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.     

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.     

Nonlinear periodic waves on the charged surface of a finite-thickness ideal liquid layer

In the fourth order of smallness in the amplitude of a periodic capillary-gravitational wave travelling over the uniformly charged free surface of an ideal incompressible conducting liquid of a finite depth, analytical expressions for the evolution of the nonlinear wave, velocity field potential of the liquid, electrostatic field potential above the liquid, and nonlinear frequency correction that is quadratic in a small parameter are derived. It is found that the dependence of the amplitude of the nonlinear correction to the frequency on the charge density on the free liquid surface and on the thickness of the liquid layer changes qualitatively when the layer gets thinner. In thin liquid layers, the resonant wavenumber depends on the surface charge density, while in thick layers, this dependence is absent.     

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.     

Stationary soliton on a charged surface of liquid helium and hydrogen films

A change in the shape of a charged surface of liquid hydrogen and helium — the formation of a solitary wave (a positively charged hump for hydrogen and a negatively charged dimple for helium)-is observed in an electric field exceeding a critical value under conditions of total compensation of the applied field by the surface charge. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 547–552 (10 April 1997)     

Capillary oscillations of a flat charged surface of liquid with finite conductivity

A dispersion relation is proposed and analyzed for the spectrum of capillary motion at a charged flat liquid surface with allowance made for the finite rate of charge redistribution accompanying equalization of the potential as a result of the wave deformation of the free surface. It is shown that when the conductivity of the liquid is low, a highly charged surface becomes unstable as a result of an increase in the amplitude of the aperiodic chargerelaxation motion of the liquid and not of the wave motion, as is observed for highly conducting media. The finite rate of charge redistribution strongly influences the structure of the capillary motion spectrum of the liquid and the conditions for the establishment of instability of its charged surface when the characteristic charge relaxation time is comparable with the characteristic time for equalization of the wave deformations of the free surface of the liquid. Zh. Tekh. Fiz. 67, 34–41 (August 1997)     

Surface waves in a crystal with switching Kerr nonlinearity

In this paper, we explore transverse electric surface waves propagating along the crystal with jump change of Kerr nonlinearity in dependence on field amplitude. The dielectric permittivity in the proposed model of nonlinearity is characterized by abruptly changing unperturbed dielectric constant and Kerr nonlinearity coefficient from one value to another when field amplitude exceeds the threshold value of the switching field. This allows to find exact solutions of model equations in different cases of nonlinearity signs, and to obtain the dependence of wave characteristics, including total power flux, on effective refractive index in explicit form. Such solutions describe two new types of nonlinear surface waves with specific structure depending on electric field amplitude. We derive the conditions of surface domain formation. It is found that the largest percentage of radiation is concentrated within the domain.     

Role of different polarization mechanisms in the self-organization of the director of a thin layer of nematic liquid crystal

A theoretical analysis of the processes occurring in a symmetric metal-liquid-crystal-metal structure is carried out to obtain the dependence of the anisotropic component of the surface free energy on the angle of deviation of the director from the direction of easy orientation. The differences between the angular dependence of the surface energy obtained in this paper from the form described by the Rapini potential are discussed. The coordinate dependence of the ionic and dipolar polarization are calculated, as is the order parameter characterizing the ordering of the dipole moments of the liquid-crystal molecules. The interrelationships of the the boundary polarization with the equilibrium orientation of the director near the surface bounding the liquid crystal and with the value of the internal electric field in the volume of the mesophase are discussed. Zh. Tekh. Fiz. 67, 23–28 (May 1997)     

Equilibrium shape and stability of a charged drop in an air flow under an electric field

The pressure balance on the surface of a charged liquid drop moving along a uniform electrostatic field is analyzed. The liquid is assumed to be nonviscous and incompressible. In the approximation linear in deformation amplitude, the equilibrium shape of the drop as a function of the charge, field strength, and velocity of travel can be both a prolate and an oblate spheroid. Critical conditions for the surface instability of such a drop are obtained analytically in the form of a relationship between the charge, field strength, and velocity of travel. An instability criterion is found by extrapolating to large Reynolds numbers. This makes it possible to fit the earlier model of a corona-initiated lightning in the vicinity of large charged water drops or hailstones to the charges of the drops, field strengths, and velocities of travel (relative to the medium) typical of thunderclouds.     

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.     

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is established that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time. Zh. éksp. Teor. Fiz. 114, 2043–2054 (December 1998)     

Exact solution of the problem of the equilibrium configuration of the charged surface of a liquid metal

A broad class of exact solutions is obtained for the problem of the equilibrium configuration of the charged surface of a conducting liquid allowing for capillary forces. An analysis of the solutions showed that when the amplitudes of the perturbations reached certain critical values, the region occupied by the liquid ceases to be singly connected, which corresponds to the formation of liquid metal droplets. It is shown that a steady-state liquid metal profile may exist for which appreciable local amplification of the electric field can be achieved. Zh. éksp. Teor. Fiz. 116, 1990–2005 (December 1999)     

Nonlinear capillary-gravitational periodic waves on the charged surface of a finite-thickness viscous liquid

An analytical expression for the time evolution of the profile of a nonlinear periodic capillary-gravitational wave traveling over the charged surface of a viscous incompressible finite-thickness liquid is found. The calculation is carried out in the second order of smallness in wave amplitude. It is shown that the dependence of a nonlinear correction to a linear solution on the liquid viscosity and liquid layer thickness changes qualitatively in going from thick to thin liquid layers.     

