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 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.     

Electrostatic stability of the liquid layer surface on a hard wettable cylindrical substrate

The wave motion in a cylindrical layer of an ideal conducting liquid on a hard rod kept at a constant electrical potential is calculated accurate to the first order of smallness in dimensional perturbation of the free surface. The instability of the free surface is also considered. A dispersion relation is derived. It is shown that the range of instability waves depends on only the electric field strength near the free surface and the instability increments of capillary waves decrease as the layer gets thinner. The influence of the hard rod becomes tangible only when its radius becomes comparable to the thickness of the liquid layer.     

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.     

The influence of electric field on the photodetachment of H- near a metal surface

The influence of electric field on the photodetachment of H-near a metal surface is investigated based on the closed-orbit theory.It is found that the photodetachment of H-near a metal surface is not only related to the electric field strength but also to the electric field direction.If the electric field is along the +z axis,it can strengthen the oscillation in the photodetachment cross section.However,if the electric field is along the -z axis,since the direction of electric field force is opposite to that of static-image force caused by the metal surface,the situation becomes much more complicated.When the electric field is very weak,its influence can be neglected.The photodetachment cross section is nearly the same as that when a single metal surface exists.When the electric field strength is strong enough,the electric field force is able to counteract the metallic attraction,therefore no closed orbit is formed.If the electric field continues to increase until its influence becomes dominant,the photodetachment cross section approaches the case of the photodetachment of H- in an electric field.Our results may be useful for guiding future experimental studies on the photodetachment of negative ions near surfaces.     

An AlGaN/GaN HEMT with a reduced surface electric field and an improved breakdown voltage

A reduced surface electric field in an AlGaN/GaN high electron mobility transistor(HEMT) is investigated by employing a localized Mg-doped layer under the two-dimensional electron gas(2-DEG) channel as an electric field shaping layer.The electric field strength around the gate edge is effectively relieved and the surface electric field is distributed evenly as compared with those of HEMTs with conventional source-connected field plate and double field plate structures with the same device physical dimensions.Compared with the HEMTs with conventional sourceconnected field plates and double field plates,the HEMT with a Mg-doped layer also shows that the breakdown location shifts from the surface of the gate edge to the bulk Mg-doped layer edge.By optimizing both the length of Mg-doped layer,L m,and the doping concentration,a 5.5 times and 3 times the reduction in the peak electric field near the drain side gate edge is observed as compared with those of the HEMTs with source-connected field plate structure and double field plate structure,respectively.In a device with V GS = -5 V,L m = 1.5 μm,a peak Mg doping concentration of 8×10 17cm-3 and a drift region length of 10 μm,the breakdown voltage is observed to increase from 560 V in a conventional device without field plate structure to over 900 V without any area overhead penalty.     

On the instability against the surface charge of a liquid meniscus at the end of a capillary

The subject of consideration is instability of the flat meniscus of a viscous liquid at the end of a capillary in the gravitational field and an electrostatic field when the symmetry axis of the capillary is arbitrarily oriented relative to the direction of free-fall acceleration. It is shown that, if the electrostatic field strength is high, the development of meniscus instability does not depend on the orientation of the capillary. The instability growth rate versus wavenumber dependence for annular waves of different types on the meniscus surface is found to be nonmonotonic.     

On the physical meaning of the critical equilibrium thickness of a film on the hailstone surface

The currently available theories of hailstone growth explain the layered structure of hailstones in two ways. Kachurin has shown that the layered structure of ice covering an object placed in the flow of a supercooled water aerosol is determined by the equilibrium thickness of the film. The other approach is based on solving the equation of heat balance on the hailstone surface and uses the notion of the critical liquid water content in a cloud. The meaning of the critical equilibrium thickness of the film is elucidated, and a relation between two existing criteria for the dry-wet hailstone growth transition is established.     

Effect of longitudinal electric field on capillary instability of a thin axisymmetric layer of liquid dielectric coating a dielectric fiber

The flow of a viscous dielectric liquid surrounded with a gas is investigated in the process of capillary disintegration of a thin axisymmetric liquid layer on an undeformable cylindrical dielectric fiber in a uniform electric field is investigated. An asymptotic analysis of the system of equations and hydrodynamic boundary conditions written with allowance for surface ponderomotive forces is carried out for the case when the average thickness of the layer is much smaller than the radius of the fiber cross section. The problem of the transition of the liquid configuration from the state of a stationary cylindrical layer to the hydrodynamic state in the form of a regular sequence of drops is formulated. In this formulation, a nonlinear parabolic equation that describes the evolution of the local thickness of the layer on the time interval to the instant of drop formation is derived. The effect of the key parameters on the capillary instability is analyzed based on the linearized version of the resultant equation and the linearized electrostatic problem of calculating the field perturbations.     

Electric field and the charge distribution on the surface of an insulator in a vacuum

The free charge steady-state distribution over the insulator surface that arises in a strong electric field in a vacuum can be found by solving the boundary-value problem for the electrostatic field strength if the angle between the field vector and vacuum-insulator interface is given. A general solution to this boundary-value problem is derived for the case of an in-plane field and rectilinear interfaces. Laws of charge and field formation that follow from the solution obtained are considered. Formulas for the electric field strength and charge density in terms of elementary functions are obtained for a number of particular cases. Power-type expressions for the electric field and a critical angle between the electrode and insulator surface that describe the field behavior and charge distribution near the vacuum-insulator-electrode contact are derived.     

