous conducting liquid are considered. A mathematical procedure modifying the well-known method of many scales is proposed for constructing an asymptotically valid solution near the resonance. It is shown that the internal nonlinear resonant interaction results in effective energy transfer from long waves to shorter ones. An increase in the viscosity of the liquid diminishes the rate of energy transfer between resonantly interacting waves.     

The physics of charging a hailstone freely falling in a thunderstorm cloud

Interaction between a charged watered coarse hailstone and likely charged droplets in a uniform electrostatic field is analyzed using the electrostatic methods of images. It is shown that, under certain external conditions characteristic of a thunderstorm cloud, the droplets are attracted to the likely charged hailstone. Owing to collisions with the droplets, the hailstone freely falling in a thunderstorm cloud can gather a charge large enough to initiate a corona discharge in its vicinity.     

Nonlinear analysis of a wave motion on the surface of a jet moving in a dielectric medium placed in a longitudinal electric field

The possibility of degenerate internal nonlinear resonance interaction between capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface of a charged cylindrical jet of an ideal incompressible conducting liquid is demonstrated. The jet moves in an ideal incompressible dielectric medium collinearly with an external uniform electrostatic field. It is shown, in particular, that six different resonance situations take place for axisymmetric waves in which primary waves and waves due to the nonlinearity of the equations of hydrodynamics exchange energy.     

Effects of an electric field on the surface electron barrier in a metal in the presence of an adsorbate. Part 2. An improved Thomas-Fermi method

An improved form of the Thomas-Fermi method (density-functional method) is used to consider the effects of an adsorbate on the screening of an external electric field near the surface of a metal. It is shown that quasihomogeneous models for the electron gas that are based on the local-density approximation do not enable one to consider the field directed towards the metal. When allowance is made for multiparticle effects and inhomogeneous corrections to the electron energy, one can calculate the damping parameter for the electron density and the coordinate of the center of gravity of the screening charge in relation to the electric field strength and adsorbate density. Various nonadditive effects are discussed that are related to the effects of the field on the structure of the double layer, which have an influence on the desorption and evaporation of surface atoms in strong electric fields.Translated from Izvestiya Vysshykeh Uchebnykh Zavedenii, Fizika, No. 11, pp. 10–14, November, 1981.     

Electric charge of a lightning ball

The electric charge of a lightning ball is found by comparing the electrohydrodynamic stabilities of a charged drop in an electrostatic suspension and a lightning ball floating in a superposition of the gravitational field and the surface electric field. It has been assumed that the electric field strength at the surface is limited by a breakdown value. For a lightning ball radius of 15 cm, its charge is estimated as several microcoulombs. Accordingly, the density of electrostatic energy accumulated in the lightning ball is on the order of one-hundredth of a joule per square centimeter. The density of the material that constitutes the lightning ball has been estimated for the case when the electric field strength at the site of its origination is several times higher than that in fine weather. The density of the lightning ball turns out to differ from that of air by only a few percents.     

On the interaction between a charged drop and an external acoustic field

An interaction between capillary oscillations of a charged drop and an external acoustic field is investigated under conditions in which nonlinear components of the acoustic pressure on the drop surface may be neglected. It is shown that equations describing the temporal evolution of modes of the capillary waves in this case may be either the Mathieu-Hill equations or ordinary inhomogeneous equations of the second order describing forced oscillations. In both cases, the drop instability (of a parametric or resonance type) may result in its disintegration due to deformation caused by the acoustic field at its own drop charge, subcritical in the sense of the Rayleigh criterion.     

Interaction of a surface glow discharge with a gas flow

A surface glow discharge in a gas flow is of particular interest as a possible tool for controlling the flow past hypersonic aircrafts. Using a hydrodynamic model of glow discharge, two-dimensional calculations for a kilovolt surface discharge in nitrogen at a pressure of 0.5 Torr are carried out in a stationary gas, as well as in a flow with a velocity of 1000 m/s. The discharge structure and plasma parameters are investigated near a charged electrode. It is shown that the electron energy in a cathode layer reaches 250–300 eV. Discharge is sustained by secondary electron emission. The influence of a high-speed gas flow on the discharge is considered. It is shown that the cathode layer configuration is flow-resistant. The distributions of the electric field and electron energy, as well as the ionization rate profile in the cathode layer, do not change qualitatively under the action of the flow. The basic effect of the flow’s influence is a sharp decrease in the region of the quasineutral plasma surrounding the cathode layer due to fast convective transport of ions.     

The surface mode supported by an asymmetrical waveguide containing left-handed materials

The propagating characteristics of surface mode supported by an asymmetrical three-layer waveguide containing left-hand materials are studied in detail. The forward and the backward surface modes have been identified respectively through the slope of dispersion curve and the total energy flux of the structure. Research shows that anti-symmetry mode corresponds to forward surface wave. Furthermore, to symmetry mode, the type of surface mode depends on the distribution of the electric field in the left-handed layer. It is found that, the conversion between backward surface wave and forward surface wave is realizable by varying the thickness of the left-handed layer and the permittivity of the substrate.     

Nonlinear Tamm states in layered metal–dielectric metamaterials

We study nonlinear surface modes at the edge of metal–dielectric nanostructured metamaterial with a nonlinear surface layer. We demonstrate that such semi‐infinite structures can support transverse electric (TE) polarized surface states with subwavelength localization near the surface, an optical analogue of the Tamm states, even in the cases when the surface modes do not exist in the linear regime. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of a strong electric field on the decay of autoionizing states formed when multiply charged ions approach a metal surface

Upon collisions of multiply charged ions with a surface, the electric field of the image charge causes Stark splitting of the ion levels; in this case, the Stark states whose energy approaches the electron binding energy in the metal with a decrease in the distance to the surface are selectively occupied. It is shown that consideration of the electric field effect leads to an increase in the probability of Auger transitions in the presence of field. This effect changes our representations about the scheme of occupation of lower levels of multiply charged ions.     

Quantum fluctuations of the refractive index near the interface between a metal and a nonlinear dielectric

Zero-point fluctuations of surface plasmon modes near the interface between a metal and a nonlinear dielectric are shown to produce a thin layer of shifted fluctuating dielectric constant near the interface. The shift of the dielectric constant in this layer may be sufficiently large to produce multiple metastable states of the surface plasmon vacuum.     

The filling of neutron star magnetospheres with plasma: Dynamics of the motion of electrons and positrons

We consider the motion of charged particles in the vacuum magnetospheres of rotating neutron stars with a strong surface magnetic field, B ≳ 10¹² G. The electrons and positrons falling into the magnetosphere or produced in it are shown to be captured by the force-free surface E · B = 0. Using the Dirac-Lorentz equation, we investigate the dynamics of particle capture and subsequent motion near the force-free surface. The particle energy far from the force-free surface has been found to be determined by the balance between the power of the forces of an accelerating electric field and the intensity of curvature radiation. When captured, the particles perform adiabatic oscillations along the magnetic field lines and simultaneously move along the force-free surface. We have found the oscillation parameters and trajectories of the captured particles. We have calculated the characteristic capture times and energy losses of the particles through the emission of both bremsstrahlung and curvature photons by them. The capture of particles is shown to lead to a monotonic increase in the thickness of the layer of charged plasma accumulating near the force-free surface. The time it takes for a vacuum magnetosphere to be filled with plasma has been estimated.