Nonlinear calculation of the electric field strength on the surface of a melting hailstone in a thundercloud

The contribution of aerodynamic pressure acting on the surface of a water layer to a total electric field near the free surface of the layer is considered. The layer covers a charged melting hailstone moving parallel to the external electrostatic field vector. An asymptotic analytical expression for the electric field strength near a water-covered hailstone is derived in an approximation that is quadratic in the amplitude of capillary oscillations of a charged conducting liquid layer on the surface of the hailstone. It is found that the motion of the hailstone in ambient air influences the total electric field near the hailstone only slightly but noticeably enhances energy exchange between neighboring oscillation modes. An air flow about the hailstone is shown to have an appreciable effect on the possibility of nonlinear resonance energy exchange between initially excited modes and modes due to the nonlinear interaction.     

On the possibility of initiating a corona discharge at the crests of nonlinear waves on the surface of a charged thin layer of a viscous conducting liquid

An analytic expression for the electrostatic field strength at the free surface of a thin layer of a uniformly charged viscous incompressible liquid is obtained in second-order asymptotic calculations in the amplitude of a periodic capillary-gravity wave propagating over the liquid surface. It is shown that a corona discharge at the crests of the waves can be initiated at subcritical values of the field strength (in the sense of possible realization of the Tonks-Frenkel instability). The electrostatic field strength at the crests of nonlinear waves increases with the wavenumber and the wave amplitude.     

Ionization of solvent molecules by the field evaporation of ions from glycerol and ethylene glycol solutions

Using an electromembrane source, mass-spectrometric investigations into the field evaporation of ions from KI solutions in a water-glycerol mixture and in ethylene glycol are performed. The concentration of negatively charged solvent ions (deprotonated molecules) on the emitting surface of the liquid is determined. It is shown that, under the conditions of intense field evaporation of ions, the surface concentration of deprotonated glycerol and ethylene glycol molecules is several orders of magnitude higher than their equilibrium concentration in the absence of an electric field. The high concentration of solvent ions is associated with an increase in the autoprotolysis constant in a strong electric field.     

Nonlinear corrections to the oscillation mode frequencies of an ideal liquid charged jet

An analytical asymptotic expression is derived for the time evolution of an ideal incompressible conducting liquid jet with a uniformly charged surface that moves with a constant velocity along the symmetry axis of an undisturbed cylindrical surface. The expression is obtained in the third order of smallness in jet oscillation amplitude under the conditions when the initial deformation of the equilibrium jet surface is specified by one (axisymmetric or nonaxisymmetric) mode. Analytical expressions are also found for the positions of internal nonlinear degenerate three-and four-mode resonances, which are typical of nonlinear corrections to the equilibrium shape of the jet, liquid velocity field potential in the jet, and electrostatic field near the jet, and also for a nonlinear frequency correction. It is established that the nonlinear oscillations of the jet take place about a surface depending on the type of initial (generally asymmetric) deformation rather than about the equilibrium cylindrical shape.     

Polarization-interference effects in the bremsstrahlung of quasiclassical electrons on ions with a core

The polarization dependence of the stimulated bremsstrahlung and inverse bremsstrahlung (SBIB) of quasiclassical electrons on highly charged ions with a core is calculated in the approximation of a specified Coulomb current. Emission frequencies close to an eigenfrequency of the ion core are considered. The contributions of the static and polarization channels are taken into account in the amplitude of the process. When the nondipole nature of the interaction between the incident particle and a resonant transition in the ion core is taken into account, interference between these channels causes the spectral-amplitude characteristics of the process to assume a specific dependence on the angle α between the electric field intensity vector of the electromagnetic wave and the initial velocity vector of the incident particle. This dependence, which persists after integration of the cross section over the scattering angle of the incident particle, causes interference effects, viz., asymmetry of the line shape and dips in the dependence of the SBIB cross section on electric field intensity, to appear for α=π/2 and significantly reduces them for α=0. Zh. éksp. Teor. Fiz. 115, 1619–1629 (May 1999)     

Effect of tilted electrostatic field on the Kelvin–Helmholtz instability in a liquid dielectric and gas flow

The effect of surface ponderomotive forces on the Kelvin–Helmholtz instability is studied in the linear formulation based on the equations and boundary conditions of the electrostatics and fluid dynamics of an ideal incompressible fluid. Conditions to be satisfied by the values of determining parameters of the problem for the transition of an unstable flow in zero electric field into a stable regime after the application of a horizontal electric field have been written in the form of inequalities. It has been shown that, at the stability bound, the wavelength of the most instable mode is independent of the ponderomotive forces. In case of a liquid with large permittivity a stable flow regime exists for which the stability condition only differs in small dimensionless values from the stability condition for the charged surface of a quiescent liquid conductor in contact with a gas at rest.     

Nonlinear analysis of the equilibrium shape of a charged conducting drop in an electrostatic suspension

An analytical asymptotic expression is derived that describes the equilibrium shape of a charged drop of an ideal incompressible conducting liquid suspended in superposed collinear uniform electrostatic and gravitational fields. The expression is obtained in an approximation quadratic in the small amplitude of deviation of the equilibrium drop from a sphere, with the electrostatic field dimensionless strength taken as a measure of the deviation amplitude. With allowance for the gravitational and electrostatic fields and interaction between the drop self-charge and external electrostatic field, the equilibrium shape of the drop is found to be very close to a spheroid when the charge and the electrostatic field strength are far from their critical values. The analysis is carried out with a refined procedure of calculation of the equilibrium shape of drops placed in external force fields.