外电场中金属表面附近里德堡氢原子的动力学行为

利用相空间分析方法研究了外电场中金属表面附近里德堡氢原子的动力学性质. 结果表明, 体系的动力学性质敏感地依赖于原子与金属表面间的距离和电场强度.通过固定原子与金属表面间的距离, 分析了外加电场作用下里德堡电子的Poincaré 截面和运动轨迹的演化过程. 研究表明: 电场的出现加速了金属表面对电子的吸附, 随着电场强度的增加,体系的动力学性质由原子与金 属表面间的距离控制逐渐变为由电场起主导作用,体系逐渐由不可积变为可积, 电子的运动轨道最终全部变为振动型轨道. 关键词： Poincaré截面 相空间分析方法 里德堡氢原子     

On the thickness of a boundary layer related to the oscillating free surface of a charged drop of a viscous liquid

The capillary oscillations of a charged drop of a viscous liquid are calculated in terms of the boundary layer theory in an approximation linear in oscillation amplitude. Calculation is accompanied with the estimation of a relative error that arises when the exact solution is replaced by an approximate one. It is shown that, for the calculation accuracy in the framework of the boundary layer theory to be about several percent, the thickness of the boundary layer near the free surface of the drop must be several times larger than that at which the intensity of the eddy flow caused by the oscillating surface decreases by e times. As the viscosity of the liquid grows, so does the thickness of the boundary layer.     

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.     

Electrocapillary instability of a conducting liquid cylinder

The electrocapillary instability of a conducting liquid cylinder is analyzed. Exact solutions to the linearized Navier-Stokes equations are examined. Growth rates are found for several unstable modes, including both axisymmetric and nonaxisymmetric ones. Special attention is given to the electric field effects on the temporal growth and length scales of unstable modes. It is shown that, whereas capillary instability is axisymmetric in the absence of electric field, nonaxisymmetric surface modes also become unstable in a nonzero electric field, growing with time. With increasing electric field strength, azimuthal modes are “switched on” (begin to grow with time) sequentially and the highest temporal growth rate monotonically increases.     

On the time evolution of the liquid meniscus at the end of a capillary placed in an external electric field

Using a linearized set of equations of electrodynamics, the stability of the uniformly charged meniscus of a viscous conducting incompressible liquid at the end of a capillary is investigated and analytical expressions are derived for the electric field outside the meniscus, velocity fields in the liquid flow and meniscus, and generatrix of the meniscus shape. It is found that, if an external electric field near the meniscus exceeds that at which the free liquid surface becomes unstable against the surface charge, a finite number of longest waves become unstable with their instability growth rates nonmonotonically depending on the wavenumber. Analysis of the time evolution of the meniscus shape under various initial conditions shows that cylindrical waves with the highest instability growth rates play a decisive role in this process, while the influence of the initial deformation amplitude is insignificant.     

Some observations on the appearance of instability of a plane charged liquid surface

A dispersion relation is obtained for the capillary oscillations of a hemispherical protrusion (oblate or prolate) on the plane surface of a conducting liquid in a uniform electrostatic field parallel to the symmetry axis of the protrusion. For the fundamental mode of the capillary oscillations realized on the protrusion the critical dependence of the parameter characterizing its stability in an external electrostatic field is obtained as a function of the square of the eccentricity as the protrusion is drawn out from the an oblate to a prolate hemisphere. Such a change in shape lowers the threshold electric field for instability of the protrusion. Zh. Tekh. Fiz. 69, 15–22 (July 1999)     

Parametric buildup of the instability of a charged flat liquid surface imposed on Kelvin-Helmholtz instability

The instability of capillary gravitational waves that is developed at the charged flat interface between media is studied for the case when the upper medium moves parallel to the interface with a velocity that has constant and time-dependent components. It is shown that the Mathieu-Hill equation, describing the temporal evolution of the capillary wave amplitudes in such a system, has unstable solutions at those values of physical parameters (electric field strength and wind velocity) meeting the conditions for Saint Elmo fire initiation in the atmosphere.     

Thickness of a boundary layer attributed to the wave motion on the charged free surface of a viscous liquid

It is shown that the analytical estimator for the boundary layer thickness that contains the wave frequency in the denominator and is proposed for approximate calculation of the wave motion on the free surface of a viscous liquid cannot be formally applied to the wave motion on the uniformly charged liquid surface. The fact is that, when the surface charge density attains a value critical in terms for the Tonks-Frenkel instability, the wave frequency tends to zero. From the analysis of liquid motions near the electric charge critical density, a technique is proposed for calculating the thickness of a boundary layer attributed to flows of various kinds. It is found that the thickness of the boundary layer due to aperiodic flows with amplitudes exponentially growing with time (such flows take place at the stage of instability against the surface charge) does not exceed a few tenths of the wavelength, whereas the thickness of the boundary layer due to exponentially decaying liquid flows is roughly equal to the wavelength.     

Mass transfer due to nonlinear capillary-gravitational waves on the surface of a viscous liquid

An analytical expression of the second order of smallness in wave amplitude-to-wavelength ratio is derived for a horizontal flow arising in a finite-depth layer of a viscous liquid under the action of a periodic nonlinear capillary wave. It is found that the liquid flow is determined by the nonlinear component of the velocity field vortex part and the flow rate increases with increasing viscosity and decreasing wavelength irrespective of the layer thickness. In thin layers, the flow rate rapidly drops from its maximal value with increasing viscosity, wavelength, and surface charge density. If the liquid surface is charged, the horizontal liquid flow decreases rapidly as the surface charge density approaches the threshold of the Tonks-Frenkel instability.